id sid tid token lemma pos 7333 1 1 SIDELIGHTS sidelight NNS 7333 1 2 ON on IN 7333 1 3 RELATIVITY RELATIVITY NNP 7333 1 4 By by IN 7333 1 5 Albert Albert NNP 7333 1 6 Einstein Einstein NNP 7333 1 7 Contents Contents NNP 7333 1 8 ETHER ETHER NNP 7333 1 9 AND and CC 7333 1 10 THE the DT 7333 1 11 THEORY theory NN 7333 1 12 OF of IN 7333 1 13 RELATIVITY RELATIVITY NNP 7333 1 14 An An NNP 7333 1 15 Address Address NNP 7333 1 16 delivered deliver VBN 7333 1 17 on on IN 7333 1 18 May May NNP 7333 1 19 5th 5th NN 7333 1 20 , , , 7333 1 21 1920 1920 CD 7333 1 22 , , , 7333 1 23 in in IN 7333 1 24 the the DT 7333 1 25 University University NNP 7333 1 26 of of IN 7333 1 27 Leyden Leyden NNP 7333 1 28 GEOMETRY GEOMETRY NNP 7333 1 29 AND and CC 7333 1 30 EXPERIENCE EXPERIENCE NNS 7333 1 31 An an DT 7333 1 32 expanded expand VBN 7333 1 33 form form NN 7333 1 34 of of IN 7333 1 35 an an DT 7333 1 36 Address address NN 7333 1 37 to to IN 7333 1 38 the the DT 7333 1 39 Prussian Prussian NNP 7333 1 40 Academy Academy NNP 7333 1 41 of of IN 7333 1 42 Sciences Sciences NNPS 7333 1 43 in in IN 7333 1 44 Berlin Berlin NNP 7333 1 45 on on IN 7333 1 46 January January NNP 7333 1 47 27th 27th NN 7333 1 48 , , , 7333 1 49 1921 1921 CD 7333 1 50 . . . 7333 2 1 ETHER ETHER NNP 7333 2 2 AND and CC 7333 2 3 THE the DT 7333 2 4 THEORY theory NN 7333 2 5 OF of IN 7333 2 6 RELATIVITY RELATIVITY NNP 7333 2 7 An An NNP 7333 2 8 Address Address NNP 7333 2 9 delivered deliver VBN 7333 2 10 on on IN 7333 2 11 May May NNP 7333 2 12 5th 5th NN 7333 2 13 , , , 7333 2 14 1920 1920 CD 7333 2 15 , , , 7333 2 16 in in IN 7333 2 17 the the DT 7333 2 18 University University NNP 7333 2 19 of of IN 7333 2 20 Leyden Leyden NNP 7333 2 21 How how WRB 7333 2 22 does do VBZ 7333 2 23 it -PRON- PRP 7333 2 24 come come VB 7333 2 25 about about IN 7333 2 26 that that DT 7333 2 27 alongside alongside NN 7333 2 28 of of IN 7333 2 29 the the DT 7333 2 30 idea idea NN 7333 2 31 of of IN 7333 2 32 ponderable ponderable JJ 7333 2 33 matter matter NN 7333 2 34 , , , 7333 2 35 which which WDT 7333 2 36 is be VBZ 7333 2 37 derived derive VBN 7333 2 38 by by IN 7333 2 39 abstraction abstraction NN 7333 2 40 from from IN 7333 2 41 everyday everyday JJ 7333 2 42 life life NN 7333 2 43 , , , 7333 2 44 the the DT 7333 2 45 physicists physicist NNS 7333 2 46 set set VBD 7333 2 47 the the DT 7333 2 48 idea idea NN 7333 2 49 of of IN 7333 2 50 the the DT 7333 2 51 existence existence NN 7333 2 52 of of IN 7333 2 53 another another DT 7333 2 54 kind kind NN 7333 2 55 of of IN 7333 2 56 matter matter NN 7333 2 57 , , , 7333 2 58 the the DT 7333 2 59 ether ether NN 7333 2 60 ? ? . 7333 3 1 The the DT 7333 3 2 explanation explanation NN 7333 3 3 is be VBZ 7333 3 4 probably probably RB 7333 3 5 to to TO 7333 3 6 be be VB 7333 3 7 sought seek VBN 7333 3 8 in in IN 7333 3 9 those those DT 7333 3 10 phenomena phenomenon NNS 7333 3 11 which which WDT 7333 3 12 have have VBP 7333 3 13 given give VBN 7333 3 14 rise rise NN 7333 3 15 to to IN 7333 3 16 the the DT 7333 3 17 theory theory NN 7333 3 18 of of IN 7333 3 19 action action NN 7333 3 20 at at IN 7333 3 21 a a DT 7333 3 22 distance distance NN 7333 3 23 , , , 7333 3 24 and and CC 7333 3 25 in in IN 7333 3 26 the the DT 7333 3 27 properties property NNS 7333 3 28 of of IN 7333 3 29 light light NN 7333 3 30 which which WDT 7333 3 31 have have VBP 7333 3 32 led lead VBN 7333 3 33 to to IN 7333 3 34 the the DT 7333 3 35 undulatory undulatory JJ 7333 3 36 theory theory NN 7333 3 37 . . . 7333 4 1 Let let VB 7333 4 2 us -PRON- PRP 7333 4 3 devote devote VB 7333 4 4 a a DT 7333 4 5 little little JJ 7333 4 6 while while NN 7333 4 7 to to IN 7333 4 8 the the DT 7333 4 9 consideration consideration NN 7333 4 10 of of IN 7333 4 11 these these DT 7333 4 12 two two CD 7333 4 13 subjects subject NNS 7333 4 14 . . . 7333 5 1 Outside outside IN 7333 5 2 of of IN 7333 5 3 physics physics NN 7333 5 4 we -PRON- PRP 7333 5 5 know know VBP 7333 5 6 nothing nothing NN 7333 5 7 of of IN 7333 5 8 action action NN 7333 5 9 at at IN 7333 5 10 a a DT 7333 5 11 distance distance NN 7333 5 12 . . . 7333 6 1 When when WRB 7333 6 2 we -PRON- PRP 7333 6 3 try try VBP 7333 6 4 to to TO 7333 6 5 connect connect VB 7333 6 6 cause cause NN 7333 6 7 and and CC 7333 6 8 effect effect NN 7333 6 9 in in IN 7333 6 10 the the DT 7333 6 11 experiences experience NNS 7333 6 12 which which WDT 7333 6 13 natural natural JJ 7333 6 14 objects object NNS 7333 6 15 afford afford VBP 7333 6 16 us -PRON- PRP 7333 6 17 , , , 7333 6 18 it -PRON- PRP 7333 6 19 seems seem VBZ 7333 6 20 at at IN 7333 6 21 first first RB 7333 6 22 as as IN 7333 6 23 if if IN 7333 6 24 there there EX 7333 6 25 were be VBD 7333 6 26 no no DT 7333 6 27 other other JJ 7333 6 28 mutual mutual JJ 7333 6 29 actions action NNS 7333 6 30 than than IN 7333 6 31 those those DT 7333 6 32 of of IN 7333 6 33 immediate immediate JJ 7333 6 34 contact contact NN 7333 6 35 , , , 7333 6 36 e.g. e.g. RB 7333 7 1 the the DT 7333 7 2 communication communication NN 7333 7 3 of of IN 7333 7 4 motion motion NN 7333 7 5 by by IN 7333 7 6 impact impact NN 7333 7 7 , , , 7333 7 8 push push VB 7333 7 9 and and CC 7333 7 10 pull pull VB 7333 7 11 , , , 7333 7 12 heating heating NN 7333 7 13 or or CC 7333 7 14 inducing induce VBG 7333 7 15 combustion combustion NN 7333 7 16 by by IN 7333 7 17 means mean NNS 7333 7 18 of of IN 7333 7 19 a a DT 7333 7 20 flame flame NN 7333 7 21 , , , 7333 7 22 etc etc FW 7333 7 23 . . . 7333 8 1 It -PRON- PRP 7333 8 2 is be VBZ 7333 8 3 true true JJ 7333 8 4 that that IN 7333 8 5 even even RB 7333 8 6 in in IN 7333 8 7 everyday everyday JJ 7333 8 8 experience experience NN 7333 8 9 weight weight NN 7333 8 10 , , , 7333 8 11 which which WDT 7333 8 12 is be VBZ 7333 8 13 in in IN 7333 8 14 a a DT 7333 8 15 sense sense NN 7333 8 16 action action NN 7333 8 17 at at IN 7333 8 18 a a DT 7333 8 19 distance distance NN 7333 8 20 , , , 7333 8 21 plays play VBZ 7333 8 22 a a DT 7333 8 23 very very RB 7333 8 24 important important JJ 7333 8 25 part part NN 7333 8 26 . . . 7333 9 1 But but CC 7333 9 2 since since IN 7333 9 3 in in IN 7333 9 4 daily daily JJ 7333 9 5 experience experience NN 7333 9 6 the the DT 7333 9 7 weight weight NN 7333 9 8 of of IN 7333 9 9 bodies body NNS 7333 9 10 meets meet VBZ 7333 9 11 us -PRON- PRP 7333 9 12 as as IN 7333 9 13 something something NN 7333 9 14 constant constant JJ 7333 9 15 , , , 7333 9 16 something something NN 7333 9 17 not not RB 7333 9 18 linked link VBN 7333 9 19 to to IN 7333 9 20 any any DT 7333 9 21 cause cause NN 7333 9 22 which which WDT 7333 9 23 is be VBZ 7333 9 24 variable variable JJ 7333 9 25 in in IN 7333 9 26 time time NN 7333 9 27 or or CC 7333 9 28 place place NN 7333 9 29 , , , 7333 9 30 we -PRON- PRP 7333 9 31 do do VBP 7333 9 32 not not RB 7333 9 33 in in IN 7333 9 34 everyday everyday JJ 7333 9 35 life life NN 7333 9 36 speculate speculate NN 7333 9 37 as as IN 7333 9 38 to to IN 7333 9 39 the the DT 7333 9 40 cause cause NN 7333 9 41 of of IN 7333 9 42 gravity gravity NN 7333 9 43 , , , 7333 9 44 and and CC 7333 9 45 therefore therefore RB 7333 9 46 do do VBP 7333 9 47 not not RB 7333 9 48 become become VB 7333 9 49 conscious conscious JJ 7333 9 50 of of IN 7333 9 51 its -PRON- PRP$ 7333 9 52 character character NN 7333 9 53 as as IN 7333 9 54 action action NN 7333 9 55 at at IN 7333 9 56 a a DT 7333 9 57 distance distance NN 7333 9 58 . . . 7333 10 1 It -PRON- PRP 7333 10 2 was be VBD 7333 10 3 Newton Newton NNP 7333 10 4 's 's POS 7333 10 5 theory theory NN 7333 10 6 of of IN 7333 10 7 gravitation gravitation NN 7333 10 8 that that WDT 7333 10 9 first first RB 7333 10 10 assigned assign VBD 7333 10 11 a a DT 7333 10 12 cause cause NN 7333 10 13 for for IN 7333 10 14 gravity gravity NN 7333 10 15 by by IN 7333 10 16 interpreting interpret VBG 7333 10 17 it -PRON- PRP 7333 10 18 as as IN 7333 10 19 action action NN 7333 10 20 at at IN 7333 10 21 a a DT 7333 10 22 distance distance NN 7333 10 23 , , , 7333 10 24 proceeding proceed VBG 7333 10 25 from from IN 7333 10 26 masses masse NNS 7333 10 27 . . . 7333 11 1 Newton Newton NNP 7333 11 2 's 's POS 7333 11 3 theory theory NN 7333 11 4 is be VBZ 7333 11 5 probably probably RB 7333 11 6 the the DT 7333 11 7 greatest great JJS 7333 11 8 stride stride NN 7333 11 9 ever ever RB 7333 11 10 made make VBN 7333 11 11 in in IN 7333 11 12 the the DT 7333 11 13 effort effort NN 7333 11 14 towards towards IN 7333 11 15 the the DT 7333 11 16 causal causal JJ 7333 11 17 nexus nexus NN 7333 11 18 of of IN 7333 11 19 natural natural JJ 7333 11 20 phenomena phenomenon NNS 7333 11 21 . . . 7333 12 1 And and CC 7333 12 2 yet yet RB 7333 12 3 this this DT 7333 12 4 theory theory NN 7333 12 5 evoked evoke VBD 7333 12 6 a a DT 7333 12 7 lively lively JJ 7333 12 8 sense sense NN 7333 12 9 of of IN 7333 12 10 discomfort discomfort NN 7333 12 11 among among IN 7333 12 12 Newton Newton NNP 7333 12 13 's 's POS 7333 12 14 contemporaries contemporary NNS 7333 12 15 , , , 7333 12 16 because because IN 7333 12 17 it -PRON- PRP 7333 12 18 seemed seem VBD 7333 12 19 to to TO 7333 12 20 be be VB 7333 12 21 in in IN 7333 12 22 conflict conflict NN 7333 12 23 with with IN 7333 12 24 the the DT 7333 12 25 principle principle JJ 7333 12 26 springing springing NN 7333 12 27 from from IN 7333 12 28 the the DT 7333 12 29 rest rest NN 7333 12 30 of of IN 7333 12 31 experience experience NN 7333 12 32 , , , 7333 12 33 that that IN 7333 12 34 there there EX 7333 12 35 can can MD 7333 12 36 be be VB 7333 12 37 reciprocal reciprocal JJ 7333 12 38 action action NN 7333 12 39 only only RB 7333 12 40 through through IN 7333 12 41 contact contact NN 7333 12 42 , , , 7333 12 43 and and CC 7333 12 44 not not RB 7333 12 45 through through IN 7333 12 46 immediate immediate JJ 7333 12 47 action action NN 7333 12 48 at at IN 7333 12 49 a a DT 7333 12 50 distance distance NN 7333 12 51 . . . 7333 13 1 It -PRON- PRP 7333 13 2 is be VBZ 7333 13 3 only only RB 7333 13 4 with with IN 7333 13 5 reluctance reluctance NN 7333 13 6 that that DT 7333 13 7 man man NN 7333 13 8 's 's POS 7333 13 9 desire desire NN 7333 13 10 for for IN 7333 13 11 knowledge knowledge NN 7333 13 12 endures endure VBZ 7333 13 13 a a DT 7333 13 14 dualism dualism NN 7333 13 15 of of IN 7333 13 16 this this DT 7333 13 17 kind kind NN 7333 13 18 . . . 7333 14 1 How how WRB 7333 14 2 was be VBD 7333 14 3 unity unity NN 7333 14 4 to to TO 7333 14 5 be be VB 7333 14 6 preserved preserve VBN 7333 14 7 in in IN 7333 14 8 his -PRON- PRP$ 7333 14 9 comprehension comprehension NN 7333 14 10 of of IN 7333 14 11 the the DT 7333 14 12 forces force NNS 7333 14 13 of of IN 7333 14 14 nature nature NN 7333 14 15 ? ? . 7333 15 1 Either either CC 7333 15 2 by by IN 7333 15 3 trying try VBG 7333 15 4 to to TO 7333 15 5 look look VB 7333 15 6 upon upon IN 7333 15 7 contact contact NN 7333 15 8 forces force NNS 7333 15 9 as as IN 7333 15 10 being be VBG 7333 15 11 themselves -PRON- PRP 7333 15 12 distant distant JJ 7333 15 13 forces force NNS 7333 15 14 which which WDT 7333 15 15 admittedly admittedly RB 7333 15 16 are be VBP 7333 15 17 observable observable JJ 7333 15 18 only only RB 7333 15 19 at at IN 7333 15 20 a a DT 7333 15 21 very very RB 7333 15 22 small small JJ 7333 15 23 distance distance NN 7333 15 24 -- -- : 7333 15 25 and and CC 7333 15 26 this this DT 7333 15 27 was be VBD 7333 15 28 the the DT 7333 15 29 road road NN 7333 15 30 which which WDT 7333 15 31 Newton Newton NNP 7333 15 32 's 's POS 7333 15 33 followers follower NNS 7333 15 34 , , , 7333 15 35 who who WP 7333 15 36 were be VBD 7333 15 37 entirely entirely RB 7333 15 38 under under IN 7333 15 39 the the DT 7333 15 40 spell spell NN 7333 15 41 of of IN 7333 15 42 his -PRON- PRP$ 7333 15 43 doctrine doctrine NN 7333 15 44 , , , 7333 15 45 mostly mostly RB 7333 15 46 preferred prefer VBN 7333 15 47 to to TO 7333 15 48 take take VB 7333 15 49 ; ; : 7333 15 50 or or CC 7333 15 51 by by IN 7333 15 52 assuming assume VBG 7333 15 53 that that IN 7333 15 54 the the DT 7333 15 55 Newtonian newtonian JJ 7333 15 56 action action NN 7333 15 57 at at IN 7333 15 58 a a DT 7333 15 59 distance distance NN 7333 15 60 is be VBZ 7333 15 61 only only RB 7333 15 62 _ _ NNP 7333 15 63 apparently apparently RB 7333 15 64 _ _ XX 7333 15 65 immediate immediate JJ 7333 15 66 action action NN 7333 15 67 at at IN 7333 15 68 a a DT 7333 15 69 distance distance NN 7333 15 70 , , , 7333 15 71 but but CC 7333 15 72 in in IN 7333 15 73 truth truth NN 7333 15 74 is be VBZ 7333 15 75 conveyed convey VBN 7333 15 76 by by IN 7333 15 77 a a DT 7333 15 78 medium medium JJ 7333 15 79 permeating permeate VBG 7333 15 80 space space NN 7333 15 81 , , , 7333 15 82 whether whether IN 7333 15 83 by by IN 7333 15 84 movements movement NNS 7333 15 85 or or CC 7333 15 86 by by IN 7333 15 87 elastic elastic JJ 7333 15 88 deformation deformation NN 7333 15 89 of of IN 7333 15 90 this this DT 7333 15 91 medium medium NN 7333 15 92 . . . 7333 16 1 Thus thus RB 7333 16 2 the the DT 7333 16 3 endeavour endeavour NN 7333 16 4 toward toward IN 7333 16 5 a a DT 7333 16 6 unified unified JJ 7333 16 7 view view NN 7333 16 8 of of IN 7333 16 9 the the DT 7333 16 10 nature nature NN 7333 16 11 of of IN 7333 16 12 forces force NNS 7333 16 13 leads lead VBZ 7333 16 14 to to IN 7333 16 15 the the DT 7333 16 16 hypothesis hypothesis NN 7333 16 17 of of IN 7333 16 18 an an DT 7333 16 19 ether ether NN 7333 16 20 . . . 7333 17 1 This this DT 7333 17 2 hypothesis hypothesis NN 7333 17 3 , , , 7333 17 4 to to TO 7333 17 5 be be VB 7333 17 6 sure sure JJ 7333 17 7 , , , 7333 17 8 did do VBD 7333 17 9 not not RB 7333 17 10 at at IN 7333 17 11 first first RB 7333 17 12 bring bring VB 7333 17 13 with with IN 7333 17 14 it -PRON- PRP 7333 17 15 any any DT 7333 17 16 advance advance NN 7333 17 17 in in IN 7333 17 18 the the DT 7333 17 19 theory theory NN 7333 17 20 of of IN 7333 17 21 gravitation gravitation NN 7333 17 22 or or CC 7333 17 23 in in IN 7333 17 24 physics physics NN 7333 17 25 generally generally RB 7333 17 26 , , , 7333 17 27 so so IN 7333 17 28 that that IN 7333 17 29 it -PRON- PRP 7333 17 30 became become VBD 7333 17 31 customary customary JJ 7333 17 32 to to TO 7333 17 33 treat treat VB 7333 17 34 Newton Newton NNP 7333 17 35 's 's POS 7333 17 36 law law NN 7333 17 37 of of IN 7333 17 38 force force NN 7333 17 39 as as IN 7333 17 40 an an DT 7333 17 41 axiom axiom NN 7333 17 42 not not RB 7333 17 43 further further RB 7333 17 44 reducible reducible JJ 7333 17 45 . . . 7333 18 1 But but CC 7333 18 2 the the DT 7333 18 3 ether ether NN 7333 18 4 hypothesis hypothesis NN 7333 18 5 was be VBD 7333 18 6 bound bind VBN 7333 18 7 always always RB 7333 18 8 to to TO 7333 18 9 play play VB 7333 18 10 some some DT 7333 18 11 part part NN 7333 18 12 in in IN 7333 18 13 physical physical JJ 7333 18 14 science science NN 7333 18 15 , , , 7333 18 16 even even RB 7333 18 17 if if IN 7333 18 18 at at IN 7333 18 19 first first RB 7333 18 20 only only RB 7333 18 21 a a DT 7333 18 22 latent latent NN 7333 18 23 part part NN 7333 18 24 . . . 7333 19 1 When when WRB 7333 19 2 in in IN 7333 19 3 the the DT 7333 19 4 first first JJ 7333 19 5 half half NN 7333 19 6 of of IN 7333 19 7 the the DT 7333 19 8 nineteenth nineteenth JJ 7333 19 9 century century NN 7333 19 10 the the DT 7333 19 11 far far RB 7333 19 12 - - HYPH 7333 19 13 reaching reach VBG 7333 19 14 similarity similarity NN 7333 19 15 was be VBD 7333 19 16 revealed reveal VBN 7333 19 17 which which WDT 7333 19 18 subsists subsist NNS 7333 19 19 between between IN 7333 19 20 the the DT 7333 19 21 properties property NNS 7333 19 22 of of IN 7333 19 23 light light NN 7333 19 24 and and CC 7333 19 25 those those DT 7333 19 26 of of IN 7333 19 27 elastic elastic JJ 7333 19 28 waves wave NNS 7333 19 29 in in IN 7333 19 30 ponderable ponderable JJ 7333 19 31 bodies body NNS 7333 19 32 , , , 7333 19 33 the the DT 7333 19 34 ether ether NN 7333 19 35 hypothesis hypothesis NN 7333 19 36 found find VBD 7333 19 37 fresh fresh JJ 7333 19 38 support support NN 7333 19 39 . . . 7333 20 1 It -PRON- PRP 7333 20 2 appeared appear VBD 7333 20 3 beyond beyond IN 7333 20 4 question question NN 7333 20 5 that that IN 7333 20 6 light light NN 7333 20 7 must must MD 7333 20 8 be be VB 7333 20 9 interpreted interpret VBN 7333 20 10 as as IN 7333 20 11 a a DT 7333 20 12 vibratory vibratory NN 7333 20 13 process process NN 7333 20 14 in in IN 7333 20 15 an an DT 7333 20 16 elastic elastic JJ 7333 20 17 , , , 7333 20 18 inert inert JJ 7333 20 19 medium medium NN 7333 20 20 filling fill VBG 7333 20 21 up up RP 7333 20 22 universal universal JJ 7333 20 23 space space NN 7333 20 24 . . . 7333 21 1 It -PRON- PRP 7333 21 2 also also RB 7333 21 3 seemed seem VBD 7333 21 4 to to TO 7333 21 5 be be VB 7333 21 6 a a DT 7333 21 7 necessary necessary JJ 7333 21 8 consequence consequence NN 7333 21 9 of of IN 7333 21 10 the the DT 7333 21 11 fact fact NN 7333 21 12 that that IN 7333 21 13 light light NN 7333 21 14 is be VBZ 7333 21 15 capable capable JJ 7333 21 16 of of IN 7333 21 17 polarisation polarisation NN 7333 21 18 that that IN 7333 21 19 this this DT 7333 21 20 medium medium NN 7333 21 21 , , , 7333 21 22 the the DT 7333 21 23 ether ether NN 7333 21 24 , , , 7333 21 25 must must MD 7333 21 26 be be VB 7333 21 27 of of IN 7333 21 28 the the DT 7333 21 29 nature nature NN 7333 21 30 of of IN 7333 21 31 a a DT 7333 21 32 solid solid JJ 7333 21 33 body body NN 7333 21 34 , , , 7333 21 35 because because IN 7333 21 36 transverse transverse JJ 7333 21 37 waves wave NNS 7333 21 38 are be VBP 7333 21 39 not not RB 7333 21 40 possible possible JJ 7333 21 41 in in IN 7333 21 42 a a DT 7333 21 43 fluid fluid NN 7333 21 44 , , , 7333 21 45 but but CC 7333 21 46 only only RB 7333 21 47 in in IN 7333 21 48 a a DT 7333 21 49 solid solid JJ 7333 21 50 . . . 7333 22 1 Thus thus RB 7333 22 2 the the DT 7333 22 3 physicists physicist NNS 7333 22 4 were be VBD 7333 22 5 bound bind VBN 7333 22 6 to to TO 7333 22 7 arrive arrive VB 7333 22 8 at at IN 7333 22 9 the the DT 7333 22 10 theory theory NN 7333 22 11 of of IN 7333 22 12 the the DT 7333 22 13 " " `` 7333 22 14 quasi quasi JJ 7333 22 15 - - JJ 7333 22 16 rigid rigid JJ 7333 22 17 " " '' 7333 22 18 luminiferous luminiferous JJ 7333 22 19 ether ether NN 7333 22 20 , , , 7333 22 21 the the DT 7333 22 22 parts part NNS 7333 22 23 of of IN 7333 22 24 which which WDT 7333 22 25 can can MD 7333 22 26 carry carry VB 7333 22 27 out out RP 7333 22 28 no no DT 7333 22 29 movements movement NNS 7333 22 30 relatively relatively RB 7333 22 31 to to IN 7333 22 32 one one CD 7333 22 33 another another DT 7333 22 34 except except IN 7333 22 35 the the DT 7333 22 36 small small JJ 7333 22 37 movements movement NNS 7333 22 38 of of IN 7333 22 39 deformation deformation NN 7333 22 40 which which WDT 7333 22 41 correspond correspond VBP 7333 22 42 to to IN 7333 22 43 light light NN 7333 22 44 - - HYPH 7333 22 45 waves wave NNS 7333 22 46 . . . 7333 23 1 This this DT 7333 23 2 theory theory NN 7333 23 3 -- -- : 7333 23 4 also also RB 7333 23 5 called call VBD 7333 23 6 the the DT 7333 23 7 theory theory NN 7333 23 8 of of IN 7333 23 9 the the DT 7333 23 10 stationary stationary JJ 7333 23 11 luminiferous luminiferous JJ 7333 23 12 ether ether NN 7333 23 13 -- -- : 7333 23 14 moreover moreover RB 7333 23 15 found find VBD 7333 23 16 a a DT 7333 23 17 strong strong JJ 7333 23 18 support support NN 7333 23 19 in in IN 7333 23 20 an an DT 7333 23 21 experiment experiment NN 7333 23 22 which which WDT 7333 23 23 is be VBZ 7333 23 24 also also RB 7333 23 25 of of IN 7333 23 26 fundamental fundamental JJ 7333 23 27 importance importance NN 7333 23 28 in in IN 7333 23 29 the the DT 7333 23 30 special special JJ 7333 23 31 theory theory NN 7333 23 32 of of IN 7333 23 33 relativity relativity NN 7333 23 34 , , , 7333 23 35 the the DT 7333 23 36 experiment experiment NN 7333 23 37 of of IN 7333 23 38 Fizeau Fizeau NNP 7333 23 39 , , , 7333 23 40 from from IN 7333 23 41 which which WDT 7333 23 42 one one NN 7333 23 43 was be VBD 7333 23 44 obliged oblige VBN 7333 23 45 to to TO 7333 23 46 infer infer VB 7333 23 47 that that IN 7333 23 48 the the DT 7333 23 49 luminiferous luminiferous JJ 7333 23 50 ether ether NN 7333 23 51 does do VBZ 7333 23 52 not not RB 7333 23 53 take take VB 7333 23 54 part part NN 7333 23 55 in in IN 7333 23 56 the the DT 7333 23 57 movements movement NNS 7333 23 58 of of IN 7333 23 59 bodies body NNS 7333 23 60 . . . 7333 24 1 The the DT 7333 24 2 phenomenon phenomenon NN 7333 24 3 of of IN 7333 24 4 aberration aberration NN 7333 24 5 also also RB 7333 24 6 favoured favour VBD 7333 24 7 the the DT 7333 24 8 theory theory NN 7333 24 9 of of IN 7333 24 10 the the DT 7333 24 11 quasi quasi JJ 7333 24 12 - - JJ 7333 24 13 rigid rigid JJ 7333 24 14 ether ether NN 7333 24 15 . . . 7333 25 1 The the DT 7333 25 2 development development NN 7333 25 3 of of IN 7333 25 4 the the DT 7333 25 5 theory theory NN 7333 25 6 of of IN 7333 25 7 electricity electricity NN 7333 25 8 along along IN 7333 25 9 the the DT 7333 25 10 path path NN 7333 25 11 opened open VBD 7333 25 12 up up RP 7333 25 13 by by IN 7333 25 14 Maxwell Maxwell NNP 7333 25 15 and and CC 7333 25 16 Lorentz Lorentz NNP 7333 25 17 gave give VBD 7333 25 18 the the DT 7333 25 19 development development NN 7333 25 20 of of IN 7333 25 21 our -PRON- PRP$ 7333 25 22 ideas idea NNS 7333 25 23 concerning concern VBG 7333 25 24 the the DT 7333 25 25 ether ether NN 7333 25 26 quite quite PDT 7333 25 27 a a DT 7333 25 28 peculiar peculiar JJ 7333 25 29 and and CC 7333 25 30 unexpected unexpected JJ 7333 25 31 turn turn NN 7333 25 32 . . . 7333 26 1 For for IN 7333 26 2 Maxwell Maxwell NNP 7333 26 3 himself -PRON- PRP 7333 26 4 the the DT 7333 26 5 ether ether NN 7333 26 6 indeed indeed RB 7333 26 7 still still RB 7333 26 8 had have VBD 7333 26 9 properties property NNS 7333 26 10 which which WDT 7333 26 11 were be VBD 7333 26 12 purely purely RB 7333 26 13 mechanical mechanical JJ 7333 26 14 , , , 7333 26 15 although although IN 7333 26 16 of of IN 7333 26 17 a a DT 7333 26 18 much much RB 7333 26 19 more more RBR 7333 26 20 complicated complicated JJ 7333 26 21 kind kind NN 7333 26 22 than than IN 7333 26 23 the the DT 7333 26 24 mechanical mechanical JJ 7333 26 25 properties property NNS 7333 26 26 of of IN 7333 26 27 tangible tangible JJ 7333 26 28 solid solid JJ 7333 26 29 bodies body NNS 7333 26 30 . . . 7333 27 1 But but CC 7333 27 2 neither neither CC 7333 27 3 Maxwell Maxwell NNP 7333 27 4 nor nor CC 7333 27 5 his -PRON- PRP$ 7333 27 6 followers follower NNS 7333 27 7 succeeded succeed VBD 7333 27 8 in in IN 7333 27 9 elaborating elaborate VBG 7333 27 10 a a DT 7333 27 11 mechanical mechanical JJ 7333 27 12 model model NN 7333 27 13 for for IN 7333 27 14 the the DT 7333 27 15 ether ether NN 7333 27 16 which which WDT 7333 27 17 might may MD 7333 27 18 furnish furnish VB 7333 27 19 a a DT 7333 27 20 satisfactory satisfactory JJ 7333 27 21 mechanical mechanical JJ 7333 27 22 interpretation interpretation NN 7333 27 23 of of IN 7333 27 24 Maxwell Maxwell NNP 7333 27 25 's 's POS 7333 27 26 laws law NNS 7333 27 27 of of IN 7333 27 28 the the DT 7333 27 29 electro electro JJ 7333 27 30 - - HYPH 7333 27 31 magnetic magnetic JJ 7333 27 32 field field NN 7333 27 33 . . . 7333 28 1 The the DT 7333 28 2 laws law NNS 7333 28 3 were be VBD 7333 28 4 clear clear JJ 7333 28 5 and and CC 7333 28 6 simple simple JJ 7333 28 7 , , , 7333 28 8 the the DT 7333 28 9 mechanical mechanical JJ 7333 28 10 interpretations interpretation NNS 7333 28 11 clumsy clumsy JJ 7333 28 12 and and CC 7333 28 13 contradictory contradictory JJ 7333 28 14 . . . 7333 29 1 Almost almost RB 7333 29 2 imperceptibly imperceptibly RB 7333 29 3 the the DT 7333 29 4 theoretical theoretical JJ 7333 29 5 physicists physicist NNS 7333 29 6 adapted adapt VBD 7333 29 7 themselves -PRON- PRP 7333 29 8 to to IN 7333 29 9 a a DT 7333 29 10 situation situation NN 7333 29 11 which which WDT 7333 29 12 , , , 7333 29 13 from from IN 7333 29 14 the the DT 7333 29 15 standpoint standpoint NN 7333 29 16 of of IN 7333 29 17 their -PRON- PRP$ 7333 29 18 mechanical mechanical JJ 7333 29 19 programme programme NN 7333 29 20 , , , 7333 29 21 was be VBD 7333 29 22 very very RB 7333 29 23 depressing depressing JJ 7333 29 24 . . . 7333 30 1 They -PRON- PRP 7333 30 2 were be VBD 7333 30 3 particularly particularly RB 7333 30 4 influenced influence VBN 7333 30 5 by by IN 7333 30 6 the the DT 7333 30 7 electro electro JJ 7333 30 8 - - HYPH 7333 30 9 dynamical dynamical JJ 7333 30 10 investigations investigation NNS 7333 30 11 of of IN 7333 30 12 Heinrich Heinrich NNP 7333 30 13 Hertz Hertz NNP 7333 30 14 . . . 7333 31 1 For for IN 7333 31 2 whereas whereas IN 7333 31 3 they -PRON- PRP 7333 31 4 previously previously RB 7333 31 5 had have VBD 7333 31 6 required require VBN 7333 31 7 of of IN 7333 31 8 a a DT 7333 31 9 conclusive conclusive JJ 7333 31 10 theory theory NN 7333 31 11 that that IN 7333 31 12 it -PRON- PRP 7333 31 13 should should MD 7333 31 14 content content VB 7333 31 15 itself -PRON- PRP 7333 31 16 with with IN 7333 31 17 the the DT 7333 31 18 fundamental fundamental JJ 7333 31 19 concepts concept NNS 7333 31 20 which which WDT 7333 31 21 belong belong VBP 7333 31 22 exclusively exclusively RB 7333 31 23 to to IN 7333 31 24 mechanics mechanic NNS 7333 31 25 ( ( -LRB- 7333 31 26 e.g. e.g. RB 7333 32 1 densities density NNS 7333 32 2 , , , 7333 32 3 velocities velocity NNS 7333 32 4 , , , 7333 32 5 deformations deformation NNS 7333 32 6 , , , 7333 32 7 stresses stress NNS 7333 32 8 ) ) -RRB- 7333 32 9 they -PRON- PRP 7333 32 10 gradually gradually RB 7333 32 11 accustomed accustom VBD 7333 32 12 themselves -PRON- PRP 7333 32 13 to to IN 7333 32 14 admitting admit VBG 7333 32 15 electric electric JJ 7333 32 16 and and CC 7333 32 17 magnetic magnetic JJ 7333 32 18 force force NN 7333 32 19 as as IN 7333 32 20 fundamental fundamental JJ 7333 32 21 concepts concept NNS 7333 32 22 side side NN 7333 32 23 by by IN 7333 32 24 side side NN 7333 32 25 with with IN 7333 32 26 those those DT 7333 32 27 of of IN 7333 32 28 mechanics mechanic NNS 7333 32 29 , , , 7333 32 30 without without IN 7333 32 31 requiring require VBG 7333 32 32 a a DT 7333 32 33 mechanical mechanical JJ 7333 32 34 interpretation interpretation NN 7333 32 35 for for IN 7333 32 36 them -PRON- PRP 7333 32 37 . . . 7333 33 1 Thus thus RB 7333 33 2 the the DT 7333 33 3 purely purely RB 7333 33 4 mechanical mechanical JJ 7333 33 5 view view NN 7333 33 6 of of IN 7333 33 7 nature nature NN 7333 33 8 was be VBD 7333 33 9 gradually gradually RB 7333 33 10 abandoned abandon VBN 7333 33 11 . . . 7333 34 1 But but CC 7333 34 2 this this DT 7333 34 3 change change NN 7333 34 4 led lead VBD 7333 34 5 to to IN 7333 34 6 a a DT 7333 34 7 fundamental fundamental JJ 7333 34 8 dualism dualism NN 7333 34 9 which which WDT 7333 34 10 in in IN 7333 34 11 the the DT 7333 34 12 long long RB 7333 34 13 - - HYPH 7333 34 14 run run NN 7333 34 15 was be VBD 7333 34 16 insupportable insupportable JJ 7333 34 17 . . . 7333 35 1 A a DT 7333 35 2 way way NN 7333 35 3 of of IN 7333 35 4 escape escape NN 7333 35 5 was be VBD 7333 35 6 now now RB 7333 35 7 sought seek VBN 7333 35 8 in in IN 7333 35 9 the the DT 7333 35 10 reverse reverse JJ 7333 35 11 direction direction NN 7333 35 12 , , , 7333 35 13 by by IN 7333 35 14 reducing reduce VBG 7333 35 15 the the DT 7333 35 16 principles principle NNS 7333 35 17 of of IN 7333 35 18 mechanics mechanic NNS 7333 35 19 to to IN 7333 35 20 those those DT 7333 35 21 of of IN 7333 35 22 electricity electricity NN 7333 35 23 , , , 7333 35 24 and and CC 7333 35 25 this this DT 7333 35 26 especially especially RB 7333 35 27 as as IN 7333 35 28 confidence confidence NN 7333 35 29 in in IN 7333 35 30 the the DT 7333 35 31 strict strict JJ 7333 35 32 validity validity NN 7333 35 33 of of IN 7333 35 34 the the DT 7333 35 35 equations equation NNS 7333 35 36 of of IN 7333 35 37 Newton Newton NNP 7333 35 38 's 's POS 7333 35 39 mechanics mechanic NNS 7333 35 40 was be VBD 7333 35 41 shaken shake VBN 7333 35 42 by by IN 7333 35 43 the the DT 7333 35 44 experiments experiment NNS 7333 35 45 with with IN 7333 35 46 beta beta NN 7333 35 47 - - HYPH 7333 35 48 rays ray NNS 7333 35 49 and and CC 7333 35 50 rapid rapid JJ 7333 35 51 kathode kathode JJ 7333 35 52 rays ray NNS 7333 35 53 . . . 7333 36 1 This this DT 7333 36 2 dualism dualism NN 7333 36 3 still still RB 7333 36 4 confronts confront VBZ 7333 36 5 us -PRON- PRP 7333 36 6 in in IN 7333 36 7 unextenuated unextenuated JJ 7333 36 8 form form NN 7333 36 9 in in IN 7333 36 10 the the DT 7333 36 11 theory theory NN 7333 36 12 of of IN 7333 36 13 Hertz Hertz NNP 7333 36 14 , , , 7333 36 15 where where WRB 7333 36 16 matter matter NN 7333 36 17 appears appear VBZ 7333 36 18 not not RB 7333 36 19 only only RB 7333 36 20 as as IN 7333 36 21 the the DT 7333 36 22 bearer bearer NN 7333 36 23 of of IN 7333 36 24 velocities velocity NNS 7333 36 25 , , , 7333 36 26 kinetic kinetic JJ 7333 36 27 energy energy NN 7333 36 28 , , , 7333 36 29 and and CC 7333 36 30 mechanical mechanical JJ 7333 36 31 pressures pressure NNS 7333 36 32 , , , 7333 36 33 but but CC 7333 36 34 also also RB 7333 36 35 as as IN 7333 36 36 the the DT 7333 36 37 bearer bearer NN 7333 36 38 of of IN 7333 36 39 electromagnetic electromagnetic JJ 7333 36 40 fields field NNS 7333 36 41 . . . 7333 37 1 Since since IN 7333 37 2 such such JJ 7333 37 3 fields field NNS 7333 37 4 also also RB 7333 37 5 occur occur VBP 7333 37 6 _ _ NNP 7333 37 7 in in IN 7333 37 8 vacuo_--i.e vacuo_--i.e NNP 7333 37 9 . . . 7333 38 1 in in IN 7333 38 2 free free JJ 7333 38 3 ether ether NN 7333 38 4 -- -- : 7333 38 5 the the DT 7333 38 6 ether ether NN 7333 38 7 also also RB 7333 38 8 appears appear VBZ 7333 38 9 as as IN 7333 38 10 bearer bearer NN 7333 38 11 of of IN 7333 38 12 electromagnetic electromagnetic JJ 7333 38 13 fields field NNS 7333 38 14 . . . 7333 39 1 The the DT 7333 39 2 ether ether NN 7333 39 3 appears appear VBZ 7333 39 4 indistinguishable indistinguishable JJ 7333 39 5 in in IN 7333 39 6 its -PRON- PRP$ 7333 39 7 functions function NNS 7333 39 8 from from IN 7333 39 9 ordinary ordinary JJ 7333 39 10 matter matter NN 7333 39 11 . . . 7333 40 1 Within within IN 7333 40 2 matter matter NN 7333 40 3 it -PRON- PRP 7333 40 4 takes take VBZ 7333 40 5 part part NN 7333 40 6 in in IN 7333 40 7 the the DT 7333 40 8 motion motion NN 7333 40 9 of of IN 7333 40 10 matter matter NN 7333 40 11 and and CC 7333 40 12 in in IN 7333 40 13 empty empty JJ 7333 40 14 space space NN 7333 40 15 it -PRON- PRP 7333 40 16 has have VBZ 7333 40 17 everywhere everywhere RB 7333 40 18 a a DT 7333 40 19 velocity velocity NN 7333 40 20 ; ; : 7333 40 21 so so IN 7333 40 22 that that IN 7333 40 23 the the DT 7333 40 24 ether ether NN 7333 40 25 has have VBZ 7333 40 26 a a DT 7333 40 27 definitely definitely RB 7333 40 28 assigned assign VBN 7333 40 29 velocity velocity NN 7333 40 30 throughout throughout IN 7333 40 31 the the DT 7333 40 32 whole whole NN 7333 40 33 of of IN 7333 40 34 space space NN 7333 40 35 . . . 7333 41 1 There there EX 7333 41 2 is be VBZ 7333 41 3 no no DT 7333 41 4 fundamental fundamental JJ 7333 41 5 difference difference NN 7333 41 6 between between IN 7333 41 7 Hertz Hertz NNP 7333 41 8 's 's POS 7333 41 9 ether ether NN 7333 41 10 and and CC 7333 41 11 ponderable ponderable JJ 7333 41 12 matter matter NN 7333 41 13 ( ( -LRB- 7333 41 14 which which WDT 7333 41 15 in in IN 7333 41 16 part part NN 7333 41 17 subsists subsist NNS 7333 41 18 in in IN 7333 41 19 the the DT 7333 41 20 ether ether NN 7333 41 21 ) ) -RRB- 7333 41 22 . . . 7333 42 1 The the DT 7333 42 2 Hertz Hertz NNP 7333 42 3 theory theory NN 7333 42 4 suffered suffer VBD 7333 42 5 not not RB 7333 42 6 only only RB 7333 42 7 from from IN 7333 42 8 the the DT 7333 42 9 defect defect NN 7333 42 10 of of IN 7333 42 11 ascribing ascribe VBG 7333 42 12 to to IN 7333 42 13 matter matter NN 7333 42 14 and and CC 7333 42 15 ether eth JJR 7333 42 16 , , , 7333 42 17 on on IN 7333 42 18 the the DT 7333 42 19 one one CD 7333 42 20 hand hand NN 7333 42 21 mechanical mechanical JJ 7333 42 22 states state NNS 7333 42 23 , , , 7333 42 24 and and CC 7333 42 25 on on IN 7333 42 26 the the DT 7333 42 27 other other JJ 7333 42 28 hand hand NN 7333 42 29 electrical electrical JJ 7333 42 30 states state NNS 7333 42 31 , , , 7333 42 32 which which WDT 7333 42 33 do do VBP 7333 42 34 not not RB 7333 42 35 stand stand VB 7333 42 36 in in IN 7333 42 37 any any DT 7333 42 38 conceivable conceivable JJ 7333 42 39 relation relation NN 7333 42 40 to to IN 7333 42 41 each each DT 7333 42 42 other other JJ 7333 42 43 ; ; : 7333 42 44 it -PRON- PRP 7333 42 45 was be VBD 7333 42 46 also also RB 7333 42 47 at at IN 7333 42 48 variance variance NN 7333 42 49 with with IN 7333 42 50 the the DT 7333 42 51 result result NN 7333 42 52 of of IN 7333 42 53 Fizeau Fizeau NNP 7333 42 54 's 's POS 7333 42 55 important important JJ 7333 42 56 experiment experiment NN 7333 42 57 on on IN 7333 42 58 the the DT 7333 42 59 velocity velocity NN 7333 42 60 of of IN 7333 42 61 the the DT 7333 42 62 propagation propagation NN 7333 42 63 of of IN 7333 42 64 light light NN 7333 42 65 in in IN 7333 42 66 moving move VBG 7333 42 67 fluids fluid NNS 7333 42 68 , , , 7333 42 69 and and CC 7333 42 70 with with IN 7333 42 71 other other JJ 7333 42 72 established establish VBN 7333 42 73 experimental experimental JJ 7333 42 74 results result NNS 7333 42 75 . . . 7333 43 1 Such such JJ 7333 43 2 was be VBD 7333 43 3 the the DT 7333 43 4 state state NN 7333 43 5 of of IN 7333 43 6 things thing NNS 7333 43 7 when when WRB 7333 43 8 H. H. NNP 7333 43 9 A. A. NNP 7333 43 10 Lorentz Lorentz NNP 7333 43 11 entered enter VBD 7333 43 12 upon upon IN 7333 43 13 the the DT 7333 43 14 scene scene NN 7333 43 15 . . . 7333 44 1 He -PRON- PRP 7333 44 2 brought bring VBD 7333 44 3 theory theory NN 7333 44 4 into into IN 7333 44 5 harmony harmony NN 7333 44 6 with with IN 7333 44 7 experience experience NN 7333 44 8 by by IN 7333 44 9 means mean NNS 7333 44 10 of of IN 7333 44 11 a a DT 7333 44 12 wonderful wonderful JJ 7333 44 13 simplification simplification NN 7333 44 14 of of IN 7333 44 15 theoretical theoretical JJ 7333 44 16 principles principle NNS 7333 44 17 . . . 7333 45 1 He -PRON- PRP 7333 45 2 achieved achieve VBD 7333 45 3 this this DT 7333 45 4 , , , 7333 45 5 the the DT 7333 45 6 most most RBS 7333 45 7 important important JJ 7333 45 8 advance advance NN 7333 45 9 in in IN 7333 45 10 the the DT 7333 45 11 theory theory NN 7333 45 12 of of IN 7333 45 13 electricity electricity NN 7333 45 14 since since IN 7333 45 15 Maxwell Maxwell NNP 7333 45 16 , , , 7333 45 17 by by IN 7333 45 18 taking take VBG 7333 45 19 from from IN 7333 45 20 ether ether NN 7333 45 21 its -PRON- PRP$ 7333 45 22 mechanical mechanical JJ 7333 45 23 , , , 7333 45 24 and and CC 7333 45 25 from from IN 7333 45 26 matter matter VB 7333 45 27 its -PRON- PRP$ 7333 45 28 electromagnetic electromagnetic JJ 7333 45 29 qualities quality NNS 7333 45 30 . . . 7333 46 1 As as IN 7333 46 2 in in IN 7333 46 3 empty empty JJ 7333 46 4 space space NN 7333 46 5 , , , 7333 46 6 so so RB 7333 46 7 too too RB 7333 46 8 in in IN 7333 46 9 the the DT 7333 46 10 interior interior NN 7333 46 11 of of IN 7333 46 12 material material JJ 7333 46 13 bodies body NNS 7333 46 14 , , , 7333 46 15 the the DT 7333 46 16 ether ether NN 7333 46 17 , , , 7333 46 18 and and CC 7333 46 19 not not RB 7333 46 20 matter matter RB 7333 46 21 viewed view VBN 7333 46 22 atomistically atomistically RB 7333 46 23 , , , 7333 46 24 was be VBD 7333 46 25 exclusively exclusively RB 7333 46 26 the the DT 7333 46 27 seat seat NN 7333 46 28 of of IN 7333 46 29 electromagnetic electromagnetic JJ 7333 46 30 fields field NNS 7333 46 31 . . . 7333 47 1 According accord VBG 7333 47 2 to to IN 7333 47 3 Lorentz Lorentz NNP 7333 47 4 the the DT 7333 47 5 elementary elementary JJ 7333 47 6 particles particle NNS 7333 47 7 of of IN 7333 47 8 matter matter NN 7333 47 9 alone alone RB 7333 47 10 are be VBP 7333 47 11 capable capable JJ 7333 47 12 of of IN 7333 47 13 carrying carry VBG 7333 47 14 out out RP 7333 47 15 movements movement NNS 7333 47 16 ; ; : 7333 47 17 their -PRON- PRP$ 7333 47 18 electromagnetic electromagnetic JJ 7333 47 19 activity activity NN 7333 47 20 is be VBZ 7333 47 21 entirely entirely RB 7333 47 22 confined confine VBN 7333 47 23 to to IN 7333 47 24 the the DT 7333 47 25 carrying carrying NN 7333 47 26 of of IN 7333 47 27 electric electric JJ 7333 47 28 charges charge NNS 7333 47 29 . . . 7333 48 1 Thus thus RB 7333 48 2 Lorentz Lorentz NNP 7333 48 3 succeeded succeed VBD 7333 48 4 in in IN 7333 48 5 reducing reduce VBG 7333 48 6 all all DT 7333 48 7 electromagnetic electromagnetic JJ 7333 48 8 happenings happening NNS 7333 48 9 to to IN 7333 48 10 Maxwell Maxwell NNP 7333 48 11 's 's POS 7333 48 12 equations equation NNS 7333 48 13 for for IN 7333 48 14 free free JJ 7333 48 15 space space NN 7333 48 16 . . . 7333 49 1 As as IN 7333 49 2 to to IN 7333 49 3 the the DT 7333 49 4 mechanical mechanical JJ 7333 49 5 nature nature NN 7333 49 6 of of IN 7333 49 7 the the DT 7333 49 8 Lorentzian lorentzian JJ 7333 49 9 ether ether NN 7333 49 10 , , , 7333 49 11 it -PRON- PRP 7333 49 12 may may MD 7333 49 13 be be VB 7333 49 14 said say VBN 7333 49 15 of of IN 7333 49 16 it -PRON- PRP 7333 49 17 , , , 7333 49 18 in in IN 7333 49 19 a a DT 7333 49 20 somewhat somewhat RB 7333 49 21 playful playful JJ 7333 49 22 spirit spirit NN 7333 49 23 , , , 7333 49 24 that that DT 7333 49 25 immobility immobility NN 7333 49 26 is be VBZ 7333 49 27 the the DT 7333 49 28 only only JJ 7333 49 29 mechanical mechanical JJ 7333 49 30 property property NN 7333 49 31 of of IN 7333 49 32 which which WDT 7333 49 33 it -PRON- PRP 7333 49 34 has have VBZ 7333 49 35 not not RB 7333 49 36 been be VBN 7333 49 37 deprived deprive VBN 7333 49 38 by by IN 7333 49 39 H. H. NNP 7333 49 40 A. A. NNP 7333 49 41 Lorentz Lorentz NNP 7333 49 42 . . . 7333 50 1 It -PRON- PRP 7333 50 2 may may MD 7333 50 3 be be VB 7333 50 4 added add VBN 7333 50 5 that that IN 7333 50 6 the the DT 7333 50 7 whole whole JJ 7333 50 8 change change NN 7333 50 9 in in IN 7333 50 10 the the DT 7333 50 11 conception conception NN 7333 50 12 of of IN 7333 50 13 the the DT 7333 50 14 ether ether NN 7333 50 15 which which WDT 7333 50 16 the the DT 7333 50 17 special special JJ 7333 50 18 theory theory NN 7333 50 19 of of IN 7333 50 20 relativity relativity NN 7333 50 21 brought bring VBN 7333 50 22 about about RP 7333 50 23 , , , 7333 50 24 consisted consist VBN 7333 50 25 in in IN 7333 50 26 taking take VBG 7333 50 27 away away RB 7333 50 28 from from IN 7333 50 29 the the DT 7333 50 30 ether ether NN 7333 50 31 its -PRON- PRP$ 7333 50 32 last last JJ 7333 50 33 mechanical mechanical JJ 7333 50 34 quality quality NN 7333 50 35 , , , 7333 50 36 namely namely RB 7333 50 37 , , , 7333 50 38 its -PRON- PRP$ 7333 50 39 immobility immobility NN 7333 50 40 . . . 7333 51 1 How how WRB 7333 51 2 this this DT 7333 51 3 is be VBZ 7333 51 4 to to TO 7333 51 5 be be VB 7333 51 6 understood understand VBN 7333 51 7 will will MD 7333 51 8 forthwith forthwith VB 7333 51 9 be be VB 7333 51 10 expounded expound VBN 7333 51 11 . . . 7333 52 1 The the DT 7333 52 2 space space NN 7333 52 3 - - HYPH 7333 52 4 time time NN 7333 52 5 theory theory NN 7333 52 6 and and CC 7333 52 7 the the DT 7333 52 8 kinematics kinematics NNPS 7333 52 9 of of IN 7333 52 10 the the DT 7333 52 11 special special JJ 7333 52 12 theory theory NN 7333 52 13 of of IN 7333 52 14 relativity relativity NN 7333 52 15 were be VBD 7333 52 16 modelled model VBN 7333 52 17 on on IN 7333 52 18 the the DT 7333 52 19 Maxwell Maxwell NNP 7333 52 20 - - HYPH 7333 52 21 Lorentz Lorentz NNP 7333 52 22 theory theory NN 7333 52 23 of of IN 7333 52 24 the the DT 7333 52 25 electromagnetic electromagnetic JJ 7333 52 26 field field NN 7333 52 27 . . . 7333 53 1 This this DT 7333 53 2 theory theory NN 7333 53 3 therefore therefore RB 7333 53 4 satisfies satisfy VBZ 7333 53 5 the the DT 7333 53 6 conditions condition NNS 7333 53 7 of of IN 7333 53 8 the the DT 7333 53 9 special special JJ 7333 53 10 theory theory NN 7333 53 11 of of IN 7333 53 12 relativity relativity NN 7333 53 13 , , , 7333 53 14 but but CC 7333 53 15 when when WRB 7333 53 16 viewed view VBN 7333 53 17 from from IN 7333 53 18 the the DT 7333 53 19 latter latter JJ 7333 53 20 it -PRON- PRP 7333 53 21 acquires acquire VBZ 7333 53 22 a a DT 7333 53 23 novel novel JJ 7333 53 24 aspect aspect NN 7333 53 25 . . . 7333 54 1 For for IN 7333 54 2 if if IN 7333 54 3 K K NNP 7333 54 4 be be VB 7333 54 5 a a DT 7333 54 6 system system NN 7333 54 7 of of IN 7333 54 8 co co NNS 7333 54 9 - - NNS 7333 54 10 ordinates ordinate NNS 7333 54 11 relatively relatively RB 7333 54 12 to to TO 7333 54 13 which which WDT 7333 54 14 the the DT 7333 54 15 Lorentzian lorentzian JJ 7333 54 16 ether ether NN 7333 54 17 is be VBZ 7333 54 18 at at IN 7333 54 19 rest rest NN 7333 54 20 , , , 7333 54 21 the the DT 7333 54 22 Maxwell Maxwell NNP 7333 54 23 - - HYPH 7333 54 24 Lorentz Lorentz NNP 7333 54 25 equations equation NNS 7333 54 26 are be VBP 7333 54 27 valid valid JJ 7333 54 28 primarily primarily RB 7333 54 29 with with IN 7333 54 30 reference reference NN 7333 54 31 to to IN 7333 54 32 K. K. NNP 7333 54 33 But but CC 7333 54 34 by by IN 7333 54 35 the the DT 7333 54 36 special special JJ 7333 54 37 theory theory NN 7333 54 38 of of IN 7333 54 39 relativity relativity NN 7333 54 40 the the DT 7333 54 41 same same JJ 7333 54 42 equations equation NNS 7333 54 43 without without IN 7333 54 44 any any DT 7333 54 45 change change NN 7333 54 46 of of IN 7333 54 47 meaning meaning NN 7333 54 48 also also RB 7333 54 49 hold hold VBP 7333 54 50 in in IN 7333 54 51 relation relation NN 7333 54 52 to to IN 7333 54 53 any any DT 7333 54 54 new new JJ 7333 54 55 system system NN 7333 54 56 of of IN 7333 54 57 co co NNS 7333 54 58 - - JJ 7333 54 59 ordinates ordinate VBZ 7333 54 60 K K NNP 7333 54 61 ' ' '' 7333 54 62 which which WDT 7333 54 63 is be VBZ 7333 54 64 moving move VBG 7333 54 65 in in IN 7333 54 66 uniform uniform JJ 7333 54 67 translation translation NN 7333 54 68 relatively relatively RB 7333 54 69 to to IN 7333 54 70 K. K. NNP 7333 54 71 Now now RB 7333 54 72 comes come VBZ 7333 54 73 the the DT 7333 54 74 anxious anxious JJ 7333 54 75 question:--Why question:--Why NNS 7333 54 76 must must MD 7333 54 77 I -PRON- PRP 7333 54 78 in in IN 7333 54 79 the the DT 7333 54 80 theory theory NN 7333 54 81 distinguish distinguish VB 7333 54 82 the the DT 7333 54 83 K k NN 7333 54 84 system system NN 7333 54 85 above above IN 7333 54 86 all all DT 7333 54 87 K K NNP 7333 54 88 ' ' POS 7333 54 89 systems system NNS 7333 54 90 , , , 7333 54 91 which which WDT 7333 54 92 are be VBP 7333 54 93 physically physically RB 7333 54 94 equivalent equivalent JJ 7333 54 95 to to IN 7333 54 96 it -PRON- PRP 7333 54 97 in in IN 7333 54 98 all all DT 7333 54 99 respects respect NNS 7333 54 100 , , , 7333 54 101 by by IN 7333 54 102 assuming assume VBG 7333 54 103 that that IN 7333 54 104 the the DT 7333 54 105 ether ether NN 7333 54 106 is be VBZ 7333 54 107 at at IN 7333 54 108 rest rest NN 7333 54 109 relatively relatively RB 7333 54 110 to to IN 7333 54 111 the the DT 7333 54 112 K k NN 7333 54 113 system system NN 7333 54 114 ? ? . 7333 55 1 For for IN 7333 55 2 the the DT 7333 55 3 theoretician theoretician NN 7333 55 4 such such PDT 7333 55 5 an an DT 7333 55 6 asymmetry asymmetry NN 7333 55 7 in in IN 7333 55 8 the the DT 7333 55 9 theoretical theoretical JJ 7333 55 10 structure structure NN 7333 55 11 , , , 7333 55 12 with with IN 7333 55 13 no no DT 7333 55 14 corresponding correspond VBG 7333 55 15 asymmetry asymmetry NN 7333 55 16 in in IN 7333 55 17 the the DT 7333 55 18 system system NN 7333 55 19 of of IN 7333 55 20 experience experience NN 7333 55 21 , , , 7333 55 22 is be VBZ 7333 55 23 intolerable intolerable JJ 7333 55 24 . . . 7333 56 1 If if IN 7333 56 2 we -PRON- PRP 7333 56 3 assume assume VBP 7333 56 4 the the DT 7333 56 5 ether ether NN 7333 56 6 to to TO 7333 56 7 be be VB 7333 56 8 at at IN 7333 56 9 rest rest NN 7333 56 10 relatively relatively RB 7333 56 11 to to IN 7333 56 12 K K NNP 7333 56 13 , , , 7333 56 14 but but CC 7333 56 15 in in IN 7333 56 16 motion motion NN 7333 56 17 relatively relatively RB 7333 56 18 to to IN 7333 56 19 K K NNP 7333 56 20 ' ' '' 7333 56 21 , , , 7333 56 22 the the DT 7333 56 23 physical physical JJ 7333 56 24 equivalence equivalence NN 7333 56 25 of of IN 7333 56 26 K K NNP 7333 56 27 and and CC 7333 56 28 K K NNP 7333 56 29 ' ' '' 7333 56 30 seems seem VBZ 7333 56 31 to to IN 7333 56 32 me -PRON- PRP 7333 56 33 from from IN 7333 56 34 the the DT 7333 56 35 logical logical JJ 7333 56 36 standpoint standpoint NN 7333 56 37 , , , 7333 56 38 not not RB 7333 56 39 indeed indeed RB 7333 56 40 downright downright RB 7333 56 41 incorrect incorrect JJ 7333 56 42 , , , 7333 56 43 but but CC 7333 56 44 nevertheless nevertheless RB 7333 56 45 inacceptable inacceptable JJ 7333 56 46 . . . 7333 57 1 The the DT 7333 57 2 next next JJ 7333 57 3 position position NN 7333 57 4 which which WDT 7333 57 5 it -PRON- PRP 7333 57 6 was be VBD 7333 57 7 possible possible JJ 7333 57 8 to to TO 7333 57 9 take take VB 7333 57 10 up up RP 7333 57 11 in in IN 7333 57 12 face face NN 7333 57 13 of of IN 7333 57 14 this this DT 7333 57 15 state state NN 7333 57 16 of of IN 7333 57 17 things thing NNS 7333 57 18 appeared appear VBD 7333 57 19 to to TO 7333 57 20 be be VB 7333 57 21 the the DT 7333 57 22 following follow VBG 7333 57 23 . . . 7333 58 1 The the DT 7333 58 2 ether ether NN 7333 58 3 does do VBZ 7333 58 4 not not RB 7333 58 5 exist exist VB 7333 58 6 at at RB 7333 58 7 all all RB 7333 58 8 . . . 7333 59 1 The the DT 7333 59 2 electromagnetic electromagnetic JJ 7333 59 3 fields field NNS 7333 59 4 are be VBP 7333 59 5 not not RB 7333 59 6 states state NNS 7333 59 7 of of IN 7333 59 8 a a DT 7333 59 9 medium medium NN 7333 59 10 , , , 7333 59 11 and and CC 7333 59 12 are be VBP 7333 59 13 not not RB 7333 59 14 bound bind VBN 7333 59 15 down down RP 7333 59 16 to to IN 7333 59 17 any any DT 7333 59 18 bearer bearer NN 7333 59 19 , , , 7333 59 20 but but CC 7333 59 21 they -PRON- PRP 7333 59 22 are be VBP 7333 59 23 independent independent JJ 7333 59 24 realities reality NNS 7333 59 25 which which WDT 7333 59 26 are be VBP 7333 59 27 not not RB 7333 59 28 reducible reducible JJ 7333 59 29 to to IN 7333 59 30 anything anything NN 7333 59 31 else else RB 7333 59 32 , , , 7333 59 33 exactly exactly RB 7333 59 34 like like IN 7333 59 35 the the DT 7333 59 36 atoms atom NNS 7333 59 37 of of IN 7333 59 38 ponderable ponderable JJ 7333 59 39 matter matter NN 7333 59 40 . . . 7333 60 1 This this DT 7333 60 2 conception conception NN 7333 60 3 suggests suggest VBZ 7333 60 4 itself -PRON- PRP 7333 60 5 the the DT 7333 60 6 more more RBR 7333 60 7 readily readily RB 7333 60 8 as as IN 7333 60 9 , , , 7333 60 10 according accord VBG 7333 60 11 to to IN 7333 60 12 Lorentz Lorentz NNP 7333 60 13 's 's POS 7333 60 14 theory theory NN 7333 60 15 , , , 7333 60 16 electromagnetic electromagnetic JJ 7333 60 17 radiation radiation NN 7333 60 18 , , , 7333 60 19 like like IN 7333 60 20 ponderable ponderable JJ 7333 60 21 matter matter NN 7333 60 22 , , , 7333 60 23 brings bring VBZ 7333 60 24 impulse impulse NN 7333 60 25 and and CC 7333 60 26 energy energy NN 7333 60 27 with with IN 7333 60 28 it -PRON- PRP 7333 60 29 , , , 7333 60 30 and and CC 7333 60 31 as as IN 7333 60 32 , , , 7333 60 33 according accord VBG 7333 60 34 to to IN 7333 60 35 the the DT 7333 60 36 special special JJ 7333 60 37 theory theory NN 7333 60 38 of of IN 7333 60 39 relativity relativity NN 7333 60 40 , , , 7333 60 41 both both CC 7333 60 42 matter matter NN 7333 60 43 and and CC 7333 60 44 radiation radiation NN 7333 60 45 are be VBP 7333 60 46 but but CC 7333 60 47 special special JJ 7333 60 48 forms form NNS 7333 60 49 of of IN 7333 60 50 distributed distribute VBN 7333 60 51 energy energy NN 7333 60 52 , , , 7333 60 53 ponderable ponderable JJ 7333 60 54 mass mass NN 7333 60 55 losing lose VBG 7333 60 56 its -PRON- PRP$ 7333 60 57 isolation isolation NN 7333 60 58 and and CC 7333 60 59 appearing appear VBG 7333 60 60 as as IN 7333 60 61 a a DT 7333 60 62 special special JJ 7333 60 63 form form NN 7333 60 64 of of IN 7333 60 65 energy energy NN 7333 60 66 . . . 7333 61 1 More more RBR 7333 61 2 careful careful JJ 7333 61 3 reflection reflection NN 7333 61 4 teaches teach VBZ 7333 61 5 us -PRON- PRP 7333 61 6 , , , 7333 61 7 however however RB 7333 61 8 , , , 7333 61 9 that that IN 7333 61 10 the the DT 7333 61 11 special special JJ 7333 61 12 theory theory NN 7333 61 13 of of IN 7333 61 14 relativity relativity NN 7333 61 15 does do VBZ 7333 61 16 not not RB 7333 61 17 compel compel VB 7333 61 18 us -PRON- PRP 7333 61 19 to to TO 7333 61 20 deny deny VB 7333 61 21 ether ether NN 7333 61 22 . . . 7333 62 1 We -PRON- PRP 7333 62 2 may may MD 7333 62 3 assume assume VB 7333 62 4 the the DT 7333 62 5 existence existence NN 7333 62 6 of of IN 7333 62 7 an an DT 7333 62 8 ether ether NN 7333 62 9 ; ; : 7333 62 10 only only RB 7333 62 11 we -PRON- PRP 7333 62 12 must must MD 7333 62 13 give give VB 7333 62 14 up up RP 7333 62 15 ascribing ascribe VBG 7333 62 16 a a DT 7333 62 17 definite definite JJ 7333 62 18 state state NN 7333 62 19 of of IN 7333 62 20 motion motion NN 7333 62 21 to to IN 7333 62 22 it -PRON- PRP 7333 62 23 , , , 7333 62 24 i.e. i.e. FW 7333 63 1 we -PRON- PRP 7333 63 2 must must MD 7333 63 3 by by IN 7333 63 4 abstraction abstraction NN 7333 63 5 take take VB 7333 63 6 from from IN 7333 63 7 it -PRON- PRP 7333 63 8 the the DT 7333 63 9 last last JJ 7333 63 10 mechanical mechanical JJ 7333 63 11 characteristic characteristic NN 7333 63 12 which which WDT 7333 63 13 Lorentz Lorentz NNP 7333 63 14 had have VBD 7333 63 15 still still RB 7333 63 16 left leave VBN 7333 63 17 it -PRON- PRP 7333 63 18 . . . 7333 64 1 We -PRON- PRP 7333 64 2 shall shall MD 7333 64 3 see see VB 7333 64 4 later later RBR 7333 64 5 that that IN 7333 64 6 this this DT 7333 64 7 point point NN 7333 64 8 of of IN 7333 64 9 view view NN 7333 64 10 , , , 7333 64 11 the the DT 7333 64 12 conceivability conceivability NN 7333 64 13 of of IN 7333 64 14 which which WDT 7333 64 15 I -PRON- PRP 7333 64 16 shall shall MD 7333 64 17 at at IN 7333 64 18 once once RB 7333 64 19 endeavour endeavour VB 7333 64 20 to to TO 7333 64 21 make make VB 7333 64 22 more more RBR 7333 64 23 intelligible intelligible JJ 7333 64 24 by by IN 7333 64 25 a a DT 7333 64 26 somewhat somewhat RB 7333 64 27 halting halting JJ 7333 64 28 comparison comparison NN 7333 64 29 , , , 7333 64 30 is be VBZ 7333 64 31 justified justify VBN 7333 64 32 by by IN 7333 64 33 the the DT 7333 64 34 results result NNS 7333 64 35 of of IN 7333 64 36 the the DT 7333 64 37 general general JJ 7333 64 38 theory theory NN 7333 64 39 of of IN 7333 64 40 relativity relativity NN 7333 64 41 . . . 7333 65 1 Think think VB 7333 65 2 of of IN 7333 65 3 waves wave NNS 7333 65 4 on on IN 7333 65 5 the the DT 7333 65 6 surface surface NN 7333 65 7 of of 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a a DT 7333 68 19 fundamental fundamental JJ 7333 68 20 impossibility impossibility NN 7333 68 21 in in IN 7333 68 22 physics physics NN 7333 68 23 -- -- : 7333 68 24 if if IN 7333 68 25 , , , 7333 68 26 in in IN 7333 68 27 fact fact NN 7333 68 28 , , , 7333 68 29 nothing nothing NN 7333 68 30 else else RB 7333 68 31 whatever whatever WDT 7333 68 32 were be VBD 7333 68 33 observable observable JJ 7333 68 34 than than IN 7333 68 35 the the DT 7333 68 36 shape shape NN 7333 68 37 of of IN 7333 68 38 the the DT 7333 68 39 space space NN 7333 68 40 occupied occupy VBN 7333 68 41 by by IN 7333 68 42 the the DT 7333 68 43 water water NN 7333 68 44 as as IN 7333 68 45 it -PRON- PRP 7333 68 46 varies vary VBZ 7333 68 47 in in IN 7333 68 48 time time NN 7333 68 49 , , , 7333 68 50 we -PRON- PRP 7333 68 51 should should MD 7333 68 52 have have VB 7333 68 53 no no DT 7333 68 54 ground ground NN 7333 68 55 for for IN 7333 68 56 the the DT 7333 68 57 assumption assumption NN 7333 68 58 that that IN 7333 68 59 water water NN 7333 68 60 consists consist VBZ 7333 68 61 of of IN 7333 68 62 movable movable JJ 7333 68 63 particles particle NNS 7333 68 64 . . . 7333 69 1 But but CC 7333 69 2 all all PDT 7333 69 3 the the DT 7333 69 4 same same JJ 7333 69 5 we -PRON- PRP 7333 69 6 could could MD 7333 69 7 characterise characterise VB 7333 69 8 it -PRON- PRP 7333 69 9 as as IN 7333 69 10 a a DT 7333 69 11 medium medium NN 7333 69 12 . . . 7333 70 1 We -PRON- PRP 7333 70 2 have have VBP 7333 70 3 something something NN 7333 70 4 like like IN 7333 70 5 this this DT 7333 70 6 in in IN 7333 70 7 the the DT 7333 70 8 electromagnetic electromagnetic JJ 7333 70 9 field field NN 7333 70 10 . . . 7333 71 1 For for IN 7333 71 2 we -PRON- PRP 7333 71 3 may may MD 7333 71 4 picture picture VB 7333 71 5 the the DT 7333 71 6 field field NN 7333 71 7 to to IN 7333 71 8 ourselves -PRON- PRP 7333 71 9 as as IN 7333 71 10 consisting consist VBG 7333 71 11 of of IN 7333 71 12 lines line NNS 7333 71 13 of of 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separate separate JJ 7333 72 40 line line NN 7333 72 41 of of IN 7333 72 42 force force NN 7333 72 43 is be VBZ 7333 72 44 tracked track VBN 7333 72 45 through through IN 7333 72 46 the the DT 7333 72 47 course course NN 7333 72 48 of of IN 7333 72 49 time time NN 7333 72 50 . . . 7333 73 1 It -PRON- PRP 7333 73 2 is be VBZ 7333 73 3 well well RB 7333 73 4 known known JJ 7333 73 5 , , , 7333 73 6 however however RB 7333 73 7 , , , 7333 73 8 that that IN 7333 73 9 this this DT 7333 73 10 way way NN 7333 73 11 of of IN 7333 73 12 regarding regard VBG 7333 73 13 the the DT 7333 73 14 electromagnetic electromagnetic JJ 7333 73 15 field field NN 7333 73 16 leads lead VBZ 7333 73 17 to to IN 7333 73 18 contradictions contradiction NNS 7333 73 19 . . . 7333 74 1 Generalising generalise VBG 7333 74 2 we -PRON- PRP 7333 74 3 must must MD 7333 74 4 say say VB 7333 74 5 this:--There this:--there RB 7333 74 6 may may MD 7333 74 7 be be VB 7333 74 8 supposed suppose VBN 7333 74 9 to to TO 7333 74 10 be be VB 7333 74 11 extended extend VBN 7333 74 12 physical physical JJ 7333 74 13 objects object NNS 7333 74 14 to to TO 7333 74 15 which which WDT 7333 74 16 the the DT 7333 74 17 idea idea NN 7333 74 18 of of IN 7333 74 19 motion motion NN 7333 74 20 can can MD 7333 74 21 not not RB 7333 74 22 be be VB 7333 74 23 applied apply VBN 7333 74 24 . . . 7333 75 1 They -PRON- PRP 7333 75 2 may may MD 7333 75 3 not not RB 7333 75 4 be be VB 7333 75 5 thought think VBN 7333 75 6 of of IN 7333 75 7 as as IN 7333 75 8 consisting consist VBG 7333 75 9 of of IN 7333 75 10 particles particle NNS 7333 75 11 which which WDT 7333 75 12 allow allow VBP 7333 75 13 themselves -PRON- PRP 7333 75 14 to to TO 7333 75 15 be be VB 7333 75 16 separately separately RB 7333 75 17 tracked track VBN 7333 75 18 through through IN 7333 75 19 time time NN 7333 75 20 . . . 7333 76 1 In in IN 7333 76 2 Minkowski Minkowski NNP 7333 76 3 's 's POS 7333 76 4 idiom idiom NN 7333 76 5 this this DT 7333 76 6 is be VBZ 7333 76 7 expressed express VBN 7333 76 8 as as IN 7333 76 9 follows:--Not follows:--Not NNS 7333 76 10 every every DT 7333 76 11 extended extend VBN 7333 76 12 conformation conformation NN 7333 76 13 in in IN 7333 76 14 the the DT 7333 76 15 four four CD 7333 76 16 - - HYPH 7333 76 17 dimensional dimensional JJ 7333 76 18 world world NN 7333 76 19 can can MD 7333 76 20 be be VB 7333 76 21 regarded regard VBN 7333 76 22 as as IN 7333 76 23 composed compose VBN 7333 76 24 of of IN 7333 76 25 world world NN 7333 76 26 - - HYPH 7333 76 27 threads thread NNS 7333 76 28 . . . 7333 77 1 The the DT 7333 77 2 special special JJ 7333 77 3 theory theory NN 7333 77 4 of of IN 7333 77 5 relativity relativity NN 7333 77 6 forbids forbid VBZ 7333 77 7 us -PRON- PRP 7333 77 8 to to TO 7333 77 9 assume assume VB 7333 77 10 the the DT 7333 77 11 ether ether NN 7333 77 12 to to TO 7333 77 13 consist consist VB 7333 77 14 of of IN 7333 77 15 particles particle NNS 7333 77 16 observable observable JJ 7333 77 17 through through IN 7333 77 18 time time NN 7333 77 19 , , , 7333 77 20 but but CC 7333 77 21 the the DT 7333 77 22 hypothesis hypothesis NN 7333 77 23 of of IN 7333 77 24 ether ether NN 7333 77 25 in in IN 7333 77 26 itself -PRON- PRP 7333 77 27 is be VBZ 7333 77 28 not not RB 7333 77 29 in in IN 7333 77 30 conflict conflict NN 7333 77 31 with with IN 7333 77 32 the the DT 7333 77 33 special special JJ 7333 77 34 theory theory NN 7333 77 35 of of IN 7333 77 36 relativity relativity NN 7333 77 37 . . . 7333 78 1 Only only RB 7333 78 2 we -PRON- PRP 7333 78 3 must must MD 7333 78 4 be be VB 7333 78 5 on on IN 7333 78 6 our -PRON- PRP$ 7333 78 7 guard guard NN 7333 78 8 against against IN 7333 78 9 ascribing ascribe VBG 7333 78 10 a a DT 7333 78 11 state state NN 7333 78 12 of of IN 7333 78 13 motion motion NN 7333 78 14 to to IN 7333 78 15 the the DT 7333 78 16 ether ether NN 7333 78 17 . . . 7333 79 1 Certainly certainly RB 7333 79 2 , , , 7333 79 3 from from IN 7333 79 4 the the DT 7333 79 5 standpoint standpoint NN 7333 79 6 of of IN 7333 79 7 the the DT 7333 79 8 special special JJ 7333 79 9 theory theory NN 7333 79 10 of of IN 7333 79 11 relativity relativity NN 7333 79 12 , , , 7333 79 13 the the DT 7333 79 14 ether ether NN 7333 79 15 hypothesis hypothesis NN 7333 79 16 appears appear VBZ 7333 79 17 at at IN 7333 79 18 first first RB 7333 79 19 to to TO 7333 79 20 be be VB 7333 79 21 an an DT 7333 79 22 empty empty JJ 7333 79 23 hypothesis hypothesis NN 7333 79 24 . . . 7333 80 1 In in IN 7333 80 2 the the DT 7333 80 3 equations equation NNS 7333 80 4 of of IN 7333 80 5 the the DT 7333 80 6 electromagnetic electromagnetic JJ 7333 80 7 field field NN 7333 80 8 there there RB 7333 80 9 occur occur VBP 7333 80 10 , , , 7333 80 11 in in IN 7333 80 12 addition addition NN 7333 80 13 to to IN 7333 80 14 the the DT 7333 80 15 densities density NNS 7333 80 16 of of IN 7333 80 17 the the DT 7333 80 18 electric electric JJ 7333 80 19 charge charge NN 7333 80 20 , , , 7333 80 21 _ _ NNP 7333 80 22 only only RB 7333 80 23 _ _ NNP 7333 80 24 the the DT 7333 80 25 intensities intensity NNS 7333 80 26 of of IN 7333 80 27 the the DT 7333 80 28 field field NN 7333 80 29 . . . 7333 81 1 The the DT 7333 81 2 career career NN 7333 81 3 of of IN 7333 81 4 electromagnetic electromagnetic JJ 7333 81 5 processes process NNS 7333 81 6 _ _ NNP 7333 81 7 in in IN 7333 81 8 vacuo vacuo NNS 7333 81 9 _ _ NNP 7333 81 10 appears appear VBZ 7333 81 11 to to TO 7333 81 12 be be VB 7333 81 13 completely completely RB 7333 81 14 determined determine VBN 7333 81 15 by by IN 7333 81 16 these these DT 7333 81 17 equations equation NNS 7333 81 18 , , , 7333 81 19 uninfluenced uninfluence VBN 7333 81 20 by by IN 7333 81 21 other other JJ 7333 81 22 physical physical JJ 7333 81 23 quantities quantity NNS 7333 81 24 . . . 7333 82 1 The the DT 7333 82 2 electromagnetic electromagnetic JJ 7333 82 3 fields field NNS 7333 82 4 appear appear VBP 7333 82 5 as as IN 7333 82 6 ultimate ultimate JJ 7333 82 7 , , , 7333 82 8 irreducible irreducible JJ 7333 82 9 realities reality NNS 7333 82 10 , , , 7333 82 11 and and CC 7333 82 12 at at IN 7333 82 13 first first RB 7333 82 14 it -PRON- PRP 7333 82 15 seems seem VBZ 7333 82 16 superfluous superfluous JJ 7333 82 17 to to TO 7333 82 18 postulate postulate VB 7333 82 19 a a DT 7333 82 20 homogeneous homogeneous JJ 7333 82 21 , , , 7333 82 22 isotropic isotropic JJ 7333 82 23 ether ether NN 7333 82 24 - - HYPH 7333 82 25 medium medium NN 7333 82 26 , , , 7333 82 27 and and CC 7333 82 28 to to TO 7333 82 29 envisage envisage VB 7333 82 30 electromagnetic electromagnetic JJ 7333 82 31 fields field NNS 7333 82 32 as as IN 7333 82 33 states state NNS 7333 82 34 of of IN 7333 82 35 this this DT 7333 82 36 medium medium NN 7333 82 37 . . . 7333 83 1 But but CC 7333 83 2 on on IN 7333 83 3 the the DT 7333 83 4 other other JJ 7333 83 5 hand hand NN 7333 83 6 there there EX 7333 83 7 is be VBZ 7333 83 8 a a DT 7333 83 9 weighty weighty JJ 7333 83 10 argument argument NN 7333 83 11 to to TO 7333 83 12 be be VB 7333 83 13 adduced adduce VBN 7333 83 14 in in IN 7333 83 15 favour favour NN 7333 83 16 of of IN 7333 83 17 the the DT 7333 83 18 ether ether NN 7333 83 19 hypothesis hypothesis NN 7333 83 20 . . . 7333 84 1 To to TO 7333 84 2 deny deny VB 7333 84 3 the the DT 7333 84 4 ether ether NN 7333 84 5 is be VBZ 7333 84 6 ultimately ultimately RB 7333 84 7 to to TO 7333 84 8 assume assume VB 7333 84 9 that that IN 7333 84 10 empty empty JJ 7333 84 11 space space NN 7333 84 12 has have VBZ 7333 84 13 no no DT 7333 84 14 physical physical JJ 7333 84 15 qualities quality NNS 7333 84 16 whatever whatever WDT 7333 84 17 . . . 7333 85 1 The the DT 7333 85 2 fundamental fundamental JJ 7333 85 3 facts fact NNS 7333 85 4 of of IN 7333 85 5 mechanics mechanic NNS 7333 85 6 do do VBP 7333 85 7 not not RB 7333 85 8 harmonize harmonize VB 7333 85 9 with with IN 7333 85 10 this this DT 7333 85 11 view view NN 7333 85 12 . . . 7333 86 1 For for IN 7333 86 2 the the DT 7333 86 3 mechanical mechanical JJ 7333 86 4 behaviour behaviour NN 7333 86 5 of of IN 7333 86 6 a a DT 7333 86 7 corporeal corporeal NN 7333 86 8 system system NN 7333 86 9 hovering hover VBG 7333 86 10 freely freely RB 7333 86 11 in in IN 7333 86 12 empty empty JJ 7333 86 13 space space NN 7333 86 14 depends depend VBZ 7333 86 15 not not RB 7333 86 16 only only RB 7333 86 17 on on IN 7333 86 18 relative relative JJ 7333 86 19 positions position NNS 7333 86 20 ( ( -LRB- 7333 86 21 distances distance NNS 7333 86 22 ) ) -RRB- 7333 86 23 and and CC 7333 86 24 relative relative JJ 7333 86 25 velocities velocity NNS 7333 86 26 , , , 7333 86 27 but but CC 7333 86 28 also also RB 7333 86 29 on on IN 7333 86 30 its -PRON- PRP$ 7333 86 31 state state NN 7333 86 32 of of IN 7333 86 33 rotation rotation NN 7333 86 34 , , , 7333 86 35 which which WDT 7333 86 36 physically physically RB 7333 86 37 may may MD 7333 86 38 be be VB 7333 86 39 taken take VBN 7333 86 40 as as IN 7333 86 41 a a DT 7333 86 42 characteristic characteristic NN 7333 86 43 not not RB 7333 86 44 appertaining appertain VBG 7333 86 45 to to IN 7333 86 46 the the DT 7333 86 47 system system NN 7333 86 48 in in IN 7333 86 49 itself -PRON- PRP 7333 86 50 . . . 7333 87 1 In in IN 7333 87 2 order order NN 7333 87 3 to to TO 7333 87 4 be be VB 7333 87 5 able able JJ 7333 87 6 to to TO 7333 87 7 look look VB 7333 87 8 upon upon IN 7333 87 9 the the DT 7333 87 10 rotation rotation NN 7333 87 11 of of IN 7333 87 12 the the DT 7333 87 13 system system NN 7333 87 14 , , , 7333 87 15 at at IN 7333 87 16 least least JJS 7333 87 17 formally formally RB 7333 87 18 , , , 7333 87 19 as as IN 7333 87 20 something something NN 7333 87 21 real real JJ 7333 87 22 , , , 7333 87 23 Newton Newton NNP 7333 87 24 objectivises objectivise VBZ 7333 87 25 space space NN 7333 87 26 . . . 7333 88 1 Since since IN 7333 88 2 he -PRON- PRP 7333 88 3 classes class VBZ 7333 88 4 his -PRON- PRP$ 7333 88 5 absolute absolute JJ 7333 88 6 space space NN 7333 88 7 together together RB 7333 88 8 with with IN 7333 88 9 real real JJ 7333 88 10 things thing NNS 7333 88 11 , , , 7333 88 12 for for IN 7333 88 13 him -PRON- PRP 7333 88 14 rotation rotation NN 7333 88 15 relative relative JJ 7333 88 16 to to IN 7333 88 17 an an DT 7333 88 18 absolute absolute JJ 7333 88 19 space space NN 7333 88 20 is be VBZ 7333 88 21 also also RB 7333 88 22 something something NN 7333 88 23 real real JJ 7333 88 24 . . . 7333 89 1 Newton Newton NNP 7333 89 2 might may MD 7333 89 3 no no RB 7333 89 4 less less RBR 7333 89 5 well well RB 7333 89 6 have have VB 7333 89 7 called call VBN 7333 89 8 his -PRON- PRP$ 7333 89 9 absolute absolute JJ 7333 89 10 space space NN 7333 89 11 " " `` 7333 89 12 Ether Ether NNP 7333 89 13 " " '' 7333 89 14 ; ; : 7333 89 15 what what WP 7333 89 16 is be VBZ 7333 89 17 essential essential JJ 7333 89 18 is be VBZ 7333 89 19 merely merely RB 7333 89 20 that that DT 7333 89 21 besides besides IN 7333 89 22 observable observable JJ 7333 89 23 objects object NNS 7333 89 24 , , , 7333 89 25 another another DT 7333 89 26 thing thing NN 7333 89 27 , , , 7333 89 28 which which WDT 7333 89 29 is be VBZ 7333 89 30 not not RB 7333 89 31 perceptible perceptible JJ 7333 89 32 , , , 7333 89 33 must must MD 7333 89 34 be be VB 7333 89 35 looked look VBN 7333 89 36 upon upon IN 7333 89 37 as as IN 7333 89 38 real real JJ 7333 89 39 , , , 7333 89 40 to to TO 7333 89 41 enable enable VB 7333 89 42 acceleration acceleration NN 7333 89 43 or or CC 7333 89 44 rotation rotation NN 7333 89 45 to to TO 7333 89 46 be be VB 7333 89 47 looked look VBN 7333 89 48 upon upon IN 7333 89 49 as as IN 7333 89 50 something something NN 7333 89 51 real real JJ 7333 89 52 . . . 7333 90 1 It -PRON- PRP 7333 90 2 is be VBZ 7333 90 3 true true JJ 7333 90 4 that that IN 7333 90 5 Mach Mach NNP 7333 90 6 tried try VBD 7333 90 7 to to TO 7333 90 8 avoid avoid VB 7333 90 9 having have VBG 7333 90 10 to to TO 7333 90 11 accept accept VB 7333 90 12 as as IN 7333 90 13 real real JJ 7333 90 14 something something NN 7333 90 15 which which WDT 7333 90 16 is be VBZ 7333 90 17 not not RB 7333 90 18 observable observable JJ 7333 90 19 by by IN 7333 90 20 endeavouring endeavour VBG 7333 90 21 to to TO 7333 90 22 substitute substitute VB 7333 90 23 in in IN 7333 90 24 mechanics mechanic NNS 7333 90 25 a a DT 7333 90 26 mean mean JJ 7333 90 27 acceleration acceleration NN 7333 90 28 with with IN 7333 90 29 reference reference NN 7333 90 30 to to IN 7333 90 31 the the DT 7333 90 32 totality totality NN 7333 90 33 of of IN 7333 90 34 the the DT 7333 90 35 masses masse NNS 7333 90 36 in in IN 7333 90 37 the the DT 7333 90 38 universe universe NN 7333 90 39 in in IN 7333 90 40 place place NN 7333 90 41 of of IN 7333 90 42 an an DT 7333 90 43 acceleration acceleration NN 7333 90 44 with with IN 7333 90 45 reference reference NN 7333 90 46 to to IN 7333 90 47 absolute absolute JJ 7333 90 48 space space NN 7333 90 49 . . . 7333 91 1 But but CC 7333 91 2 inertial inertial JJ 7333 91 3 resistance resistance NN 7333 91 4 opposed oppose VBN 7333 91 5 to to TO 7333 91 6 relative relative JJ 7333 91 7 acceleration acceleration NN 7333 91 8 of of IN 7333 91 9 distant distant JJ 7333 91 10 masses masse NNS 7333 91 11 presupposes presuppose VBZ 7333 91 12 action action NN 7333 91 13 at at IN 7333 91 14 a a DT 7333 91 15 distance distance NN 7333 91 16 ; ; : 7333 91 17 and and CC 7333 91 18 as as IN 7333 91 19 the the DT 7333 91 20 modern modern JJ 7333 91 21 physicist physicist NN 7333 91 22 does do VBZ 7333 91 23 not not RB 7333 91 24 believe believe VB 7333 91 25 that that IN 7333 91 26 he -PRON- PRP 7333 91 27 may may MD 7333 91 28 accept accept VB 7333 91 29 this this DT 7333 91 30 action action NN 7333 91 31 at at IN 7333 91 32 a a DT 7333 91 33 distance distance NN 7333 91 34 , , , 7333 91 35 he -PRON- PRP 7333 91 36 comes come VBZ 7333 91 37 back back RB 7333 91 38 once once RB 7333 91 39 more more RBR 7333 91 40 , , , 7333 91 41 if if IN 7333 91 42 he -PRON- PRP 7333 91 43 follows follow VBZ 7333 91 44 Mach Mach NNP 7333 91 45 , , , 7333 91 46 to to IN 7333 91 47 the the DT 7333 91 48 ether ether NN 7333 91 49 , , , 7333 91 50 which which WDT 7333 91 51 has have VBZ 7333 91 52 to to TO 7333 91 53 serve serve VB 7333 91 54 as as IN 7333 91 55 medium medium NN 7333 91 56 for for IN 7333 91 57 the the DT 7333 91 58 effects effect NNS 7333 91 59 of of IN 7333 91 60 inertia inertia NN 7333 91 61 . . . 7333 92 1 But but CC 7333 92 2 this this DT 7333 92 3 conception conception NN 7333 92 4 of of IN 7333 92 5 the the DT 7333 92 6 ether ether NN 7333 92 7 to to TO 7333 92 8 which which WDT 7333 92 9 we -PRON- PRP 7333 92 10 are be VBP 7333 92 11 led lead VBN 7333 92 12 by by IN 7333 92 13 Mach Mach NNP 7333 92 14 's 's POS 7333 92 15 way way NN 7333 92 16 of of IN 7333 92 17 thinking thinking NN 7333 92 18 differs differ VBZ 7333 92 19 essentially essentially RB 7333 92 20 from from IN 7333 92 21 the the DT 7333 92 22 ether ether NN 7333 92 23 as as IN 7333 92 24 conceived conceive VBN 7333 92 25 by by IN 7333 92 26 Newton Newton NNP 7333 92 27 , , , 7333 92 28 by by IN 7333 92 29 Fresnel Fresnel NNP 7333 92 30 , , , 7333 92 31 and and CC 7333 92 32 by by IN 7333 92 33 Lorentz Lorentz NNP 7333 92 34 . . . 7333 93 1 Mach Mach NNP 7333 93 2 's 's POS 7333 93 3 ether ether NN 7333 93 4 not not RB 7333 93 5 only only RB 7333 93 6 _ _ NNP 7333 93 7 conditions condition NNS 7333 93 8 _ _ IN 7333 93 9 the the DT 7333 93 10 behaviour behaviour NN 7333 93 11 of of IN 7333 93 12 inert inert JJ 7333 93 13 masses masse NNS 7333 93 14 , , , 7333 93 15 but but CC 7333 93 16 _ _ NNP 7333 93 17 is be VBZ 7333 93 18 also also RB 7333 93 19 conditioned condition VBN 7333 93 20 _ _ NNP 7333 93 21 in in IN 7333 93 22 its -PRON- PRP$ 7333 93 23 state state NN 7333 93 24 by by IN 7333 93 25 them -PRON- PRP 7333 93 26 . . . 7333 94 1 Mach Mach NNP 7333 94 2 's 's POS 7333 94 3 idea idea NN 7333 94 4 finds find VBZ 7333 94 5 its -PRON- PRP$ 7333 94 6 full full JJ 7333 94 7 development development NN 7333 94 8 in in IN 7333 94 9 the the DT 7333 94 10 ether ether NN 7333 94 11 of of IN 7333 94 12 the the DT 7333 94 13 general general JJ 7333 94 14 theory theory NN 7333 94 15 of of IN 7333 94 16 relativity relativity NN 7333 94 17 . . . 7333 95 1 According accord VBG 7333 95 2 to to IN 7333 95 3 this this DT 7333 95 4 theory theory NN 7333 95 5 the the DT 7333 95 6 metrical metrical JJ 7333 95 7 qualities quality NNS 7333 95 8 of of IN 7333 95 9 the the DT 7333 95 10 continuum continuum NN 7333 95 11 of of IN 7333 95 12 space space NN 7333 95 13 - - HYPH 7333 95 14 time time NN 7333 95 15 differ differ VBP 7333 95 16 in in IN 7333 95 17 the the DT 7333 95 18 environment environment NN 7333 95 19 of of IN 7333 95 20 different different JJ 7333 95 21 points point NNS 7333 95 22 of of IN 7333 95 23 space space NN 7333 95 24 - - HYPH 7333 95 25 time time NN 7333 95 26 , , , 7333 95 27 and and CC 7333 95 28 are be VBP 7333 95 29 partly partly RB 7333 95 30 conditioned condition VBN 7333 95 31 by by IN 7333 95 32 the the DT 7333 95 33 matter matter NN 7333 95 34 existing exist VBG 7333 95 35 outside outside RB 7333 95 36 of of IN 7333 95 37 the the DT 7333 95 38 territory territory NN 7333 95 39 under under IN 7333 95 40 consideration consideration NN 7333 95 41 . . . 7333 96 1 This this DT 7333 96 2 space space NN 7333 96 3 - - HYPH 7333 96 4 time time NN 7333 96 5 variability variability NN 7333 96 6 of of IN 7333 96 7 the the DT 7333 96 8 reciprocal reciprocal JJ 7333 96 9 relations relation NNS 7333 96 10 of of IN 7333 96 11 the the DT 7333 96 12 standards standard NNS 7333 96 13 of of IN 7333 96 14 space space NN 7333 96 15 and and CC 7333 96 16 time time NN 7333 96 17 , , , 7333 96 18 or or CC 7333 96 19 , , , 7333 96 20 perhaps perhaps RB 7333 96 21 , , , 7333 96 22 the the DT 7333 96 23 recognition recognition NN 7333 96 24 of of IN 7333 96 25 the the DT 7333 96 26 fact fact NN 7333 96 27 that that IN 7333 96 28 " " `` 7333 96 29 empty empty JJ 7333 96 30 space space NN 7333 96 31 " " '' 7333 96 32 in in IN 7333 96 33 its -PRON- PRP$ 7333 96 34 physical physical JJ 7333 96 35 relation relation NN 7333 96 36 is be VBZ 7333 96 37 neither neither CC 7333 96 38 homogeneous homogeneous JJ 7333 96 39 nor nor CC 7333 96 40 isotropic isotropic JJ 7333 96 41 , , , 7333 96 42 compelling compel VBG 7333 96 43 us -PRON- PRP 7333 96 44 to to TO 7333 96 45 describe describe VB 7333 96 46 its -PRON- PRP$ 7333 96 47 state state NN 7333 96 48 by by IN 7333 96 49 ten ten CD 7333 96 50 functions function NNS 7333 96 51 ( ( -LRB- 7333 96 52 the the DT 7333 96 53 gravitation gravitation NN 7333 96 54 potentials potential NNS 7333 96 55 g_(mn g_(mn NNP 7333 96 56 ) ) -RRB- 7333 96 57 ) ) -RRB- 7333 96 58 , , , 7333 96 59 has have VBZ 7333 96 60 , , , 7333 96 61 I -PRON- PRP 7333 96 62 think think VBP 7333 96 63 , , , 7333 96 64 finally finally RB 7333 96 65 disposed dispose VBN 7333 96 66 of of IN 7333 96 67 the the DT 7333 96 68 view view NN 7333 96 69 that that DT 7333 96 70 space space NN 7333 96 71 is be VBZ 7333 96 72 physically physically RB 7333 96 73 empty empty JJ 7333 96 74 . . . 7333 97 1 But but CC 7333 97 2 therewith therewith NNP 7333 97 3 the the DT 7333 97 4 conception conception NN 7333 97 5 of of IN 7333 97 6 the the DT 7333 97 7 ether ether NN 7333 97 8 has have VBZ 7333 97 9 again again RB 7333 97 10 acquired acquire VBN 7333 97 11 an an DT 7333 97 12 intelligible intelligible JJ 7333 97 13 content content NN 7333 97 14 , , , 7333 97 15 although although IN 7333 97 16 this this DT 7333 97 17 content content NN 7333 97 18 differs differ VBZ 7333 97 19 widely widely RB 7333 97 20 from from IN 7333 97 21 that that DT 7333 97 22 of of IN 7333 97 23 the the DT 7333 97 24 ether ether NN 7333 97 25 of of IN 7333 97 26 the the DT 7333 97 27 mechanical mechanical JJ 7333 97 28 undulatory undulatory JJ 7333 97 29 theory theory NN 7333 97 30 of of IN 7333 97 31 light light NN 7333 97 32 . . . 7333 98 1 The the DT 7333 98 2 ether ether NN 7333 98 3 of of IN 7333 98 4 the the DT 7333 98 5 general general JJ 7333 98 6 theory theory NN 7333 98 7 of of IN 7333 98 8 relativity relativity NN 7333 98 9 is be VBZ 7333 98 10 a a DT 7333 98 11 medium medium NN 7333 98 12 which which WDT 7333 98 13 is be VBZ 7333 98 14 itself -PRON- PRP 7333 98 15 devoid devoid JJ 7333 98 16 of of IN 7333 98 17 _ _ NNP 7333 98 18 all all DT 7333 98 19 _ _ NNP 7333 98 20 mechanical mechanical JJ 7333 98 21 and and CC 7333 98 22 kinematical kinematical JJ 7333 98 23 qualities quality NNS 7333 98 24 , , , 7333 98 25 but but CC 7333 98 26 helps help VBZ 7333 98 27 to to TO 7333 98 28 determine determine VB 7333 98 29 mechanical mechanical JJ 7333 98 30 ( ( -LRB- 7333 98 31 and and CC 7333 98 32 electromagnetic electromagnetic JJ 7333 98 33 ) ) -RRB- 7333 98 34 events event NNS 7333 98 35 . . . 7333 99 1 What what WP 7333 99 2 is be VBZ 7333 99 3 fundamentally fundamentally RB 7333 99 4 new new JJ 7333 99 5 in in IN 7333 99 6 the the DT 7333 99 7 ether ether NN 7333 99 8 of of IN 7333 99 9 the the DT 7333 99 10 general general JJ 7333 99 11 theory theory NN 7333 99 12 of of IN 7333 99 13 relativity relativity NN 7333 99 14 as as IN 7333 99 15 opposed oppose VBN 7333 99 16 to to IN 7333 99 17 the the DT 7333 99 18 ether ether NN 7333 99 19 of of IN 7333 99 20 Lorentz Lorentz NNP 7333 99 21 consists consist VBZ 7333 99 22 in in IN 7333 99 23 this this DT 7333 99 24 , , , 7333 99 25 that that IN 7333 99 26 the the DT 7333 99 27 state state NN 7333 99 28 of of IN 7333 99 29 the the DT 7333 99 30 former former JJ 7333 99 31 is be VBZ 7333 99 32 at at IN 7333 99 33 every every DT 7333 99 34 place place NN 7333 99 35 determined determine VBN 7333 99 36 by by IN 7333 99 37 connections connection NNS 7333 99 38 with with IN 7333 99 39 the the DT 7333 99 40 matter matter NN 7333 99 41 and and CC 7333 99 42 the the DT 7333 99 43 state state NN 7333 99 44 of of IN 7333 99 45 the the DT 7333 99 46 ether ether NN 7333 99 47 in in IN 7333 99 48 neighbouring neighbouring NN 7333 99 49 places place NNS 7333 99 50 , , , 7333 99 51 which which WDT 7333 99 52 are be VBP 7333 99 53 amenable amenable JJ 7333 99 54 to to IN 7333 99 55 law law NN 7333 99 56 in in IN 7333 99 57 the the DT 7333 99 58 form form NN 7333 99 59 of of IN 7333 99 60 differential differential JJ 7333 99 61 equations equation NNS 7333 99 62 ; ; : 7333 99 63 whereas whereas IN 7333 99 64 the the DT 7333 99 65 state state NN 7333 99 66 of of IN 7333 99 67 the the DT 7333 99 68 Lorentzian lorentzian JJ 7333 99 69 ether ether NN 7333 99 70 in in IN 7333 99 71 the the DT 7333 99 72 absence absence NN 7333 99 73 of of IN 7333 99 74 electromagnetic electromagnetic JJ 7333 99 75 fields field NNS 7333 99 76 is be VBZ 7333 99 77 conditioned condition VBN 7333 99 78 by by IN 7333 99 79 nothing nothing NN 7333 99 80 outside outside IN 7333 99 81 itself -PRON- PRP 7333 99 82 , , , 7333 99 83 and and CC 7333 99 84 is be VBZ 7333 99 85 everywhere everywhere RB 7333 99 86 the the DT 7333 99 87 same same JJ 7333 99 88 . . . 7333 100 1 The the DT 7333 100 2 ether ether NN 7333 100 3 of of IN 7333 100 4 the the DT 7333 100 5 general general JJ 7333 100 6 theory theory NN 7333 100 7 of of IN 7333 100 8 relativity relativity NN 7333 100 9 is be VBZ 7333 100 10 transmuted transmute VBN 7333 100 11 conceptually conceptually RB 7333 100 12 into into IN 7333 100 13 the the DT 7333 100 14 ether ether NN 7333 100 15 of of IN 7333 100 16 Lorentz Lorentz NNP 7333 100 17 if if IN 7333 100 18 we -PRON- PRP 7333 100 19 substitute substitute VBP 7333 100 20 constants constant NNS 7333 100 21 for for IN 7333 100 22 the the DT 7333 100 23 functions function NNS 7333 100 24 of of IN 7333 100 25 space space NN 7333 100 26 which which WDT 7333 100 27 describe describe VBP 7333 100 28 the the DT 7333 100 29 former former JJ 7333 100 30 , , , 7333 100 31 disregarding disregard VBG 7333 100 32 the the DT 7333 100 33 causes cause NNS 7333 100 34 which which WDT 7333 100 35 condition condition NN 7333 100 36 its -PRON- PRP$ 7333 100 37 state state NN 7333 100 38 . . . 7333 101 1 Thus thus RB 7333 101 2 we -PRON- PRP 7333 101 3 may may MD 7333 101 4 also also RB 7333 101 5 say say VB 7333 101 6 , , , 7333 101 7 I -PRON- PRP 7333 101 8 think think VBP 7333 101 9 , , , 7333 101 10 that that IN 7333 101 11 the the DT 7333 101 12 ether ether NN 7333 101 13 of of IN 7333 101 14 the the DT 7333 101 15 general general JJ 7333 101 16 theory theory NN 7333 101 17 of of IN 7333 101 18 relativity relativity NN 7333 101 19 is be VBZ 7333 101 20 the the DT 7333 101 21 outcome outcome NN 7333 101 22 of of IN 7333 101 23 the the DT 7333 101 24 Lorentzian lorentzian JJ 7333 101 25 ether ether NN 7333 101 26 , , , 7333 101 27 through through IN 7333 101 28 relativation relativation NN 7333 101 29 . . . 7333 102 1 As as IN 7333 102 2 to to IN 7333 102 3 the the DT 7333 102 4 part part NN 7333 102 5 which which WDT 7333 102 6 the the DT 7333 102 7 new new JJ 7333 102 8 ether ether NN 7333 102 9 is be VBZ 7333 102 10 to to TO 7333 102 11 play play VB 7333 102 12 in in IN 7333 102 13 the the DT 7333 102 14 physics physics NN 7333 102 15 of of IN 7333 102 16 the the DT 7333 102 17 future future NN 7333 102 18 we -PRON- PRP 7333 102 19 are be VBP 7333 102 20 not not RB 7333 102 21 yet yet RB 7333 102 22 clear clear JJ 7333 102 23 . . . 7333 103 1 We -PRON- PRP 7333 103 2 know know VBP 7333 103 3 that that IN 7333 103 4 it -PRON- PRP 7333 103 5 determines determine VBZ 7333 103 6 the the DT 7333 103 7 metrical metrical JJ 7333 103 8 relations relation NNS 7333 103 9 in in IN 7333 103 10 the the DT 7333 103 11 space space NN 7333 103 12 - - HYPH 7333 103 13 time time NN 7333 103 14 continuum continuum NN 7333 103 15 , , , 7333 103 16 e.g. e.g. RB 7333 104 1 the the DT 7333 104 2 configurative configurative JJ 7333 104 3 possibilities possibility NNS 7333 104 4 of of IN 7333 104 5 solid solid JJ 7333 104 6 bodies body NNS 7333 104 7 as as RB 7333 104 8 well well RB 7333 104 9 as as IN 7333 104 10 the the DT 7333 104 11 gravitational gravitational JJ 7333 104 12 fields field NNS 7333 104 13 ; ; : 7333 104 14 but but CC 7333 104 15 we -PRON- PRP 7333 104 16 do do VBP 7333 104 17 not not RB 7333 104 18 know know VB 7333 104 19 whether whether IN 7333 104 20 it -PRON- PRP 7333 104 21 has have VBZ 7333 104 22 an an DT 7333 104 23 essential essential JJ 7333 104 24 share share NN 7333 104 25 in in IN 7333 104 26 the the DT 7333 104 27 structure structure NN 7333 104 28 of of IN 7333 104 29 the the DT 7333 104 30 electrical electrical JJ 7333 104 31 elementary elementary JJ 7333 104 32 particles particle NNS 7333 104 33 constituting constitute VBG 7333 104 34 matter matter NN 7333 104 35 . . . 7333 105 1 Nor nor CC 7333 105 2 do do VBP 7333 105 3 we -PRON- PRP 7333 105 4 know know VB 7333 105 5 whether whether IN 7333 105 6 it -PRON- PRP 7333 105 7 is be VBZ 7333 105 8 only only RB 7333 105 9 in in IN 7333 105 10 the the DT 7333 105 11 proximity proximity NN 7333 105 12 of of IN 7333 105 13 ponderable ponderable JJ 7333 105 14 masses masse NNS 7333 105 15 that that IN 7333 105 16 its -PRON- PRP$ 7333 105 17 structure structure NN 7333 105 18 differs differ VBZ 7333 105 19 essentially essentially RB 7333 105 20 from from IN 7333 105 21 that that DT 7333 105 22 of of IN 7333 105 23 the the DT 7333 105 24 Lorentzian lorentzian JJ 7333 105 25 ether ether NN 7333 105 26 ; ; : 7333 105 27 whether whether IN 7333 105 28 the the DT 7333 105 29 geometry geometry NN 7333 105 30 of of IN 7333 105 31 spaces space NNS 7333 105 32 of of IN 7333 105 33 cosmic cosmic JJ 7333 105 34 extent extent NN 7333 105 35 is be VBZ 7333 105 36 approximately approximately RB 7333 105 37 Euclidean euclidean JJ 7333 105 38 . . . 7333 106 1 But but CC 7333 106 2 we -PRON- PRP 7333 106 3 can can MD 7333 106 4 assert assert VB 7333 106 5 by by IN 7333 106 6 reason reason NN 7333 106 7 of of IN 7333 106 8 the the DT 7333 106 9 relativistic relativistic JJ 7333 106 10 equations equation NNS 7333 106 11 of of IN 7333 106 12 gravitation gravitation NN 7333 106 13 that that IN 7333 106 14 there there EX 7333 106 15 must must MD 7333 106 16 be be VB 7333 106 17 a a DT 7333 106 18 departure departure NN 7333 106 19 from from IN 7333 106 20 Euclidean euclidean JJ 7333 106 21 relations relation NNS 7333 106 22 , , , 7333 106 23 with with IN 7333 106 24 spaces space NNS 7333 106 25 of of IN 7333 106 26 cosmic cosmic JJ 7333 106 27 order order NN 7333 106 28 of of IN 7333 106 29 magnitude magnitude NN 7333 106 30 , , , 7333 106 31 if if IN 7333 106 32 there there EX 7333 106 33 exists exist VBZ 7333 106 34 a a DT 7333 106 35 positive positive JJ 7333 106 36 mean mean JJ 7333 106 37 density density NN 7333 106 38 , , , 7333 106 39 no no RB 7333 106 40 matter matter RB 7333 106 41 how how WRB 7333 106 42 small small JJ 7333 106 43 , , , 7333 106 44 of of IN 7333 106 45 the the DT 7333 106 46 matter matter NN 7333 106 47 in in IN 7333 106 48 the the DT 7333 106 49 universe universe NN 7333 106 50 . . . 7333 107 1 In in IN 7333 107 2 this this DT 7333 107 3 case case NN 7333 107 4 the the DT 7333 107 5 universe universe NN 7333 107 6 must must MD 7333 107 7 of of IN 7333 107 8 necessity necessity NN 7333 107 9 be be VB 7333 107 10 spatially spatially RB 7333 107 11 unbounded unbounded JJ 7333 107 12 and and CC 7333 107 13 of of IN 7333 107 14 finite finite NN 7333 107 15 magnitude magnitude NN 7333 107 16 , , , 7333 107 17 its -PRON- PRP$ 7333 107 18 magnitude magnitude NN 7333 107 19 being be VBG 7333 107 20 determined determine VBN 7333 107 21 by by IN 7333 107 22 the the DT 7333 107 23 value value NN 7333 107 24 of of IN 7333 107 25 that that DT 7333 107 26 mean mean JJ 7333 107 27 density density NN 7333 107 28 . . . 7333 108 1 If if IN 7333 108 2 we -PRON- PRP 7333 108 3 consider consider VBP 7333 108 4 the the DT 7333 108 5 gravitational gravitational JJ 7333 108 6 field field NN 7333 108 7 and and CC 7333 108 8 the the DT 7333 108 9 electromagnetic electromagnetic JJ 7333 108 10 field field NN 7333 108 11 from from IN 7333 108 12 the the DT 7333 108 13 stand stand NN 7333 108 14 - - HYPH 7333 108 15 point point NN 7333 108 16 of of IN 7333 108 17 the the DT 7333 108 18 ether ether NN 7333 108 19 hypothesis hypothesis NN 7333 108 20 , , , 7333 108 21 we -PRON- PRP 7333 108 22 find find VBP 7333 108 23 a a DT 7333 108 24 remarkable remarkable JJ 7333 108 25 difference difference NN 7333 108 26 between between IN 7333 108 27 the the DT 7333 108 28 two two CD 7333 108 29 . . . 7333 109 1 There there EX 7333 109 2 can can MD 7333 109 3 be be VB 7333 109 4 no no DT 7333 109 5 space space NN 7333 109 6 nor nor CC 7333 109 7 any any DT 7333 109 8 part part NN 7333 109 9 of of IN 7333 109 10 space space NN 7333 109 11 without without IN 7333 109 12 gravitational gravitational JJ 7333 109 13 potentials potential NNS 7333 109 14 ; ; : 7333 109 15 for for IN 7333 109 16 these these DT 7333 109 17 confer confer NN 7333 109 18 upon upon IN 7333 109 19 space space NN 7333 109 20 its -PRON- PRP$ 7333 109 21 metrical metrical JJ 7333 109 22 qualities quality NNS 7333 109 23 , , , 7333 109 24 without without IN 7333 109 25 which which WDT 7333 109 26 it -PRON- PRP 7333 109 27 can can MD 7333 109 28 not not RB 7333 109 29 be be VB 7333 109 30 imagined imagine VBN 7333 109 31 at at RB 7333 109 32 all all RB 7333 109 33 . . . 7333 110 1 The the DT 7333 110 2 existence existence NN 7333 110 3 of of IN 7333 110 4 the the DT 7333 110 5 gravitational gravitational JJ 7333 110 6 field field NN 7333 110 7 is be VBZ 7333 110 8 inseparably inseparably RB 7333 110 9 bound bind VBN 7333 110 10 up up RP 7333 110 11 with with IN 7333 110 12 the the DT 7333 110 13 existence existence NN 7333 110 14 of of IN 7333 110 15 space space NN 7333 110 16 . . . 7333 111 1 On on IN 7333 111 2 the the DT 7333 111 3 other other JJ 7333 111 4 hand hand NN 7333 111 5 a a DT 7333 111 6 part part NN 7333 111 7 of of IN 7333 111 8 space space NN 7333 111 9 may may MD 7333 111 10 very very RB 7333 111 11 well well RB 7333 111 12 be be VB 7333 111 13 imagined imagine VBN 7333 111 14 without without IN 7333 111 15 an an DT 7333 111 16 electromagnetic electromagnetic JJ 7333 111 17 field field NN 7333 111 18 ; ; : 7333 111 19 thus thus RB 7333 111 20 in in IN 7333 111 21 contrast contrast NN 7333 111 22 with with IN 7333 111 23 the the DT 7333 111 24 gravitational gravitational JJ 7333 111 25 field field NN 7333 111 26 , , , 7333 111 27 the the DT 7333 111 28 electromagnetic electromagnetic JJ 7333 111 29 field field NN 7333 111 30 seems seem VBZ 7333 111 31 to to TO 7333 111 32 be be VB 7333 111 33 only only RB 7333 111 34 secondarily secondarily RB 7333 111 35 linked link VBN 7333 111 36 to to IN 7333 111 37 the the DT 7333 111 38 ether ether NN 7333 111 39 , , , 7333 111 40 the the DT 7333 111 41 formal formal JJ 7333 111 42 nature nature NN 7333 111 43 of of IN 7333 111 44 the the DT 7333 111 45 electromagnetic electromagnetic JJ 7333 111 46 field field NN 7333 111 47 being be VBG 7333 111 48 as as RB 7333 111 49 yet yet RB 7333 111 50 in in IN 7333 111 51 no no DT 7333 111 52 way way NN 7333 111 53 determined determine VBN 7333 111 54 by by IN 7333 111 55 that that DT 7333 111 56 of of IN 7333 111 57 gravitational gravitational JJ 7333 111 58 ether ether NN 7333 111 59 . . . 7333 112 1 From from IN 7333 112 2 the the DT 7333 112 3 present present JJ 7333 112 4 state state NN 7333 112 5 of of IN 7333 112 6 theory theory NN 7333 112 7 it -PRON- PRP 7333 112 8 looks look VBZ 7333 112 9 as as IN 7333 112 10 if if IN 7333 112 11 the the DT 7333 112 12 electromagnetic electromagnetic JJ 7333 112 13 field field NN 7333 112 14 , , , 7333 112 15 as as IN 7333 112 16 opposed oppose VBN 7333 112 17 to to IN 7333 112 18 the the DT 7333 112 19 gravitational gravitational JJ 7333 112 20 field field NN 7333 112 21 , , , 7333 112 22 rests rest VBZ 7333 112 23 upon upon IN 7333 112 24 an an DT 7333 112 25 entirely entirely RB 7333 112 26 new new JJ 7333 112 27 formal formal JJ 7333 112 28 _ _ NNP 7333 112 29 motif motif NN 7333 112 30 _ _ NNP 7333 112 31 , , , 7333 112 32 as as IN 7333 112 33 though though IN 7333 112 34 nature nature NN 7333 112 35 might may MD 7333 112 36 just just RB 7333 112 37 as as RB 7333 112 38 well well RB 7333 112 39 have have VBP 7333 112 40 endowed endow VBN 7333 112 41 the the DT 7333 112 42 gravitational gravitational JJ 7333 112 43 ether ether NN 7333 112 44 with with IN 7333 112 45 fields field NNS 7333 112 46 of of IN 7333 112 47 quite quite PDT 7333 112 48 another another DT 7333 112 49 type type NN 7333 112 50 , , , 7333 112 51 for for IN 7333 112 52 example example NN 7333 112 53 , , , 7333 112 54 with with IN 7333 112 55 fields field NNS 7333 112 56 of of IN 7333 112 57 a a DT 7333 112 58 scalar scalar JJ 7333 112 59 potential potential NN 7333 112 60 , , , 7333 112 61 instead instead RB 7333 112 62 of of IN 7333 112 63 fields field NNS 7333 112 64 of of IN 7333 112 65 the the DT 7333 112 66 electromagnetic electromagnetic JJ 7333 112 67 type type NN 7333 112 68 . . . 7333 113 1 Since since IN 7333 113 2 according accord VBG 7333 113 3 to to IN 7333 113 4 our -PRON- PRP$ 7333 113 5 present present JJ 7333 113 6 conceptions conception NNS 7333 113 7 the the DT 7333 113 8 elementary elementary JJ 7333 113 9 particles particle NNS 7333 113 10 of of IN 7333 113 11 matter matter NN 7333 113 12 are be VBP 7333 113 13 also also RB 7333 113 14 , , , 7333 113 15 in in IN 7333 113 16 their -PRON- PRP$ 7333 113 17 essence essence NN 7333 113 18 , , , 7333 113 19 nothing nothing NN 7333 113 20 else else RB 7333 113 21 than than IN 7333 113 22 condensations condensation NNS 7333 113 23 of of IN 7333 113 24 the the DT 7333 113 25 electromagnetic electromagnetic JJ 7333 113 26 field field NN 7333 113 27 , , , 7333 113 28 our -PRON- PRP$ 7333 113 29 present present JJ 7333 113 30 view view NN 7333 113 31 of of IN 7333 113 32 the the DT 7333 113 33 universe universe NNP 7333 113 34 presents present VBZ 7333 113 35 two two CD 7333 113 36 realities reality NNS 7333 113 37 which which WDT 7333 113 38 are be VBP 7333 113 39 completely completely RB 7333 113 40 separated separate VBN 7333 113 41 from from IN 7333 113 42 each each DT 7333 113 43 other other JJ 7333 113 44 conceptually conceptually RB 7333 113 45 , , , 7333 113 46 although although IN 7333 113 47 connected connect VBN 7333 113 48 causally causally RB 7333 113 49 , , , 7333 113 50 namely namely RB 7333 113 51 , , , 7333 113 52 gravitational gravitational JJ 7333 113 53 ether ether NN 7333 113 54 and and CC 7333 113 55 electromagnetic electromagnetic JJ 7333 113 56 field field NN 7333 113 57 , , , 7333 113 58 or or CC 7333 113 59 -- -- : 7333 113 60 as as IN 7333 113 61 they -PRON- PRP 7333 113 62 might may MD 7333 113 63 also also RB 7333 113 64 be be VB 7333 113 65 called call VBN 7333 113 66 -- -- : 7333 113 67 space space NN 7333 113 68 and and CC 7333 113 69 matter matter NN 7333 113 70 . . . 7333 114 1 Of of RB 7333 114 2 course course RB 7333 114 3 it -PRON- PRP 7333 114 4 would would MD 7333 114 5 be be VB 7333 114 6 a a DT 7333 114 7 great great JJ 7333 114 8 advance advance NN 7333 114 9 if if IN 7333 114 10 we -PRON- PRP 7333 114 11 could could MD 7333 114 12 succeed succeed VB 7333 114 13 in in IN 7333 114 14 comprehending comprehend VBG 7333 114 15 the the DT 7333 114 16 gravitational gravitational JJ 7333 114 17 field field NN 7333 114 18 and and CC 7333 114 19 the the DT 7333 114 20 electromagnetic electromagnetic JJ 7333 114 21 field field NN 7333 114 22 together together RB 7333 114 23 as as IN 7333 114 24 one one CD 7333 114 25 unified unify VBN 7333 114 26 conformation conformation NN 7333 114 27 . . . 7333 115 1 Then then RB 7333 115 2 for for IN 7333 115 3 the the DT 7333 115 4 first first JJ 7333 115 5 time time NN 7333 115 6 the the DT 7333 115 7 epoch epoch NN 7333 115 8 of of IN 7333 115 9 theoretical theoretical JJ 7333 115 10 physics physics NN 7333 115 11 founded found VBN 7333 115 12 by by IN 7333 115 13 Faraday Faraday NNP 7333 115 14 and and CC 7333 115 15 Maxwell Maxwell NNP 7333 115 16 would would MD 7333 115 17 reach reach VB 7333 115 18 a a DT 7333 115 19 satisfactory satisfactory JJ 7333 115 20 conclusion conclusion NN 7333 115 21 . . . 7333 116 1 The the DT 7333 116 2 contrast contrast NN 7333 116 3 between between IN 7333 116 4 ether ether NN 7333 116 5 and and CC 7333 116 6 matter matter NN 7333 116 7 would would MD 7333 116 8 fade fade VB 7333 116 9 away away RB 7333 116 10 , , , 7333 116 11 and and CC 7333 116 12 , , , 7333 116 13 through through IN 7333 116 14 the the DT 7333 116 15 general general JJ 7333 116 16 theory theory NN 7333 116 17 of of IN 7333 116 18 relativity relativity NN 7333 116 19 , , , 7333 116 20 the the DT 7333 116 21 whole whole NN 7333 116 22 of of IN 7333 116 23 physics physics NN 7333 116 24 would would MD 7333 116 25 become become VB 7333 116 26 a a DT 7333 116 27 complete complete JJ 7333 116 28 system system NN 7333 116 29 of of IN 7333 116 30 thought thought NN 7333 116 31 , , , 7333 116 32 like like IN 7333 116 33 geometry geometry NN 7333 116 34 , , , 7333 116 35 kinematics kinematic NNS 7333 116 36 , , , 7333 116 37 and and CC 7333 116 38 the the DT 7333 116 39 theory theory NN 7333 116 40 of of IN 7333 116 41 gravitation gravitation NN 7333 116 42 . . . 7333 117 1 An an DT 7333 117 2 exceedingly exceedingly RB 7333 117 3 ingenious ingenious JJ 7333 117 4 attempt attempt NN 7333 117 5 in in IN 7333 117 6 this this DT 7333 117 7 direction direction NN 7333 117 8 has have VBZ 7333 117 9 been be VBN 7333 117 10 made make VBN 7333 117 11 by by IN 7333 117 12 the the DT 7333 117 13 mathematician mathematician JJ 7333 117 14 H. H. NNP 7333 117 15 Weyl Weyl NNP 7333 117 16 ; ; : 7333 117 17 but but CC 7333 117 18 I -PRON- PRP 7333 117 19 do do VBP 7333 117 20 not not RB 7333 117 21 believe believe VB 7333 117 22 that that IN 7333 117 23 his -PRON- PRP$ 7333 117 24 theory theory NN 7333 117 25 will will MD 7333 117 26 hold hold VB 7333 117 27 its -PRON- PRP$ 7333 117 28 ground ground NN 7333 117 29 in in IN 7333 117 30 relation relation NN 7333 117 31 to to IN 7333 117 32 reality reality NN 7333 117 33 . . . 7333 118 1 Further further RB 7333 118 2 , , , 7333 118 3 in in IN 7333 118 4 contemplating contemplate VBG 7333 118 5 the the DT 7333 118 6 immediate immediate JJ 7333 118 7 future future NN 7333 118 8 of of IN 7333 118 9 theoretical theoretical JJ 7333 118 10 physics physics NN 7333 118 11 we -PRON- PRP 7333 118 12 ought ought MD 7333 118 13 not not RB 7333 118 14 unconditionally unconditionally RB 7333 118 15 to to TO 7333 118 16 reject reject VB 7333 118 17 the the DT 7333 118 18 possibility possibility NN 7333 118 19 that that IN 7333 118 20 the the DT 7333 118 21 facts fact NNS 7333 118 22 comprised comprise VBN 7333 118 23 in in IN 7333 118 24 the the DT 7333 118 25 quantum quantum NN 7333 118 26 theory theory NN 7333 118 27 may may MD 7333 118 28 set set VB 7333 118 29 bounds bound NNS 7333 118 30 to to IN 7333 118 31 the the DT 7333 118 32 field field NN 7333 118 33 theory theory NN 7333 118 34 beyond beyond IN 7333 118 35 which which WDT 7333 118 36 it -PRON- PRP 7333 118 37 can can MD 7333 118 38 not not RB 7333 118 39 pass pass VB 7333 118 40 . . . 7333 119 1 Recapitulating recapitulate VBG 7333 119 2 , , , 7333 119 3 we -PRON- PRP 7333 119 4 may may MD 7333 119 5 say say VB 7333 119 6 that that IN 7333 119 7 according accord VBG 7333 119 8 to to IN 7333 119 9 the the DT 7333 119 10 general general JJ 7333 119 11 theory theory NN 7333 119 12 of of IN 7333 119 13 relativity relativity NN 7333 119 14 space space NN 7333 119 15 is be VBZ 7333 119 16 endowed endow VBN 7333 119 17 with with IN 7333 119 18 physical physical JJ 7333 119 19 qualities quality NNS 7333 119 20 ; ; : 7333 119 21 in in IN 7333 119 22 this this DT 7333 119 23 sense sense NN 7333 119 24 , , , 7333 119 25 therefore therefore RB 7333 119 26 , , , 7333 119 27 there there EX 7333 119 28 exists exist VBZ 7333 119 29 an an DT 7333 119 30 ether ether NN 7333 119 31 . . . 7333 120 1 According accord VBG 7333 120 2 to to IN 7333 120 3 the the DT 7333 120 4 general general JJ 7333 120 5 theory theory NN 7333 120 6 of of IN 7333 120 7 relativity relativity NN 7333 120 8 space space NN 7333 120 9 without without IN 7333 120 10 ether ether NN 7333 120 11 is be VBZ 7333 120 12 unthinkable unthinkable JJ 7333 120 13 ; ; : 7333 120 14 for for IN 7333 120 15 in in IN 7333 120 16 such such JJ 7333 120 17 space space NN 7333 120 18 there there RB 7333 120 19 not not RB 7333 120 20 only only RB 7333 120 21 would would MD 7333 120 22 be be VB 7333 120 23 no no DT 7333 120 24 propagation propagation NN 7333 120 25 of of IN 7333 120 26 light light NN 7333 120 27 , , , 7333 120 28 but but CC 7333 120 29 also also RB 7333 120 30 no no DT 7333 120 31 possibility possibility NN 7333 120 32 of of IN 7333 120 33 existence existence NN 7333 120 34 for for IN 7333 120 35 standards standard NNS 7333 120 36 of of IN 7333 120 37 space space NN 7333 120 38 and and CC 7333 120 39 time time NN 7333 120 40 ( ( -LRB- 7333 120 41 measuring measure VBG 7333 120 42 - - HYPH 7333 120 43 rods rod NNS 7333 120 44 and and CC 7333 120 45 clocks clock NNS 7333 120 46 ) ) -RRB- 7333 120 47 , , , 7333 120 48 nor nor CC 7333 120 49 therefore therefore RB 7333 120 50 any any DT 7333 120 51 space space NN 7333 120 52 - - HYPH 7333 120 53 time time NN 7333 120 54 intervals interval NNS 7333 120 55 in in IN 7333 120 56 the the DT 7333 120 57 physical physical JJ 7333 120 58 sense sense NN 7333 120 59 . . . 7333 121 1 But but CC 7333 121 2 this this DT 7333 121 3 ether ether NN 7333 121 4 may may MD 7333 121 5 not not RB 7333 121 6 be be VB 7333 121 7 thought think VBN 7333 121 8 of of IN 7333 121 9 as as IN 7333 121 10 endowed endow VBN 7333 121 11 with with IN 7333 121 12 the the DT 7333 121 13 quality quality NN 7333 121 14 characteristic characteristic NN 7333 121 15 of of IN 7333 121 16 ponderable ponderable JJ 7333 121 17 media medium NNS 7333 121 18 , , , 7333 121 19 as as IN 7333 121 20 consisting consist VBG 7333 121 21 of of IN 7333 121 22 parts part NNS 7333 121 23 which which WDT 7333 121 24 may may MD 7333 121 25 be be VB 7333 121 26 tracked track VBN 7333 121 27 through through IN 7333 121 28 time time NN 7333 121 29 . . . 7333 122 1 The the DT 7333 122 2 idea idea NN 7333 122 3 of of IN 7333 122 4 motion motion NN 7333 122 5 may may MD 7333 122 6 not not RB 7333 122 7 be be VB 7333 122 8 applied apply VBN 7333 122 9 to to IN 7333 122 10 it -PRON- PRP 7333 122 11 . . . 7333 123 1 GEOMETRY GEOMETRY NNP 7333 123 2 AND and CC 7333 123 3 EXPERIENCE EXPERIENCE NNS 7333 123 4 An an DT 7333 123 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JJ 7333 124 21 and and CC 7333 124 22 indisputable indisputable JJ 7333 124 23 , , , 7333 124 24 while while IN 7333 124 25 those those DT 7333 124 26 of of IN 7333 124 27 all all DT 7333 124 28 other other JJ 7333 124 29 sciences science NNS 7333 124 30 are be VBP 7333 124 31 to to IN 7333 124 32 some some DT 7333 124 33 extent extent NN 7333 124 34 debatable debatable JJ 7333 124 35 and and CC 7333 124 36 in in IN 7333 124 37 constant constant JJ 7333 124 38 danger danger NN 7333 124 39 of of IN 7333 124 40 being be VBG 7333 124 41 overthrown overthrow VBN 7333 124 42 by by IN 7333 124 43 newly newly RB 7333 124 44 discovered discover VBN 7333 124 45 facts fact NNS 7333 124 46 . . . 7333 125 1 In in IN 7333 125 2 spite spite NN 7333 125 3 of of IN 7333 125 4 this this DT 7333 125 5 , , , 7333 125 6 the the DT 7333 125 7 investigator investigator NN 7333 125 8 in in IN 7333 125 9 another another DT 7333 125 10 department department NN 7333 125 11 of of IN 7333 125 12 science science NN 7333 125 13 would would MD 7333 125 14 not not RB 7333 125 15 need need VB 7333 125 16 to to TO 7333 125 17 envy envy VB 7333 125 18 the the DT 7333 125 19 mathematician mathematician NN 7333 125 20 if if IN 7333 125 21 the the DT 7333 125 22 laws law NNS 7333 125 23 of of IN 7333 125 24 mathematics mathematic NNS 7333 125 25 referred refer VBD 7333 125 26 to to IN 7333 125 27 objects object NNS 7333 125 28 of of IN 7333 125 29 our -PRON- PRP$ 7333 125 30 mere mere JJ 7333 125 31 imagination imagination NN 7333 125 32 , , , 7333 125 33 and and CC 7333 125 34 not not RB 7333 125 35 to to IN 7333 125 36 objects object NNS 7333 125 37 of of IN 7333 125 38 reality reality NN 7333 125 39 . . . 7333 126 1 For for IN 7333 126 2 it -PRON- PRP 7333 126 3 can can MD 7333 126 4 not not RB 7333 126 5 occasion occasion VB 7333 126 6 surprise surprise NN 7333 126 7 that that IN 7333 126 8 different different JJ 7333 126 9 persons person NNS 7333 126 10 should should MD 7333 126 11 arrive arrive 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present VBZ 7333 128 7 itself -PRON- PRP 7333 128 8 which which WDT 7333 128 9 in in IN 7333 128 10 all all DT 7333 128 11 ages age NNS 7333 128 12 has have VBZ 7333 128 13 agitated agitate VBN 7333 128 14 inquiring inquire VBG 7333 128 15 minds mind NNS 7333 128 16 . . . 7333 129 1 How how WRB 7333 129 2 can can MD 7333 129 3 it -PRON- PRP 7333 129 4 be be VB 7333 129 5 that that IN 7333 129 6 mathematics mathematic NNS 7333 129 7 , , , 7333 129 8 being be VBG 7333 129 9 after after RB 7333 129 10 all all PDT 7333 129 11 a a DT 7333 129 12 product product NN 7333 129 13 of of IN 7333 129 14 human human JJ 7333 129 15 thought thought NN 7333 129 16 which which WDT 7333 129 17 is be VBZ 7333 129 18 independent independent JJ 7333 129 19 of of IN 7333 129 20 experience experience NN 7333 129 21 , , , 7333 129 22 is be VBZ 7333 129 23 so so RB 7333 129 24 admirably admirably RB 7333 129 25 appropriate appropriate JJ 7333 129 26 to to IN 7333 129 27 the the DT 7333 129 28 objects object 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15 as as IN 7333 131 16 the the DT 7333 131 17 laws law NNS 7333 131 18 of of IN 7333 131 19 mathematics mathematic NNS 7333 131 20 refer refer VBP 7333 131 21 to to IN 7333 131 22 reality reality NN 7333 131 23 , , , 7333 131 24 they -PRON- PRP 7333 131 25 are be VBP 7333 131 26 not not RB 7333 131 27 certain certain JJ 7333 131 28 ; ; : 7333 131 29 and and CC 7333 131 30 as as RB 7333 131 31 far far RB 7333 131 32 as as IN 7333 131 33 they -PRON- PRP 7333 131 34 are be VBP 7333 131 35 certain certain JJ 7333 131 36 , , , 7333 131 37 they -PRON- PRP 7333 131 38 do do VBP 7333 131 39 not not RB 7333 131 40 refer refer VB 7333 131 41 to to IN 7333 131 42 reality reality NN 7333 131 43 . . . 7333 132 1 It -PRON- PRP 7333 132 2 seems seem VBZ 7333 132 3 to to IN 7333 132 4 me -PRON- PRP 7333 132 5 that that DT 7333 132 6 complete complete JJ 7333 132 7 clearness clearness NN 7333 132 8 as as IN 7333 132 9 to to IN 7333 132 10 this this DT 7333 132 11 state state NN 7333 132 12 of of IN 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the DT 7333 133 13 logical logical JJ 7333 133 14 - - HYPH 7333 133 15 formal formal JJ 7333 133 16 from from IN 7333 133 17 its -PRON- PRP$ 7333 133 18 objective objective JJ 7333 133 19 or or CC 7333 133 20 intuitive intuitive JJ 7333 133 21 content content NN 7333 133 22 ; ; : 7333 133 23 according accord VBG 7333 133 24 to to IN 7333 133 25 axiomatics axiomatic NNS 7333 133 26 the the DT 7333 133 27 logical logical JJ 7333 133 28 - - HYPH 7333 133 29 formal formal JJ 7333 133 30 alone alone JJ 7333 133 31 forms form VBZ 7333 133 32 the the DT 7333 133 33 subject subject JJ 7333 133 34 - - HYPH 7333 133 35 matter matter NN 7333 133 36 of of IN 7333 133 37 mathematics mathematic NNS 7333 133 38 , , , 7333 133 39 which which WDT 7333 133 40 is be VBZ 7333 133 41 not not RB 7333 133 42 concerned concerned JJ 7333 133 43 with with IN 7333 133 44 the the DT 7333 133 45 intuitive intuitive JJ 7333 133 46 or or CC 7333 133 47 other other JJ 7333 133 48 content content NN 7333 133 49 associated associate VBN 7333 133 50 with with IN 7333 133 51 the the DT 7333 133 52 logical logical JJ 7333 133 53 - - HYPH 7333 133 54 formal formal JJ 7333 133 55 . . . 7333 134 1 Let let VB 7333 134 2 us -PRON- PRP 7333 134 3 for for IN 7333 134 4 a a DT 7333 134 5 moment moment NN 7333 134 6 consider consider VB 7333 134 7 from from IN 7333 134 8 this this DT 7333 134 9 point point NN 7333 134 10 of of IN 7333 134 11 view view NN 7333 134 12 any any DT 7333 134 13 axiom axiom NN 7333 134 14 of of IN 7333 134 15 geometry geometry NN 7333 134 16 , , , 7333 134 17 for for IN 7333 134 18 instance instance NN 7333 134 19 , , , 7333 134 20 the the DT 7333 134 21 following:--Through following:--through JJ 7333 134 22 two two CD 7333 134 23 points point NNS 7333 134 24 in in IN 7333 134 25 space space NN 7333 134 26 there there RB 7333 134 27 always always RB 7333 134 28 passes pass VBZ 7333 134 29 one one CD 7333 134 30 and and CC 7333 134 31 only only RB 7333 134 32 one one CD 7333 134 33 straight straight JJ 7333 134 34 line line NN 7333 134 35 . . . 7333 135 1 How how WRB 7333 135 2 is be VBZ 7333 135 3 this this DT 7333 135 4 axiom axiom NN 7333 135 5 to to TO 7333 135 6 be be VB 7333 135 7 interpreted interpret VBN 7333 135 8 in in IN 7333 135 9 the the DT 7333 135 10 older old JJR 7333 135 11 sense sense NN 7333 135 12 and and CC 7333 135 13 in in IN 7333 135 14 the the DT 7333 135 15 more more RBR 7333 135 16 modern modern JJ 7333 135 17 sense sense NN 7333 135 18 ? ? . 7333 136 1 The the DT 7333 136 2 older old JJR 7333 136 3 interpretation:--Every interpretation:--every NN 7333 136 4 one one NN 7333 136 5 knows know VBZ 7333 136 6 what what WP 7333 136 7 a a DT 7333 136 8 straight straight JJ 7333 136 9 line line NN 7333 136 10 is be VBZ 7333 136 11 , , , 7333 136 12 and and CC 7333 136 13 what what WP 7333 136 14 a a DT 7333 136 15 point point NN 7333 136 16 is be VBZ 7333 136 17 . . . 7333 137 1 Whether whether IN 7333 137 2 this this DT 7333 137 3 knowledge knowledge NN 7333 137 4 springs spring NNS 7333 137 5 from from IN 7333 137 6 an an DT 7333 137 7 ability ability NN 7333 137 8 of of IN 7333 137 9 the the DT 7333 137 10 human human JJ 7333 137 11 mind mind NN 7333 137 12 or or CC 7333 137 13 from from IN 7333 137 14 experience experience NN 7333 137 15 , , , 7333 137 16 from from IN 7333 137 17 some some DT 7333 137 18 collaboration collaboration NN 7333 137 19 of of IN 7333 137 20 the the DT 7333 137 21 two two CD 7333 137 22 or or CC 7333 137 23 from from IN 7333 137 24 some some DT 7333 137 25 other other JJ 7333 137 26 source source NN 7333 137 27 , , , 7333 137 28 is be VBZ 7333 137 29 not not RB 7333 137 30 for for IN 7333 137 31 the the DT 7333 137 32 mathematician mathematician NN 7333 137 33 to to TO 7333 137 34 decide decide VB 7333 137 35 . . . 7333 138 1 He -PRON- PRP 7333 138 2 leaves leave VBZ 7333 138 3 the the DT 7333 138 4 question question NN 7333 138 5 to to IN 7333 138 6 the the DT 7333 138 7 philosopher philosopher NN 7333 138 8 . . . 7333 139 1 Being be VBG 7333 139 2 based base VBN 7333 139 3 upon upon IN 7333 139 4 this this DT 7333 139 5 knowledge knowledge NN 7333 139 6 , , , 7333 139 7 which which WDT 7333 139 8 precedes precede VBZ 7333 139 9 all all DT 7333 139 10 mathematics mathematic NNS 7333 139 11 , , , 7333 139 12 the the DT 7333 139 13 axiom axiom NN 7333 139 14 stated state VBN 7333 139 15 above above RB 7333 139 16 is be VBZ 7333 139 17 , , , 7333 139 18 like like IN 7333 139 19 all all DT 7333 139 20 other other JJ 7333 139 21 axioms axiom NNS 7333 139 22 , , , 7333 139 23 self self NN 7333 139 24 - - HYPH 7333 139 25 evident evident JJ 7333 139 26 , , , 7333 139 27 that that RB 7333 139 28 is is RB 7333 139 29 , , , 7333 139 30 it -PRON- PRP 7333 139 31 is be VBZ 7333 139 32 the the DT 7333 139 33 expression expression NN 7333 139 34 of of IN 7333 139 35 a a DT 7333 139 36 part part NN 7333 139 37 of of IN 7333 139 38 this this DT 7333 139 39 _ _ NNP 7333 139 40 a a DT 7333 139 41 priori priori FW 7333 139 42 _ _ NNP 7333 139 43 knowledge knowledge NN 7333 139 44 . . . 7333 140 1 The the DT 7333 140 2 more more RBR 7333 140 3 modern modern JJ 7333 140 4 interpretation:--Geometry interpretation:--geometry NN 7333 140 5 treats treat NNS 7333 140 6 of of IN 7333 140 7 entities entity NNS 7333 140 8 which which WDT 7333 140 9 are be VBP 7333 140 10 denoted denote VBN 7333 140 11 by by IN 7333 140 12 the the DT 7333 140 13 words word NNS 7333 140 14 straight straight JJ 7333 140 15 line line NN 7333 140 16 , , , 7333 140 17 point point NN 7333 140 18 , , , 7333 140 19 etc etc FW 7333 140 20 . . . 7333 141 1 These these DT 7333 141 2 entities entity NNS 7333 141 3 do do VBP 7333 141 4 not not RB 7333 141 5 take take VB 7333 141 6 for for IN 7333 141 7 granted grant VBN 7333 141 8 any any DT 7333 141 9 knowledge knowledge NN 7333 141 10 or or CC 7333 141 11 intuition intuition NN 7333 141 12 whatever whatever WDT 7333 141 13 , , , 7333 141 14 but but CC 7333 141 15 they -PRON- PRP 7333 141 16 presuppose presuppose VBP 7333 141 17 only only RB 7333 141 18 the the DT 7333 141 19 validity validity NN 7333 141 20 of of IN 7333 141 21 the the DT 7333 141 22 axioms axiom NNS 7333 141 23 , , , 7333 141 24 such such JJ 7333 141 25 as as IN 7333 141 26 the the DT 7333 141 27 one one NN 7333 141 28 stated state VBN 7333 141 29 above above RB 7333 141 30 , , , 7333 141 31 which which WDT 7333 141 32 are be VBP 7333 141 33 to to TO 7333 141 34 be be VB 7333 141 35 taken take VBN 7333 141 36 in in IN 7333 141 37 a a DT 7333 141 38 purely purely RB 7333 141 39 formal formal JJ 7333 141 40 sense sense NN 7333 141 41 , , , 7333 141 42 i.e. i.e. FW 7333 142 1 as as IN 7333 142 2 void void RB 7333 142 3 of of IN 7333 142 4 all all DT 7333 142 5 content content NN 7333 142 6 of of IN 7333 142 7 intuition intuition NN 7333 142 8 or or CC 7333 142 9 experience experience NN 7333 142 10 . . . 7333 143 1 These these DT 7333 143 2 axioms axiom NNS 7333 143 3 are be VBP 7333 143 4 free free JJ 7333 143 5 creations creation NNS 7333 143 6 of of IN 7333 143 7 the the DT 7333 143 8 human human JJ 7333 143 9 mind mind NN 7333 143 10 . . . 7333 144 1 All all DT 7333 144 2 other other JJ 7333 144 3 propositions proposition NNS 7333 144 4 of of IN 7333 144 5 geometry geometry NN 7333 144 6 are be VBP 7333 144 7 logical logical JJ 7333 144 8 inferences inference NNS 7333 144 9 from from IN 7333 144 10 the the DT 7333 144 11 axioms axiom NNS 7333 144 12 ( ( -LRB- 7333 144 13 which which WDT 7333 144 14 are be VBP 7333 144 15 to to TO 7333 144 16 be be VB 7333 144 17 taken take VBN 7333 144 18 in in IN 7333 144 19 the the DT 7333 144 20 nominalistic nominalistic JJ 7333 144 21 sense sense NN 7333 144 22 only only RB 7333 144 23 ) ) -RRB- 7333 144 24 . . . 7333 145 1 The the DT 7333 145 2 matter matter NN 7333 145 3 of of IN 7333 145 4 which which WDT 7333 145 5 geometry geometry NN 7333 145 6 treats treat NNS 7333 145 7 is be VBZ 7333 145 8 first first RB 7333 145 9 defined define VBN 7333 145 10 by by IN 7333 145 11 the the DT 7333 145 12 axioms axiom NNS 7333 145 13 . . . 7333 146 1 Schlick schlick VB 7333 146 2 in in IN 7333 146 3 his -PRON- PRP$ 7333 146 4 book book NN 7333 146 5 on on IN 7333 146 6 epistemology epistemology NN 7333 146 7 has have VBZ 7333 146 8 therefore therefore RB 7333 146 9 characterised characterise VBN 7333 146 10 axioms axiom NNS 7333 146 11 very very RB 7333 146 12 aptly aptly RB 7333 146 13 as as IN 7333 146 14 " " `` 7333 146 15 implicit implicit JJ 7333 146 16 definitions definition NNS 7333 146 17 . . . 7333 146 18 " " '' 7333 147 1 This this DT 7333 147 2 view view NN 7333 147 3 of of IN 7333 147 4 axioms axiom NNS 7333 147 5 , , , 7333 147 6 advocated advocate VBN 7333 147 7 by by IN 7333 147 8 modern modern JJ 7333 147 9 axiomatics axiomatic NNS 7333 147 10 , , , 7333 147 11 purges purge NNS 7333 147 12 mathematics mathematic NNS 7333 147 13 of of IN 7333 147 14 all all DT 7333 147 15 extraneous extraneous JJ 7333 147 16 elements element NNS 7333 147 17 , , , 7333 147 18 and and CC 7333 147 19 thus thus RB 7333 147 20 dispels dispel VBZ 7333 147 21 the the DT 7333 147 22 mystic mystic JJ 7333 147 23 obscurity obscurity NN 7333 147 24 which which WDT 7333 147 25 formerly formerly RB 7333 147 26 surrounded surround VBD 7333 147 27 the the DT 7333 147 28 principles principle NNS 7333 147 29 of of IN 7333 147 30 mathematics mathematic NNS 7333 147 31 . . . 7333 148 1 But but CC 7333 148 2 a a DT 7333 148 3 presentation presentation NN 7333 148 4 of of IN 7333 148 5 its -PRON- PRP$ 7333 148 6 principles principle NNS 7333 148 7 thus thus RB 7333 148 8 clarified clarify VBD 7333 148 9 makes make VBZ 7333 148 10 it -PRON- PRP 7333 148 11 also also RB 7333 148 12 evident evident JJ 7333 148 13 that that IN 7333 148 14 mathematics mathematic NNS 7333 148 15 as as IN 7333 148 16 such such JJ 7333 148 17 can can MD 7333 148 18 not not RB 7333 148 19 predicate predicate VB 7333 148 20 anything anything NN 7333 148 21 about about IN 7333 148 22 perceptual perceptual JJ 7333 148 23 objects object NNS 7333 148 24 or or CC 7333 148 25 real real JJ 7333 148 26 objects object NNS 7333 148 27 . . . 7333 149 1 In in IN 7333 149 2 axiomatic axiomatic JJ 7333 149 3 geometry geometry NN 7333 149 4 the the DT 7333 149 5 words word NNS 7333 149 6 " " `` 7333 149 7 point point NN 7333 149 8 , , , 7333 149 9 " " '' 7333 149 10 " " `` 7333 149 11 straight straight JJ 7333 149 12 line line NN 7333 149 13 , , , 7333 149 14 " " '' 7333 149 15 etc etc FW 7333 149 16 . . . 7333 149 17 , , , 7333 149 18 stand stand VB 7333 149 19 only only RB 7333 149 20 for for IN 7333 149 21 empty empty JJ 7333 149 22 conceptual conceptual JJ 7333 149 23 schemata schemata NN 7333 149 24 . . . 7333 150 1 That that DT 7333 150 2 which which WDT 7333 150 3 gives give VBZ 7333 150 4 them -PRON- PRP 7333 150 5 substance substance NN 7333 150 6 is be VBZ 7333 150 7 not not RB 7333 150 8 relevant relevant JJ 7333 150 9 to to IN 7333 150 10 mathematics mathematic NNS 7333 150 11 . . . 7333 151 1 Yet yet CC 7333 151 2 on on IN 7333 151 3 the the DT 7333 151 4 other other JJ 7333 151 5 hand hand NN 7333 151 6 it -PRON- PRP 7333 151 7 is be VBZ 7333 151 8 certain certain JJ 7333 151 9 that that IN 7333 151 10 mathematics mathematic NNS 7333 151 11 generally generally RB 7333 151 12 , , , 7333 151 13 and and CC 7333 151 14 particularly particularly RB 7333 151 15 geometry geometry NN 7333 151 16 , , , 7333 151 17 owes owe VBZ 7333 151 18 its -PRON- PRP$ 7333 151 19 existence existence NN 7333 151 20 to to IN 7333 151 21 the the DT 7333 151 22 need need NN 7333 151 23 which which WDT 7333 151 24 was be VBD 7333 151 25 felt feel VBN 7333 151 26 of of IN 7333 151 27 learning learn VBG 7333 151 28 something something NN 7333 151 29 about about IN 7333 151 30 the the DT 7333 151 31 relations relation NNS 7333 151 32 of of IN 7333 151 33 real real JJ 7333 151 34 things thing NNS 7333 151 35 to to IN 7333 151 36 one one CD 7333 151 37 another another DT 7333 151 38 . . . 7333 152 1 The the DT 7333 152 2 very very JJ 7333 152 3 word word NN 7333 152 4 geometry geometry NN 7333 152 5 , , , 7333 152 6 which which WDT 7333 152 7 , , , 7333 152 8 of of IN 7333 152 9 course course NN 7333 152 10 , , , 7333 152 11 means mean VBZ 7333 152 12 earth earth NN 7333 152 13 - - HYPH 7333 152 14 measuring measure VBG 7333 152 15 , , , 7333 152 16 proves prove VBZ 7333 152 17 this this DT 7333 152 18 . . . 7333 153 1 For for IN 7333 153 2 earth earth NN 7333 153 3 - - HYPH 7333 153 4 measuring measuring NN 7333 153 5 has have VBZ 7333 153 6 to to TO 7333 153 7 do do VB 7333 153 8 with with IN 7333 153 9 the the DT 7333 153 10 possibilities possibility NNS 7333 153 11 of of IN 7333 153 12 the the DT 7333 153 13 disposition disposition NN 7333 153 14 of of IN 7333 153 15 certain certain JJ 7333 153 16 natural natural JJ 7333 153 17 objects object NNS 7333 153 18 with with IN 7333 153 19 respect respect NN 7333 153 20 to to IN 7333 153 21 one one CD 7333 153 22 another another DT 7333 153 23 , , , 7333 153 24 namely namely RB 7333 153 25 , , , 7333 153 26 with with IN 7333 153 27 parts part NNS 7333 153 28 of of IN 7333 153 29 the the DT 7333 153 30 earth earth NN 7333 153 31 , , , 7333 153 32 measuring measure VBG 7333 153 33 - - HYPH 7333 153 34 lines line NNS 7333 153 35 , , , 7333 153 36 measuring measure VBG 7333 153 37 - - HYPH 7333 153 38 wands wand NNS 7333 153 39 , , , 7333 153 40 etc etc FW 7333 153 41 . . . 7333 154 1 It -PRON- PRP 7333 154 2 is be VBZ 7333 154 3 clear clear JJ 7333 154 4 that that IN 7333 154 5 the the DT 7333 154 6 system system NN 7333 154 7 of of IN 7333 154 8 concepts concept NNS 7333 154 9 of of IN 7333 154 10 axiomatic axiomatic JJ 7333 154 11 geometry geometry NN 7333 154 12 alone alone RB 7333 154 13 can can MD 7333 154 14 not not RB 7333 154 15 make make VB 7333 154 16 any any DT 7333 154 17 assertions assertion NNS 7333 154 18 as as IN 7333 154 19 to to IN 7333 154 20 the the DT 7333 154 21 relations relation NNS 7333 154 22 of of IN 7333 154 23 real real JJ 7333 154 24 objects object NNS 7333 154 25 of of IN 7333 154 26 this this DT 7333 154 27 kind kind NN 7333 154 28 , , , 7333 154 29 which which WDT 7333 154 30 we -PRON- PRP 7333 154 31 will will MD 7333 154 32 call call VB 7333 154 33 practically practically RB 7333 154 34 - - HYPH 7333 154 35 rigid rigid JJ 7333 154 36 bodies body NNS 7333 154 37 . . . 7333 155 1 To to TO 7333 155 2 be be VB 7333 155 3 able able JJ 7333 155 4 to to TO 7333 155 5 make make VB 7333 155 6 such such JJ 7333 155 7 assertions assertion NNS 7333 155 8 , , , 7333 155 9 geometry geometry NN 7333 155 10 must must MD 7333 155 11 be be VB 7333 155 12 stripped strip VBN 7333 155 13 of of IN 7333 155 14 its -PRON- PRP$ 7333 155 15 merely merely RB 7333 155 16 logical logical JJ 7333 155 17 - - HYPH 7333 155 18 formal formal JJ 7333 155 19 character character NN 7333 155 20 by by IN 7333 155 21 the the DT 7333 155 22 co co NN 7333 155 23 - - NN 7333 155 24 ordination ordination NN 7333 155 25 of of IN 7333 155 26 real real JJ 7333 155 27 objects object NNS 7333 155 28 of of IN 7333 155 29 experience experience NN 7333 155 30 with with IN 7333 155 31 the the DT 7333 155 32 empty empty JJ 7333 155 33 conceptual conceptual JJ 7333 155 34 frame frame NN 7333 155 35 - - HYPH 7333 155 36 work work NN 7333 155 37 of of IN 7333 155 38 axiomatic axiomatic JJ 7333 155 39 geometry geometry NN 7333 155 40 . . . 7333 156 1 To to TO 7333 156 2 accomplish accomplish VB 7333 156 3 this this DT 7333 156 4 , , , 7333 156 5 we -PRON- PRP 7333 156 6 need need VBP 7333 156 7 only only RB 7333 156 8 add add VB 7333 156 9 the the DT 7333 156 10 proposition:--Solid proposition:--solid JJ 7333 156 11 bodies body NNS 7333 156 12 are be VBP 7333 156 13 related relate VBN 7333 156 14 , , , 7333 156 15 with with IN 7333 156 16 respect respect NN 7333 156 17 to to IN 7333 156 18 their -PRON- PRP$ 7333 156 19 possible possible JJ 7333 156 20 dispositions disposition NNS 7333 156 21 , , , 7333 156 22 as as IN 7333 156 23 are be VBP 7333 156 24 bodies body NNS 7333 156 25 in in IN 7333 156 26 Euclidean Euclidean NNP 7333 156 27 geometry geometry NN 7333 156 28 of of IN 7333 156 29 three three CD 7333 156 30 dimensions dimension NNS 7333 156 31 . . . 7333 157 1 Then then RB 7333 157 2 the the DT 7333 157 3 propositions proposition NNS 7333 157 4 of of IN 7333 157 5 Euclid euclid JJ 7333 157 6 contain contain NN 7333 157 7 affirmations affirmation NNS 7333 157 8 as as IN 7333 157 9 to to IN 7333 157 10 the the DT 7333 157 11 relations relation NNS 7333 157 12 of of IN 7333 157 13 practically practically RB 7333 157 14 - - HYPH 7333 157 15 rigid rigid JJ 7333 157 16 bodies body NNS 7333 157 17 . . . 7333 158 1 Geometry geometry NN 7333 158 2 thus thus RB 7333 158 3 completed complete VBD 7333 158 4 is be VBZ 7333 158 5 evidently evidently RB 7333 158 6 a a DT 7333 158 7 natural natural JJ 7333 158 8 science science NN 7333 158 9 ; ; : 7333 158 10 we -PRON- PRP 7333 158 11 may may MD 7333 158 12 in in IN 7333 158 13 fact fact NN 7333 158 14 regard regard VB 7333 158 15 it -PRON- PRP 7333 158 16 as as IN 7333 158 17 the the DT 7333 158 18 most most RBS 7333 158 19 ancient ancient JJ 7333 158 20 branch branch NN 7333 158 21 of of IN 7333 158 22 physics physics NN 7333 158 23 . . . 7333 159 1 Its -PRON- PRP$ 7333 159 2 affirmations affirmation NNS 7333 159 3 rest rest VBP 7333 159 4 essentially essentially RB 7333 159 5 on on IN 7333 159 6 induction induction NN 7333 159 7 from from IN 7333 159 8 experience experience NN 7333 159 9 , , , 7333 159 10 but but CC 7333 159 11 not not RB 7333 159 12 on on IN 7333 159 13 logical logical JJ 7333 159 14 inferences inference NNS 7333 159 15 only only RB 7333 159 16 . . . 7333 160 1 We -PRON- PRP 7333 160 2 will will MD 7333 160 3 call call VB 7333 160 4 this this DT 7333 160 5 completed complete VBN 7333 160 6 geometry geometry NN 7333 160 7 " " `` 7333 160 8 practical practical JJ 7333 160 9 geometry geometry NN 7333 160 10 , , , 7333 160 11 " " '' 7333 160 12 and and CC 7333 160 13 shall shall MD 7333 160 14 distinguish distinguish VB 7333 160 15 it -PRON- PRP 7333 160 16 in in IN 7333 160 17 what what WP 7333 160 18 follows follow VBZ 7333 160 19 from from IN 7333 160 20 " " `` 7333 160 21 purely purely RB 7333 160 22 axiomatic axiomatic JJ 7333 160 23 geometry geometry NN 7333 160 24 . . . 7333 160 25 " " '' 7333 161 1 The the DT 7333 161 2 question question NN 7333 161 3 whether whether IN 7333 161 4 the the DT 7333 161 5 practical practical JJ 7333 161 6 geometry geometry NN 7333 161 7 of of IN 7333 161 8 the the DT 7333 161 9 universe universe NN 7333 161 10 is be VBZ 7333 161 11 Euclidean euclidean JJ 7333 161 12 or or CC 7333 161 13 not not RB 7333 161 14 has have VBZ 7333 161 15 a a DT 7333 161 16 clear clear JJ 7333 161 17 meaning meaning NN 7333 161 18 , , , 7333 161 19 and and CC 7333 161 20 its -PRON- PRP$ 7333 161 21 answer answer NN 7333 161 22 can can MD 7333 161 23 only only RB 7333 161 24 be be VB 7333 161 25 furnished furnish VBN 7333 161 26 by by IN 7333 161 27 experience experience NN 7333 161 28 . . . 7333 162 1 All all DT 7333 162 2 linear linear JJ 7333 162 3 measurement measurement NN 7333 162 4 in in IN 7333 162 5 physics physics NN 7333 162 6 is be VBZ 7333 162 7 practical practical JJ 7333 162 8 geometry geometry NN 7333 162 9 in in IN 7333 162 10 this this DT 7333 162 11 sense sense NN 7333 162 12 , , , 7333 162 13 so so CC 7333 162 14 too too RB 7333 162 15 is be VBZ 7333 162 16 geodetic geodetic JJ 7333 162 17 and and CC 7333 162 18 astronomical astronomical JJ 7333 162 19 linear linear JJ 7333 162 20 measurement measurement NN 7333 162 21 , , , 7333 162 22 if if IN 7333 162 23 we -PRON- PRP 7333 162 24 call call VBP 7333 162 25 to to IN 7333 162 26 our -PRON- PRP$ 7333 162 27 help help NN 7333 162 28 the the DT 7333 162 29 law law NN 7333 162 30 of of IN 7333 162 31 experience experience NN 7333 162 32 that that WDT 7333 162 33 light light NN 7333 162 34 is be VBZ 7333 162 35 propagated propagate VBN 7333 162 36 in in IN 7333 162 37 a a DT 7333 162 38 straight straight JJ 7333 162 39 line line NN 7333 162 40 , , , 7333 162 41 and and CC 7333 162 42 indeed indeed RB 7333 162 43 in in IN 7333 162 44 a a DT 7333 162 45 straight straight JJ 7333 162 46 line line NN 7333 162 47 in in IN 7333 162 48 the the DT 7333 162 49 sense sense NN 7333 162 50 of of IN 7333 162 51 practical practical JJ 7333 162 52 geometry geometry NN 7333 162 53 . . . 7333 163 1 I -PRON- PRP 7333 163 2 attach attach VBP 7333 163 3 special special JJ 7333 163 4 importance importance NN 7333 163 5 to to IN 7333 163 6 the the DT 7333 163 7 view view NN 7333 163 8 of of IN 7333 163 9 geometry geometry NN 7333 163 10 which which WDT 7333 163 11 I -PRON- PRP 7333 163 12 have have VBP 7333 163 13 just just RB 7333 163 14 set set VBN 7333 163 15 forth forth RP 7333 163 16 , , , 7333 163 17 because because IN 7333 163 18 without without IN 7333 163 19 it -PRON- PRP 7333 163 20 I -PRON- PRP 7333 163 21 should should MD 7333 163 22 have have VB 7333 163 23 been be VBN 7333 163 24 unable unable JJ 7333 163 25 to to TO 7333 163 26 formulate formulate VB 7333 163 27 the the DT 7333 163 28 theory theory NN 7333 163 29 of of IN 7333 163 30 relativity relativity NN 7333 163 31 . . . 7333 164 1 Without without IN 7333 164 2 it -PRON- PRP 7333 164 3 the the DT 7333 164 4 following follow VBG 7333 164 5 reflection reflection NN 7333 164 6 would would MD 7333 164 7 have have VB 7333 164 8 been be VBN 7333 164 9 impossible:--In impossible:--in ADD 7333 164 10 a a DT 7333 164 11 system system NN 7333 164 12 of of IN 7333 164 13 reference reference NN 7333 164 14 rotating rotate VBG 7333 164 15 relatively relatively RB 7333 164 16 to to IN 7333 164 17 an an DT 7333 164 18 inert inert JJ 7333 164 19 system system NN 7333 164 20 , , , 7333 164 21 the the DT 7333 164 22 laws law NNS 7333 164 23 of of IN 7333 164 24 disposition disposition NN 7333 164 25 of of IN 7333 164 26 rigid rigid JJ 7333 164 27 bodies body NNS 7333 164 28 do do VBP 7333 164 29 not not RB 7333 164 30 correspond correspond VB 7333 164 31 to to IN 7333 164 32 the the DT 7333 164 33 rules rule NNS 7333 164 34 of of IN 7333 164 35 Euclidean euclidean JJ 7333 164 36 geometry geometry NN 7333 164 37 on on IN 7333 164 38 account account NN 7333 164 39 of of IN 7333 164 40 the the DT 7333 164 41 Lorentz Lorentz NNP 7333 164 42 contraction contraction NN 7333 164 43 ; ; : 7333 164 44 thus thus RB 7333 164 45 if if IN 7333 164 46 we -PRON- PRP 7333 164 47 admit admit VBP 7333 164 48 non non JJ 7333 164 49 - - JJ 7333 164 50 inert inert JJ 7333 164 51 systems system NNS 7333 164 52 we -PRON- PRP 7333 164 53 must must MD 7333 164 54 abandon abandon VB 7333 164 55 Euclidean Euclidean NNP 7333 164 56 geometry geometry NN 7333 164 57 . . . 7333 165 1 The the DT 7333 165 2 decisive decisive JJ 7333 165 3 step step NN 7333 165 4 in in IN 7333 165 5 the the DT 7333 165 6 transition transition NN 7333 165 7 to to IN 7333 165 8 general general JJ 7333 165 9 co co JJ 7333 165 10 - - JJ 7333 165 11 variant variant JJ 7333 165 12 equations equation NNS 7333 165 13 would would MD 7333 165 14 certainly certainly RB 7333 165 15 not not RB 7333 165 16 have have VB 7333 165 17 been be VBN 7333 165 18 taken take VBN 7333 165 19 if if IN 7333 165 20 the the DT 7333 165 21 above above JJ 7333 165 22 interpretation interpretation NN 7333 165 23 had have VBD 7333 165 24 not not RB 7333 165 25 served serve VBN 7333 165 26 as as IN 7333 165 27 a a DT 7333 165 28 stepping stepping JJ 7333 165 29 - - HYPH 7333 165 30 stone stone NN 7333 165 31 . . . 7333 166 1 If if IN 7333 166 2 we -PRON- PRP 7333 166 3 deny deny VBP 7333 166 4 the the DT 7333 166 5 relation relation NN 7333 166 6 between between IN 7333 166 7 the the DT 7333 166 8 body body NN 7333 166 9 of of IN 7333 166 10 axiomatic axiomatic JJ 7333 166 11 Euclidean euclidean JJ 7333 166 12 geometry geometry NN 7333 166 13 and and CC 7333 166 14 the the DT 7333 166 15 practically practically RB 7333 166 16 - - HYPH 7333 166 17 rigid rigid JJ 7333 166 18 body body NN 7333 166 19 of of IN 7333 166 20 reality reality NN 7333 166 21 , , , 7333 166 22 we -PRON- PRP 7333 166 23 readily readily RB 7333 166 24 arrive arrive VBP 7333 166 25 at at IN 7333 166 26 the the DT 7333 166 27 following follow VBG 7333 166 28 view view NN 7333 166 29 , , , 7333 166 30 which which WDT 7333 166 31 was be VBD 7333 166 32 entertained entertain VBN 7333 166 33 by by IN 7333 166 34 that that DT 7333 166 35 acute acute JJ 7333 166 36 and and CC 7333 166 37 profound profound JJ 7333 166 38 thinker thinker NN 7333 166 39 , , , 7333 166 40 H. H. NNP 7333 166 41 Poincare:--Euclidean Poincare:--Euclidean NNP 7333 166 42 geometry geometry NN 7333 166 43 is be VBZ 7333 166 44 distinguished distinguish VBN 7333 166 45 above above IN 7333 166 46 all all DT 7333 166 47 other other JJ 7333 166 48 imaginable imaginable JJ 7333 166 49 axiomatic axiomatic JJ 7333 166 50 geometries geometry NNS 7333 166 51 by by IN 7333 166 52 its -PRON- PRP$ 7333 166 53 simplicity simplicity NN 7333 166 54 . . . 7333 167 1 Now now RB 7333 167 2 since since IN 7333 167 3 axiomatic axiomatic JJ 7333 167 4 geometry geometry NN 7333 167 5 by by IN 7333 167 6 itself -PRON- PRP 7333 167 7 contains contain VBZ 7333 167 8 no no DT 7333 167 9 assertions assertion NNS 7333 167 10 as as IN 7333 167 11 to to IN 7333 167 12 the the DT 7333 167 13 reality reality NN 7333 167 14 which which WDT 7333 167 15 can can MD 7333 167 16 be be VB 7333 167 17 experienced experience VBN 7333 167 18 , , , 7333 167 19 but but CC 7333 167 20 can can MD 7333 167 21 do do VB 7333 167 22 so so RB 7333 167 23 only only RB 7333 167 24 in in IN 7333 167 25 combination combination NN 7333 167 26 with with IN 7333 167 27 physical physical JJ 7333 167 28 laws law NNS 7333 167 29 , , , 7333 167 30 it -PRON- PRP 7333 167 31 should should MD 7333 167 32 be be VB 7333 167 33 possible possible JJ 7333 167 34 and and CC 7333 167 35 reasonable reasonable JJ 7333 167 36 -- -- : 7333 167 37 whatever whatever WDT 7333 167 38 may may MD 7333 167 39 be be VB 7333 167 40 the the DT 7333 167 41 nature nature NN 7333 167 42 of of IN 7333 167 43 reality reality NN 7333 167 44 -- -- : 7333 167 45 to to TO 7333 167 46 retain retain VB 7333 167 47 Euclidean Euclidean NNP 7333 167 48 geometry geometry NN 7333 167 49 . . . 7333 168 1 For for IN 7333 168 2 if if IN 7333 168 3 contradictions contradiction NNS 7333 168 4 between between IN 7333 168 5 theory theory NN 7333 168 6 and and CC 7333 168 7 experience experience NN 7333 168 8 manifest manifest VBP 7333 168 9 themselves -PRON- PRP 7333 168 10 , , , 7333 168 11 we -PRON- PRP 7333 168 12 should should MD 7333 168 13 rather rather RB 7333 168 14 decide decide VB 7333 168 15 to to TO 7333 168 16 change change VB 7333 168 17 physical physical JJ 7333 168 18 laws law NNS 7333 168 19 than than IN 7333 168 20 to to TO 7333 168 21 change change VB 7333 168 22 axiomatic axiomatic JJ 7333 168 23 Euclidean euclidean JJ 7333 168 24 geometry geometry NN 7333 168 25 . . . 7333 169 1 If if IN 7333 169 2 we -PRON- PRP 7333 169 3 deny deny VBP 7333 169 4 the the DT 7333 169 5 relation relation NN 7333 169 6 between between IN 7333 169 7 the the DT 7333 169 8 practically practically RB 7333 169 9 - - HYPH 7333 169 10 rigid rigid JJ 7333 169 11 body body NN 7333 169 12 and and CC 7333 169 13 geometry geometry NN 7333 169 14 , , , 7333 169 15 we -PRON- PRP 7333 169 16 shall shall MD 7333 169 17 indeed indeed RB 7333 169 18 not not RB 7333 169 19 easily easily RB 7333 169 20 free free JJ 7333 169 21 ourselves -PRON- PRP 7333 169 22 from from IN 7333 169 23 the the DT 7333 169 24 convention convention NN 7333 169 25 that that WDT 7333 169 26 Euclidean Euclidean NNP 7333 169 27 geometry geometry NN 7333 169 28 is be VBZ 7333 169 29 to to TO 7333 169 30 be be VB 7333 169 31 retained retain VBN 7333 169 32 as as IN 7333 169 33 the the DT 7333 169 34 simplest simple JJS 7333 169 35 . . . 7333 170 1 Why why WRB 7333 170 2 is be VBZ 7333 170 3 the the DT 7333 170 4 equivalence equivalence NN 7333 170 5 of of IN 7333 170 6 the the DT 7333 170 7 practically practically RB 7333 170 8 - - HYPH 7333 170 9 rigid rigid JJ 7333 170 10 body body NN 7333 170 11 and and CC 7333 170 12 the the DT 7333 170 13 body body NN 7333 170 14 of of IN 7333 170 15 geometry geometry NN 7333 170 16 -- -- : 7333 170 17 which which WDT 7333 170 18 suggests suggest VBZ 7333 170 19 itself -PRON- PRP 7333 170 20 so so RB 7333 170 21 readily readily RB 7333 170 22 -- -- : 7333 170 23 denied deny VBN 7333 170 24 by by IN 7333 170 25 Poincare Poincare NNP 7333 170 26 and and CC 7333 170 27 other other JJ 7333 170 28 investigators investigator NNS 7333 170 29 ? ? . 7333 171 1 Simply simply RB 7333 171 2 because because IN 7333 171 3 under under IN 7333 171 4 closer close JJR 7333 171 5 inspection inspection NN 7333 171 6 the the DT 7333 171 7 real real JJ 7333 171 8 solid solid JJ 7333 171 9 bodies body NNS 7333 171 10 in in IN 7333 171 11 nature nature NN 7333 171 12 are be VBP 7333 171 13 not not RB 7333 171 14 rigid rigid JJ 7333 171 15 , , , 7333 171 16 because because IN 7333 171 17 their -PRON- PRP$ 7333 171 18 geometrical geometrical JJ 7333 171 19 behaviour behaviour NN 7333 171 20 , , , 7333 171 21 that that RB 7333 171 22 is is RB 7333 171 23 , , , 7333 171 24 their -PRON- PRP$ 7333 171 25 possibilities possibility NNS 7333 171 26 of of IN 7333 171 27 relative relative JJ 7333 171 28 disposition disposition NN 7333 171 29 , , , 7333 171 30 depend depend VBP 7333 171 31 upon upon IN 7333 171 32 temperature temperature NN 7333 171 33 , , , 7333 171 34 external external JJ 7333 171 35 forces force NNS 7333 171 36 , , , 7333 171 37 etc etc FW 7333 171 38 . . . 7333 172 1 Thus thus RB 7333 172 2 the the DT 7333 172 3 original original JJ 7333 172 4 , , , 7333 172 5 immediate immediate JJ 7333 172 6 relation relation NN 7333 172 7 between between IN 7333 172 8 geometry geometry NN 7333 172 9 and and CC 7333 172 10 physical physical JJ 7333 172 11 reality reality NN 7333 172 12 appears appear VBZ 7333 172 13 destroyed destroy VBN 7333 172 14 , , , 7333 172 15 and and CC 7333 172 16 we -PRON- PRP 7333 172 17 feel feel VBP 7333 172 18 impelled impel VBN 7333 172 19 toward toward IN 7333 172 20 the the DT 7333 172 21 following follow VBG 7333 172 22 more more RBR 7333 172 23 general general JJ 7333 172 24 view view NN 7333 172 25 , , , 7333 172 26 which which WDT 7333 172 27 characterizes characterize VBZ 7333 172 28 Poincare Poincare NNP 7333 172 29 's 's POS 7333 172 30 standpoint standpoint NN 7333 172 31 . . . 7333 173 1 Geometry Geometry NNP 7333 173 2 ( ( -LRB- 7333 173 3 G g NN 7333 173 4 ) ) -RRB- 7333 173 5 predicates predicate VBZ 7333 173 6 nothing nothing NN 7333 173 7 about about IN 7333 173 8 the the DT 7333 173 9 relations relation NNS 7333 173 10 of of IN 7333 173 11 real real JJ 7333 173 12 things thing NNS 7333 173 13 , , , 7333 173 14 but but CC 7333 173 15 only only RB 7333 173 16 geometry geometry NN 7333 173 17 together together RB 7333 173 18 with with IN 7333 173 19 the the DT 7333 173 20 purport purport NN 7333 173 21 ( ( -LRB- 7333 173 22 P p NN 7333 173 23 ) ) -RRB- 7333 173 24 of of IN 7333 173 25 physical physical JJ 7333 173 26 laws law NNS 7333 173 27 can can MD 7333 173 28 do do VB 7333 173 29 so so RB 7333 173 30 . . . 7333 174 1 Using use VBG 7333 174 2 symbols symbol NNS 7333 174 3 , , , 7333 174 4 we -PRON- PRP 7333 174 5 may may MD 7333 174 6 say say VB 7333 174 7 that that IN 7333 174 8 only only RB 7333 174 9 the the DT 7333 174 10 sum sum NN 7333 174 11 of of IN 7333 174 12 ( ( -LRB- 7333 174 13 G g NN 7333 174 14 ) ) -RRB- 7333 174 15 + + NFP 7333 174 16 ( ( -LRB- 7333 174 17 P p NN 7333 174 18 ) ) -RRB- 7333 174 19 is be VBZ 7333 174 20 subject subject JJ 7333 174 21 to to IN 7333 174 22 the the DT 7333 174 23 control control NN 7333 174 24 of of IN 7333 174 25 experience experience NN 7333 174 26 . . . 7333 175 1 Thus thus RB 7333 175 2 ( ( -LRB- 7333 175 3 G g NN 7333 175 4 ) ) -RRB- 7333 175 5 may may MD 7333 175 6 be be VB 7333 175 7 chosen choose VBN 7333 175 8 arbitrarily arbitrarily RB 7333 175 9 , , , 7333 175 10 and and CC 7333 175 11 also also RB 7333 175 12 parts part NNS 7333 175 13 of of IN 7333 175 14 ( ( -LRB- 7333 175 15 P p NN 7333 175 16 ) ) -RRB- 7333 175 17 ; ; : 7333 175 18 all all PDT 7333 175 19 these these DT 7333 175 20 laws law NNS 7333 175 21 are be VBP 7333 175 22 conventions convention NNS 7333 175 23 . . . 7333 176 1 All all DT 7333 176 2 that that WDT 7333 176 3 is be VBZ 7333 176 4 necessary necessary JJ 7333 176 5 to to TO 7333 176 6 avoid avoid VB 7333 176 7 contradictions contradiction NNS 7333 176 8 is be VBZ 7333 176 9 to to TO 7333 176 10 choose choose VB 7333 176 11 the the DT 7333 176 12 remainder remainder NN 7333 176 13 of of IN 7333 176 14 ( ( -LRB- 7333 176 15 P p NN 7333 176 16 ) ) -RRB- 7333 176 17 so so IN 7333 176 18 that that DT 7333 176 19 ( ( -LRB- 7333 176 20 G g NN 7333 176 21 ) ) -RRB- 7333 176 22 and and CC 7333 176 23 the the DT 7333 176 24 whole whole NN 7333 176 25 of of IN 7333 176 26 ( ( -LRB- 7333 176 27 P p NN 7333 176 28 ) ) -RRB- 7333 176 29 are be VBP 7333 176 30 together together RB 7333 176 31 in in IN 7333 176 32 accord accord NN 7333 176 33 with with IN 7333 176 34 experience experience NN 7333 176 35 . . . 7333 177 1 Envisaged envisage VBN 7333 177 2 in in IN 7333 177 3 this this DT 7333 177 4 way way NN 7333 177 5 , , , 7333 177 6 axiomatic axiomatic JJ 7333 177 7 geometry geometry NN 7333 177 8 and and CC 7333 177 9 the the DT 7333 177 10 part part NN 7333 177 11 of of IN 7333 177 12 natural natural JJ 7333 177 13 law law NN 7333 177 14 which which WDT 7333 177 15 has have VBZ 7333 177 16 been be VBN 7333 177 17 given give VBN 7333 177 18 a a DT 7333 177 19 conventional conventional JJ 7333 177 20 status status NN 7333 177 21 appear appear VBP 7333 177 22 as as RB 7333 177 23 epistemologically epistemologically RB 7333 177 24 equivalent equivalent JJ 7333 177 25 . . . 7333 178 1 _ _ NNP 7333 178 2 Sub Sub NNP 7333 178 3 specie specie VBD 7333 178 4 aeterni aeterni NN 7333 178 5 _ _ NNP 7333 178 6 Poincare Poincare NNP 7333 178 7 , , , 7333 178 8 in in IN 7333 178 9 my -PRON- PRP$ 7333 178 10 opinion opinion NN 7333 178 11 , , , 7333 178 12 is be VBZ 7333 178 13 right right JJ 7333 178 14 . . . 7333 179 1 The the DT 7333 179 2 idea idea NN 7333 179 3 of of IN 7333 179 4 the the DT 7333 179 5 measuring measure VBG 7333 179 6 - - HYPH 7333 179 7 rod rod NN 7333 179 8 and and CC 7333 179 9 the the DT 7333 179 10 idea idea NN 7333 179 11 of of IN 7333 179 12 the the DT 7333 179 13 clock clock NN 7333 179 14 co co VBN 7333 179 15 - - JJ 7333 179 16 ordinated ordinated JJ 7333 179 17 with with IN 7333 179 18 it -PRON- PRP 7333 179 19 in in IN 7333 179 20 the the DT 7333 179 21 theory theory NN 7333 179 22 of of IN 7333 179 23 relativity relativity NN 7333 179 24 do do VBP 7333 179 25 not not RB 7333 179 26 find find VB 7333 179 27 their -PRON- PRP$ 7333 179 28 exact exact JJ 7333 179 29 correspondence correspondence NN 7333 179 30 in in IN 7333 179 31 the the DT 7333 179 32 real real JJ 7333 179 33 world world NN 7333 179 34 . . . 7333 180 1 It -PRON- PRP 7333 180 2 is be VBZ 7333 180 3 also also RB 7333 180 4 clear clear JJ 7333 180 5 that that IN 7333 180 6 the the DT 7333 180 7 solid solid JJ 7333 180 8 body body NN 7333 180 9 and and CC 7333 180 10 the the DT 7333 180 11 clock clock NN 7333 180 12 do do VBP 7333 180 13 not not RB 7333 180 14 in in IN 7333 180 15 the the DT 7333 180 16 conceptual conceptual JJ 7333 180 17 edifice edifice NN 7333 180 18 of of IN 7333 180 19 physics physics NN 7333 180 20 play play VBP 7333 180 21 the the DT 7333 180 22 part part NN 7333 180 23 of of IN 7333 180 24 irreducible irreducible JJ 7333 180 25 elements element NNS 7333 180 26 , , , 7333 180 27 but but CC 7333 180 28 that that DT 7333 180 29 of of IN 7333 180 30 composite composite JJ 7333 180 31 structures structure NNS 7333 180 32 , , , 7333 180 33 which which WDT 7333 180 34 may may MD 7333 180 35 not not RB 7333 180 36 play play VB 7333 180 37 any any DT 7333 180 38 independent independent JJ 7333 180 39 part part NN 7333 180 40 in in IN 7333 180 41 theoretical theoretical JJ 7333 180 42 physics physics NN 7333 180 43 . . . 7333 181 1 But but CC 7333 181 2 it -PRON- PRP 7333 181 3 is be VBZ 7333 181 4 my -PRON- PRP$ 7333 181 5 conviction conviction NN 7333 181 6 that that IN 7333 181 7 in in IN 7333 181 8 the the DT 7333 181 9 present present JJ 7333 181 10 stage stage NN 7333 181 11 of of IN 7333 181 12 development development NN 7333 181 13 of of IN 7333 181 14 theoretical theoretical JJ 7333 181 15 physics physics NN 7333 181 16 these these DT 7333 181 17 ideas idea NNS 7333 181 18 must must MD 7333 181 19 still still RB 7333 181 20 be be VB 7333 181 21 employed employ VBN 7333 181 22 as as IN 7333 181 23 independent independent JJ 7333 181 24 ideas idea NNS 7333 181 25 ; ; : 7333 181 26 for for IN 7333 181 27 we -PRON- PRP 7333 181 28 are be VBP 7333 181 29 still still RB 7333 181 30 far far RB 7333 181 31 from from IN 7333 181 32 possessing possess VBG 7333 181 33 such such JJ 7333 181 34 certain certain JJ 7333 181 35 knowledge knowledge NN 7333 181 36 of of IN 7333 181 37 theoretical theoretical JJ 7333 181 38 principles principle NNS 7333 181 39 as as IN 7333 181 40 to to TO 7333 181 41 be be VB 7333 181 42 able able JJ 7333 181 43 to to TO 7333 181 44 give give VB 7333 181 45 exact exact JJ 7333 181 46 theoretical theoretical JJ 7333 181 47 constructions construction NNS 7333 181 48 of of IN 7333 181 49 solid solid JJ 7333 181 50 bodies body NNS 7333 181 51 and and CC 7333 181 52 clocks clock NNS 7333 181 53 . . . 7333 182 1 Further further RB 7333 182 2 , , , 7333 182 3 as as IN 7333 182 4 to to IN 7333 182 5 the the DT 7333 182 6 objection objection NN 7333 182 7 that that IN 7333 182 8 there there EX 7333 182 9 are be VBP 7333 182 10 no no DT 7333 182 11 really really RB 7333 182 12 rigid rigid JJ 7333 182 13 bodies body NNS 7333 182 14 in in IN 7333 182 15 nature nature NN 7333 182 16 , , , 7333 182 17 and and CC 7333 182 18 that that IN 7333 182 19 therefore therefore RB 7333 182 20 the the DT 7333 182 21 properties property NNS 7333 182 22 predicated predicate VBN 7333 182 23 of of IN 7333 182 24 rigid rigid JJ 7333 182 25 bodies body NNS 7333 182 26 do do VBP 7333 182 27 not not RB 7333 182 28 apply apply VB 7333 182 29 to to IN 7333 182 30 physical physical NNP 7333 182 31 reality,--this reality,--this DT 7333 182 32 objection objection NN 7333 182 33 is be VBZ 7333 182 34 by by IN 7333 182 35 no no DT 7333 182 36 means means NN 7333 182 37 so so RB 7333 182 38 radical radical JJ 7333 182 39 as as IN 7333 182 40 might may MD 7333 182 41 appear appear VB 7333 182 42 from from IN 7333 182 43 a a DT 7333 182 44 hasty hasty JJ 7333 182 45 examination examination NN 7333 182 46 . . . 7333 183 1 For for IN 7333 183 2 it -PRON- PRP 7333 183 3 is be VBZ 7333 183 4 not not RB 7333 183 5 a a DT 7333 183 6 difficult difficult JJ 7333 183 7 task task NN 7333 183 8 to to TO 7333 183 9 determine determine VB 7333 183 10 the the DT 7333 183 11 physical physical JJ 7333 183 12 state state NN 7333 183 13 of of IN 7333 183 14 a a DT 7333 183 15 measuring measure VBG 7333 183 16 - - HYPH 7333 183 17 rod rod NN 7333 183 18 so so RB 7333 183 19 accurately accurately RB 7333 183 20 that that IN 7333 183 21 its -PRON- PRP$ 7333 183 22 behaviour behaviour NN 7333 183 23 relatively relatively RB 7333 183 24 to to IN 7333 183 25 other other JJ 7333 183 26 measuring measuring NN 7333 183 27 - - HYPH 7333 183 28 bodies body NNS 7333 183 29 shall shall MD 7333 183 30 be be VB 7333 183 31 sufficiently sufficiently RB 7333 183 32 free free JJ 7333 183 33 from from IN 7333 183 34 ambiguity ambiguity NN 7333 183 35 to to TO 7333 183 36 allow allow VB 7333 183 37 it -PRON- PRP 7333 183 38 to to TO 7333 183 39 be be VB 7333 183 40 substituted substitute VBN 7333 183 41 for for IN 7333 183 42 the the DT 7333 183 43 " " `` 7333 183 44 rigid rigid JJ 7333 183 45 " " '' 7333 183 46 body body NN 7333 183 47 . . . 7333 184 1 It -PRON- PRP 7333 184 2 is be VBZ 7333 184 3 to to IN 7333 184 4 measuring measure VBG 7333 184 5 - - HYPH 7333 184 6 bodies body NNS 7333 184 7 of of IN 7333 184 8 this this DT 7333 184 9 kind kind NN 7333 184 10 that that WDT 7333 184 11 statements statement VBZ 7333 184 12 as as IN 7333 184 13 to to IN 7333 184 14 rigid rigid JJ 7333 184 15 bodies body NNS 7333 184 16 must must MD 7333 184 17 be be VB 7333 184 18 referred refer VBN 7333 184 19 . . . 7333 185 1 All all DT 7333 185 2 practical practical JJ 7333 185 3 geometry geometry NN 7333 185 4 is be VBZ 7333 185 5 based base VBN 7333 185 6 upon upon IN 7333 185 7 a a DT 7333 185 8 principle principle NN 7333 185 9 which which WDT 7333 185 10 is be VBZ 7333 185 11 accessible accessible JJ 7333 185 12 to to TO 7333 185 13 experience experience VB 7333 185 14 , , , 7333 185 15 and and CC 7333 185 16 which which WDT 7333 185 17 we -PRON- PRP 7333 185 18 will will MD 7333 185 19 now now RB 7333 185 20 try try VB 7333 185 21 to to TO 7333 185 22 realise realise VB 7333 185 23 . . . 7333 186 1 We -PRON- PRP 7333 186 2 will will MD 7333 186 3 call call VB 7333 186 4 that that DT 7333 186 5 which which WDT 7333 186 6 is be VBZ 7333 186 7 enclosed enclose VBN 7333 186 8 between between IN 7333 186 9 two two CD 7333 186 10 boundaries boundary NNS 7333 186 11 , , , 7333 186 12 marked mark VBN 7333 186 13 upon upon IN 7333 186 14 a a DT 7333 186 15 practically practically RB 7333 186 16 - - HYPH 7333 186 17 rigid rigid JJ 7333 186 18 body body NN 7333 186 19 , , , 7333 186 20 a a DT 7333 186 21 tract tract NN 7333 186 22 . . . 7333 187 1 We -PRON- PRP 7333 187 2 imagine imagine VBP 7333 187 3 two two CD 7333 187 4 practically practically RB 7333 187 5 - - HYPH 7333 187 6 rigid rigid JJ 7333 187 7 bodies body NNS 7333 187 8 , , , 7333 187 9 each each DT 7333 187 10 with with IN 7333 187 11 a a DT 7333 187 12 tract tract NN 7333 187 13 marked mark VBN 7333 187 14 out out RP 7333 187 15 on on IN 7333 187 16 it -PRON- PRP 7333 187 17 . . . 7333 188 1 These these DT 7333 188 2 two two CD 7333 188 3 tracts tract NNS 7333 188 4 are be VBP 7333 188 5 said say VBN 7333 188 6 to to TO 7333 188 7 be be VB 7333 188 8 " " `` 7333 188 9 equal equal JJ 7333 188 10 to to IN 7333 188 11 one one CD 7333 188 12 another another DT 7333 188 13 " " `` 7333 188 14 if if IN 7333 188 15 the the DT 7333 188 16 boundaries boundary NNS 7333 188 17 of of IN 7333 188 18 the the DT 7333 188 19 one one CD 7333 188 20 tract tract NN 7333 188 21 can can MD 7333 188 22 be be VB 7333 188 23 brought bring VBN 7333 188 24 to to TO 7333 188 25 coincide coincide VB 7333 188 26 permanently permanently RB 7333 188 27 with with IN 7333 188 28 the the DT 7333 188 29 boundaries boundary NNS 7333 188 30 of of IN 7333 188 31 the the DT 7333 188 32 other other JJ 7333 188 33 . . . 7333 189 1 We -PRON- PRP 7333 189 2 now now RB 7333 189 3 assume assume VBP 7333 189 4 that that IN 7333 189 5 : : : 7333 189 6 If if IN 7333 189 7 two two CD 7333 189 8 tracts tract NNS 7333 189 9 are be VBP 7333 189 10 found find VBN 7333 189 11 to to TO 7333 189 12 be be VB 7333 189 13 equal equal JJ 7333 189 14 once once RB 7333 189 15 and and CC 7333 189 16 anywhere anywhere RB 7333 189 17 , , , 7333 189 18 they -PRON- PRP 7333 189 19 are be VBP 7333 189 20 equal equal JJ 7333 189 21 always always RB 7333 189 22 and and CC 7333 189 23 everywhere everywhere RB 7333 189 24 . . . 7333 190 1 Not not RB 7333 190 2 only only RB 7333 190 3 the the DT 7333 190 4 practical practical JJ 7333 190 5 geometry geometry NN 7333 190 6 of of IN 7333 190 7 Euclid Euclid NNP 7333 190 8 , , , 7333 190 9 but but CC 7333 190 10 also also RB 7333 190 11 its -PRON- PRP$ 7333 190 12 nearest near JJS 7333 190 13 generalisation generalisation NN 7333 190 14 , , , 7333 190 15 the the DT 7333 190 16 practical practical JJ 7333 190 17 geometry geometry NN 7333 190 18 of of IN 7333 190 19 Riemann Riemann NNP 7333 190 20 , , , 7333 190 21 and and CC 7333 190 22 therewith therewith NNP 7333 190 23 the the DT 7333 190 24 general general JJ 7333 190 25 theory theory NN 7333 190 26 of of IN 7333 190 27 relativity relativity NN 7333 190 28 , , , 7333 190 29 rest rest VB 7333 190 30 upon upon IN 7333 190 31 this this DT 7333 190 32 assumption assumption NN 7333 190 33 . . . 7333 191 1 Of of IN 7333 191 2 the the DT 7333 191 3 experimental experimental JJ 7333 191 4 reasons reason NNS 7333 191 5 which which WDT 7333 191 6 warrant warrant VBP 7333 191 7 this this DT 7333 191 8 assumption assumption NN 7333 191 9 I -PRON- PRP 7333 191 10 will will MD 7333 191 11 mention mention VB 7333 191 12 only only RB 7333 191 13 one one CD 7333 191 14 . . . 7333 192 1 The the DT 7333 192 2 phenomenon phenomenon NN 7333 192 3 of of IN 7333 192 4 the the DT 7333 192 5 propagation propagation NN 7333 192 6 of of IN 7333 192 7 light light NN 7333 192 8 in in IN 7333 192 9 empty empty JJ 7333 192 10 space space NN 7333 192 11 assigns assign VBZ 7333 192 12 a a DT 7333 192 13 tract tract NN 7333 192 14 , , , 7333 192 15 namely namely RB 7333 192 16 , , , 7333 192 17 the the DT 7333 192 18 appropriate appropriate JJ 7333 192 19 path path NN 7333 192 20 of of IN 7333 192 21 light light NN 7333 192 22 , , , 7333 192 23 to to IN 7333 192 24 each each DT 7333 192 25 interval interval NN 7333 192 26 of of IN 7333 192 27 local local JJ 7333 192 28 time time NN 7333 192 29 , , , 7333 192 30 and and CC 7333 192 31 conversely conversely RB 7333 192 32 . . . 7333 193 1 Thence thence NN 7333 193 2 it -PRON- PRP 7333 193 3 follows follow VBZ 7333 193 4 that that IN 7333 193 5 the the DT 7333 193 6 above above JJ 7333 193 7 assumption assumption NN 7333 193 8 for for IN 7333 193 9 tracts tract NNS 7333 193 10 must must MD 7333 193 11 also also RB 7333 193 12 hold hold VB 7333 193 13 good good JJ 7333 193 14 for for IN 7333 193 15 intervals interval NNS 7333 193 16 of of IN 7333 193 17 clock clock NN 7333 193 18 - - HYPH 7333 193 19 time time NN 7333 193 20 in in IN 7333 193 21 the the DT 7333 193 22 theory theory NN 7333 193 23 of of IN 7333 193 24 relativity relativity NN 7333 193 25 . . . 7333 194 1 Consequently consequently RB 7333 194 2 it -PRON- PRP 7333 194 3 may may MD 7333 194 4 be be VB 7333 194 5 formulated formulate VBN 7333 194 6 as as IN 7333 194 7 follows:--If follows:--If NNP 7333 194 8 two two CD 7333 194 9 ideal ideal JJ 7333 194 10 clocks clock NNS 7333 194 11 are be VBP 7333 194 12 going go VBG 7333 194 13 at at IN 7333 194 14 the the DT 7333 194 15 same same JJ 7333 194 16 rate rate NN 7333 194 17 at at IN 7333 194 18 any any DT 7333 194 19 time time NN 7333 194 20 and and CC 7333 194 21 at at IN 7333 194 22 any any DT 7333 194 23 place place NN 7333 194 24 ( ( -LRB- 7333 194 25 being be VBG 7333 194 26 then then RB 7333 194 27 in in IN 7333 194 28 immediate immediate JJ 7333 194 29 proximity proximity NN 7333 194 30 to to IN 7333 194 31 each each DT 7333 194 32 other other JJ 7333 194 33 ) ) -RRB- 7333 194 34 , , , 7333 194 35 they -PRON- PRP 7333 194 36 will will MD 7333 194 37 always always RB 7333 194 38 go go VB 7333 194 39 at at IN 7333 194 40 the the DT 7333 194 41 same same JJ 7333 194 42 rate rate NN 7333 194 43 , , , 7333 194 44 no no RB 7333 194 45 matter matter RB 7333 194 46 where where WRB 7333 194 47 and and CC 7333 194 48 when when WRB 7333 194 49 they -PRON- PRP 7333 194 50 are be VBP 7333 194 51 again again RB 7333 194 52 compared compare VBN 7333 194 53 with with IN 7333 194 54 each each DT 7333 194 55 other other JJ 7333 194 56 at at IN 7333 194 57 one one CD 7333 194 58 place.--If place.--if NN 7333 194 59 this this DT 7333 194 60 law law NN 7333 194 61 were be VBD 7333 194 62 not not RB 7333 194 63 valid valid JJ 7333 194 64 for for IN 7333 194 65 real real JJ 7333 194 66 clocks clock NNS 7333 194 67 , , , 7333 194 68 the the DT 7333 194 69 proper proper JJ 7333 194 70 frequencies frequency NNS 7333 194 71 for for IN 7333 194 72 the the DT 7333 194 73 separate separate JJ 7333 194 74 atoms atom NNS 7333 194 75 of of IN 7333 194 76 the the DT 7333 194 77 same same JJ 7333 194 78 chemical chemical NN 7333 194 79 element element NN 7333 194 80 would would MD 7333 194 81 not not RB 7333 194 82 be be VB 7333 194 83 in in IN 7333 194 84 such such JJ 7333 194 85 exact exact JJ 7333 194 86 agreement agreement NN 7333 194 87 as as IN 7333 194 88 experience experience NN 7333 194 89 demonstrates demonstrate VBZ 7333 194 90 . . . 7333 195 1 The the DT 7333 195 2 existence existence NN 7333 195 3 of of IN 7333 195 4 sharp sharp JJ 7333 195 5 spectral spectral JJ 7333 195 6 lines line NNS 7333 195 7 is be VBZ 7333 195 8 a a DT 7333 195 9 convincing convincing JJ 7333 195 10 experimental experimental JJ 7333 195 11 proof proof NN 7333 195 12 of of IN 7333 195 13 the the DT 7333 195 14 above above RB 7333 195 15 - - HYPH 7333 195 16 mentioned mention VBN 7333 195 17 principle principle NN 7333 195 18 of of IN 7333 195 19 practical practical JJ 7333 195 20 geometry geometry NN 7333 195 21 . . . 7333 196 1 This this DT 7333 196 2 is be VBZ 7333 196 3 the the DT 7333 196 4 ultimate ultimate JJ 7333 196 5 foundation foundation NN 7333 196 6 in in IN 7333 196 7 fact fact NN 7333 196 8 which which WDT 7333 196 9 enables enable VBZ 7333 196 10 us -PRON- PRP 7333 196 11 to to TO 7333 196 12 speak speak VB 7333 196 13 with with IN 7333 196 14 meaning meaning NN 7333 196 15 of of IN 7333 196 16 the the DT 7333 196 17 mensuration mensuration NN 7333 196 18 , , , 7333 196 19 in in IN 7333 196 20 Riemann Riemann NNP 7333 196 21 's 's POS 7333 196 22 sense sense NN 7333 196 23 of of IN 7333 196 24 the the DT 7333 196 25 word word NN 7333 196 26 , , , 7333 196 27 of of IN 7333 196 28 the the DT 7333 196 29 four four CD 7333 196 30 - - HYPH 7333 196 31 dimensional dimensional JJ 7333 196 32 continuum continuum NN 7333 196 33 of of IN 7333 196 34 space space NN 7333 196 35 - - HYPH 7333 196 36 time time NN 7333 196 37 . . . 7333 197 1 The the DT 7333 197 2 question question NN 7333 197 3 whether whether IN 7333 197 4 the the DT 7333 197 5 structure structure NN 7333 197 6 of of IN 7333 197 7 this this DT 7333 197 8 continuum continuum NN 7333 197 9 is be VBZ 7333 197 10 Euclidean Euclidean NNP 7333 197 11 , , , 7333 197 12 or or CC 7333 197 13 in in IN 7333 197 14 accordance accordance NN 7333 197 15 with with IN 7333 197 16 Riemann Riemann NNP 7333 197 17 's 's POS 7333 197 18 general general JJ 7333 197 19 scheme scheme NN 7333 197 20 , , , 7333 197 21 or or CC 7333 197 22 otherwise otherwise RB 7333 197 23 , , , 7333 197 24 is be VBZ 7333 197 25 , , , 7333 197 26 according accord VBG 7333 197 27 to to IN 7333 197 28 the the DT 7333 197 29 view view NN 7333 197 30 which which WDT 7333 197 31 is be VBZ 7333 197 32 here here RB 7333 197 33 being be VBG 7333 197 34 advocated advocate VBN 7333 197 35 , , , 7333 197 36 properly properly RB 7333 197 37 speaking speak VBG 7333 197 38 a a DT 7333 197 39 physical physical JJ 7333 197 40 question question NN 7333 197 41 which which WDT 7333 197 42 must must MD 7333 197 43 be be VB 7333 197 44 answered answer VBN 7333 197 45 by by IN 7333 197 46 experience experience NN 7333 197 47 , , , 7333 197 48 and and CC 7333 197 49 not not RB 7333 197 50 a a DT 7333 197 51 question question NN 7333 197 52 of of IN 7333 197 53 a a DT 7333 197 54 mere mere JJ 7333 197 55 convention convention NN 7333 197 56 to to TO 7333 197 57 be be VB 7333 197 58 selected select VBN 7333 197 59 on on IN 7333 197 60 practical practical JJ 7333 197 61 grounds ground NNS 7333 197 62 . . . 7333 198 1 Riemann Riemann NNP 7333 198 2 's 's POS 7333 198 3 geometry geometry NN 7333 198 4 will will MD 7333 198 5 be be VB 7333 198 6 the the DT 7333 198 7 right right JJ 7333 198 8 thing thing NN 7333 198 9 if if IN 7333 198 10 the the DT 7333 198 11 laws law NNS 7333 198 12 of of IN 7333 198 13 disposition disposition NN 7333 198 14 of of IN 7333 198 15 practically practically RB 7333 198 16 - - HYPH 7333 198 17 rigid rigid JJ 7333 198 18 bodies body NNS 7333 198 19 are be VBP 7333 198 20 transformable transformable JJ 7333 198 21 into into IN 7333 198 22 those those DT 7333 198 23 of of IN 7333 198 24 the the DT 7333 198 25 bodies body NNS 7333 198 26 of of IN 7333 198 27 Euclid Euclid NNP 7333 198 28 's 's POS 7333 198 29 geometry geometry NN 7333 198 30 with with IN 7333 198 31 an an DT 7333 198 32 exactitude exactitude NN 7333 198 33 which which WDT 7333 198 34 increases increase VBZ 7333 198 35 in in IN 7333 198 36 proportion proportion NN 7333 198 37 as as IN 7333 198 38 the the DT 7333 198 39 dimensions dimension NNS 7333 198 40 of of IN 7333 198 41 the the DT 7333 198 42 part part NN 7333 198 43 of of IN 7333 198 44 space space NN 7333 198 45 - - HYPH 7333 198 46 time time NN 7333 198 47 under under IN 7333 198 48 consideration consideration NN 7333 198 49 are be VBP 7333 198 50 diminished diminish VBN 7333 198 51 . . . 7333 199 1 It -PRON- PRP 7333 199 2 is be VBZ 7333 199 3 true true JJ 7333 199 4 that that IN 7333 199 5 this this DT 7333 199 6 proposed propose VBN 7333 199 7 physical physical JJ 7333 199 8 interpretation interpretation NN 7333 199 9 of of IN 7333 199 10 geometry geometry NN 7333 199 11 breaks break VBZ 7333 199 12 down down RP 7333 199 13 when when WRB 7333 199 14 applied apply VBN 7333 199 15 immediately immediately RB 7333 199 16 to to IN 7333 199 17 spaces space NNS 7333 199 18 of of IN 7333 199 19 sub sub JJ 7333 199 20 - - JJ 7333 199 21 molecular molecular JJ 7333 199 22 order order NN 7333 199 23 of of IN 7333 199 24 magnitude magnitude NN 7333 199 25 . . . 7333 200 1 But but CC 7333 200 2 nevertheless nevertheless RB 7333 200 3 , , , 7333 200 4 even even RB 7333 200 5 in in IN 7333 200 6 questions question NNS 7333 200 7 as as IN 7333 200 8 to to IN 7333 200 9 the the DT 7333 200 10 constitution constitution NN 7333 200 11 of of IN 7333 200 12 elementary elementary JJ 7333 200 13 particles particle NNS 7333 200 14 , , , 7333 200 15 it -PRON- PRP 7333 200 16 retains retain VBZ 7333 200 17 part part NN 7333 200 18 of of IN 7333 200 19 its -PRON- PRP$ 7333 200 20 importance importance NN 7333 200 21 . . . 7333 201 1 For for IN 7333 201 2 even even RB 7333 201 3 when when WRB 7333 201 4 it -PRON- PRP 7333 201 5 is be VBZ 7333 201 6 a a DT 7333 201 7 question question NN 7333 201 8 of of IN 7333 201 9 describing describe VBG 7333 201 10 the the DT 7333 201 11 electrical electrical JJ 7333 201 12 elementary elementary JJ 7333 201 13 particles particle NNS 7333 201 14 constituting constitute VBG 7333 201 15 matter matter NN 7333 201 16 , , , 7333 201 17 the the DT 7333 201 18 attempt attempt NN 7333 201 19 may may MD 7333 201 20 still still RB 7333 201 21 be be VB 7333 201 22 made make VBN 7333 201 23 to to TO 7333 201 24 ascribe ascribe VB 7333 201 25 physical physical JJ 7333 201 26 importance importance NN 7333 201 27 to to IN 7333 201 28 those those DT 7333 201 29 ideas idea NNS 7333 201 30 of of IN 7333 201 31 fields field NNS 7333 201 32 which which WDT 7333 201 33 have have VBP 7333 201 34 been be VBN 7333 201 35 physically physically RB 7333 201 36 defined define VBN 7333 201 37 for for IN 7333 201 38 the the DT 7333 201 39 purpose purpose NN 7333 201 40 of of IN 7333 201 41 describing describe VBG 7333 201 42 the the DT 7333 201 43 geometrical geometrical JJ 7333 201 44 behaviour behaviour NN 7333 201 45 of of IN 7333 201 46 bodies body NNS 7333 201 47 which which WDT 7333 201 48 are be VBP 7333 201 49 large large JJ 7333 201 50 as as IN 7333 201 51 compared compare VBN 7333 201 52 with with IN 7333 201 53 the the DT 7333 201 54 molecule molecule NN 7333 201 55 . . . 7333 202 1 Success success NN 7333 202 2 alone alone RB 7333 202 3 can can MD 7333 202 4 decide decide VB 7333 202 5 as as IN 7333 202 6 to to IN 7333 202 7 the the DT 7333 202 8 justification justification NN 7333 202 9 of of IN 7333 202 10 such such PDT 7333 202 11 an an DT 7333 202 12 attempt attempt NN 7333 202 13 , , , 7333 202 14 which which WDT 7333 202 15 postulates postulate VBZ 7333 202 16 physical physical JJ 7333 202 17 reality reality NN 7333 202 18 for for IN 7333 202 19 the the DT 7333 202 20 fundamental fundamental JJ 7333 202 21 principles principle NNS 7333 202 22 of of IN 7333 202 23 Riemann Riemann NNP 7333 202 24 's 's POS 7333 202 25 geometry geometry NN 7333 202 26 outside outside IN 7333 202 27 of of IN 7333 202 28 the the DT 7333 202 29 domain domain NN 7333 202 30 of of IN 7333 202 31 their -PRON- PRP$ 7333 202 32 physical physical JJ 7333 202 33 definitions definition NNS 7333 202 34 . . . 7333 203 1 It -PRON- PRP 7333 203 2 might may MD 7333 203 3 possibly possibly RB 7333 203 4 turn turn VB 7333 203 5 out out RP 7333 203 6 that that IN 7333 203 7 this this DT 7333 203 8 extrapolation extrapolation NN 7333 203 9 has have VBZ 7333 203 10 no no DT 7333 203 11 better well JJR 7333 203 12 warrant warrant NN 7333 203 13 than than IN 7333 203 14 the the DT 7333 203 15 extrapolation extrapolation NN 7333 203 16 of of IN 7333 203 17 the the DT 7333 203 18 idea idea NN 7333 203 19 of of IN 7333 203 20 temperature temperature NN 7333 203 21 to to IN 7333 203 22 parts part NNS 7333 203 23 of of IN 7333 203 24 a a DT 7333 203 25 body body NN 7333 203 26 of of IN 7333 203 27 molecular molecular JJ 7333 203 28 order order NN 7333 203 29 of of IN 7333 203 30 magnitude magnitude NN 7333 203 31 . . . 7333 204 1 It -PRON- PRP 7333 204 2 appears appear VBZ 7333 204 3 less less RBR 7333 204 4 problematical problematical JJ 7333 204 5 to to TO 7333 204 6 extend extend VB 7333 204 7 the the DT 7333 204 8 ideas idea NNS 7333 204 9 of of IN 7333 204 10 practical practical JJ 7333 204 11 geometry geometry NN 7333 204 12 to to IN 7333 204 13 spaces space NNS 7333 204 14 of of IN 7333 204 15 cosmic cosmic JJ 7333 204 16 order order NN 7333 204 17 of of IN 7333 204 18 magnitude magnitude NN 7333 204 19 . . . 7333 205 1 It -PRON- PRP 7333 205 2 might may MD 7333 205 3 , , , 7333 205 4 of of IN 7333 205 5 course course NN 7333 205 6 , , , 7333 205 7 be be VB 7333 205 8 objected object VBN 7333 205 9 that that IN 7333 205 10 a a DT 7333 205 11 construction construction NN 7333 205 12 composed compose VBN 7333 205 13 of of IN 7333 205 14 solid solid JJ 7333 205 15 rods rod NNS 7333 205 16 departs depart VBZ 7333 205 17 more more JJR 7333 205 18 and and CC 7333 205 19 more more RBR 7333 205 20 from from IN 7333 205 21 ideal ideal JJ 7333 205 22 rigidity rigidity NN 7333 205 23 in in IN 7333 205 24 proportion proportion NN 7333 205 25 as as IN 7333 205 26 its -PRON- PRP$ 7333 205 27 spatial spatial JJ 7333 205 28 extent extent NN 7333 205 29 becomes become VBZ 7333 205 30 greater great JJR 7333 205 31 . . . 7333 206 1 But but CC 7333 206 2 it -PRON- PRP 7333 206 3 will will MD 7333 206 4 hardly hardly RB 7333 206 5 be be VB 7333 206 6 possible possible JJ 7333 206 7 , , , 7333 206 8 I -PRON- PRP 7333 206 9 think think VBP 7333 206 10 , , , 7333 206 11 to to TO 7333 206 12 assign assign VB 7333 206 13 fundamental fundamental JJ 7333 206 14 significance significance NN 7333 206 15 to to IN 7333 206 16 this this DT 7333 206 17 objection objection NN 7333 206 18 . . . 7333 207 1 Therefore therefore RB 7333 207 2 the the DT 7333 207 3 question question NN 7333 207 4 whether whether IN 7333 207 5 the the DT 7333 207 6 universe universe NN 7333 207 7 is be VBZ 7333 207 8 spatially spatially RB 7333 207 9 finite finite JJ 7333 207 10 or or CC 7333 207 11 not not RB 7333 207 12 seems seem VBZ 7333 207 13 to to IN 7333 207 14 me -PRON- PRP 7333 207 15 decidedly decidedly RB 7333 207 16 a a DT 7333 207 17 pregnant pregnant JJ 7333 207 18 question question NN 7333 207 19 in in IN 7333 207 20 the the DT 7333 207 21 sense sense NN 7333 207 22 of of IN 7333 207 23 practical practical JJ 7333 207 24 geometry geometry NN 7333 207 25 . . . 7333 208 1 I -PRON- PRP 7333 208 2 do do VBP 7333 208 3 not not RB 7333 208 4 even even RB 7333 208 5 consider consider VB 7333 208 6 it -PRON- PRP 7333 208 7 impossible impossible JJ 7333 208 8 that that IN 7333 208 9 this this DT 7333 208 10 question question NN 7333 208 11 will will MD 7333 208 12 be be VB 7333 208 13 answered answer VBN 7333 208 14 before before RB 7333 208 15 long long RB 7333 208 16 by by IN 7333 208 17 astronomy astronomy NN 7333 208 18 . . . 7333 209 1 Let let VB 7333 209 2 us -PRON- PRP 7333 209 3 call call VB 7333 209 4 to to TO 7333 209 5 mind mind VB 7333 209 6 what what WP 7333 209 7 the the DT 7333 209 8 general general JJ 7333 209 9 theory theory NN 7333 209 10 of of IN 7333 209 11 relativity relativity NN 7333 209 12 teaches teach VBZ 7333 209 13 in in IN 7333 209 14 this this DT 7333 209 15 respect respect NN 7333 209 16 . . . 7333 210 1 It -PRON- PRP 7333 210 2 offers offer VBZ 7333 210 3 two two CD 7333 210 4 possibilities:-- possibilities:-- SYM 7333 210 5 1 1 CD 7333 210 6 . . . 7333 211 1 The the DT 7333 211 2 universe universe NN 7333 211 3 is be VBZ 7333 211 4 spatially spatially RB 7333 211 5 infinite infinite JJ 7333 211 6 . . . 7333 212 1 This this DT 7333 212 2 can can MD 7333 212 3 be be VB 7333 212 4 so so RB 7333 212 5 only only RB 7333 212 6 if if IN 7333 212 7 the the DT 7333 212 8 average average JJ 7333 212 9 spatial spatial JJ 7333 212 10 density density NN 7333 212 11 of of IN 7333 212 12 the the DT 7333 212 13 matter matter NN 7333 212 14 in in IN 7333 212 15 universal universal JJ 7333 212 16 space space NN 7333 212 17 , , , 7333 212 18 concentrated concentrate VBD 7333 212 19 in in IN 7333 212 20 the the DT 7333 212 21 stars star NNS 7333 212 22 , , , 7333 212 23 vanishes vanishe NNS 7333 212 24 , , , 7333 212 25 i.e. i.e. FW 7333 213 1 if if IN 7333 213 2 the the DT 7333 213 3 ratio ratio NN 7333 213 4 of of IN 7333 213 5 the the DT 7333 213 6 total total JJ 7333 213 7 mass mass NN 7333 213 8 of of IN 7333 213 9 the the DT 7333 213 10 stars star NNS 7333 213 11 to to IN 7333 213 12 the the DT 7333 213 13 magnitude magnitude NN 7333 213 14 of of IN 7333 213 15 the the DT 7333 213 16 space space NN 7333 213 17 through through IN 7333 213 18 which which WDT 7333 213 19 they -PRON- PRP 7333 213 20 are be VBP 7333 213 21 scattered scatter VBN 7333 213 22 approximates approximate NNS 7333 213 23 indefinitely indefinitely RB 7333 213 24 to to IN 7333 213 25 the the DT 7333 213 26 value value NN 7333 213 27 zero zero CD 7333 213 28 when when WRB 7333 213 29 the the DT 7333 213 30 spaces space NNS 7333 213 31 taken take VBN 7333 213 32 into into IN 7333 213 33 consideration consideration NN 7333 213 34 are be VBP 7333 213 35 constantly constantly RB 7333 213 36 greater great JJR 7333 213 37 and and CC 7333 213 38 greater great JJR 7333 213 39 . . . 7333 214 1 2 2 LS 7333 214 2 . . . 7333 215 1 The the DT 7333 215 2 universe universe NN 7333 215 3 is be VBZ 7333 215 4 spatially spatially RB 7333 215 5 finite finite JJ 7333 215 6 . . . 7333 216 1 This this DT 7333 216 2 must must MD 7333 216 3 be be VB 7333 216 4 so so RB 7333 216 5 , , , 7333 216 6 if if IN 7333 216 7 there there EX 7333 216 8 is be VBZ 7333 216 9 a a DT 7333 216 10 mean mean JJ 7333 216 11 density density NN 7333 216 12 of of IN 7333 216 13 the the DT 7333 216 14 ponderable ponderable JJ 7333 216 15 matter matter NN 7333 216 16 in in IN 7333 216 17 universal universal JJ 7333 216 18 space space NN 7333 216 19 differing differ VBG 7333 216 20 from from IN 7333 216 21 zero zero CD 7333 216 22 . . . 7333 217 1 The the DT 7333 217 2 smaller small JJR 7333 217 3 that that WDT 7333 217 4 mean mean VBP 7333 217 5 density density NN 7333 217 6 , , , 7333 217 7 the the DT 7333 217 8 greater great JJR 7333 217 9 is be VBZ 7333 217 10 the the DT 7333 217 11 volume volume NN 7333 217 12 of of IN 7333 217 13 universal universal JJ 7333 217 14 space space NN 7333 217 15 . . . 7333 218 1 I -PRON- PRP 7333 218 2 must must MD 7333 218 3 not not RB 7333 218 4 fail fail VB 7333 218 5 to to TO 7333 218 6 mention mention VB 7333 218 7 that that IN 7333 218 8 a a DT 7333 218 9 theoretical theoretical JJ 7333 218 10 argument argument NN 7333 218 11 can can MD 7333 218 12 be be VB 7333 218 13 adduced adduce VBN 7333 218 14 in in IN 7333 218 15 favour favour NN 7333 218 16 of of IN 7333 218 17 the the DT 7333 218 18 hypothesis hypothesis NN 7333 218 19 of of IN 7333 218 20 a a DT 7333 218 21 finite finite JJ 7333 218 22 universe universe NN 7333 218 23 . . . 7333 219 1 The the DT 7333 219 2 general general JJ 7333 219 3 theory theory NN 7333 219 4 of of IN 7333 219 5 relativity relativity NN 7333 219 6 teaches teach VBZ 7333 219 7 that that IN 7333 219 8 the the DT 7333 219 9 inertia inertia NN 7333 219 10 of of IN 7333 219 11 a a DT 7333 219 12 given give VBN 7333 219 13 body body NN 7333 219 14 is be VBZ 7333 219 15 greater great JJR 7333 219 16 as as IN 7333 219 17 there there EX 7333 219 18 are be VBP 7333 219 19 more more JJR 7333 219 20 ponderable ponderable JJ 7333 219 21 masses masse NNS 7333 219 22 in in IN 7333 219 23 proximity proximity NN 7333 219 24 to to IN 7333 219 25 it -PRON- PRP 7333 219 26 ; ; : 7333 219 27 thus thus RB 7333 219 28 it -PRON- PRP 7333 219 29 seems seem VBZ 7333 219 30 very very RB 7333 219 31 natural natural JJ 7333 219 32 to to TO 7333 219 33 reduce reduce VB 7333 219 34 the the DT 7333 219 35 total total JJ 7333 219 36 effect effect NN 7333 219 37 of of IN 7333 219 38 inertia inertia NN 7333 219 39 of of IN 7333 219 40 a a DT 7333 219 41 body body NN 7333 219 42 to to IN 7333 219 43 action action NN 7333 219 44 and and CC 7333 219 45 reaction reaction NN 7333 219 46 between between IN 7333 219 47 it -PRON- PRP 7333 219 48 and and CC 7333 219 49 the the DT 7333 219 50 other other JJ 7333 219 51 bodies body NNS 7333 219 52 in in IN 7333 219 53 the the DT 7333 219 54 universe universe NN 7333 219 55 , , , 7333 219 56 as as RB 7333 219 57 indeed indeed RB 7333 219 58 , , , 7333 219 59 ever ever RB 7333 219 60 since since IN 7333 219 61 Newton Newton NNP 7333 219 62 's 's POS 7333 219 63 time time NN 7333 219 64 , , , 7333 219 65 gravity gravity NN 7333 219 66 has have VBZ 7333 219 67 been be VBN 7333 219 68 completely completely RB 7333 219 69 reduced reduce VBN 7333 219 70 to to IN 7333 219 71 action action NN 7333 219 72 and and CC 7333 219 73 reaction reaction NN 7333 219 74 between between IN 7333 219 75 bodies body NNS 7333 219 76 . . . 7333 220 1 From from IN 7333 220 2 the the DT 7333 220 3 equations equation NNS 7333 220 4 of of IN 7333 220 5 the the DT 7333 220 6 general general JJ 7333 220 7 theory theory NN 7333 220 8 of of IN 7333 220 9 relativity relativity NN 7333 220 10 it -PRON- PRP 7333 220 11 can can MD 7333 220 12 be be VB 7333 220 13 deduced deduce VBN 7333 220 14 that that IN 7333 220 15 this this DT 7333 220 16 total total JJ 7333 220 17 reduction reduction NN 7333 220 18 of of IN 7333 220 19 inertia inertia NN 7333 220 20 to to IN 7333 220 21 reciprocal reciprocal JJ 7333 220 22 action action NN 7333 220 23 between between IN 7333 220 24 masses masse NNS 7333 220 25 -- -- : 7333 220 26 as as IN 7333 220 27 required require VBN 7333 220 28 by by IN 7333 220 29 E. E. NNP 7333 220 30 Mach Mach NNP 7333 220 31 , , , 7333 220 32 for for IN 7333 220 33 example example NN 7333 220 34 -- -- : 7333 220 35 is be VBZ 7333 220 36 possible possible JJ 7333 220 37 only only RB 7333 220 38 if if IN 7333 220 39 the the DT 7333 220 40 universe universe NN 7333 220 41 is be VBZ 7333 220 42 spatially spatially RB 7333 220 43 finite finite JJ 7333 220 44 . . . 7333 221 1 On on IN 7333 221 2 many many JJ 7333 221 3 physicists physicist NNS 7333 221 4 and and CC 7333 221 5 astronomers astronomer NNS 7333 221 6 this this DT 7333 221 7 argument argument NN 7333 221 8 makes make VBZ 7333 221 9 no no DT 7333 221 10 impression impression NN 7333 221 11 . . . 7333 222 1 Experience experience NN 7333 222 2 alone alone RB 7333 222 3 can can MD 7333 222 4 finally finally RB 7333 222 5 decide decide VB 7333 222 6 which which WDT 7333 222 7 of of IN 7333 222 8 the the DT 7333 222 9 two two CD 7333 222 10 possibilities possibility NNS 7333 222 11 is be VBZ 7333 222 12 realised realise VBN 7333 222 13 in in IN 7333 222 14 nature nature NN 7333 222 15 . . . 7333 223 1 How how WRB 7333 223 2 can can MD 7333 223 3 experience experience VB 7333 223 4 furnish furnish VB 7333 223 5 an an DT 7333 223 6 answer answer NN 7333 223 7 ? ? . 7333 224 1 At at IN 7333 224 2 first first RB 7333 224 3 it -PRON- PRP 7333 224 4 might may MD 7333 224 5 seem seem VB 7333 224 6 possible possible JJ 7333 224 7 to to TO 7333 224 8 determine determine VB 7333 224 9 the the DT 7333 224 10 mean mean JJ 7333 224 11 density density NN 7333 224 12 of of IN 7333 224 13 matter matter NN 7333 224 14 by by IN 7333 224 15 observation observation NN 7333 224 16 of of IN 7333 224 17 that that DT 7333 224 18 part part NN 7333 224 19 of of IN 7333 224 20 the the DT 7333 224 21 universe universe NN 7333 224 22 which which WDT 7333 224 23 is be VBZ 7333 224 24 accessible accessible JJ 7333 224 25 to to IN 7333 224 26 our -PRON- PRP$ 7333 224 27 perception perception NN 7333 224 28 . . . 7333 225 1 This this DT 7333 225 2 hope hope NN 7333 225 3 is be VBZ 7333 225 4 illusory illusory JJ 7333 225 5 . . . 7333 226 1 The the DT 7333 226 2 distribution distribution NN 7333 226 3 of of IN 7333 226 4 the the DT 7333 226 5 visible visible JJ 7333 226 6 stars star NNS 7333 226 7 is be VBZ 7333 226 8 extremely extremely RB 7333 226 9 irregular irregular JJ 7333 226 10 , , , 7333 226 11 so so IN 7333 226 12 that that IN 7333 226 13 we -PRON- PRP 7333 226 14 on on IN 7333 226 15 no no DT 7333 226 16 account account NN 7333 226 17 may may MD 7333 226 18 venture venture VB 7333 226 19 to to TO 7333 226 20 set set VB 7333 226 21 down down RP 7333 226 22 the the DT 7333 226 23 mean mean JJ 7333 226 24 density density NN 7333 226 25 of of IN 7333 226 26 star star NN 7333 226 27 - - HYPH 7333 226 28 matter matter NN 7333 226 29 in in IN 7333 226 30 the the DT 7333 226 31 universe universe NN 7333 226 32 as as IN 7333 226 33 equal equal JJ 7333 226 34 , , , 7333 226 35 let let VB 7333 226 36 us -PRON- PRP 7333 226 37 say say VB 7333 226 38 , , , 7333 226 39 to to IN 7333 226 40 the the DT 7333 226 41 mean mean JJ 7333 226 42 density density NN 7333 226 43 in in IN 7333 226 44 the the DT 7333 226 45 Milky Milky NNP 7333 226 46 Way Way NNP 7333 226 47 . . . 7333 227 1 In in IN 7333 227 2 any any DT 7333 227 3 case case NN 7333 227 4 , , , 7333 227 5 however however RB 7333 227 6 great great JJ 7333 227 7 the the DT 7333 227 8 space space NN 7333 227 9 examined examine VBN 7333 227 10 may may MD 7333 227 11 be be VB 7333 227 12 , , , 7333 227 13 we -PRON- PRP 7333 227 14 could could MD 7333 227 15 not not RB 7333 227 16 feel feel VB 7333 227 17 convinced convinced JJ 7333 227 18 that that IN 7333 227 19 there there EX 7333 227 20 were be VBD 7333 227 21 no no DT 7333 227 22 more more JJR 7333 227 23 stars star NNS 7333 227 24 beyond beyond IN 7333 227 25 that that DT 7333 227 26 space space NN 7333 227 27 . . . 7333 228 1 So so CC 7333 228 2 it -PRON- PRP 7333 228 3 seems seem VBZ 7333 228 4 impossible impossible JJ 7333 228 5 to to TO 7333 228 6 estimate estimate VB 7333 228 7 the the DT 7333 228 8 mean mean JJ 7333 228 9 density density NN 7333 228 10 . . . 7333 229 1 But but CC 7333 229 2 there there EX 7333 229 3 is be VBZ 7333 229 4 another another DT 7333 229 5 road road NN 7333 229 6 , , , 7333 229 7 which which WDT 7333 229 8 seems seem VBZ 7333 229 9 to to IN 7333 229 10 me -PRON- PRP 7333 229 11 more more RBR 7333 229 12 practicable practicable JJ 7333 229 13 , , , 7333 229 14 although although IN 7333 229 15 it -PRON- PRP 7333 229 16 also also RB 7333 229 17 presents present VBZ 7333 229 18 great great JJ 7333 229 19 difficulties difficulty NNS 7333 229 20 . . . 7333 230 1 For for CC 7333 230 2 if if IN 7333 230 3 we -PRON- PRP 7333 230 4 inquire inquire VBP 7333 230 5 into into IN 7333 230 6 the the DT 7333 230 7 deviations deviation NNS 7333 230 8 shown show VBN 7333 230 9 by by IN 7333 230 10 the the DT 7333 230 11 consequences consequence NNS 7333 230 12 of of IN 7333 230 13 the the DT 7333 230 14 general general JJ 7333 230 15 theory theory NN 7333 230 16 of of IN 7333 230 17 relativity relativity NN 7333 230 18 which which WDT 7333 230 19 are be VBP 7333 230 20 accessible accessible JJ 7333 230 21 to to TO 7333 230 22 experience experience VB 7333 230 23 , , , 7333 230 24 when when WRB 7333 230 25 these these DT 7333 230 26 are be VBP 7333 230 27 compared compare VBN 7333 230 28 with with IN 7333 230 29 the the DT 7333 230 30 consequences consequence NNS 7333 230 31 of of IN 7333 230 32 the the DT 7333 230 33 Newtonian newtonian JJ 7333 230 34 theory theory NN 7333 230 35 , , , 7333 230 36 we -PRON- PRP 7333 230 37 first first RB 7333 230 38 of of IN 7333 230 39 all all DT 7333 230 40 find find VBP 7333 230 41 a a DT 7333 230 42 deviation deviation NN 7333 230 43 which which WDT 7333 230 44 shows show VBZ 7333 230 45 itself -PRON- PRP 7333 230 46 in in IN 7333 230 47 close close JJ 7333 230 48 proximity proximity NN 7333 230 49 to to IN 7333 230 50 gravitating gravitate VBG 7333 230 51 mass mass NN 7333 230 52 , , , 7333 230 53 and and CC 7333 230 54 has have VBZ 7333 230 55 been be VBN 7333 230 56 confirmed confirm VBN 7333 230 57 in in IN 7333 230 58 the the DT 7333 230 59 case case NN 7333 230 60 of of IN 7333 230 61 the the DT 7333 230 62 planet planet NN 7333 230 63 Mercury Mercury NNP 7333 230 64 . . . 7333 231 1 But but CC 7333 231 2 if if IN 7333 231 3 the the DT 7333 231 4 universe universe NN 7333 231 5 is be VBZ 7333 231 6 spatially spatially RB 7333 231 7 finite finite JJ 7333 231 8 there there EX 7333 231 9 is be VBZ 7333 231 10 a a DT 7333 231 11 second second JJ 7333 231 12 deviation deviation NN 7333 231 13 from from IN 7333 231 14 the the DT 7333 231 15 Newtonian newtonian JJ 7333 231 16 theory theory NN 7333 231 17 , , , 7333 231 18 which which WDT 7333 231 19 , , , 7333 231 20 in in IN 7333 231 21 the the DT 7333 231 22 language language NN 7333 231 23 of of IN 7333 231 24 the the DT 7333 231 25 Newtonian newtonian JJ 7333 231 26 theory theory NN 7333 231 27 , , , 7333 231 28 may may MD 7333 231 29 be be VB 7333 231 30 expressed express VBN 7333 231 31 thus:--The thus:--The NNP 7333 231 32 gravitational gravitational JJ 7333 231 33 field field NN 7333 231 34 is be VBZ 7333 231 35 in in IN 7333 231 36 its -PRON- PRP$ 7333 231 37 nature nature NN 7333 231 38 such such JJ 7333 231 39 as as IN 7333 231 40 if if IN 7333 231 41 it -PRON- PRP 7333 231 42 were be VBD 7333 231 43 produced produce VBN 7333 231 44 , , , 7333 231 45 not not RB 7333 231 46 only only RB 7333 231 47 by by IN 7333 231 48 the the DT 7333 231 49 ponderable ponderable JJ 7333 231 50 masses masse NNS 7333 231 51 , , , 7333 231 52 but but CC 7333 231 53 also also RB 7333 231 54 by by IN 7333 231 55 a a DT 7333 231 56 mass mass NN 7333 231 57 - - HYPH 7333 231 58 density density NN 7333 231 59 of of IN 7333 231 60 negative negative JJ 7333 231 61 sign sign NN 7333 231 62 , , , 7333 231 63 distributed distribute VBD 7333 231 64 uniformly uniformly RB 7333 231 65 throughout throughout IN 7333 231 66 space space NN 7333 231 67 . . . 7333 232 1 Since since IN 7333 232 2 this this DT 7333 232 3 factitious factitious JJ 7333 232 4 mass mass NN 7333 232 5 - - HYPH 7333 232 6 density density NN 7333 232 7 would would MD 7333 232 8 have have VB 7333 232 9 to to TO 7333 232 10 be be VB 7333 232 11 enormously enormously RB 7333 232 12 small small JJ 7333 232 13 , , , 7333 232 14 it -PRON- PRP 7333 232 15 could could MD 7333 232 16 make make VB 7333 232 17 its -PRON- PRP$ 7333 232 18 presence presence NN 7333 232 19 felt feel VBN 7333 232 20 only only RB 7333 232 21 in in IN 7333 232 22 gravitating gravitate VBG 7333 232 23 systems system NNS 7333 232 24 of of IN 7333 232 25 very very RB 7333 232 26 great great JJ 7333 232 27 extent extent NN 7333 232 28 . . . 7333 233 1 Assuming assume VBG 7333 233 2 that that IN 7333 233 3 we -PRON- PRP 7333 233 4 know know VBP 7333 233 5 , , , 7333 233 6 let let VB 7333 233 7 us -PRON- PRP 7333 233 8 say say VB 7333 233 9 , , , 7333 233 10 the the DT 7333 233 11 statistical statistical JJ 7333 233 12 distribution distribution NN 7333 233 13 of of IN 7333 233 14 the the DT 7333 233 15 stars star NNS 7333 233 16 in in IN 7333 233 17 the the DT 7333 233 18 Milky Milky NNP 7333 233 19 Way Way NNP 7333 233 20 , , , 7333 233 21 as as RB 7333 233 22 well well RB 7333 233 23 as as IN 7333 233 24 their -PRON- PRP$ 7333 233 25 masses masse NNS 7333 233 26 , , , 7333 233 27 then then RB 7333 233 28 by by IN 7333 233 29 Newton Newton NNP 7333 233 30 's 's POS 7333 233 31 law law NN 7333 233 32 we -PRON- PRP 7333 233 33 can can MD 7333 233 34 calculate calculate VB 7333 233 35 the the DT 7333 233 36 gravitational gravitational JJ 7333 233 37 field field NN 7333 233 38 and and CC 7333 233 39 the the DT 7333 233 40 mean mean JJ 7333 233 41 velocities velocity NNS 7333 233 42 which which WDT 7333 233 43 the the DT 7333 233 44 stars star NNS 7333 233 45 must must MD 7333 233 46 have have VB 7333 233 47 , , , 7333 233 48 so so IN 7333 233 49 that that IN 7333 233 50 the the DT 7333 233 51 Milky Milky NNP 7333 233 52 Way Way NNP 7333 233 53 should should MD 7333 233 54 not not RB 7333 233 55 collapse collapse VB 7333 233 56 under under IN 7333 233 57 the the DT 7333 233 58 mutual mutual JJ 7333 233 59 attraction attraction NN 7333 233 60 of of IN 7333 233 61 its -PRON- PRP$ 7333 233 62 stars star NNS 7333 233 63 , , , 7333 233 64 but but CC 7333 233 65 should should MD 7333 233 66 maintain maintain VB 7333 233 67 its -PRON- PRP$ 7333 233 68 actual actual JJ 7333 233 69 extent extent NN 7333 233 70 . . . 7333 234 1 Now now RB 7333 234 2 if if IN 7333 234 3 the the DT 7333 234 4 actual actual JJ 7333 234 5 velocities velocity NNS 7333 234 6 of of IN 7333 234 7 the the DT 7333 234 8 stars star NNS 7333 234 9 , , , 7333 234 10 which which WDT 7333 234 11 can can MD 7333 234 12 , , , 7333 234 13 of of IN 7333 234 14 course course NN 7333 234 15 , , , 7333 234 16 be be VB 7333 234 17 measured measure VBN 7333 234 18 , , , 7333 234 19 were be VBD 7333 234 20 smaller small JJR 7333 234 21 than than IN 7333 234 22 the the DT 7333 234 23 calculated calculate VBN 7333 234 24 velocities velocity NNS 7333 234 25 , , , 7333 234 26 we -PRON- PRP 7333 234 27 should should MD 7333 234 28 have have VB 7333 234 29 a a DT 7333 234 30 proof proof NN 7333 234 31 that that IN 7333 234 32 the the DT 7333 234 33 actual actual JJ 7333 234 34 attractions attraction NNS 7333 234 35 at at IN 7333 234 36 great great JJ 7333 234 37 distances distance NNS 7333 234 38 are be VBP 7333 234 39 smaller small JJR 7333 234 40 than than IN 7333 234 41 by by IN 7333 234 42 Newton Newton NNP 7333 234 43 's 's POS 7333 234 44 law law NN 7333 234 45 . . . 7333 235 1 From from IN 7333 235 2 such such PDT 7333 235 3 a a DT 7333 235 4 deviation deviation NN 7333 235 5 it -PRON- PRP 7333 235 6 could could MD 7333 235 7 be be VB 7333 235 8 proved prove VBN 7333 235 9 indirectly indirectly RB 7333 235 10 that that IN 7333 235 11 the the DT 7333 235 12 universe universe NN 7333 235 13 is be VBZ 7333 235 14 finite finite JJ 7333 235 15 . . . 7333 236 1 It -PRON- PRP 7333 236 2 would would MD 7333 236 3 even even RB 7333 236 4 be be VB 7333 236 5 possible possible JJ 7333 236 6 to to TO 7333 236 7 estimate estimate VB 7333 236 8 its -PRON- PRP$ 7333 236 9 spatial spatial JJ 7333 236 10 magnitude magnitude NN 7333 236 11 . . . 7333 237 1 Can Can MD 7333 237 2 we -PRON- PRP 7333 237 3 picture picture VB 7333 237 4 to to IN 7333 237 5 ourselves -PRON- PRP 7333 237 6 a a DT 7333 237 7 three three CD 7333 237 8 - - HYPH 7333 237 9 dimensional dimensional JJ 7333 237 10 universe universe NN 7333 237 11 which which WDT 7333 237 12 is be VBZ 7333 237 13 finite finite JJ 7333 237 14 , , , 7333 237 15 yet yet CC 7333 237 16 unbounded unbounded JJ 7333 237 17 ? ? . 7333 238 1 The the DT 7333 238 2 usual usual JJ 7333 238 3 answer answer NN 7333 238 4 to to IN 7333 238 5 this this DT 7333 238 6 question question NN 7333 238 7 is be VBZ 7333 238 8 " " `` 7333 238 9 No no UH 7333 238 10 , , , 7333 238 11 " " '' 7333 238 12 but but CC 7333 238 13 that that DT 7333 238 14 is be VBZ 7333 238 15 not not RB 7333 238 16 the the DT 7333 238 17 right right JJ 7333 238 18 answer answer NN 7333 238 19 . . . 7333 239 1 The the DT 7333 239 2 purpose purpose NN 7333 239 3 of of IN 7333 239 4 the the DT 7333 239 5 following follow VBG 7333 239 6 remarks remark NNS 7333 239 7 is be VBZ 7333 239 8 to to TO 7333 239 9 show show VB 7333 239 10 that that IN 7333 239 11 the the DT 7333 239 12 answer answer NN 7333 239 13 should should MD 7333 239 14 be be VB 7333 239 15 " " `` 7333 239 16 Yes yes UH 7333 239 17 . . . 7333 239 18 " " '' 7333 240 1 I -PRON- PRP 7333 240 2 want want VBP 7333 240 3 to to TO 7333 240 4 show show VB 7333 240 5 that that IN 7333 240 6 without without IN 7333 240 7 any any DT 7333 240 8 extraordinary extraordinary JJ 7333 240 9 difficulty difficulty NN 7333 240 10 we -PRON- PRP 7333 240 11 can can MD 7333 240 12 illustrate illustrate VB 7333 240 13 the the DT 7333 240 14 theory theory NN 7333 240 15 of of IN 7333 240 16 a a DT 7333 240 17 finite finite JJ 7333 240 18 universe universe NN 7333 240 19 by by IN 7333 240 20 means mean NNS 7333 240 21 of of IN 7333 240 22 a a DT 7333 240 23 mental mental JJ 7333 240 24 image image NN 7333 240 25 to to IN 7333 240 26 which which WDT 7333 240 27 , , , 7333 240 28 with with IN 7333 240 29 some some DT 7333 240 30 practice practice NN 7333 240 31 , , , 7333 240 32 we -PRON- PRP 7333 240 33 shall shall MD 7333 240 34 soon soon RB 7333 240 35 grow grow VB 7333 240 36 accustomed accustom VBN 7333 240 37 . . . 7333 241 1 First first RB 7333 241 2 of of IN 7333 241 3 all all DT 7333 241 4 , , , 7333 241 5 an an DT 7333 241 6 observation observation NN 7333 241 7 of of IN 7333 241 8 epistemological epistemological JJ 7333 241 9 nature nature NN 7333 241 10 . . . 7333 242 1 A a DT 7333 242 2 geometrical geometrical JJ 7333 242 3 - - HYPH 7333 242 4 physical physical JJ 7333 242 5 theory theory NN 7333 242 6 as as IN 7333 242 7 such such JJ 7333 242 8 is be VBZ 7333 242 9 incapable incapable JJ 7333 242 10 of of IN 7333 242 11 being be VBG 7333 242 12 directly directly RB 7333 242 13 pictured picture VBN 7333 242 14 , , , 7333 242 15 being be VBG 7333 242 16 merely merely RB 7333 242 17 a a DT 7333 242 18 system system NN 7333 242 19 of of IN 7333 242 20 concepts concept NNS 7333 242 21 . . . 7333 243 1 But but CC 7333 243 2 these these DT 7333 243 3 concepts concept NNS 7333 243 4 serve serve VBP 7333 243 5 the the DT 7333 243 6 purpose purpose NN 7333 243 7 of of IN 7333 243 8 bringing bring VBG 7333 243 9 a a DT 7333 243 10 multiplicity multiplicity NN 7333 243 11 of of IN 7333 243 12 real real JJ 7333 243 13 or or CC 7333 243 14 imaginary imaginary JJ 7333 243 15 sensory sensory JJ 7333 243 16 experiences experience NNS 7333 243 17 into into IN 7333 243 18 connection connection NN 7333 243 19 in in IN 7333 243 20 the the DT 7333 243 21 mind mind NN 7333 243 22 . . . 7333 244 1 To to TO 7333 244 2 " " `` 7333 244 3 visualise visualise VB 7333 244 4 " " '' 7333 244 5 a a DT 7333 244 6 theory theory NN 7333 244 7 , , , 7333 244 8 or or CC 7333 244 9 bring bring VB 7333 244 10 it -PRON- PRP 7333 244 11 home home RB 7333 244 12 to to IN 7333 244 13 one one NN 7333 244 14 's 's POS 7333 244 15 mind mind NN 7333 244 16 , , , 7333 244 17 therefore therefore RB 7333 244 18 means mean VBZ 7333 244 19 to to TO 7333 244 20 give give VB 7333 244 21 a a DT 7333 244 22 representation representation NN 7333 244 23 to to IN 7333 244 24 that that DT 7333 244 25 abundance abundance NN 7333 244 26 of of IN 7333 244 27 experiences experience NNS 7333 244 28 for for IN 7333 244 29 which which WDT 7333 244 30 the the DT 7333 244 31 theory theory NN 7333 244 32 supplies supply VBZ 7333 244 33 the the DT 7333 244 34 schematic schematic JJ 7333 244 35 arrangement arrangement NN 7333 244 36 . . . 7333 245 1 In in IN 7333 245 2 the the DT 7333 245 3 present present JJ 7333 245 4 case case NN 7333 245 5 we -PRON- PRP 7333 245 6 have have VBP 7333 245 7 to to TO 7333 245 8 ask ask VB 7333 245 9 ourselves -PRON- PRP 7333 245 10 how how WRB 7333 245 11 we -PRON- PRP 7333 245 12 can can MD 7333 245 13 represent represent VB 7333 245 14 that that DT 7333 245 15 relation relation NN 7333 245 16 of of IN 7333 245 17 solid solid JJ 7333 245 18 bodies body NNS 7333 245 19 with with IN 7333 245 20 respect respect NN 7333 245 21 to to IN 7333 245 22 their -PRON- PRP$ 7333 245 23 reciprocal reciprocal JJ 7333 245 24 disposition disposition NN 7333 245 25 ( ( -LRB- 7333 245 26 contact contact NN 7333 245 27 ) ) -RRB- 7333 245 28 which which WDT 7333 245 29 corresponds correspond VBZ 7333 245 30 to to IN 7333 245 31 the the DT 7333 245 32 theory theory NN 7333 245 33 of of IN 7333 245 34 a a DT 7333 245 35 finite finite JJ 7333 245 36 universe universe NN 7333 245 37 . . . 7333 246 1 There there EX 7333 246 2 is be VBZ 7333 246 3 really really RB 7333 246 4 nothing nothing NN 7333 246 5 new new JJ 7333 246 6 in in IN 7333 246 7 what what WP 7333 246 8 I -PRON- PRP 7333 246 9 have have VBP 7333 246 10 to to TO 7333 246 11 say say VB 7333 246 12 about about IN 7333 246 13 this this DT 7333 246 14 ; ; : 7333 246 15 but but CC 7333 246 16 innumerable innumerable JJ 7333 246 17 questions question NNS 7333 246 18 addressed address VBD 7333 246 19 to to IN 7333 246 20 me -PRON- PRP 7333 246 21 prove prove VB 7333 246 22 that that IN 7333 246 23 the the DT 7333 246 24 requirements requirement NNS 7333 246 25 of of IN 7333 246 26 those those DT 7333 246 27 who who WP 7333 246 28 thirst thirst VBP 7333 246 29 for for IN 7333 246 30 knowledge knowledge NN 7333 246 31 of of IN 7333 246 32 these these DT 7333 246 33 matters matter NNS 7333 246 34 have have VBP 7333 246 35 not not RB 7333 246 36 yet yet RB 7333 246 37 been be VBN 7333 246 38 completely completely RB 7333 246 39 satisfied satisfied JJ 7333 246 40 . . . 7333 247 1 So so RB 7333 247 2 , , , 7333 247 3 will will MD 7333 247 4 the the DT 7333 247 5 initiated initiated JJ 7333 247 6 please please UH 7333 247 7 pardon pardon VB 7333 247 8 me -PRON- PRP 7333 247 9 , , , 7333 247 10 if if IN 7333 247 11 part part NN 7333 247 12 of of IN 7333 247 13 what what WP 7333 247 14 I -PRON- PRP 7333 247 15 shall shall MD 7333 247 16 bring bring VB 7333 247 17 forward forward RB 7333 247 18 has have VBZ 7333 247 19 long long RB 7333 247 20 been be VBN 7333 247 21 known know VBN 7333 247 22 ? ? . 7333 248 1 What what WP 7333 248 2 do do VBP 7333 248 3 we -PRON- PRP 7333 248 4 wish wish VB 7333 248 5 to to TO 7333 248 6 express express VB 7333 248 7 when when WRB 7333 248 8 we -PRON- PRP 7333 248 9 say say VBP 7333 248 10 that that IN 7333 248 11 our -PRON- PRP$ 7333 248 12 space space NN 7333 248 13 is be VBZ 7333 248 14 infinite infinite JJ 7333 248 15 ? ? . 7333 249 1 Nothing nothing NN 7333 249 2 more more JJR 7333 249 3 than than IN 7333 249 4 that that IN 7333 249 5 we -PRON- PRP 7333 249 6 might may MD 7333 249 7 lay lay VB 7333 249 8 any any DT 7333 249 9 number number NN 7333 249 10 whatever whatever WDT 7333 249 11 of of IN 7333 249 12 bodies body NNS 7333 249 13 of of IN 7333 249 14 equal equal JJ 7333 249 15 sizes size NNS 7333 249 16 side side NN 7333 249 17 by by IN 7333 249 18 side side NN 7333 249 19 without without IN 7333 249 20 ever ever RB 7333 249 21 filling fill VBG 7333 249 22 space space NN 7333 249 23 . . . 7333 250 1 Suppose suppose VB 7333 250 2 that that IN 7333 250 3 we -PRON- PRP 7333 250 4 are be VBP 7333 250 5 provided provide VBN 7333 250 6 with with IN 7333 250 7 a a DT 7333 250 8 great great JJ 7333 250 9 many many JJ 7333 250 10 wooden wooden JJ 7333 250 11 cubes cube NNS 7333 250 12 all all DT 7333 250 13 of of IN 7333 250 14 the the DT 7333 250 15 same same JJ 7333 250 16 size size NN 7333 250 17 . . . 7333 251 1 In in IN 7333 251 2 accordance accordance NN 7333 251 3 with with IN 7333 251 4 Euclidean euclidean JJ 7333 251 5 geometry geometry NN 7333 251 6 we -PRON- PRP 7333 251 7 can can MD 7333 251 8 place place VB 7333 251 9 them -PRON- PRP 7333 251 10 above above IN 7333 251 11 , , , 7333 251 12 beside beside RB 7333 251 13 , , , 7333 251 14 and and CC 7333 251 15 behind behind IN 7333 251 16 one one CD 7333 251 17 another another DT 7333 251 18 so so IN 7333 251 19 as as IN 7333 251 20 to to TO 7333 251 21 fill fill VB 7333 251 22 a a DT 7333 251 23 part part NN 7333 251 24 of of IN 7333 251 25 space space NN 7333 251 26 of of IN 7333 251 27 any any DT 7333 251 28 dimensions dimension NNS 7333 251 29 ; ; : 7333 251 30 but but CC 7333 251 31 this this DT 7333 251 32 construction construction NN 7333 251 33 would would MD 7333 251 34 never never RB 7333 251 35 be be VB 7333 251 36 finished finish VBN 7333 251 37 ; ; : 7333 251 38 we -PRON- PRP 7333 251 39 could could MD 7333 251 40 go go VB 7333 251 41 on on RP 7333 251 42 adding add VBG 7333 251 43 more more JJR 7333 251 44 and and CC 7333 251 45 more more JJR 7333 251 46 cubes cube NNS 7333 251 47 without without IN 7333 251 48 ever ever RB 7333 251 49 finding find VBG 7333 251 50 that that IN 7333 251 51 there there EX 7333 251 52 was be VBD 7333 251 53 no no DT 7333 251 54 more more JJR 7333 251 55 room room NN 7333 251 56 . . . 7333 252 1 That that DT 7333 252 2 is be VBZ 7333 252 3 what what WP 7333 252 4 we -PRON- PRP 7333 252 5 wish wish VBP 7333 252 6 to to TO 7333 252 7 express express VB 7333 252 8 when when WRB 7333 252 9 we -PRON- PRP 7333 252 10 say say VBP 7333 252 11 that that IN 7333 252 12 space space NN 7333 252 13 is be VBZ 7333 252 14 infinite infinite JJ 7333 252 15 . . . 7333 253 1 It -PRON- PRP 7333 253 2 would would MD 7333 253 3 be be VB 7333 253 4 better well JJR 7333 253 5 to to TO 7333 253 6 say say VB 7333 253 7 that that IN 7333 253 8 space space NN 7333 253 9 is be VBZ 7333 253 10 infinite infinite JJ 7333 253 11 in in IN 7333 253 12 relation relation NN 7333 253 13 to to IN 7333 253 14 practically practically RB 7333 253 15 - - HYPH 7333 253 16 rigid rigid JJ 7333 253 17 bodies body NNS 7333 253 18 , , , 7333 253 19 assuming assume VBG 7333 253 20 that that IN 7333 253 21 the the DT 7333 253 22 laws law NNS 7333 253 23 of of IN 7333 253 24 disposition disposition NN 7333 253 25 for for IN 7333 253 26 these these DT 7333 253 27 bodies body NNS 7333 253 28 are be VBP 7333 253 29 given give VBN 7333 253 30 by by IN 7333 253 31 Euclidean euclidean JJ 7333 253 32 geometry geometry NN 7333 253 33 . . . 7333 254 1 Another another DT 7333 254 2 example example NN 7333 254 3 of of IN 7333 254 4 an an DT 7333 254 5 infinite infinite JJ 7333 254 6 continuum continuum NN 7333 254 7 is be VBZ 7333 254 8 the the DT 7333 254 9 plane plane NN 7333 254 10 . . . 7333 255 1 On on IN 7333 255 2 a a DT 7333 255 3 plane plane NN 7333 255 4 surface surface NN 7333 255 5 we -PRON- PRP 7333 255 6 may may MD 7333 255 7 lay lay VB 7333 255 8 squares square NNS 7333 255 9 of of IN 7333 255 10 cardboard cardboard NN 7333 255 11 so so IN 7333 255 12 that that IN 7333 255 13 each each DT 7333 255 14 side side NN 7333 255 15 of of IN 7333 255 16 any any DT 7333 255 17 square square NN 7333 255 18 has have VBZ 7333 255 19 the the DT 7333 255 20 side side NN 7333 255 21 of of IN 7333 255 22 another another DT 7333 255 23 square square NN 7333 255 24 adjacent adjacent JJ 7333 255 25 to to IN 7333 255 26 it -PRON- PRP 7333 255 27 . . . 7333 256 1 The the DT 7333 256 2 construction construction NN 7333 256 3 is be VBZ 7333 256 4 never never RB 7333 256 5 finished finish VBN 7333 256 6 ; ; : 7333 256 7 we -PRON- PRP 7333 256 8 can can MD 7333 256 9 always always RB 7333 256 10 go go VB 7333 256 11 on on RP 7333 256 12 laying lay VBG 7333 256 13 squares square NNS 7333 256 14 -- -- : 7333 256 15 if if IN 7333 256 16 their -PRON- PRP$ 7333 256 17 laws law NNS 7333 256 18 of of IN 7333 256 19 disposition disposition NN 7333 256 20 correspond correspond NNP 7333 256 21 to to IN 7333 256 22 those those DT 7333 256 23 of of IN 7333 256 24 plane plane NN 7333 256 25 figures figure NNS 7333 256 26 of of IN 7333 256 27 Euclidean euclidean JJ 7333 256 28 geometry geometry NN 7333 256 29 . . . 7333 257 1 The the DT 7333 257 2 plane plane NN 7333 257 3 is be VBZ 7333 257 4 therefore therefore RB 7333 257 5 infinite infinite JJ 7333 257 6 in in IN 7333 257 7 relation relation NN 7333 257 8 to to IN 7333 257 9 the the DT 7333 257 10 cardboard cardboard NN 7333 257 11 squares square NNS 7333 257 12 . . . 7333 258 1 Accordingly accordingly RB 7333 258 2 we -PRON- PRP 7333 258 3 say say VBP 7333 258 4 that that IN 7333 258 5 the the DT 7333 258 6 plane plane NN 7333 258 7 is be VBZ 7333 258 8 an an DT 7333 258 9 infinite infinite JJ 7333 258 10 continuum continuum NN 7333 258 11 of of IN 7333 258 12 two two CD 7333 258 13 dimensions dimension NNS 7333 258 14 , , , 7333 258 15 and and CC 7333 258 16 space space NN 7333 258 17 an an DT 7333 258 18 infinite infinite JJ 7333 258 19 continuum continuum NN 7333 258 20 of of IN 7333 258 21 three three CD 7333 258 22 dimensions dimension NNS 7333 258 23 . . . 7333 259 1 What what WP 7333 259 2 is be VBZ 7333 259 3 here here RB 7333 259 4 meant mean VBN 7333 259 5 by by IN 7333 259 6 the the DT 7333 259 7 number number NN 7333 259 8 of of IN 7333 259 9 dimensions dimension NNS 7333 259 10 , , , 7333 259 11 I -PRON- PRP 7333 259 12 think think VBP 7333 259 13 I -PRON- PRP 7333 259 14 may may MD 7333 259 15 assume assume VB 7333 259 16 to to TO 7333 259 17 be be VB 7333 259 18 known know VBN 7333 259 19 . . . 7333 260 1 Now now RB 7333 260 2 we -PRON- PRP 7333 260 3 take take VBP 7333 260 4 an an DT 7333 260 5 example example NN 7333 260 6 of of IN 7333 260 7 a a DT 7333 260 8 two two CD 7333 260 9 - - HYPH 7333 260 10 dimensional dimensional JJ 7333 260 11 continuum continuum NN 7333 260 12 which which WDT 7333 260 13 is be VBZ 7333 260 14 finite finite JJ 7333 260 15 , , , 7333 260 16 but but CC 7333 260 17 unbounded unbounded JJ 7333 260 18 . . . 7333 261 1 We -PRON- PRP 7333 261 2 imagine imagine VBP 7333 261 3 the the DT 7333 261 4 surface surface NN 7333 261 5 of of IN 7333 261 6 a a DT 7333 261 7 large large JJ 7333 261 8 globe globe NN 7333 261 9 and and CC 7333 261 10 a a DT 7333 261 11 quantity quantity NN 7333 261 12 of of IN 7333 261 13 small small JJ 7333 261 14 paper paper NN 7333 261 15 discs disc NNS 7333 261 16 , , , 7333 261 17 all all DT 7333 261 18 of of IN 7333 261 19 the the DT 7333 261 20 same same JJ 7333 261 21 size size NN 7333 261 22 . . . 7333 262 1 We -PRON- PRP 7333 262 2 place place VBP 7333 262 3 one one CD 7333 262 4 of of IN 7333 262 5 the the DT 7333 262 6 discs disc NNS 7333 262 7 anywhere anywhere RB 7333 262 8 on on IN 7333 262 9 the the DT 7333 262 10 surface surface NN 7333 262 11 of of IN 7333 262 12 the the DT 7333 262 13 globe globe NN 7333 262 14 . . . 7333 263 1 If if IN 7333 263 2 we -PRON- PRP 7333 263 3 move move VBP 7333 263 4 the the DT 7333 263 5 disc disc NN 7333 263 6 about about IN 7333 263 7 , , , 7333 263 8 anywhere anywhere RB 7333 263 9 we -PRON- PRP 7333 263 10 like like VBP 7333 263 11 , , , 7333 263 12 on on IN 7333 263 13 the the DT 7333 263 14 surface surface NN 7333 263 15 of of IN 7333 263 16 the the DT 7333 263 17 globe globe NN 7333 263 18 , , , 7333 263 19 we -PRON- PRP 7333 263 20 do do VBP 7333 263 21 not not RB 7333 263 22 come come VB 7333 263 23 upon upon IN 7333 263 24 a a DT 7333 263 25 limit limit NN 7333 263 26 or or CC 7333 263 27 boundary boundary NN 7333 263 28 anywhere anywhere RB 7333 263 29 on on IN 7333 263 30 the the DT 7333 263 31 journey journey NN 7333 263 32 . . . 7333 264 1 Therefore therefore RB 7333 264 2 we -PRON- PRP 7333 264 3 say say VBP 7333 264 4 that that IN 7333 264 5 the the DT 7333 264 6 spherical spherical JJ 7333 264 7 surface surface NN 7333 264 8 of of IN 7333 264 9 the the DT 7333 264 10 globe globe NN 7333 264 11 is be VBZ 7333 264 12 an an DT 7333 264 13 unbounded unbounded JJ 7333 264 14 continuum continuum NN 7333 264 15 . . . 7333 265 1 Moreover moreover RB 7333 265 2 , , , 7333 265 3 the the DT 7333 265 4 spherical spherical JJ 7333 265 5 surface surface NN 7333 265 6 is be VBZ 7333 265 7 a a DT 7333 265 8 finite finite JJ 7333 265 9 continuum continuum NN 7333 265 10 . . . 7333 266 1 For for IN 7333 266 2 if if IN 7333 266 3 we -PRON- PRP 7333 266 4 stick stick VBP 7333 266 5 the the DT 7333 266 6 paper paper NN 7333 266 7 discs disc NNS 7333 266 8 on on IN 7333 266 9 the the DT 7333 266 10 globe globe NN 7333 266 11 , , , 7333 266 12 so so IN 7333 266 13 that that IN 7333 266 14 no no DT 7333 266 15 disc disc NN 7333 266 16 overlaps overlap VBZ 7333 266 17 another another DT 7333 266 18 , , , 7333 266 19 the the DT 7333 266 20 surface surface NN 7333 266 21 of of IN 7333 266 22 the the DT 7333 266 23 globe globe NN 7333 266 24 will will MD 7333 266 25 finally finally RB 7333 266 26 become become VB 7333 266 27 so so RB 7333 266 28 full full JJ 7333 266 29 that that IN 7333 266 30 there there EX 7333 266 31 is be VBZ 7333 266 32 no no DT 7333 266 33 room room NN 7333 266 34 for for IN 7333 266 35 another another DT 7333 266 36 disc disc NN 7333 266 37 . . . 7333 267 1 This this DT 7333 267 2 simply simply RB 7333 267 3 means mean VBZ 7333 267 4 that that IN 7333 267 5 the the DT 7333 267 6 spherical spherical JJ 7333 267 7 surface surface NN 7333 267 8 of of IN 7333 267 9 the the DT 7333 267 10 globe globe NN 7333 267 11 is be VBZ 7333 267 12 finite finite JJ 7333 267 13 in in IN 7333 267 14 relation relation NN 7333 267 15 to to IN 7333 267 16 the the DT 7333 267 17 paper paper NN 7333 267 18 discs disc NNS 7333 267 19 . . . 7333 268 1 Further further RB 7333 268 2 , , , 7333 268 3 the the DT 7333 268 4 spherical spherical JJ 7333 268 5 surface surface NN 7333 268 6 is be VBZ 7333 268 7 a a DT 7333 268 8 non non JJ 7333 268 9 - - JJ 7333 268 10 Euclidean euclidean JJ 7333 268 11 continuum continuum NN 7333 268 12 of of IN 7333 268 13 two two CD 7333 268 14 dimensions dimension NNS 7333 268 15 , , , 7333 268 16 that that DT 7333 268 17 is be VBZ 7333 268 18 to to TO 7333 268 19 say say VB 7333 268 20 , , , 7333 268 21 the the DT 7333 268 22 laws law NNS 7333 268 23 of of IN 7333 268 24 disposition disposition NN 7333 268 25 for for IN 7333 268 26 the the DT 7333 268 27 rigid rigid JJ 7333 268 28 figures figure NNS 7333 268 29 lying lie VBG 7333 268 30 in in IN 7333 268 31 it -PRON- PRP 7333 268 32 do do VBP 7333 268 33 not not RB 7333 268 34 agree agree VB 7333 268 35 with with IN 7333 268 36 those those DT 7333 268 37 of of IN 7333 268 38 the the DT 7333 268 39 Euclidean euclidean JJ 7333 268 40 plane plane NN 7333 268 41 . . . 7333 269 1 This this DT 7333 269 2 can can MD 7333 269 3 be be VB 7333 269 4 shown show VBN 7333 269 5 in in IN 7333 269 6 the the DT 7333 269 7 following following JJ 7333 269 8 way way NN 7333 269 9 . . . 7333 270 1 Place place VB 7333 270 2 a a DT 7333 270 3 paper paper NN 7333 270 4 disc disc NN 7333 270 5 on on IN 7333 270 6 the the DT 7333 270 7 spherical spherical JJ 7333 270 8 surface surface NN 7333 270 9 , , , 7333 270 10 and and CC 7333 270 11 around around IN 7333 270 12 it -PRON- PRP 7333 270 13 in in IN 7333 270 14 a a DT 7333 270 15 circle circle NN 7333 270 16 place place NN 7333 270 17 six six CD 7333 270 18 more more JJR 7333 270 19 discs disc NNS 7333 270 20 , , , 7333 270 21 each each DT 7333 270 22 of of IN 7333 270 23 which which WDT 7333 270 24 is be VBZ 7333 270 25 to to TO 7333 270 26 be be VB 7333 270 27 surrounded surround VBN 7333 270 28 in in IN 7333 270 29 turn turn NN 7333 270 30 by by IN 7333 270 31 six six CD 7333 270 32 discs disc NNS 7333 270 33 , , , 7333 270 34 and and CC 7333 270 35 so so RB 7333 270 36 on on RB 7333 270 37 . . . 7333 271 1 If if IN 7333 271 2 this this DT 7333 271 3 construction construction NN 7333 271 4 is be VBZ 7333 271 5 made make VBN 7333 271 6 on on IN 7333 271 7 a a DT 7333 271 8 plane plane NN 7333 271 9 surface surface NN 7333 271 10 , , , 7333 271 11 we -PRON- PRP 7333 271 12 have have VBP 7333 271 13 an an DT 7333 271 14 uninterrupted uninterrupted JJ 7333 271 15 disposition disposition NN 7333 271 16 in in IN 7333 271 17 which which WDT 7333 271 18 there there EX 7333 271 19 are be VBP 7333 271 20 six six CD 7333 271 21 discs disc NNS 7333 271 22 touching touch VBG 7333 271 23 every every DT 7333 271 24 disc disc NN 7333 271 25 except except IN 7333 271 26 those those DT 7333 271 27 which which WDT 7333 271 28 lie lie VBP 7333 271 29 on on IN 7333 271 30 the the DT 7333 271 31 outside outside NN 7333 271 32 . . . 7333 272 1 [ [ -LRB- 7333 272 2 Figure figure NN 7333 272 3 1 1 CD 7333 272 4 : : : 7333 272 5 Discs Discs NNP 7333 272 6 maximally maximally RB 7333 272 7 packed pack VBD 7333 272 8 on on IN 7333 272 9 a a DT 7333 272 10 plane plane NN 7333 272 11 ] ] -RRB- 7333 272 12 On on IN 7333 272 13 the the DT 7333 272 14 spherical spherical JJ 7333 272 15 surface surface NN 7333 272 16 the the DT 7333 272 17 construction construction NN 7333 272 18 also also RB 7333 272 19 seems seem VBZ 7333 272 20 to to TO 7333 272 21 promise promise VB 7333 272 22 success success NN 7333 272 23 at at IN 7333 272 24 the the DT 7333 272 25 outset outset NN 7333 272 26 , , , 7333 272 27 and and CC 7333 272 28 the the DT 7333 272 29 smaller small JJR 7333 272 30 the the DT 7333 272 31 radius radius NN 7333 272 32 of of IN 7333 272 33 the the DT 7333 272 34 disc disc NN 7333 272 35 in in IN 7333 272 36 proportion proportion NN 7333 272 37 to to IN 7333 272 38 that that DT 7333 272 39 of of IN 7333 272 40 the the DT 7333 272 41 sphere sphere NN 7333 272 42 , , , 7333 272 43 the the DT 7333 272 44 more more RBR 7333 272 45 promising promising JJ 7333 272 46 it -PRON- PRP 7333 272 47 seems seem VBZ 7333 272 48 . . . 7333 273 1 But but CC 7333 273 2 as as IN 7333 273 3 the the DT 7333 273 4 construction construction NN 7333 273 5 progresses progress VBZ 7333 273 6 it -PRON- PRP 7333 273 7 becomes become VBZ 7333 273 8 more more JJR 7333 273 9 and and CC 7333 273 10 more more JJR 7333 273 11 patent patent NN 7333 273 12 that that WDT 7333 273 13 the the DT 7333 273 14 disposition disposition NN 7333 273 15 of of IN 7333 273 16 the the DT 7333 273 17 discs disc NNS 7333 273 18 in in IN 7333 273 19 the the DT 7333 273 20 manner manner NN 7333 273 21 indicated indicate VBD 7333 273 22 , , , 7333 273 23 without without IN 7333 273 24 interruption interruption NN 7333 273 25 , , , 7333 273 26 is be VBZ 7333 273 27 not not RB 7333 273 28 possible possible JJ 7333 273 29 , , , 7333 273 30 as as IN 7333 273 31 it -PRON- PRP 7333 273 32 should should MD 7333 273 33 be be VB 7333 273 34 possible possible JJ 7333 273 35 by by IN 7333 273 36 Euclidean euclidean JJ 7333 273 37 geometry geometry NN 7333 273 38 of of IN 7333 273 39 the the DT 7333 273 40 the the DT 7333 273 41 plane plane NN 7333 273 42 surface surface NN 7333 273 43 . . . 7333 274 1 In in IN 7333 274 2 this this DT 7333 274 3 way way NN 7333 274 4 creatures creature NNS 7333 274 5 which which WDT 7333 274 6 can can MD 7333 274 7 not not RB 7333 274 8 leave leave VB 7333 274 9 the the DT 7333 274 10 spherical spherical JJ 7333 274 11 surface surface NN 7333 274 12 , , , 7333 274 13 and and CC 7333 274 14 can can MD 7333 274 15 not not RB 7333 274 16 even even RB 7333 274 17 peep peep VB 7333 274 18 out out RP 7333 274 19 from from IN 7333 274 20 the the DT 7333 274 21 spherical spherical JJ 7333 274 22 surface surface NN 7333 274 23 into into IN 7333 274 24 three three CD 7333 274 25 - - HYPH 7333 274 26 dimensional dimensional JJ 7333 274 27 space space NN 7333 274 28 , , , 7333 274 29 might may MD 7333 274 30 discover discover VB 7333 274 31 , , , 7333 274 32 merely merely RB 7333 274 33 by by IN 7333 274 34 experimenting experiment VBG 7333 274 35 with with IN 7333 274 36 discs disc NNS 7333 274 37 , , , 7333 274 38 that that IN 7333 274 39 their -PRON- PRP$ 7333 274 40 two two CD 7333 274 41 - - HYPH 7333 274 42 dimensional dimensional JJ 7333 274 43 " " `` 7333 274 44 space space NN 7333 274 45 " " '' 7333 274 46 is be VBZ 7333 274 47 not not RB 7333 274 48 Euclidean euclidean JJ 7333 274 49 , , , 7333 274 50 but but CC 7333 274 51 spherical spherical JJ 7333 274 52 space space NN 7333 274 53 . . . 7333 275 1 From from IN 7333 275 2 the the DT 7333 275 3 latest late JJS 7333 275 4 results result NNS 7333 275 5 of of IN 7333 275 6 the the DT 7333 275 7 theory theory NN 7333 275 8 of of IN 7333 275 9 relativity relativity NN 7333 275 10 it -PRON- PRP 7333 275 11 is be VBZ 7333 275 12 probable probable JJ 7333 275 13 that that IN 7333 275 14 our -PRON- PRP$ 7333 275 15 three three CD 7333 275 16 - - HYPH 7333 275 17 dimensional dimensional JJ 7333 275 18 space space NN 7333 275 19 is be VBZ 7333 275 20 also also RB 7333 275 21 approximately approximately RB 7333 275 22 spherical spherical JJ 7333 275 23 , , , 7333 275 24 that that RB 7333 275 25 is is RB 7333 275 26 , , , 7333 275 27 that that IN 7333 275 28 the the DT 7333 275 29 laws law NNS 7333 275 30 of of IN 7333 275 31 disposition disposition NN 7333 275 32 of of IN 7333 275 33 rigid rigid JJ 7333 275 34 bodies body NNS 7333 275 35 in in IN 7333 275 36 it -PRON- PRP 7333 275 37 are be VBP 7333 275 38 not not RB 7333 275 39 given give VBN 7333 275 40 by by IN 7333 275 41 Euclidean euclidean JJ 7333 275 42 geometry geometry NN 7333 275 43 , , , 7333 275 44 but but CC 7333 275 45 approximately approximately RB 7333 275 46 by by IN 7333 275 47 spherical spherical JJ 7333 275 48 geometry geometry NN 7333 275 49 , , , 7333 275 50 if if IN 7333 275 51 only only RB 7333 275 52 we -PRON- PRP 7333 275 53 consider consider VBP 7333 275 54 parts part NNS 7333 275 55 of of IN 7333 275 56 space space NN 7333 275 57 which which WDT 7333 275 58 are be VBP 7333 275 59 sufficiently sufficiently RB 7333 275 60 great great JJ 7333 275 61 . . . 7333 276 1 Now now RB 7333 276 2 this this DT 7333 276 3 is be VBZ 7333 276 4 the the DT 7333 276 5 place place NN 7333 276 6 where where WRB 7333 276 7 the the DT 7333 276 8 reader reader NN 7333 276 9 's 's POS 7333 276 10 imagination imagination NN 7333 276 11 boggles boggle NNS 7333 276 12 . . . 7333 277 1 " " `` 7333 277 2 Nobody nobody NN 7333 277 3 can can MD 7333 277 4 imagine imagine VB 7333 277 5 this this DT 7333 277 6 thing thing NN 7333 277 7 , , , 7333 277 8 " " '' 7333 277 9 he -PRON- PRP 7333 277 10 cries cry VBZ 7333 277 11 indignantly indignantly RB 7333 277 12 . . . 7333 278 1 " " `` 7333 278 2 It -PRON- PRP 7333 278 3 can can MD 7333 278 4 be be VB 7333 278 5 said say VBN 7333 278 6 , , , 7333 278 7 but but CC 7333 278 8 can can MD 7333 278 9 not not RB 7333 278 10 be be VB 7333 278 11 thought think VBN 7333 278 12 . . . 7333 279 1 I -PRON- PRP 7333 279 2 can can MD 7333 279 3 represent represent VB 7333 279 4 to to IN 7333 279 5 myself -PRON- PRP 7333 279 6 a a DT 7333 279 7 spherical spherical JJ 7333 279 8 surface surface NN 7333 279 9 well well RB 7333 279 10 enough enough RB 7333 279 11 , , , 7333 279 12 but but CC 7333 279 13 nothing nothing NN 7333 279 14 analogous analogous JJ 7333 279 15 to to IN 7333 279 16 it -PRON- PRP 7333 279 17 in in IN 7333 279 18 three three CD 7333 279 19 dimensions dimension NNS 7333 279 20 . . . 7333 279 21 " " '' 7333 280 1 [ [ -LRB- 7333 280 2 Figure figure NN 7333 280 3 2 2 CD 7333 280 4 : : : 7333 280 5 A a DT 7333 280 6 circle circle NN 7333 280 7 projected project VBN 7333 280 8 from from IN 7333 280 9 a a DT 7333 280 10 sphere sphere NN 7333 280 11 onto onto IN 7333 280 12 a a DT 7333 280 13 plane plane NN 7333 280 14 ] ] -RRB- 7333 280 15 We -PRON- PRP 7333 280 16 must must MD 7333 280 17 try try VB 7333 280 18 to to TO 7333 280 19 surmount surmount VB 7333 280 20 this this DT 7333 280 21 barrier barrier NN 7333 280 22 in in IN 7333 280 23 the the DT 7333 280 24 mind mind NN 7333 280 25 , , , 7333 280 26 and and CC 7333 280 27 the the DT 7333 280 28 patient patient JJ 7333 280 29 reader reader NN 7333 280 30 will will MD 7333 280 31 see see VB 7333 280 32 that that IN 7333 280 33 it -PRON- PRP 7333 280 34 is be VBZ 7333 280 35 by by IN 7333 280 36 no no DT 7333 280 37 means means NN 7333 280 38 a a DT 7333 280 39 particularly particularly RB 7333 280 40 difficult difficult JJ 7333 280 41 task task NN 7333 280 42 . . . 7333 281 1 For for IN 7333 281 2 this this DT 7333 281 3 purpose purpose NN 7333 281 4 we -PRON- PRP 7333 281 5 will will MD 7333 281 6 first first RB 7333 281 7 give give VB 7333 281 8 our -PRON- PRP$ 7333 281 9 attention attention NN 7333 281 10 once once RB 7333 281 11 more more JJR 7333 281 12 to to IN 7333 281 13 the the DT 7333 281 14 geometry geometry NN 7333 281 15 of of IN 7333 281 16 two two CD 7333 281 17 - - HYPH 7333 281 18 dimensional dimensional JJ 7333 281 19 spherical spherical JJ 7333 281 20 surfaces surface NNS 7333 281 21 . . . 7333 282 1 In in IN 7333 282 2 the the DT 7333 282 3 adjoining adjoining JJ 7333 282 4 figure figure NN 7333 282 5 let let VBD 7333 282 6 _ _ NNP 7333 282 7 K K NNP 7333 282 8 _ _ NNP 7333 282 9 be be VB 7333 282 10 the the DT 7333 282 11 spherical spherical JJ 7333 282 12 surface surface NN 7333 282 13 , , , 7333 282 14 touched touch VBD 7333 282 15 at at IN 7333 282 16 _ _ NNP 7333 282 17 S S NNP 7333 282 18 _ _ NNP 7333 282 19 by by IN 7333 282 20 a a DT 7333 282 21 plane plane NN 7333 282 22 , , , 7333 282 23 _ _ NNP 7333 282 24 E E NNP 7333 282 25 _ _ NNP 7333 282 26 , , , 7333 282 27 which which WDT 7333 282 28 , , , 7333 282 29 for for IN 7333 282 30 facility facility NN 7333 282 31 of of IN 7333 282 32 presentation presentation NN 7333 282 33 , , , 7333 282 34 is be VBZ 7333 282 35 shown show VBN 7333 282 36 in in IN 7333 282 37 the the DT 7333 282 38 drawing drawing NN 7333 282 39 as as IN 7333 282 40 a a DT 7333 282 41 bounded bound VBN 7333 282 42 surface surface NN 7333 282 43 . . . 7333 283 1 Let let VB 7333 283 2 _ _ NNP 7333 283 3 L L NNP 7333 283 4 _ _ NNP 7333 283 5 be be VB 7333 283 6 a a DT 7333 283 7 disc disc NN 7333 283 8 on on IN 7333 283 9 the the DT 7333 283 10 spherical spherical JJ 7333 283 11 surface surface NN 7333 283 12 . . . 7333 284 1 Now now RB 7333 284 2 let let VB 7333 284 3 us -PRON- PRP 7333 284 4 imagine imagine VB 7333 284 5 that that IN 7333 284 6 at at IN 7333 284 7 the the DT 7333 284 8 point point NN 7333 284 9 _ _ NNP 7333 284 10 N N NNP 7333 284 11 _ _ NNP 7333 284 12 of of IN 7333 284 13 the the DT 7333 284 14 spherical spherical JJ 7333 284 15 surface surface NN 7333 284 16 , , , 7333 284 17 diametrically diametrically RB 7333 284 18 opposite opposite JJ 7333 284 19 to to IN 7333 284 20 _ _ NNP 7333 284 21 S S NNP 7333 284 22 _ _ NNP 7333 284 23 , , , 7333 284 24 there there EX 7333 284 25 is be VBZ 7333 284 26 a a DT 7333 284 27 luminous luminous JJ 7333 284 28 point point NN 7333 284 29 , , , 7333 284 30 throwing throw VBG 7333 284 31 a a DT 7333 284 32 shadow shadow NN 7333 284 33 _ _ NNP 7333 284 34 L L NNP 7333 284 35 ' ' '' 7333 284 36 _ _ NNP 7333 284 37 of of IN 7333 284 38 the the DT 7333 284 39 disc disc NN 7333 284 40 _ _ NNP 7333 284 41 L L NNP 7333 284 42 _ _ NNP 7333 284 43 upon upon IN 7333 284 44 the the DT 7333 284 45 plane plane NN 7333 284 46 _ _ NNP 7333 284 47 E E NNP 7333 284 48 _ _ NNP 7333 284 49 . . . 7333 285 1 Every every DT 7333 285 2 point point NN 7333 285 3 on on IN 7333 285 4 the the DT 7333 285 5 sphere sphere NN 7333 285 6 has have VBZ 7333 285 7 its -PRON- PRP$ 7333 285 8 shadow shadow NN 7333 285 9 on on IN 7333 285 10 the the DT 7333 285 11 plane plane NN 7333 285 12 . . . 7333 286 1 If if IN 7333 286 2 the the DT 7333 286 3 disc disc NN 7333 286 4 on on IN 7333 286 5 the the DT 7333 286 6 sphere sphere NN 7333 286 7 _ _ NNP 7333 286 8 K K NNP 7333 286 9 _ _ NNP 7333 286 10 is be VBZ 7333 286 11 moved move VBN 7333 286 12 , , , 7333 286 13 its -PRON- PRP$ 7333 286 14 shadow shadow NN 7333 286 15 _ _ NNP 7333 286 16 L L NNP 7333 286 17 ' ' '' 7333 286 18 _ _ NNP 7333 286 19 on on IN 7333 286 20 the the DT 7333 286 21 plane plane NN 7333 286 22 _ _ NNP 7333 286 23 E E NNP 7333 286 24 _ _ NNP 7333 286 25 also also RB 7333 286 26 moves move VBZ 7333 286 27 . . . 7333 287 1 When when WRB 7333 287 2 the the DT 7333 287 3 disc disc NN 7333 287 4 _ _ NNP 7333 287 5 L L NNP 7333 287 6 _ _ NNP 7333 287 7 is be VBZ 7333 287 8 at at IN 7333 287 9 _ _ NNP 7333 287 10 S S NNP 7333 287 11 _ _ NNP 7333 287 12 , , , 7333 287 13 it -PRON- PRP 7333 287 14 almost almost RB 7333 287 15 exactly exactly RB 7333 287 16 coincides coincide VBZ 7333 287 17 with with IN 7333 287 18 its -PRON- PRP$ 7333 287 19 shadow shadow NN 7333 287 20 . . . 7333 288 1 If if IN 7333 288 2 it -PRON- PRP 7333 288 3 moves move VBZ 7333 288 4 on on IN 7333 288 5 the the DT 7333 288 6 spherical spherical JJ 7333 288 7 surface surface NN 7333 288 8 away away RB 7333 288 9 from from IN 7333 288 10 _ _ NNP 7333 288 11 S S NNP 7333 288 12 _ _ NNP 7333 288 13 upwards upwards RB 7333 288 14 , , , 7333 288 15 the the DT 7333 288 16 disc disc NN 7333 288 17 shadow shadow NN 7333 288 18 _ _ NNP 7333 288 19 L L NNP 7333 288 20 ' ' '' 7333 288 21 _ _ NNP 7333 288 22 on on IN 7333 288 23 the the DT 7333 288 24 plane plane NN 7333 288 25 also also RB 7333 288 26 moves move VBZ 7333 288 27 away away RB 7333 288 28 from from IN 7333 288 29 _ _ NNP 7333 288 30 S S NNP 7333 288 31 _ _ NNP 7333 288 32 on on IN 7333 288 33 the the DT 7333 288 34 plane plane NN 7333 288 35 outwards outward NNS 7333 288 36 , , , 7333 288 37 growing grow VBG 7333 288 38 bigger big JJR 7333 288 39 and and CC 7333 288 40 bigger big JJR 7333 288 41 . . . 7333 289 1 As as IN 7333 289 2 the the DT 7333 289 3 disc disc NN 7333 289 4 _ _ NNP 7333 289 5 L L NNP 7333 289 6 _ _ NNP 7333 289 7 approaches approach VBZ 7333 289 8 the the DT 7333 289 9 luminous luminous JJ 7333 289 10 point point NN 7333 289 11 _ _ NNP 7333 289 12 N N NNP 7333 289 13 _ _ NNP 7333 289 14 , , , 7333 289 15 the the DT 7333 289 16 shadow shadow NN 7333 289 17 moves move VBZ 7333 289 18 off off RP 7333 289 19 to to IN 7333 289 20 infinity infinity NN 7333 289 21 , , , 7333 289 22 and and CC 7333 289 23 becomes become VBZ 7333 289 24 infinitely infinitely RB 7333 289 25 great great JJ 7333 289 26 . . . 7333 290 1 Now now RB 7333 290 2 we -PRON- PRP 7333 290 3 put put VBP 7333 290 4 the the DT 7333 290 5 question question NN 7333 290 6 , , , 7333 290 7 What what WP 7333 290 8 are be VBP 7333 290 9 the the DT 7333 290 10 laws law NNS 7333 290 11 of of IN 7333 290 12 disposition disposition NN 7333 290 13 of of IN 7333 290 14 the the DT 7333 290 15 disc disc NN 7333 290 16 - - HYPH 7333 290 17 shadows shadow NNS 7333 290 18 _ _ NNP 7333 290 19 L L NNP 7333 290 20 ' ' '' 7333 290 21 _ _ NNP 7333 290 22 on on IN 7333 290 23 the the DT 7333 290 24 plane plane NN 7333 290 25 _ _ NNP 7333 290 26 E E NNP 7333 290 27 _ _ NNP 7333 290 28 ? ? . 7333 291 1 Evidently evidently RB 7333 291 2 they -PRON- PRP 7333 291 3 are be VBP 7333 291 4 exactly exactly RB 7333 291 5 the the DT 7333 291 6 same same JJ 7333 291 7 as as IN 7333 291 8 the the DT 7333 291 9 laws law NNS 7333 291 10 of of IN 7333 291 11 disposition disposition NN 7333 291 12 of of IN 7333 291 13 the the DT 7333 291 14 discs disc NNS 7333 291 15 _ _ NNP 7333 291 16 L L NNP 7333 291 17 _ _ NNP 7333 291 18 on on IN 7333 291 19 the the DT 7333 291 20 spherical spherical JJ 7333 291 21 surface surface NN 7333 291 22 . . . 7333 292 1 For for IN 7333 292 2 to to IN 7333 292 3 each each DT 7333 292 4 original original JJ 7333 292 5 figure figure NN 7333 292 6 on on IN 7333 292 7 _ _ NNP 7333 292 8 K K NNP 7333 292 9 _ _ NNP 7333 292 10 there there EX 7333 292 11 is be VBZ 7333 292 12 a a DT 7333 292 13 corresponding correspond VBG 7333 292 14 shadow shadow NN 7333 292 15 figure figure NN 7333 292 16 on on IN 7333 292 17 _ _ NNP 7333 292 18 E E NNP 7333 292 19 _ _ NNP 7333 292 20 . . . 7333 293 1 If if IN 7333 293 2 two two CD 7333 293 3 discs disc NNS 7333 293 4 on on IN 7333 293 5 _ _ NNP 7333 293 6 K K NNP 7333 293 7 _ _ NNP 7333 293 8 are be VBP 7333 293 9 touching touch VBG 7333 293 10 , , , 7333 293 11 their -PRON- PRP$ 7333 293 12 shadows shadow NNS 7333 293 13 on on IN 7333 293 14 _ _ NNP 7333 293 15 E E NNP 7333 293 16 _ _ NNP 7333 293 17 also also RB 7333 293 18 touch touch NN 7333 293 19 . . . 7333 294 1 The the DT 7333 294 2 shadow shadow NN 7333 294 3 - - HYPH 7333 294 4 geometry geometry NN 7333 294 5 on on IN 7333 294 6 the the DT 7333 294 7 plane plane NN 7333 294 8 agrees agree VBZ 7333 294 9 with with IN 7333 294 10 the the DT 7333 294 11 the the DT 7333 294 12 disc disc NN 7333 294 13 - - HYPH 7333 294 14 geometry geometry NN 7333 294 15 on on IN 7333 294 16 the the DT 7333 294 17 sphere sphere NN 7333 294 18 . . . 7333 295 1 If if IN 7333 295 2 we -PRON- PRP 7333 295 3 call call VBP 7333 295 4 the the DT 7333 295 5 disc disc NN 7333 295 6 - - HYPH 7333 295 7 shadows shadow NNS 7333 295 8 rigid rigid JJ 7333 295 9 figures figure NNS 7333 295 10 , , , 7333 295 11 then then RB 7333 295 12 spherical spherical JJ 7333 295 13 geometry geometry NN 7333 295 14 holds hold VBZ 7333 295 15 good good JJ 7333 295 16 on on IN 7333 295 17 the the DT 7333 295 18 plane plane NN 7333 295 19 _ _ NNP 7333 295 20 E E NNP 7333 295 21 _ _ NNP 7333 295 22 with with IN 7333 295 23 respect respect NN 7333 295 24 to to IN 7333 295 25 these these DT 7333 295 26 rigid rigid JJ 7333 295 27 figures figure NNS 7333 295 28 . . . 7333 296 1 Moreover moreover RB 7333 296 2 , , , 7333 296 3 the the DT 7333 296 4 plane plane NN 7333 296 5 is be VBZ 7333 296 6 finite finite JJ 7333 296 7 with with IN 7333 296 8 respect respect NN 7333 296 9 to to IN 7333 296 10 the the DT 7333 296 11 disc disc NN 7333 296 12 - - HYPH 7333 296 13 shadows shadow NNS 7333 296 14 , , , 7333 296 15 since since IN 7333 296 16 only only RB 7333 296 17 a a DT 7333 296 18 finite finite JJ 7333 296 19 number number NN 7333 296 20 of of IN 7333 296 21 the the DT 7333 296 22 shadows shadow NNS 7333 296 23 can can MD 7333 296 24 find find VB 7333 296 25 room room NN 7333 296 26 on on IN 7333 296 27 the the DT 7333 296 28 plane plane NN 7333 296 29 . . . 7333 297 1 At at IN 7333 297 2 this this DT 7333 297 3 point point NN 7333 297 4 somebody somebody NN 7333 297 5 will will MD 7333 297 6 say say VB 7333 297 7 , , , 7333 297 8 " " `` 7333 297 9 That that DT 7333 297 10 is be VBZ 7333 297 11 nonsense nonsense NN 7333 297 12 . . . 7333 298 1 The the DT 7333 298 2 disc disc NN 7333 298 3 - - HYPH 7333 298 4 shadows shadow NNS 7333 298 5 are be VBP 7333 298 6 _ _ NNP 7333 298 7 not not RB 7333 298 8 _ _ NNP 7333 298 9 rigid rigid JJ 7333 298 10 figures figure NNS 7333 298 11 . . . 7333 299 1 We -PRON- PRP 7333 299 2 have have VBP 7333 299 3 only only RB 7333 299 4 to to TO 7333 299 5 move move VB 7333 299 6 a a DT 7333 299 7 two two CD 7333 299 8 - - HYPH 7333 299 9 foot foot NN 7333 299 10 rule rule NN 7333 299 11 about about IN 7333 299 12 on on IN 7333 299 13 the the DT 7333 299 14 plane plane NN 7333 299 15 _ _ NNP 7333 299 16 E E NNP 7333 299 17 _ _ NNP 7333 299 18 to to TO 7333 299 19 convince convince VB 7333 299 20 ourselves -PRON- PRP 7333 299 21 that that IN 7333 299 22 the the DT 7333 299 23 shadows shadow NNS 7333 299 24 constantly constantly RB 7333 299 25 increase increase VBP 7333 299 26 in in IN 7333 299 27 size size NN 7333 299 28 as as IN 7333 299 29 they -PRON- PRP 7333 299 30 move move VBP 7333 299 31 away away RB 7333 299 32 from from IN 7333 299 33 _ _ NNP 7333 299 34 S S NNP 7333 299 35 _ _ NNP 7333 299 36 on on IN 7333 299 37 the the DT 7333 299 38 plane plane NN 7333 299 39 towards towards IN 7333 299 40 infinity infinity NN 7333 299 41 . . . 7333 299 42 " " '' 7333 300 1 But but CC 7333 300 2 what what WP 7333 300 3 if if IN 7333 300 4 the the DT 7333 300 5 two two CD 7333 300 6 - - HYPH 7333 300 7 foot foot NN 7333 300 8 rule rule NN 7333 300 9 were be VBD 7333 300 10 to to TO 7333 300 11 behave behave VB 7333 300 12 on on IN 7333 300 13 the the DT 7333 300 14 plane plane NN 7333 300 15 _ _ NNP 7333 300 16 E E NNP 7333 300 17 _ _ NNP 7333 300 18 in in IN 7333 300 19 the the DT 7333 300 20 same same JJ 7333 300 21 way way NN 7333 300 22 as as IN 7333 300 23 the the DT 7333 300 24 disc disc NN 7333 300 25 - - HYPH 7333 300 26 shadows shadow NNS 7333 300 27 _ _ NNP 7333 300 28 L L NNP 7333 300 29 ' ' '' 7333 300 30 _ _ NNP 7333 300 31 ? ? . 7333 301 1 It -PRON- PRP 7333 301 2 would would MD 7333 301 3 then then RB 7333 301 4 be be VB 7333 301 5 impossible impossible JJ 7333 301 6 to to TO 7333 301 7 show show VB 7333 301 8 that that IN 7333 301 9 the the DT 7333 301 10 shadows shadow NNS 7333 301 11 increase increase VBP 7333 301 12 in in IN 7333 301 13 size size NN 7333 301 14 as as IN 7333 301 15 they -PRON- PRP 7333 301 16 move move VBP 7333 301 17 away away RB 7333 301 18 from from IN 7333 301 19 _ _ NNP 7333 301 20 S S NNP 7333 301 21 _ _ NNP 7333 301 22 ; ; : 7333 301 23 such such PDT 7333 301 24 an an DT 7333 301 25 assertion assertion NN 7333 301 26 would would MD 7333 301 27 then then RB 7333 301 28 no no RB 7333 301 29 longer long RBR 7333 301 30 have have VB 7333 301 31 any any DT 7333 301 32 meaning meaning NN 7333 301 33 whatever whatever WDT 7333 301 34 . . . 7333 302 1 In in IN 7333 302 2 fact fact NN 7333 302 3 the the DT 7333 302 4 only only JJ 7333 302 5 objective objective JJ 7333 302 6 assertion assertion NN 7333 302 7 that that WDT 7333 302 8 can can MD 7333 302 9 be be VB 7333 302 10 made make VBN 7333 302 11 about about IN 7333 302 12 the the DT 7333 302 13 disc disc NN 7333 302 14 - - HYPH 7333 302 15 shadows shadow NNS 7333 302 16 is be VBZ 7333 302 17 just just RB 7333 302 18 this this DT 7333 302 19 , , , 7333 302 20 that that IN 7333 302 21 they -PRON- PRP 7333 302 22 are be VBP 7333 302 23 related relate VBN 7333 302 24 in in IN 7333 302 25 exactly exactly RB 7333 302 26 the the DT 7333 302 27 same same JJ 7333 302 28 way way NN 7333 302 29 as as IN 7333 302 30 are be VBP 7333 302 31 the the DT 7333 302 32 rigid rigid JJ 7333 302 33 discs disc NNS 7333 302 34 on on IN 7333 302 35 the the DT 7333 302 36 spherical spherical JJ 7333 302 37 surface surface NN 7333 302 38 in in IN 7333 302 39 the the DT 7333 302 40 sense sense NN 7333 302 41 of of IN 7333 302 42 Euclidean euclidean JJ 7333 302 43 geometry geometry NN 7333 302 44 . . . 7333 303 1 We -PRON- PRP 7333 303 2 must must MD 7333 303 3 carefully carefully RB 7333 303 4 bear bear VB 7333 303 5 in in IN 7333 303 6 mind mind NN 7333 303 7 that that IN 7333 303 8 our -PRON- PRP$ 7333 303 9 statement statement NN 7333 303 10 as as IN 7333 303 11 to to IN 7333 303 12 the the DT 7333 303 13 growth growth NN 7333 303 14 of of IN 7333 303 15 the the DT 7333 303 16 disc disc NN 7333 303 17 - - HYPH 7333 303 18 shadows shadow NNS 7333 303 19 , , , 7333 303 20 as as IN 7333 303 21 they -PRON- PRP 7333 303 22 move move VBP 7333 303 23 away away RB 7333 303 24 from from IN 7333 303 25 _ _ NNP 7333 303 26 S S NNP 7333 303 27 _ _ NNP 7333 303 28 towards towards IN 7333 303 29 infinity infinity NN 7333 303 30 , , , 7333 303 31 has have VBZ 7333 303 32 in in IN 7333 303 33 itself -PRON- PRP 7333 303 34 no no DT 7333 303 35 objective objective JJ 7333 303 36 meaning meaning NN 7333 303 37 , , , 7333 303 38 as as RB 7333 303 39 long long RB 7333 303 40 as as IN 7333 303 41 we -PRON- PRP 7333 303 42 are be VBP 7333 303 43 unable unable JJ 7333 303 44 to to TO 7333 303 45 employ employ VB 7333 303 46 Euclidean euclidean JJ 7333 303 47 rigid rigid JJ 7333 303 48 bodies body NNS 7333 303 49 which which WDT 7333 303 50 can can MD 7333 303 51 be be VB 7333 303 52 moved move VBN 7333 303 53 about about RB 7333 303 54 on on IN 7333 303 55 the the DT 7333 303 56 plane plane NN 7333 303 57 _ _ NNP 7333 303 58 E E NNP 7333 303 59 _ _ NNP 7333 303 60 for for IN 7333 303 61 the the DT 7333 303 62 purpose purpose NN 7333 303 63 of of IN 7333 303 64 comparing compare VBG 7333 303 65 the the DT 7333 303 66 size size NN 7333 303 67 of of IN 7333 303 68 the the DT 7333 303 69 disc disc NN 7333 303 70 - - HYPH 7333 303 71 shadows shadow NNS 7333 303 72 . . . 7333 304 1 In in IN 7333 304 2 respect respect NN 7333 304 3 of of IN 7333 304 4 the the DT 7333 304 5 laws law NNS 7333 304 6 of of IN 7333 304 7 disposition disposition NN 7333 304 8 of of IN 7333 304 9 the the DT 7333 304 10 shadows shadow NNS 7333 304 11 _ _ NNP 7333 304 12 L L NNP 7333 304 13 ' ' '' 7333 304 14 _ _ NNP 7333 304 15 , , , 7333 304 16 the the DT 7333 304 17 point point NN 7333 304 18 _ _ NNP 7333 304 19 S S NNP 7333 304 20 _ _ NNP 7333 304 21 has have VBZ 7333 304 22 no no DT 7333 304 23 special special JJ 7333 304 24 privileges privilege NNS 7333 304 25 on on IN 7333 304 26 the the DT 7333 304 27 plane plane NN 7333 304 28 any any RB 7333 304 29 more more RBR 7333 304 30 than than IN 7333 304 31 on on IN 7333 304 32 the the DT 7333 304 33 spherical spherical JJ 7333 304 34 surface surface NN 7333 304 35 . . . 7333 305 1 The the DT 7333 305 2 representation representation NN 7333 305 3 given give VBN 7333 305 4 above above RB 7333 305 5 of of IN 7333 305 6 spherical spherical JJ 7333 305 7 geometry geometry NN 7333 305 8 on on IN 7333 305 9 the the DT 7333 305 10 plane plane NN 7333 305 11 is be VBZ 7333 305 12 important important JJ 7333 305 13 for for IN 7333 305 14 us -PRON- PRP 7333 305 15 , , , 7333 305 16 because because IN 7333 305 17 it -PRON- PRP 7333 305 18 readily readily RB 7333 305 19 allows allow VBZ 7333 305 20 itself -PRON- PRP 7333 305 21 to to TO 7333 305 22 be be VB 7333 305 23 transferred transfer VBN 7333 305 24 to to IN 7333 305 25 the the DT 7333 305 26 three three CD 7333 305 27 - - HYPH 7333 305 28 dimensional dimensional JJ 7333 305 29 case case NN 7333 305 30 . . . 7333 306 1 Let let VB 7333 306 2 us -PRON- PRP 7333 306 3 imagine imagine VB 7333 306 4 a a DT 7333 306 5 point point NN 7333 306 6 _ _ NNP 7333 306 7 S S NNP 7333 306 8 _ _ NNP 7333 306 9 of of IN 7333 306 10 our -PRON- PRP$ 7333 306 11 space space NN 7333 306 12 , , , 7333 306 13 and and CC 7333 306 14 a a DT 7333 306 15 great great JJ 7333 306 16 number number NN 7333 306 17 of of IN 7333 306 18 small small JJ 7333 306 19 spheres sphere NNS 7333 306 20 , , , 7333 306 21 _ _ NNP 7333 306 22 L L NNP 7333 306 23 ' ' '' 7333 306 24 _ _ NNP 7333 306 25 , , , 7333 306 26 which which WDT 7333 306 27 can can MD 7333 306 28 all all DT 7333 306 29 be be VB 7333 306 30 brought bring VBN 7333 306 31 to to TO 7333 306 32 coincide coincide VB 7333 306 33 with with IN 7333 306 34 one one NN 7333 306 35 another another DT 7333 306 36 . . . 7333 307 1 But but CC 7333 307 2 these these DT 7333 307 3 spheres sphere NNS 7333 307 4 are be VBP 7333 307 5 not not RB 7333 307 6 to to TO 7333 307 7 be be VB 7333 307 8 rigid rigid JJ 7333 307 9 in in IN 7333 307 10 the the DT 7333 307 11 sense sense NN 7333 307 12 of of IN 7333 307 13 Euclidean euclidean JJ 7333 307 14 geometry geometry NN 7333 307 15 ; ; : 7333 307 16 their -PRON- PRP$ 7333 307 17 radius radius NN 7333 307 18 is be VBZ 7333 307 19 to to TO 7333 307 20 increase increase VB 7333 307 21 ( ( -LRB- 7333 307 22 in in IN 7333 307 23 the the DT 7333 307 24 sense sense NN 7333 307 25 of of IN 7333 307 26 Euclidean euclidean JJ 7333 307 27 geometry geometry NN 7333 307 28 ) ) -RRB- 7333 307 29 when when WRB 7333 307 30 they -PRON- PRP 7333 307 31 are be VBP 7333 307 32 moved move VBN 7333 307 33 away away RB 7333 307 34 from from IN 7333 307 35 _ _ NNP 7333 307 36 S S NNP 7333 307 37 _ _ NNP 7333 307 38 towards towards IN 7333 307 39 infinity infinity NN 7333 307 40 , , , 7333 307 41 and and CC 7333 307 42 this this DT 7333 307 43 increase increase NN 7333 307 44 is be VBZ 7333 307 45 to to TO 7333 307 46 take take VB 7333 307 47 place place NN 7333 307 48 in in IN 7333 307 49 exact exact JJ 7333 307 50 accordance accordance NN 7333 307 51 with with IN 7333 307 52 the the DT 7333 307 53 same same JJ 7333 307 54 law law NN 7333 307 55 as as IN 7333 307 56 applies apply VBZ 7333 307 57 to to IN 7333 307 58 the the DT 7333 307 59 increase increase NN 7333 307 60 of of IN 7333 307 61 the the DT 7333 307 62 radii radii NN 7333 307 63 of of IN 7333 307 64 the the DT 7333 307 65 disc disc NN 7333 307 66 - - HYPH 7333 307 67 shadows shadow NNS 7333 307 68 _ _ NNP 7333 307 69 L L NNP 7333 307 70 ' ' '' 7333 307 71 _ _ NNP 7333 307 72 on on IN 7333 307 73 the the DT 7333 307 74 plane plane NN 7333 307 75 . . . 7333 308 1 After after IN 7333 308 2 having have VBG 7333 308 3 gained gain VBN 7333 308 4 a a DT 7333 308 5 vivid vivid JJ 7333 308 6 mental mental JJ 7333 308 7 image image NN 7333 308 8 of of IN 7333 308 9 the the DT 7333 308 10 geometrical geometrical JJ 7333 308 11 behaviour behaviour NN 7333 308 12 of of IN 7333 308 13 our -PRON- PRP$ 7333 308 14 _ _ NNP 7333 308 15 L L NNP 7333 308 16 ' ' POS 7333 308 17 _ _ NNP 7333 308 18 spheres sphere NNS 7333 308 19 , , , 7333 308 20 let let VB 7333 308 21 us -PRON- PRP 7333 308 22 assume assume VB 7333 308 23 that that IN 7333 308 24 in in IN 7333 308 25 our -PRON- PRP$ 7333 308 26 space space NN 7333 308 27 there there EX 7333 308 28 are be VBP 7333 308 29 no no DT 7333 308 30 rigid rigid JJ 7333 308 31 bodies body NNS 7333 308 32 at at RB 7333 308 33 all all RB 7333 308 34 in in IN 7333 308 35 the the DT 7333 308 36 sense sense NN 7333 308 37 of of IN 7333 308 38 Euclidean euclidean JJ 7333 308 39 geometry geometry NN 7333 308 40 , , , 7333 308 41 but but CC 7333 308 42 only only RB 7333 308 43 bodies body NNS 7333 308 44 having have VBG 7333 308 45 the the DT 7333 308 46 behaviour behaviour NN 7333 308 47 of of IN 7333 308 48 our -PRON- PRP$ 7333 308 49 _ _ NNP 7333 308 50 L L NNP 7333 308 51 ' ' POS 7333 308 52 _ _ NNP 7333 308 53 spheres sphere NNS 7333 308 54 . . . 7333 309 1 Then then RB 7333 309 2 we -PRON- PRP 7333 309 3 shall shall MD 7333 309 4 have have VB 7333 309 5 a a DT 7333 309 6 vivid vivid JJ 7333 309 7 representation representation NN 7333 309 8 of of IN 7333 309 9 three three CD 7333 309 10 - - HYPH 7333 309 11 dimensional dimensional JJ 7333 309 12 spherical spherical JJ 7333 309 13 space space NN 7333 309 14 , , , 7333 309 15 or or CC 7333 309 16 , , , 7333 309 17 rather rather RB 7333 309 18 of of IN 7333 309 19 three three CD 7333 309 20 - - HYPH 7333 309 21 dimensional dimensional JJ 7333 309 22 spherical spherical JJ 7333 309 23 geometry geometry NN 7333 309 24 . . . 7333 310 1 Here here RB 7333 310 2 our -PRON- PRP$ 7333 310 3 spheres sphere NNS 7333 310 4 must must MD 7333 310 5 be be VB 7333 310 6 called call VBN 7333 310 7 " " `` 7333 310 8 rigid rigid JJ 7333 310 9 " " '' 7333 310 10 spheres sphere NNS 7333 310 11 . . . 7333 311 1 Their -PRON- PRP$ 7333 311 2 increase increase NN 7333 311 3 in in IN 7333 311 4 size size NN 7333 311 5 as as IN 7333 311 6 they -PRON- PRP 7333 311 7 depart depart VBP 7333 311 8 from from IN 7333 311 9 _ _ NNP 7333 311 10 S S NNP 7333 311 11 _ _ NNP 7333 311 12 is be VBZ 7333 311 13 not not RB 7333 311 14 to to TO 7333 311 15 be be VB 7333 311 16 detected detect VBN 7333 311 17 by by IN 7333 311 18 measuring measure VBG 7333 311 19 with with IN 7333 311 20 measuring measure VBG 7333 311 21 - - HYPH 7333 311 22 rods rod NNS 7333 311 23 , , , 7333 311 24 any any DT 7333 311 25 more more RBR 7333 311 26 than than IN 7333 311 27 in in IN 7333 311 28 the the DT 7333 311 29 case case NN 7333 311 30 of of IN 7333 311 31 the the DT 7333 311 32 disc disc NN 7333 311 33 - - HYPH 7333 311 34 shadows shadow NNS 7333 311 35 on on IN 7333 311 36 _ _ NNP 7333 311 37 E E NNP 7333 311 38 _ _ NNP 7333 311 39 , , , 7333 311 40 because because IN 7333 311 41 the the DT 7333 311 42 standards standard NNS 7333 311 43 of of IN 7333 311 44 measurement measurement NN 7333 311 45 behave behave NN 7333 311 46 in in IN 7333 311 47 the the DT 7333 311 48 same same JJ 7333 311 49 way way NN 7333 311 50 as as IN 7333 311 51 the the DT 7333 311 52 spheres sphere NNS 7333 311 53 . . . 7333 312 1 Space space NN 7333 312 2 is be VBZ 7333 312 3 homogeneous homogeneous JJ 7333 312 4 , , , 7333 312 5 that that DT 7333 312 6 is be VBZ 7333 312 7 to to TO 7333 312 8 say say VB 7333 312 9 , , , 7333 312 10 the the DT 7333 312 11 same same JJ 7333 312 12 spherical spherical JJ 7333 312 13 configurations configuration NNS 7333 312 14 are be VBP 7333 312 15 possible possible JJ 7333 312 16 in in IN 7333 312 17 the the DT 7333 312 18 environment environment NN 7333 312 19 of of IN 7333 312 20 all all DT 7333 312 21 points point NNS 7333 312 22 . . . 7333 313 1 * * NFP 7333 313 2 Our -PRON- PRP$ 7333 313 3 space space NN 7333 313 4 is be VBZ 7333 313 5 finite finite JJ 7333 313 6 , , , 7333 313 7 because because IN 7333 313 8 , , , 7333 313 9 in in IN 7333 313 10 consequence consequence NN 7333 313 11 of of IN 7333 313 12 the the DT 7333 313 13 " " `` 7333 313 14 growth growth NN 7333 313 15 " " '' 7333 313 16 of of IN 7333 313 17 the the DT 7333 313 18 spheres sphere NNS 7333 313 19 , , , 7333 313 20 only only RB 7333 313 21 a a DT 7333 313 22 finite finite JJ 7333 313 23 number number NN 7333 313 24 of of IN 7333 313 25 them -PRON- PRP 7333 313 26 can can MD 7333 313 27 find find VB 7333 313 28 room room NN 7333 313 29 in in IN 7333 313 30 space space NN 7333 313 31 . . . 7333 314 1 * * NFP 7333 314 2 This this DT 7333 314 3 is be VBZ 7333 314 4 intelligible intelligible JJ 7333 314 5 without without IN 7333 314 6 calculation calculation NN 7333 314 7 -- -- : 7333 314 8 but but CC 7333 314 9 only only RB 7333 314 10 for for IN 7333 314 11 the the DT 7333 314 12 two two CD 7333 314 13 - - HYPH 7333 314 14 dimensional dimensional JJ 7333 314 15 case case NN 7333 314 16 -- -- : 7333 314 17 if if IN 7333 314 18 we -PRON- PRP 7333 314 19 revert revert VBP 7333 314 20 once once RB 7333 314 21 more more RBR 7333 314 22 to to IN 7333 314 23 the the DT 7333 314 24 case case NN 7333 314 25 of of IN 7333 314 26 the the DT 7333 314 27 disc disc NN 7333 314 28 on on IN 7333 314 29 the the DT 7333 314 30 surface surface NN 7333 314 31 of of IN 7333 314 32 the the DT 7333 314 33 sphere sphere NN 7333 314 34 . . . 7333 315 1 In in IN 7333 315 2 this this DT 7333 315 3 way way NN 7333 315 4 , , , 7333 315 5 by by IN 7333 315 6 using use VBG 7333 315 7 as as RB 7333 315 8 stepping stepping JJ 7333 315 9 - - : 7333 315 10 stones stone NNS 7333 315 11 the the DT 7333 315 12 practice practice NN 7333 315 13 in in IN 7333 315 14 thinking thinking NN 7333 315 15 and and CC 7333 315 16 visualisation visualisation NN 7333 315 17 which which WDT 7333 315 18 Euclidean Euclidean NNP 7333 315 19 geometry geometry NN 7333 315 20 gives give VBZ 7333 315 21 us -PRON- PRP 7333 315 22 , , , 7333 315 23 we -PRON- PRP 7333 315 24 have have VBP 7333 315 25 acquired acquire VBN 7333 315 26 a a DT 7333 315 27 mental mental JJ 7333 315 28 picture picture NN 7333 315 29 of of IN 7333 315 30 spherical spherical JJ 7333 315 31 geometry geometry NN 7333 315 32 . . . 7333 316 1 We -PRON- PRP 7333 316 2 may may MD 7333 316 3 without without IN 7333 316 4 difficulty difficulty NN 7333 316 5 impart impart VB 7333 316 6 more more JJR 7333 316 7 depth depth NN 7333 316 8 and and CC 7333 316 9 vigour vigour NN 7333 316 10 to to IN 7333 316 11 these these DT 7333 316 12 ideas idea NNS 7333 316 13 by by IN 7333 316 14 carrying carry VBG 7333 316 15 out out RP 7333 316 16 special special JJ 7333 316 17 imaginary imaginary JJ 7333 316 18 constructions construction NNS 7333 316 19 . . . 7333 317 1 Nor nor CC 7333 317 2 would would MD 7333 317 3 it -PRON- PRP 7333 317 4 be be VB 7333 317 5 difficult difficult JJ 7333 317 6 to to TO 7333 317 7 represent represent VB 7333 317 8 the the DT 7333 317 9 case case NN 7333 317 10 of of IN 7333 317 11 what what WP 7333 317 12 is be VBZ 7333 317 13 called call VBN 7333 317 14 elliptical elliptical JJ 7333 317 15 geometry geometry NN 7333 317 16 in in IN 7333 317 17 an an DT 7333 317 18 analogous analogous JJ 7333 317 19 manner manner NN 7333 317 20 . . . 7333 318 1 My -PRON- PRP$ 7333 318 2 only only JJ 7333 318 3 aim aim NN 7333 318 4 to to IN 7333 318 5 - - HYPH 7333 318 6 day day NN 7333 318 7 has have VBZ 7333 318 8 been be VBN 7333 318 9 to to TO 7333 318 10 show show VB 7333 318 11 that that IN 7333 318 12 the the DT 7333 318 13 human human JJ 7333 318 14 faculty faculty NN 7333 318 15 of of IN 7333 318 16 visualisation visualisation NN 7333 318 17 is be VBZ 7333 318 18 by by IN 7333 318 19 no no DT 7333 318 20 means means NN 7333 318 21 bound bind VBN 7333 318 22 to to TO 7333 318 23 capitulate capitulate VB 7333 318 24 to to IN 7333 318 25 non non JJ 7333 318 26 - - JJ 7333 318 27 Euclidean euclidean JJ 7333 318 28 geometry geometry NN 7333 318 29 . . .