From Cubist Simultaneity to Quantum Complementarity


From Cubist Simultaneity to Quantum Complementarity

Christophe Schinckus1

Published online: 12 May 2016
� The Author(s) 2016. This article is published with open access at Springerlink.com

Abstract This article offers a contribution to the history of scientific ideas by proposing an
epistemological argument supporting the assumption made by Miller whereby Niels Bohr

has been influenced by cubism (Jean Metzinger) when he developed his non-intuitive

complementarity principle. More specifically, this essay will identify the Bergsonian durée

as the conceptual bridge between Metzinger and Bohr. Beyond this conceptual link

between the painter and the physicist, this paper aims to emphasize the key role played by

art in the development of human knowledge.

Keywords Cubism � Quantum physics � Simultaneity � Bergsonian durée

1 Introduction: Cubism and Science

Cubism is usually associated with a movement in art in which the single viewpoint per-

spective has been abandoned. Actually, the term ‘‘Cubism’’ refers to a heterogeneous

movement that was composed by ‘‘several Cubisms’’: the Gris’s Cubism was different

from the works of Villion or Leger whereas the Metzinger conception of Cubism was far

from the way of painting of the two masters Picasso and Braque (who worked together

during several years). Despite existing dissimilarities between these works, they usually

appear under the same umbrella of Cubism because they all proposed an innovative way of

painting the world by representing, at the same time, several dimensions of a reality/object

(Fauchereau 1982). Precisely, ‘‘a cubist painting requires us to recognize that our confusion

about what is implied in this new method of representation is the result of misplaced

expectations […] about our own ability to identify and organize our word’’ (Vargish and
Mook 1999 p. 34). In other words, although ‘‘Cubisms’’ differ in terms of colour themes,

& Christophe Schinckus
cs354@le.ac.uk

1
School of Management, University of Leicester, Leicester, UK

123

Found Sci (2017) 22:709–716
DOI 10.1007/s10699-016-9494-7

http://crossmark.crossref.org/dialog/?doi=10.1007/s10699-016-9494-7&domain=pdf
http://crossmark.crossref.org/dialog/?doi=10.1007/s10699-016-9494-7&domain=pdf


level of abstraction and materials used, they all suggest that there is no there because it is

all here in a view where ‘‘all the points in space along the path of observation occupy the

same location simultaneously’’ (Shlain 2007, p. 188). Such an intellectual evolution in the

way of thinking the notion of representation echoed scientific debates that emerged in the

early twentieth Century in physics. There exists a specific literature showing that Cubism

serves very well to illustrate the conceptual shift generated by the scientific environment at

that time. Among other works, one can mention, for instance, Laporte (1966), Richardson

(1971) and Fry (1988) who studied the potential link between Cubism and the Einsteinian

relativity, Fauchereau (1982), Vargish and Mook (1999) or Henderson (2013) who

investigated the influence of no-Euclidian geometry on Cubism or Shlain (2007) and

Willette (2012) who rather discussed how Cubism, by using neutral tones, dull colors and

specific contour drawing would have tampered the expression in painting in accordance

with an increasing importance of science in society.

This article aims at contributing to these debates between Cubism and science by

focusing on a very specific point: the influence of Cubism on Niels Bohr’s works. So doing,

this paper offers a contribution to the history of scientific ideas by proposing an episte-

mological argument in favour of the assumption made by Miller whereby Niels Bohr has

been influenced by a particular form of Cubism (Jean Metzinger) when he developed his

non-intuitive complementarity principle.

2 Miller’s Assumption on the Visual Dimension of the Principle
of Complementarity

In the 1920s, the physicist Niels Bohr understood that the classical visual representation of

the atom (a solar metaphor in which the atom’s nucleus acts as the central sun while its

electrons move in planetary orbits) was inappropriate. At that time, recent experimental

evidence suggested that the atom should simultaneously be seen as a corpuscular and as a

wave object. The idea that an electron could be both wave and particle generated much

debate and it confused scientists, for whom these two perceptions appear to be ontologi-

cally incompatible. Beyond the scientific/ontological debates, this particle-wave duality

could also be looked upon as a challenge from a visual (or artistic) point of view. Such a

duality was difficult to represent visually because its two components are seemingly in

opposition: a particle is often visually represented as a dense body (as a point or a geo-

metric form) while a wave is usually seen as a wavy line or curve.

In 1927, Bohr modified this common way of thinking by proposing his complementarity

principle, in which the atomic level is no longer governed by the Newtonian perspective

based on interrelated electrons in space and time. This atomic level must instead be

analysed using a wave-particle duality framework within which an electron is seen as the

sum of its wave and particle properties complementing one another. Depending on the

experimental configuration, electrons can exhibit either their wave or particle modes of

existence, not both.

How Bohr conceived this complementarity view is sometimes presented as a puzzle in

the history of scientific ideas (Miller 2001, p. 395). The complementarity principle can be

metaphorically assimilated to psychological studies about the simultaneous existence of

reason and emotion and the notion that ‘‘we are both onlookers and actors in the great

drama of existence’’ (Favrholdt 1999, p. 40). In this context, several authors have discussed

the potential influences of psychology on Niels Bohr’s complementarity principle. For

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Holton (1970) and Feuer (1974), Kierkegaard, James and Hoffding played an intellectual

role in the development of this principle. In the same vein, Pind (2014) explained that

Rubin (who was Bohr’s second cousin) also influenced the Danish physicist in his con-

ceptualization of the dual complementarity. It bears mentioning that these influences still

generate a lot of debate since Pais (1991), Favrholdt (2009) and Kragh (2012), for example,

argued that none of the philosophers previously evoked had any influence on Bohr (see

Kragh 2012; or Favrholdt 2009 for further details on this point).

In this article, I will not address these links between simultaneous dualities coming from

psychology and the development of the complementarity principle but will rather inves-

tigate the visual dimensions which potentially inspired Niels Bohr when he worked on this

principle. According to Miller, a part of the solution can be found in the historical influence

of cubism on Bohr’s way of thinking. About this influence, Miller (2001) wrote, ‘‘The

connection with Cubism (Metzinger) is straightforward and not accidental.’’ However,

Miller never explained in details why he thought that this influence is straightforward. All

contextual information provided by Miller in his remarkable works informed us about how

a link can be made between Bohr and Cubism but a question is still open: what is the

intellectual reason for why one can consider a straightforward link between them? This

specific question is at the origin of this article. In different references Miller (1995, 2001)

gave historical indications about this relationship between Cubism and Bohr’s works like,

for instance, that, in the early 1930s, Bohr moved into a mansion (owned by the Carlsberg

Foundation), which he refurbished by buying a Cubist painting (Woman on a horse,

Metzinger).

This painting (Fig. 1) represents a woman on a horse in a fuzzy and geometrical

juxtaposition of facets breaking the image into a provocative multiplicity of perspectives.

Although this painting represents an object that, at first sight, could appeared as frag-

mented, it rather offers ‘‘a representation of visual fragments that are rearranged so that the

viewer would not have to move through space in an allotted period of time in order to view

them in sequence. Visual segments of the front, back, top, bottom and sides of an object

jump out and assault the viewer’s eye simultaneously’’ (Shlain 2007, p. 189). Combined

with the book entitled Du Cubisme, this painting is usually presented as a telling example

of cubist simultaneity as explained by Fauchereau (1982), Cottington (2004) and Shlain

(2007).

The purchase of this painting by Bohr, combined with the testimonies of Mogens

Andersen (Bohr’s friend and Danish artist), led Miller to assume that Metzinger had had an

influence on Bohr’s way of thinking: ‘‘this choice [purchase of the Metzinger’s painting by

Bohr] indicates quite an interest in Cubism perhaps [by Bohr], a clue to yet another path to

complementarity—that is assuming that Bohr knew about Metzinger prior 1927’’ (Miller

2001, p. 189, my italics). In the following sections, I will investigate this assumption,

whose significance goes beyond the mere historical\contextual influence of Metzinger on

Bohr. Actually, this plausible influence of Cubism on Quantum Physics goes beyond

Miller’s claim since it echoes a vast literature about the epistemic dimension of art and the

extent to which art can contribute to an improvement of knowledge (Klinke 2014).

Jean Metzinger (1883–1956) was a French painter, writer and theorist who was initially

influenced by neo-impressionism before joining the Cubist movement in 1907. Although

Metzinger produced several pieces of art in which he explicitly showed his adhesion to

Cubism,
1
he is nowadays well known for having been at the center of Cubism as one of the

first theorist to identify the movement when it first emerged. Metzinger is sometimes

1
See Serullaz (1963) or Robbins (1985) for an exhaustive list of Metzinger’s paintings.

From Cubist Simultaneity to Quantum Complementarity 711

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presented as a cubist painter ‘‘without daring’’ (Serullaz 1963) who is more famous for his

conceptual understanding of the movement that, along with another cubist (A. Gleizes), he

summarized in a book entitled Du Cubisme (1912). As almost all painters involved in

Cubism, Metzinger had several periods in his work: between 1907 and 1913, his works

corresponded to what art specialists called ‘‘Analytic Cubism’’ that ‘‘describes the early

phase of cubism, generally considered to run from 1908 to 1912, characterized by a

fragmentary appearance of multiple viewpoints and overlapping plane’’ (Tate 2016). The

major characteristics of this Cubism refers to the rupture with the classical tradition and the

importance of the multiple perspectives giving a feeling of simultaneity in the vision

(Serullaz 1963). Starting from 1913, Serullaz (1963) explained that Metzinger tried to

follow unsuccessfully the Synthetic period of Cubism that mainly corresponded to a

systematic used of collages and other materials in works. This evolution showed a more

colourful Cubism with simpler lines and shapes introducing some elements of reality in the

works. This evolution of Cubism was not really in accordance with what Metzinger was

doing and progressively distanced himself from Cubism to focus more on what he called a

‘‘realisme constructif’’ (Metzinger 1972).

In this article will focus on the Metzinger’s Analytic Cubism in order to understand its

potential impact on Bohr’s works. There are some works on the Metzinger’s Cubism and

its influence on science generated much debates among scholars. Lehrer (2011) wrote, ‘‘It

is hard to believe that a work of abstract art might have actually affected the history of

Fig. 1 La Femme au Cheval (Woman with a Horse), 1911–1912, Jean Metzinger, oil on canvas,
162 cm 9 130.5 cm (63.8 in 9 51.2 in), Statens Museum for Kunst

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science. Cubism seems to have nothing in common with modern physics’’ (this claim could

be reinforced by Laporte 1966 or Richardson 1971). These doubts call for an additional

argument to support Miller’s perspective. The purpose of this article is to offer an addi-

tional argument and to contribute to these debates by providing an epistemological reason

for why the association between Metzinger’s Cubism and Bohr’s works is intellectually

justified. In the rest of the paper, I will identify what Bohr found in Metzinger’s cubism.

That question led me to identify the Bergsonian durée (with its diachronic simultaneity) as

the epistemological bridge between Metzinger and Bohr, confirming Miller’s claim

according to which Cubism has influenced Niels Bohr in his conception of the comple-

mentarity principle.

3 From Metzinger’s Simultaneity to Complementarity in Physics

In 1911, room 41 of the Salon d’Automne organized in Paris exhibited a collection of

cubist experimentations presented as a rivalry with the futurist paintings (Cottington 2004,

p. 74). Although ‘‘simultaneity’’ was a buzzword for both of these artistic movements, they

did not use the term to refer to the same concept: futurists mainly painted a visual per-

ception of simultaneity by working on the cinematographic depiction of movement while

cubists dealt with a geometric understanding of simultaneity. The futurist simultaneity

refers to the simultaneous representation of all subsequent events, but it does not deal with

the visual dimensions/perspective of these subsequent events. In contrast, cubists focused

on a diachronic simultaneity, in which all visual aspects are holistically captured by

juxtaposing all successive aspects of an object in a single pictorial entity. On this point,

Vargish and Mook (1999, p. 69) wrote, ‘‘When early analysts of Cubism spoke about

simultaneity, they meant the representation in cubist art of more than one perspective or of

what would represent more than one perspective in the traditional of optical verisimili-

tude’’. This simultaneity is called diachronic simply because this holistic perception of all

dimensions is captured as a unique image directly dependent on the observer’s perspec-

tive—any physical or temporal changes would therefore generate a new visual represen-

tation. According to Cottington (2004), the importance of diachronic simultaneity lies in

the visual representation of the Bergsonian durée reasserting temporal continuity/unity.

The difference between Cubism and Futurism is clearly explained in the now famous book

entitled Du Cubisme (1912), written by Metzinger and Gleizes in 1912 who contrasted this

sense of simultaneity: ‘‘the fact of moving around an object [like Cubists do] to seize it

from several successive appearances, which, fused into a single image, reconstitute it in

time’’—in contrast with—‘‘those [futurists] who mistake the bustle of the street for plastic

dynamism will eventually appreciate the differences’’ (Gleizes and Metzinger 1912, p. 15).

The book Du Cubisme played an important role in Miller’s assumption since he

assumed that Niels Bohr has read the book before buying Metzinger’s masterpiece: ‘‘Since

Bohr read widely we can safely assume that he read their [Metzinger and Gleizes] book

before 1927.’’ I claim here that what is important in the potential influence of Metzinger on

Bohr’s work is the holistic understanding of the concept of simultaneity promoted by the

cubist painter in Du Cubisme. By codifying diachronic simultaneity as the ‘‘programmatic

means [of cubism] to the representation of Bergsonian durée’’ (Bergson 1911, p. 94),

Metzinger opened the door to the idea of complementarity. The Bergsoninan durée refers

to a theory of consciousness according to which heterogeneity and continuity of phe-

nomena can be unified in a consistent way. Precisely, the durée can be conceptualized as a

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unified flow of reality (i.e. unified way of perceiving reality). In this perspective, Bergson

considered that space and time are not a void that would be filled by reality. Phenomena are

not in space and time but, conversely, the latters are in the former. In other words, time

cannot be seen as a multiplicity of moments neither as an abstract eternity—time represents

a heterogeneous whole that continually interact with space in a constantly changing flux of

renewal. This non-ending and simultaneous repetition of time and space in things can be

seen as the Bergsionian durée.

By promoting a holistic perspective where all aspects (even those which are not visible) of

an object are depicted in a single image, Metzinger proposed a visual interpretation of

Bergsonian simultaneity which refers to the idea that ‘‘the real Whole has no parts but is

repeated to infinity, each time integrally (though diversely) within itself, and that all these

repetitions are complementary to each other’’ (Bergson 1911, p. 351). The interest of Met-

zinger in Berson’s simultaneity was evidenced in an article published in 1913 in a daily

newspaper (‘‘Celui qui ignore les cubistes’’, G.M, L’Eclair, 29th of June, 1913)—this interest

has also been evoked by Antliff (1988, p. 341) who wrote ‘‘I believe that Du Cubisme was

written with Bergson in mind’’. The diachronic simultaneity promoted by Metzinger implied

a Bergsonian complementarity in which all visual aspects of an object (colours, shadows,

perspectives etc.) combine with each other in a complementary but unique cubist image. In

this context, cubism can be seen as a visual translation of the unextended durée into an

extended and homogeneous multiplicity or juxtaposition of distinct but complementary parts.

In line with Bergson’ simultaneity, Metzinger did not promote an absolute simultaneity nor

the possibility of having a simultaneity of spatially separated events. Although time, motion

and all visual aspects of an object are pictorially fragmented, they are chosen and rearranged

by the artist (the observer), permitting the viewer to see them in a single image which is

contextually defined: any changes in time or in the observer’s perspective would imply a

modification of the image. In accordance with the Bergsonian durée, Metzinger’s simul-

taneity emerged as a unique event (image) repeated ad infinitum.

According to Miller, the influence of Metzinger on Bohr’s way of thinking has two

sources: the purchase of the painter’s masterpiece Woman with a horse and a potential

reading of Du Cubisme. I support this claim by arguing that Bergsonian simultaneity is the

epistemological bridge between Metzinger and Bohr. Indeed, when Bohr (1928) defined

his principle of complementarity, he implicitly referred to a Bergsonian form of comple-

mentarity in which the atomic particle-wave duality must be looked at as a single phe-

nomenon (Lofgren 1992). By considering that an electron can be seen as the sum of its

wave and particle properties, which complement one another, the principle of comple-

mentarity assumed a diachronic simultaneity (wave and particle at the same time in a

single phenomenon). The influence of Bergsonian durée on modern physics is well doc-

umented (Guerlac 2006) but what is interesting for this paper is the parallelism between the

Bergsonian concept of durée and the principle of complementarity, which, for both Met-

zinger and Bohr, appears as an epistemic way of understanding a fragmented world.

Although all situations are physically composed of a large number of parts, these parts are

perceived, at every moment (and ad infinitum), as a complementary unified perception of

time (durée). In the same vein, although the universe appears to be fragmented through two

incompatible descriptions of matter (particle-wave duality), the complementarity principle

proposed by Bohr offers an epistemic way of understanding that complex world as a

unified perception at a specific time. This parallelism led Louis de Broglie (1969) to

suggest that Bergson anticipated the conceptual framework developed by Bohr. The

complementarity principle defined by Bohr implied a Bergsonian durée (with its diachronic

simultaneity) that the physicist has possibly found in Metzinger’s works. This influence of

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the painter on Bohr is enhanced by the idea that, although the perspective (or explanation)

given by the observer is presented as a unique image (event), it is directly associated with

the angle of observation taken by the observer. As Bohr (Bohr 1928, p. 580) wrote, ‘‘in the

description of atomic phenomena, the quantum postulate presents us with the task of

developing a ‘complementarity’ theory the consistency of which can be judged only by

weighing the possibilities of definition and observation’’. Regarding the visualization of

this theory, the physicist wrote, in accordance with the cubist style, ‘‘a more compre-

hensive generalization of the complementary mode of description will demand a still more

radical renunciation of the usual claims of so-called visualization’’ (Bohr 1937, p. 294).

The elements presented here support Miller’s claim that the analytic cubism of Metzinger

had a significant influence on the Bohr’s way of thinking.

4 Conclusion

In different places, Arthur Miller (1995, 2001) claimed that Metzinger’s Cubism influenced

the Bohr’s works. Although Miller gave historical and contextual evidences showing how

this influence operated, he did not explain why the association between Cubism and Bohr’s

works is intellectually founded. The contribution of this article is to offer an epistemo-

logical argument supporting the assumption made by Miller whereby Niels Bohr has been

influenced by Cubism (Jean Metzinger) when he developed his non-intuitive comple-

mentarity principle. I explained here that the plausible conceptual bridge between Cubism

and Quantum Physics is the concept of Bergsonian durée. More precisely, I identified a

parallelism between the Bergsonian concept of durée and the principle of complementarity,

which appear, for both Metzinger and Bohr, as an epistemic way of understanding a

fragmented world: the physicist and the painter considered that, although all situations are

physically composed of vast numbers of parts, these parts are perceived, at every moment

(and ad infinitum), as a complementary unified perception of time (durée).

This article is a contribution to the field of history of scientific ideas in which there is,

unfortunately, very few historical (physical) evidences. By definition, the history of ideas

implies another ‘‘proof regime’’ which is rather based on what philosophers of science call

a ‘‘rational reconstruction a posteriori’’ (Lakatos 1978). This paper is a telling example of

such as rational reconstruction that refers to a combination of plausible historical facts

(enhanced by Arthur Miller) with a rational\logical reasoning (proposed in this paper).

Beyond the contribution to the history of scientific ideas evoked above, this short paper

also emphasizes that art can also play a key role in the development of human knowledge.

Indeed, while one can find a lot of articles on how art is influenced by science, this paper

suggests the reciprocal link since science can also be influenced by art.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 Inter-
national License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made.

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History Unstuffed Publications.

Christophe Schinckus Christophe is Senior Lecturer in Finance at the University of Leicester, he published
more than 50 papers in peer-reviewed journals. He is currently finishing on a book on Econophysics (Oxford
University Press) while doing a second Ph.D. in Philosophy of Science at the University of Cambridge.

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http://www.tate.org.uk/learn/online-resources/glossary/a/analytical-cubism
http://www.tate.org.uk/learn/online-resources/glossary/a/analytical-cubism

	From Cubist Simultaneity to Quantum Complementarity
	Abstract
	Introduction: Cubism and Science
	Miller’s Assumption on the Visual Dimension of the Principle of Complementarity
	From Metzinger’s Simultaneity to Complementarity in Physics
	Conclusion
	Open Access
	References