Revealing Affinities between Art and Science

Philip F. Palmedo studied art history and physics as an undergraduate at Williams College, and received his PhD in nuclear engineering from MIT. He carried out nuclear reactor physics research at the French nuclear laboratory at Saclay and at Brookhaven National Laboratory. He then initiated and headed the International Resources Group and the Long Island Research Institute. He has written extensively in many areas, including several books on modern sculpture. His most recent book is ‘Deep Affinities: Art and Science’, on which this article is based.

When did art originate? And why? How about science: when did that first appear? And was there any connection between the two – at their origins and through time? Those are the basic questions that I explore in this article. It turns out that the origins of art are far easier to identify than the origins of science. But the abundant physical evidence for the origins of our aesthetic instincts provides clues for the origins of science.[1]

Let’s start with what have been called “the first artists,” those who painted the walls of caves some 40,000 to 15,000 years ago (known as the Upper Paleolithic period).

Fig. 1 Chauvet Cave. Panel of the Lions, 35,500 -31,500 BCE. Official replica.

There have been many explanations for cave art but all have been criticized for lack of supporting evidence. But it is generally agreed that cave art was some form of communication, most probably intended to affect the understanding or behavior of those who experienced it. Thus, the artists must have been concerned with effectiveness. In viewing a work of representational art, two kinds of recognition come into play. First is the recognition of something in the real world, a horse or a tree. Then there is a more subtle form of recognition, of aesthetic qualities – lines, forms, and colors. It is the combination of those two aspects that accounts for the effectiveness of a work of representative art. Effectiveness also entails what Paul Bahn  and Jean Vertut call a “schematization,” the reduction of a figure to its essential traits.[2] That concept of “essential traits” brings us close to the nature of science.

Fig. 2 Signs in the cave of El Castillo

There are other paintings in caves that relate to science: the groups of dots and geometric forms that appear on many cave walls. There are several elements at the origin of science. The most fundamental is careful, curiosity-driven observation of the natural world. That is also the starting point of art. Then, after the idea of numbers (which we get from our animal ancestors), the recognition of concepts such as time, velocity, and weight, and the application of numbers to those concepts. Then the recognition of relationships between those concepts. Further on, the representation of those concepts by symbols, V for velocity, M for mass, and so forth. And, finally, discovering and representing those relationships by equations. Here, in the geometric signs in Upper Paleolithic caves, we see the first evidence of the use of symbols. We don’t know what they mean, but the fact that there is a finite number of them, and that they are repeated in many caves, indicates that they did have meaning.[3]

Fig. 3. Upper Paleolithic cave signs. From von Petzinger[4]

Early humans, our hunter-gatherer ancestors, were faced with a baffling, chaotic natural world. Their survival depended on figuring out nature but they had no concept of the physical laws that nature obeyed. Those who had a greater curiosity and sought regularities and patterns in nature had a higher probability of survival. Humans were equipped to find that order by a highly evolved visual system from the eye to the visual cortex. That system automatically separated patterned signal from noise.[5] The early seeking of order in nature was at the origin of both art and science.

By the time humans found their way to Europe and started to produce cave paintings, figurines, and the abstract signs on cave walls, their minds were highly developed. The earliest cave paintings were as sophisticated as the later ones. And the walls of caves in Indonesia were being decorated at the same time as the earliest paintings on the walls of French and Spanish caves. We have to search much further far back in time to find the actual first artists.

It is fortunate for those of us who are curious about human evolution that our ancestors evolved where there were rocks and stones, for the dominant physical evidence we have of how early humans interacted with their environment is the vast number of stone tools that have been unearthed and studied.  Hand axes evolved with humans over something like a million years, but around 700,000 BCE, for some individuals in some places, the form itself took on more importance than the function.

Fig. 4. Hand axe from Kathu Pan, South Africa, ironstone, 9¼ × 4½ in. c. 600,000 BCE. McGregor Museum, Kimberley, South Africa.

The clean shapes and perfect symmetry of these hand axes were achieved at a huge cost of time and effort with no practical benefit. They were the first crafted aesthetic objects, the first sculptures. A hand ax found at Kathu Pan, South Africa, and dating to 600,000 BCE is a fine example. Note that this was crafted some 300,000 years before our species, Homo sapiens, first appeared.

Symmetry would be a fundamental characteristic of both art and science. During our evolution, having two equally strong legs, and arms, and eyes had survival value. Symmetry is built into our shape, and into our genes. There are various kind of symmetry, and we are bilaterally symmetric, as famously depicted by Leonardo da Vinci in his Vitruvian man. Note that Leonardo connects our symmetry to geometry, to the square and the circle.

Fig. 5. Leonardo da Vinci c. 1490  Pen and ink with wash over metalpoint on paper. 13.6 in × 10.0 in. Gallerie dell’Accademia, Venice, Italy

The second root of our taste for symmetry is in nature. Survival value could be ascribed to early humans’ appreciation of formal aspects of the outside world. Nature is not symmetrical throughout, but the parts of nature that are symmetrical in some way tend to be important. They are the plants and animals on which our survival depended. Asymmetry indicates abnormality, in an animal being hunted or a fruit being gathered.

Fig. 6. Symmetrical Ascidiacea (sea squids) from Ernst Haeckel.[6]

The symmetries found in nature derive from the symmetrical laws of biophysics that are the foundations of the processes of growth. Small deep-sea organisms can be spherically symmetric, for in their domain they float in zero net gravity and have no preferred direction of movement. It’s been shown that insects prefer symmetrical flowers of a given species. That preference might have stemmed from the fact that healthy, symmetrical flowers produce more pollen, but it has become an independent – aesthetic – preference.

Fig. 7. Ancient Greek frieze pattern showing linear symmetry and mirror symmetry around a vertical axis.[7]

Symmetry is a recurrent theme in the art of diverse cultures through time and space. There are few architectural buildings from the Parthenon to the Taj Mahal, and down through the ages, that don’t display some degree of symmetry.

Fig. 8. Taj Mahal. Agra, Uttar Pradesh, India. Completed 1653.

It was Thales of Miletus, in the 6th century BCE, who first declared the grand symmetry: that everything in the world is governed by natural laws. Cycles and circles were integral parts of that origin of science. It was also the ancient Greeks who demonstrated that the earth was round (and measured its diameter quite accurately). Symmetry is a form of invariance, on rotation or reflection; but also posits that physical things behave the same here as they do there. When Newton declared that the force that kept the planets in their orbits was the same force that brought the apple to earth, he was declaring a grand symmetry. Ever since the days of Newton, the concept of symmetry has played an important role in science, and is a fundamental tenet of modern physics. Beneath specific explanations, or laws, there are fundamental beliefs or hypotheses. The most fundamental is that the universe has universal regularities, or laws, and that there are symmetries in space and time.

Einstein’s thinking that produced his theory of special relativity reveals the scientist’s concern with symmetry and its connection with simplicity. The first sentence in Einstein’s revolutionary 1905 paper (titled “On the Electrodynamics of Moving Bodies”) reads, “That Maxwell’s electrodynamics – as usually understood at the present time – when applied to moving bodies, leads to asymmetries that do not appear to be inherent in the phenomena is well known.” Einstein was concerned with the inconsistency between how Maxwell’s theory considered a conducting coil passing by a magnet and a magnet passing by a coil. Einstein found the existence of two views, this asymmetry, as “unbearable.” The more holistic view presented in his paper eliminated the redundancy and thus created a “simpler” explanation.

In modern physics, mathematics is taken to reveal physical truth. That, and the underlying belief in symmetry drove the search for new particles in the early twentieth century. Paul Dirac published a paper in 1931 that predicted the existence of an as-yet-unobserved particle that he called an “anti-electron” that would have the same mass and the opposite charge as an electron and that would mutually annihilate upon contact with an electron. The prediction was based on a belief that since the equation describing the electron had that solution, that particle had to exist. That belief was based on the principle of the deep symmetry of nature. The positron was discovered the next year. In his Nobel Prize speech in 1933, Dirac, on the basis of symmetry being “really fundamental in nature,” also predicted that the positively charged proton would have its negatively charged counterpart. The anti-proton was found experimentally twenty-two years later.

The goal of physics is to provide a complete mathematical description of the physical world. At the end of the 19th century, it seemed that we were close to achieving that objective, but as the 20th century progressed the picture became ever more complex. There are four forces at work in the universe, but the best model we have of microscopic phenomena describes only three of them. The theory that includes gravity, the theory of general relativity, doesn’t connect with our description of the very small.

The hypothetical model that would reconcile the two descriptions of the world, of the very small and the very large, is termed Supersymmetry.  A paradigm of the belief in symmetry, that model posits a number of new particles, symmetric to existing ones. Unfortunately, experiments have not found those particles. But, as Leon Lederman expresses it, the language of that quest has been learned, and “whatever new answers are found, and deeper questions spawned, about the universe or its mathematical fabric, at the center will be symmetry.”[8]

Our early ancestors were faced with a seemingly chaotic world. Those who were curious, who looked for order in that chaos and found it, and found ways of communicating it, became the first artists and scientists. Hundreds of thousands of years later, their descendants painted the walls of caves around the world. Of the first instances of order those early humans found in nature, symmetry is the deepest and most resilient. It has formed a foundation of both art and science since before the emergence of our species, and constitutes a profound link between those two domains.

There are kinds and degrees of symmetry, and the purest symmetrical geometric shapes are the circle and sphere. The circle may well have been at the origin of humans’ recognition of pure form. As expressed by Black Elk, holy man of the Oglala Sioux:

…everything the Power of the world does is done in a circle. . . . The wind, in its greatest power, whirls. Birds make their nests in a circle, for theirs is the same religion as ours.”[9]

It’s silly romanticism to think that our concept of geometric form arose from a single event, but imagine an early human noticing the perfect circles made by water dripping into a pool from the roof of a cave and relating it to the circle of her friend’s eye. In contrast to

Fig. 9. Charles Yoder, Tree Rings, 2012. Linocut 16 x 27 in.

the chaotic natural world around her, she saw perfect circles. That evening she may have noted the circular moon, seen a circular spider’s web, or noted the circular splash of a flower’s petals, and thus acquired the concept of circularity. I’ll go as far as imagining the pleasure the young woman took in finding those examples of a pervasive order in nature.

Some early structures indicate that the circle was fundamental to our first concept of the heavens. One example is the Goseck Circle, in Germany. Constructed around 4900 BCE, it consists of a structure some 275 ft. in diameter, with concentric ditches, low earthen ramparts, and wooden palisade walls that have been reconstructed by archaeologists. The walls have pairs of openings aligned with the sunrise on summer and winter solstices.

Fig. 10. The reconstructed Goseck Circle, Saxony-Anhalt, Germany.

Humanity’s first conceptual models of the universe were based on the symbols of nature’s perfection: the circle and the sphere. By the sixteenth century we have artistic representations of those models, with the earth at the center. In the seventeenth century, the illustrations moved from the geocentric Ptolemaic system to more elaborate renderings of the heliocentric Copernican one, but the circle still dominated These celestial maps are some of the first examples of the use of artistic means to present scientific concepts.

Fig. 11. Oronce Fine, Illustration of the Ptolemaic system, “Le Sphere du Monde,” 1549, fol 8v. Houghton Library, Harvard University, Cambridge, MA

The fifteenth-century Catholic mystic Nicholas of Cusa referred to God as “an infinite circle whose center is everywhere and whose circumference is nowhere,” but the idea also had a sternly literal presence in dogma and in the minds of believers. The pure circle was deeply embedded in the human aesthetic/scientific consciousness. Johannes Kepler struggled for years to explain why Tycho Brahe’s observations deviated from Copernicus’s circular planetary orbits. He hesitated to accept the solution of elliptical orbits because he believed that God, in his perfection, would use only the perfectly symmetrical spherical shape when he designed his universe. But Kepler’s belief in mathematics, and the simpler explanation of the observations, finally convinced him.

The cycle is the temporal version of the circle. In Hindu sculpture, the circle of fire that surrounds Shiva represents the concept of the never-ending cycle of time, of life being reborn. The connection between the circle and the cycle of life is a concept so widespread across time periods and cultures that its origins must have been early and profound. It is reasonable to think that early humans had a sense of the circle that went deeper than simply observing it in nature. The cycle of day and night, the cycles of the moon, the cycles of the year, on which their lives depended, must have created a psychological sense of the importance of that fundamental shape.

Fig. 12. Shiva as Lord of Dance (Nataraja), c. 11th century, Copper alloy 26 7/8 in. x 22 1/4 in. diameter. Metropolitan Museum of Art, New York

The life of the circle in art was accentuated with the birth if modernism. At the origins of pure abstraction in 1913 (the year of the Bohr-Rutherford atomic model), Kazimir Malevich radically presented a painting of a black circle as a work of art. Even today there are few modern museum or gallery spaces where a circle doesn’t appear. In March of 2021, New York’s Metropolitan Museum of Art installed on its façade sculptures by Carol Bove featuring circles.

Fig. 13. Carol Bove, The séances aren’t helping. 2021. Stainless-steel and aluminum. 15 x 5 ft. Metropolitan Museum of Art, New York

In seeking the order in nature, we observed her underlying structure determined by physical laws, what Piet Mondrian called the “mutual relations that are inherent in things.”[10] Circles are not the only mathematical – and aesthetic – forms that we discover in nature. There are fractals, forms that repeat at different scales and there are logarithmic spirals: spirals where the spaces between successive curves have a constant ratio (a form of continuous fractal).

Fig. 14. Cutaway of a nautilus shell compared with a logarithmic spiral.

The laws that control the growth of the nautilus sea creature result in a logarithmic spiral. And huge galaxies take the same form.

Fig. 15 Whirlpool Galaxy, M51A.   NASA and the Hubble Space Telescope team

The spiral had spiritual meaning for many ancient civilizations, symbolizing the continuity of life and the eternal. In part because of that connection, the sculptor Robert Smithson, when he became dissatisfied with the commercialization of the art world, went into nature and created his Spiral Jetty, a giant 1,500 ft. long construction in Utah’s Great Salt Lake using 6,650 tons of earth and rock.

Fig. 16. Robert Smithson, Spiral Jetty, 1970 (Great Salt Lake, Utah) (photo: Gianfranco Gorgoni) ©Holt-Smithson Foundation

If art and science are as close as I maintain, then the making of art and the making of science should have similarities. After all, the origins of both art and science go back to the days when our early ancestors sought patterns in nature: order in the chaos that surrounded them. And indeed, the nature of the creative act, and the human emotions that accompany it, are remarkably similar in art and science, particularly at the highly creative extremes. Creativity in both areas involves understanding the current state of the field and taking a leap beyond the boundary. Although artists now avoid the word beauty, scientists often cite the search for beauty as their motivation. Einstein often evoked beauty as the ultimate criterion for the validity of a scientific explanation.

An identical feeling was expressed by James Watson and Francis Crick when they started to perceive the likely structure of DNA. When the two scientists almost completed the structure there was uncertainty whether the two bases that bridged the two helixes had the right dimensions. But they told each other that “a structure this pretty just had to exist.”[11]  It was Paul Dirac, the predictor of the positron, who stated that “it is more important to have beauty in one’s equations than to have them fit experiment.”[12]

When success arrives, when scientists achieve the “eureka” moment, they often describe their reaction in aesthetic terms. In 1957, Richard Feynman and Murray Gell-Mann developed a theory of the interactions between fundamental particles. The theory did not agree with some recent experiments but had aesthetic qualities that convinced its authors. Feynman described the moment of discovery: “There was a moment when I knew how nature worked. It had elegance and beauty. The goddamn thing was gleaming.”[13]

Given all the connections between art and science it’s difficult to point to a central connecting concept, but if you pushed me into a corner and insisted, I would say it was that basic, difficult to define concept that lies deep within us, the idea of beauty: the notion of beauty that was instilled in our brains as we succeeded in the process of evolution. Beauty has a deep and remarkably similar role in our creation and appreciation of art and of science separately. And I would maintain that beauty also describes the deep affinities between art and science. That relationship is gleaming.


[1] This article derives from the much more extensive discussion contained in my book, Deep Affinities: Art and Science, published by Abbeville Press in 2020.

[2] Paul G. Bahn and Jean Vertut.. Journey Through the Ice Age. Berkeley: University of California Press. 1997, p. 167

[3] For an analysis of these symbols, see Genevieve von Petzinger, The First Signs: Unlocking the Mysteries of the World’s Oldest Symbols. New York: Atria. 2016.

[4] Genevieve von Petzinger, The First Signs: Unlocking the Mysteries of the World’s Oldest Symbols. New York: Atria, 2016.

[5] Derek Hodgson, The Roots of Visual Depiction in Art. Newcastle upon Tyne: Cambridge Scholars Publishing, 2021, p. 7-10.

[6] Ernst Haeckel, Art Forms in Nature, New York: Dover Publications, 1974.

[7] Peter S. Stevens, Handbook of Regular Patterns: An Introduction to Symmetry in Two dimensions. Cambridge, MA: MIT Press.1980, p.3

[8] Leon Lederman and Christopher T. Hill, Symmetry and the Beautiful Universe. Amherst, NY: Prometheus Books. 2004, p. 289.

[9] The passage continues; “…our teepees were round like the nests of birds, and these were always set in a circle…. But the Wasichus (white men) have put us in these square houses. Our power is gone and we are dying.” Nicholas Black Elk as told through John G. Niehardt, Black Elk Speaks: Being the Life Story of a Holy Man of the Oglala Sioux, Lincoln NE: University of Nebraska, 2000.

[10] Piet Mondrian, Plastic Art and Pure Plastic Art.  San Francisco: Wittenborn Art Books, 2008, p. 52 (essay first published in 1936).

[11] James D. Watson, The Double Helix. New York: Athenium Press. 1968. p. 205

[12] P. A. M. Dirac, “The Evolution of the Physicist’s Picture of Nature,” Scientific American, Vol.  208, No.5, 1963.

[13] Lawrence M. Krauss, Quantum Man: Richard Feynman’s Life in Science. New York: W. W. Norton, 2011, p. 216.


DEEP AFFINITIES: Art and Science

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