Smart wax, honeycomb

The venerable institution of higher learning I Fucking Love Science reposted a TED-ed video called “Why Do Honeybees Love Hexagons” that raises some interesting questions about the thinking habits of bees. In it, educators Zach Patterson and Andy Peterson contend that honeybees are “excellent mathematicians.” Not only can they “calculate angles,” but they can “comprehend the roundness of the earth.”

Claims about the geometrical genius of bees have been pretty standard in descriptions of bees since antiquity. In describing the wax structure or hexagonal comb characteristic of beehives, first-century Roman natural historian Pliny wrote, “all cells are hexagonal, each side being the work of one of the bee’s six feet.” 1 Writers of a medieval bestiary asked, “What architect taught them to fit together six-sided chambers with their sides undistinguishably equal?” 2 The Italian Renaissance philosopher Federico Cesi claimed that “people praise the architecture and mathematics of the bees, and those are disciplines in which so many men are unskilled.” 3 Indeed, waxed Charles Darwin, “he must be a dull man who can examine the exquisite structure of a comb, so beautifully adapted to its end, without enthusiastic admiration.” 4

The Hive-Making Instinct

Bees, it has been long known, have managed to figure out that the hexagon is the most efficient shape not only for storing honey, but for conserving wax. Wax is a precious resource: bees produce it by processing honey in their own bodies and excreting wax from glands on their abdomen. It takes 7 or 8 pounds of honey to produce a single pound of wax, and it takes the nectar of something like 2 million flowers to produce a single pound of honey. A single bee in its lifetime will produce only around 1/12th of a teaspoon of honey. This means that a pound of wax requires the lifetime labor of around 7300 bees visiting 15 or 16 million flowers, if my math is correct (but I’m no bee so double check this. 5

Darwin first speculated that bees might have evolved their economical engineering instinct through natural selection. Wax production is a key limitation on bee colony success: it makes sense that the colonies that stored the most honey with the least wax would have a survival advantage. And over time, this very material advantage would be passed on to future colonies in the form of higher reproductive success rates, which would in turn result in selection for instincts that improved upon the hive design until it reached maximum efficiency:

The motive power of the process of natural selection having been economy of wax; that individual swarm which wasted least honey in the secretion of wax, having succeeded best, and having transmitted by inheritance its newly acquired economical instinct to new swarms, which in their turn will have had the best chance of succeeding in the struggle for existence. 6

That’s a very different way to describe the hive-making instinct than saying, as the TED video does, that bees have managed to “figure out” the best way to make a hive: they first “decide what the cells should be made out of,” they “may have noticed problems in their design,” and finally they “found that the hexagon was the ideal storage space” after much “trial and error.” This kind of language makes it seem that hive construction is the result of conscious choices on the part of bees: they learn and pass this learning on to the next generation.

At heart lies the question of whether bees can learn, decide, and comprehend the way we do, as the TED video states and as thinkers have thought for ages. That kind of anthropomorphic language would seem to take us far afield of natural selection. In other words, can we really understand what it means, as they say, “to think like a bee?” Or is any such attempt merely an exercise in anthropomorphism, in imposing human thought processes on an inhuman world?

In this, Darwin is little help, since he himself might have introduced a ghost in the machine–that is, he might have suggested something like intelligence where there is none. Like the TED video, Darwin argues that the cell-making instinct is not perfect. Bees make mistakes. They start over:

It was really curious to note in cases of difficulty, as when two pieces of comb met at an angle, how often the bees would pull down and rebuild in different ways the same cells, sometimes recurring to a shape which they had first rejected. 7

If bees can make mistakes, then they are not simply machines outputting pre-programmed behaviors. Honeycomb is not produced with machine precision–it’s a process of trial and error and craftsmanship. Bees inherit the behavior of economic comb-making, but that doesn’t mean that they do it perfectly every time. This makes it seem like bees are, to some degree, designing their cells.

Melipona beecheii

Melipona beecheii (Darwin’s Melipona domestica)

For Darwin, the important thing to show in his chapter on “Instinct” was that natural selection can produce even highly specialized behaviors like the comb-making instinct in bees, or the slave-making instinct in ants. These are the hard cases–that is, a potential detractor to his theory of natural selection could argue that no way could such complex and specialized behaviors be produced by increments over time. For what would be the stages on the way to such apparently perfect products like the hexagonal, mathematically precise cell of the honeycomb?

Melipona beecheii comb

Melipona beecheii honeycomb

As evidence, Darwin examines the “imperfect” comb of Melipona domestica (renamed Melipona beecheii), a hive-making stingless bee native to Mexico. These honey-making bees produce round honeycomb rather than hexagonal, which Darwin saw as an intermediary example between the more architecturally advanced Apis mellifera, or honeybee, and the more primitive, globular structures of bumblebees, who don’t produce honey. These intermediary and primitive stages show that something as complex as the cell-making instinct of the honeybee could evolve from simpler nest-building instincts. A “mistake” in the craftsmanship of honeycomb could well be a beneficial mutation that leads to improved design.

bumble bee nest

Bumble bee nest

As interested as he was in his bees (and his worms and his beetles), Darwin was using such behaviors to make a larger point, about natural selection’s almost limitless ability to produce complex phenomena, like instincts. But even he couldn’t resist the comparison to human workmanship:

We hear from mathematicians that bees have practically solved a recondite problem, and have made their cells of the proper shape to hold the greatest possible  amount of honey…. It has been remarked that a skilful [sic] workman, with fitting tools and measures, would find it very difficult to make cells of wax of the true form, though this is perfectly effected by a crowd of bees working in a dark hive. 8

The intelligence of bees is up for debate, and such anthropomorphic language only muddies the waters. Do bees calculate? Do they decide? Are they mathematicians? Geniuses of engineering? Or are these simply, as one IFLS commenter notes, “genetically encoded behaviour pattern[s], that might seem intelligent,” in which case insect “intelligence” is “a mere illusion”?

smart wax, circle combSmart Wax

Or is the answer something in between? A 2013 study in the Journal of the Royal Society: Interface on “Honeybee Combs: How the Circular Cells Transform into Rounded Hexagons,” by B. L. Karihaloo, K. Zhang and J. Wang, suggests that the shape of the honeycomb has less to do with deliberation or even skill than with the physical properties of wax. Bees, the writers observed, first create cylindrical shapes, like bundles of straws (see [a]). The size of the honeycomb cell is the same as the size of young nurse bees that make the cells. So in essence they make the cells by proscribing a circle their bodies. Honeycomb takes on its characteristic hexagonal shape only later, because of the way wax settles into this shape after being heated to a molten state by the bodies of the bees (b). 9

(And in my own unscientific observations as an amateur beekeeper, I have noticed, too, that beeswax in the hive takes on different qualities and dimensions according to age: for example newly made comb begins at an angle, with cell openings facing fairly sharply skyward, at about around a 45 degree angle. As this comb is filled with honey, it tends to settle at 90 degrees, presumably from the weight of its contents and the interior temperature of the hive. Bees “know” this feature of wax construction beforehand and build accordingly.)

The value of the hexagon in the human imagination seems greater, however, than the circle, which is why the architect metaphor persists. Hexagons suggest geometry and calculation, things possible only through reason, deliberation, and planning. It suggests intelligence. But the metaphor has value, ironically, because hexagons do not generally occur in nature: they could be produced only by an intelligence that reminds us of our own. Drawing a circle by spinning around in the same spot is a primitive behavior, easily explained by instinct. However, it’s also far less humanizing to argue that the “intelligence” might be in the matter itself: that the form of hexagon is self-organizing due to properties of wax. It’s as different as arguing that bees are “industrious insect architects” (TED talk) and claiming that bees “heat up wax during the building process, which then flows thermoplastically into regular hexagons as a liquid equilibrium process.” 10

There are lots of other reasons for thinking that bees think in ways that might be familiar to us–bees, it has been shown, can learn from watching other bees; they can make predictions about the location of food sources; and they can make decisions about flight patterns. But anthropomorphizing bees doesn’t get us any closer to understanding intelligence in nature. Bees don’t have to be individually bright, they don’t have to be tiny humans: to call wax structures self-organizing and not the product of complex geometrical thinking on the part of bees is not to take away from the intelligence of bees. Rather, it’s to broaden what we mean by “intelligence” to include forms of “thought” and “mind” that do not look like ours, and which are not limited to the bee’s brain, but which extend beyond the bee to include its habitat and environment. Mind might come in different varieties, and wax might be one of them.

Think of it this way: What is beeswax?  It’s a bio-material for building construction produced through the collective organization of thousands of bees seamlessly interacting with each other and with their environment, which–partly through bees’ inherited behaviors, partly through their individual agency, and partly through the self-organizing tendency of matter–is molded into useful shapes and patterns, one of whose function is to act as incubators for more bees. That’s pretty smart to me. In fact it’s fucking genius–not because bees “do” math, but because bees facilitate the math that nature wants to manifest: it’s just as easy to say wax “wants” to be a hexagon as it is to say that bees “do” math. But both would be wrong. They’re anthropomorphisms, attempts to describe something that might not be expressible in human terms.

Hot Wax

It’s ironic that Rene Descartes, one of the architects of the Enlightenment, saw warmed-up beeswax and came to the exact opposite conclusion: namely, that mind exists independent of nature, of matter. In his Divine Meditations II, in which he sought to provide a solid basis for reason, Descartes hypothesized that mind alone is responsible for the impressions made on it by things in the environment. His illustration was wax, which produces different impressions on the mind according to its different physical states, such as when it’s cold or hot:

Take for example, this piece of wax; it is quite fresh, having been but recently taken from the beehive; it has not yet lost the sweetness of the honey it contained; it still retains somewhat of the odor of the flowers from which it was gathered; its color, figure, size, are apparent ( to the sight); it is hard, cold, easily handled; and sounds when struck upon with the finger. In fine, all that contributes to make a body as distinctly known as possible, is found in the one before us. But, while I am speaking, let it be placed near the fire–what remained of the taste exhales, the smell evaporates, the color changes, its figure is destroyed, its size increases, it becomes liquid, it grows hot, it can hardly be handled, and, although struck upon, it emits no sound. Does the same wax still remain after this change? It must be admitted that it does remain; no one doubts it, or judges otherwise. What, then, was it I knew with so much distinctness in the piece of wax? Assuredly, it could be nothing of all that I observed by means of the senses, since all the things that fell under taste, smell, sight, touch, and hearing are changed, and yet the same wax remains.

His conclusion from this experiment was that the only certain foundation of knowledge is our own mind: “I must, therefore, admit that I cannot even comprehend by imagination what the piece of wax is, and that it is the mind alone which perceives it.” We can celebrate Descartes for freeing us from some bad old ideas, but we can blame him for turning mind into pure form, distinct from matter: In Descartes’s dualism, mind triumphs over matter, which is merely inert, mindless stuff.

This is what anthropomorphism does: it understands mind as a purely formal quality that animals either possess or don’t.  This is a naive way of conceptualizing the relationship between mind and nature. Anthropomorphism naturalizes Descartes’s dualism as a simple metaphor, a figure of speech: the bee as architect, wax as lifeless stuff. Such easy figures of language preserve the integrity of the human mind against the human-decentering prospect that mind comes in different forms, only one of which looks and thinks like ours. Like Descartes’s dualism, anthropomorphism keeps us ignorant of the ways mind and nature connect. To graduate beyond this naive thinking, it’s more useful–and more awesome, to this mind–to consider, rather, mind in nature: that wax–that self-organizing collaborative creation of bees and flowers–is “smart.” No doubt we have a lot to learn from bees, but my guess is that none of it is about our own minds. In a beehive, wax may not be a metaphor, but it does matter.


  1. Pliny, Natural History: A Selection. Trans. John F. Healy. Oxford: Penguin, 29.
  2. T. H. White, The Book of Beasts: Being a Translation from a Latin Bestiary of the Twelfth Century. 1954. New York: Dover, 1984. 156
  3. Federico Cesi. Apiarium. Trans. Clara Sue Kidwell. Dissertation: U Oklahoma, 149.
  4. Charles Darwin. On the Origin of Species. London: John Murray, 1859. 224.
  5. Actual mathematician, friend, colleague, and possible bee Mike Gagliardo has corrected my math on this. Originally I was off by a factor of 10! No bee indeed.
  6. Darwin, 235.
  7. Darwin, 232.
  8. Darwin, 224
  9. See Karihaloo et al., “Honeybee combs: how the circular cells transform into rounded hexagons.” Journal of the Royal Society: Interface 10 (July 2013).
  10. Pirk et al., “Honeybee combs: construction through a liquid equilibrium process?” Naturwissenschaften (2004) 91:350–353.