The Star Trek fans among you are no doubt familiar with “The Menagerie,” a two-episode story from the first season in 1966. The crew of the Enterprise gets trapped on a planet occupied by aliens called Talosions who look like humans, except for their massive, vein-encircled brains.*

That story was produced the year I was born, and when I saw it about a decade later, it made a big impression on me. Could brains get that big? Would they wind up with that cantaloupe shape? Would they provide Talosians with super-intelligence?

My ten-year-old brain was too underdeveloped to process the paradox that these were aliens living on another planet–and therefore would have likely followed an unimaginably different route of evolution. Chances are, the Talosians wouldn’t look like short middle-aged men wearing smocks, with foam padding pasted to their scalps. But as a grown man, I can still picture those Talosians in full Technicolor. They embody an interesting question: what are the possible shapes of the brain?

All of this is to explain the delight I experienced when I stumbled today across a recent paper entitled, “On the Possible Shapes of the Brain.”

The paper is the work of Roberto Toro of the Insitut Pasteur in Paris. Toro investigates a couple key features of the brain: its size and the folds on its surface. Some mammals have smooth surfaces, while others have crumpled ones. This difference is important, because the outer layer of the mammal brain does most of the cognitive heavy lifting. The neocortex, as it’s known, is packed with neurons that have dense interconnections, enabling it to do sophisticated information processing. The interior of the mammal brain is taken up, in large part, with fibers that link different parts of the neocortex to one another, enabling them to share their information with one another.

The more wrinkled a brain gets, the bigger the surface of the cortext becomes. The human brain is especially wrinkled. If you look at a human brain, you only see about a third of its surface–the other two-thirds are hidden in its folds. If you could spread it out flat on a table, it would be 2500 square centimeters (a small tablecloth). A shrew’s brain surface would be .8 square centimeters.

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The human brain isn’t just wrinkly, of course. It’s also big–three times bigger than the brains of chimpanzees, our closest relatives. And the relationship between the the size of brains and their surface area is what interests Toro in particular. If our brains were like balloons, increasing their volume would increase their surface area proportionally.

But our brains, it turns out, are not just like balloons. Bigger brains have a much bigger surface than you’d predict from just scaling up their volume like a balloon. Big-brained mammals have much more gray matter (the stuff of the neocortex) than small-brained mammals, in proportion to the connecting fibers.

This extra surface comes to use courtesy of our especially wrinkled brains. But there’s another intriguing thing about those wrinkles: they are not spread uniformly across our heads. The front of the neocortex is more wrinkly than the back. This is intriguing, because the front of the cortex handles much of the most abstract sorts of thinking. Our brains pack extra real estate there with additional folds. And if you look at mammals in general, they tend to have more wrinkles at the front than the back.

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Given the importance of this architecture of the human brain, a question naturally arises: is the shape of the human brain precisely encoded by genes, or does it emerge from its enormous size? Toro and his colleagues have created mathematical models of the growing brain, which suggest that size does indeed matter. As a brain grows, the different regions of the cortex get further apart from each other. The white matter fibers that link them start to stretch. To avoid snapping these fibers, the brain needs to start wrinkling, so that neighboring regions of the cortext can stay close to each other. Wrinkles, in other words, are a natural result of a bigger brain. Wrinkles may develop more at the front of the brain because the back of the brain finishes developing earlier, when the brain is still small.

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You can see the link between the size of brains and their wrinkles not just by comparing different species, but by comparing people. Toro and his colleagues have compared the brains of 300 Canadian teenagers. As the graph here shows, there’s a remarkable range in the sizes of their brains, from 800 to 1400 cubic centimeters. The total surface of the brain is proportional to the volume of the brain. But if our brains were mere balloons, people’s brains should fall along the dotted line. Instead, the surface of the brain increases faster as its volume expands. This expansion is the result of extra wrinkles–with more wrinkles towards the front than the back.

One of the most striking patterns in human evolution is the expansion of our brains, especially over the past two million years. If Toros is right, this expansion led to its reorganization. Simply making a mammal brain bigger forces it to take on other features, such as extra wrinkles on its front end, increasing its surface allowing it to get parcelled up into specialized areas.

These patterns are not the whole story of why our brains are shaped the way they are. A Talosian brain might be impossible to evolve for other reasons, such as the strain it would put on mothers in childbirth, or the huge amount of fuel it would demand. But if natural selection could favor even bigger brains than we have today, perhaps we’d end up as Talosians. But if we did, our brains would become fiercely wrinkled.

*If any Star Trek fans are tempted to correct me and point out that “The Menagerie” was originally a pilot for Star Trek called “The Cage,”, I’ve just done your work for you. You can thank me later.