It is a density thing. Think of the wrinkles in the brain being like an air filter.
Those cheap fiberglass air filters work, but they’re really not the best. The folded paper ones are significantly more effective as they have far more surface area to collect debris.
The more wrinkles in the brain the more surface area there is for neurons.
It is about density. The more brain matter you have the more neurons you have. A wrinkly brain can fit more mass in the same volume. Imagine you had a ball of dough and had to fit it in a box. If the ball of dough is as big as the box it can remain smooth, but if you wanted to fit a bigger ball of dough in the same box you’d have to squish it in and it would get wrinkly.
Your brain is folded in order to increased the amount of neurons and axons (as well as connections, which could be more important than the other two) that can fit via available surface area. A more wrinkled brain and higher density of neurons is correlated with more complex thought in mammals. Of course, this is mainly with mammals.
The answer is that most of what you think is your brain is just wiring. Only the very surface layer is actual “gray matter” , the part that does the actual brain stuff. If your brain was smooth then the part of your brain that’s you , that’s doing the actual thinking, would be much smaller.
Imagine your brain is a computer chip that’s the size of a sheet of normal printer paper. Ok that’s about as big a sheet as would fit in your skull if it was smooth . But i could take a sheet of paper as big as a bed sheet and crumple it up and stuff that into your skull too. By crumpling and folding you get a much larger surface area and there for much more processing power.
There is another benefit too. Imagine again this huge sheet of paper on your bed. Now take a marker and mark two spots on the paper that are 4 feet apart. If your brain was smooth, a signal traveling from one mark to the other has to travel 4 feet. But if I crumple up the paper, those two spots could be right next to each other. Much faster to communicate
For some reason, possibly even just random luck, evolution has made it so the surface of the brain is where the “thinking” happens, with the inside of the brain being more about connections between different areas of the brain.
So more wrinkles = more surface area = more of the thinky parts of the brain.
[Further reading](https://www.technologynetworks.com/neuroscience/articles/gray-matter-vs-white-matter-322973)
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