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When we look at the cortex of the brain, it has a folded structure. It is said that this is because this enables a greater number of neurons to exist, which is obviously advantageous.

However, we could pack in the same amount of 'volume' into a smaller space without any folding, sacrificing that surface area it results in. Why does this lead to fewer neurons? Can neurons only exist near surfaces?

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The key point is that the brain is not a uniform structure. The outer layer, known as grey matter, is a relatively uniform and flat structure. Underneath the grey matter is white matter. An overly-simple characterization of these two areas is that grey matter performs computations, and white matter lets different areas of grey matter talk to each other. Here's an image of a dissected brain from wikipedia where you can clearly see the ring of grey matter.

One reason for the folds might be that if you want to fit a flat structure (like grey matter) into a tight space, folding it is one way to fit more of it. Another aspect of this is that the folds bring different areas of grey matter closer together, which means less white matter is needed to connect the areas together.

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This answer is great. Thanks for sticking around and lending us your expertise :) –  Chuck Sherrington May 26 at 18:24
Thanks for the answer. Am I right in saying that the grey matter band we see surrounding the white matter in the image comprises of layers 1-6 of the cortex? According to wikipedia, the 6 layers would be around 2-4mm thick, which looks about right. –  ddriver1 May 26 at 18:47
Right. The neocortex is the grey matter. –  Josh May 26 at 18:56

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