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Going to actual citation in that article, "Males have on average larger overall absolute volumes (i.e. not corrected for body size) in each volume category (see Table 3), ranging from 8% to 13% larger volume in males." ... aren't males generally physically larger overall? Granted, 8-13% feels like it's disproportionate, but I'd want to check that before drawing any conclusions.

Is correcting for body size correct? If it takes X mass of brain to run the human body, than the larger brain has more cells free to do something other than run the body. Or in other words, how much of a larger brain is required to run a larger body - if the scale isn't linear then I'd expect the larger brain to be "smarter"

As the other posters have said, size doesn't seem to correlate to anything. More than that I don't know.

That's a fair question. I'm given to understand that brain size doesn't directly scale with intelligence (consider sperm whale vs dolphin vs human), but for all I know that's only true between species? Actually now that I'm thinking about it, I'm pretty sure there are pathologies where the brain is too big, but one shouldn't conclude much on pathological cases. So.... I dunno. Maybe?

Anyway one complication between species is we know that brains are composed and are laid out differently which affects density and distribution. Cephalopods for instance lack mylenation and appear to have their brain functions a bit more distributes to the point that they occasionally have "rogue arms" which act dysfunctional to the point the host decides to just chew it off and eventually regenerate a "sane" replacement.

It is probably a very rough approximation anyway as it doesn't account for what a given body is. A brain the size of a gnat would be insufficient to handle a body the size of an elephant but that doesn't say how relevant the difference is even in the same order of magnitude. A morbid observation of hunters and tanners is that anything the brain of anything they skin is enough to tan its hide. Now that is clearly a chemical process with a very remote relation to actual processing capability given that tanin can subsitute for tanning but not thinking but it does hint at a lower bound size constraint for even the dumbest vertabrate.

That aside the point is there would be less nerve input for the brain to process from five grams of fat, five grams of skin, or say an organ like the eye. Let alone any other other details it must acount or provide for. Further complicating things is neural plasticity - if I recall correctly "optical" areas of the born blind tend to be repurposed for other senses as opposed to say mathematical ability.

TL;DR: There is evidence but certainly not good enough to tell us anything about sex differences in humans.

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