Commenter pumpkinhead doubts Oprah’s head is as big as I say it it, writing:

Given this information of 1358 cc cranial capacity(for white females mind you) and 91 SD, Oprah would be 7.45 SD above average making her 1 in the tens of trillions.

I don’t want to argue about Oprah’s head size here since we’re already having that argument in the previous thread, but rather I want to make a more general point.

The problem with pumpkinhead’s argument is it assumes cranial capacity fits the Gaussian curve which is a reasonable assumption for non-pathological heads, but there’s just one problem with it. If head circumference is normally distributed, and head circumference has a cubic relationship with cranial capacity, then extreme cranial capacity can not be normally distributed.

For example, the late J.P. Rushton suggested that at least in very young children, cranial capacity ( cm^{3} ) = circumfence^{3}/118.4. This is the formula for a volume of a hemisphere, which as Rushton acknowledged, is an oversimplification, because the cranium is not a perfect hemisphere and there is massive individual variation in head shape.

But let’s imagine a world where all crania were perfect hemispheres. I randomly generated 60 crania and these had a mean of 54.7 cm (SD 1.28 cm which because of my small sample size, is slightly smaller than the actual U.S. female SD). In this sample, the one in several billion level (+6.3 SD) would be reached at 62.76 cm.

Now what happens when all the circumferences are converted into cranial capacity using the hemisphere formula. The mean becomes 1387 cm^{3} and the SD becomes 97. What this means is that a head that is +6.3 SD in circumference (62.38 cm), becomes +7.2 SD in cranial capacity (2088 cm^{3} ). So the cubic effect of going from circumference to volume make extreme humans seem superhuman.

Of course our crania are not perfect hemispheres, but the cubic effect still applies.

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swank is too racist not to use his talents IN AFRICA.

said:swank is the most racist person i’ve ever encountered.

pumpkinhead

said:You are using the formula incorrectly. CC = C^3/118.4 is used only for kids. For adults the correct formula to use is CC = C^3/118.4 – 200. Using the latter this gives us a CC of about 1850 cc and a SD of 4.77 making her roughly one in a million. However that is neither here nor there, cranial capacity from head circumference is an extremely crude way to work out brain size. Personally I do not see any reason why CC would not fit a Gaussian distribution curve, however if CSF and bone thickness and skin fat throw a spanner in the works then actual brain size should definitely fit the curve(within races or sub-populations).

pumpkinperson

said:You are using the formula incorrectly. CC = C^3/118.4 is used only for kids. For adults the correct formula to use is CC = C^3/118.4 – 200I’m the one who suggested subtracting 200 cm for adults on my other blog, but that was speculative

pumpkinhead

said:Really, well that’s good thinking! I think I ran into this on one of the papers while doing research. I think there is a slightly altered one for men but I can’t remember the exact figures for it. Another one using HC for women is V = 59.74*HC-1912.18 It works out a little more conservative but around the same ballpark figure.

pumpkinhead

said:Outside of pathological cases like encephalitis or gigantism.

pumpkinhead

said:The largest female brain ever recorded was 1742 grams. That gives us a cranial capacity of 1800 to 1900 cc. However that isn’t even the clincher in all this, the point remains that using Lee Pearson formula, the absolute upper limits of head dimensions, and careful analysis from the right sort of images we see that 2000+ is a pipe dream. 215x160x145 exceeds an educated and generous guess by 5 mm on each dimension and that still is 200 cc short of what you claim to be her brain size.

According to my calculations and data taken from US army anthropometric measurements an HC of 25.25 in puts her at 5.7 SD above average or 1 in 137 million. Considering that the data is taken from a majority white population where the bottom 10% of the population is cut off one can easily deduce that when applied to her race and sex 25.25 inches would comfortably exceed 6 SD making her a statistical impossibility considering she has no obvious pathological disorder like encephalitis or gigantism.

Furthermore, a HC of 62.38 cm sits at 4.5 SD which then translates to a 4.77 SD in cranial capacity. Fair point about the cubing effect but I feel that is significantly mitigated by the positive correlation between brain size and and skull thickness and CSF volume while simply put 25.25 is simply outside the realm of possibilities while the cranial capacity it implies is even more preposterous.