As commenter pumpkinhead noted, the following formula is used to calculate cranial capacity in living people.
Source J.P. Rushton
This regression equation is over 100 years old so it may underestimate the crania of people today, though if everyone in the modern developed world is underestimated to a similar degree, it might still be useful for measuring relative differences.
It’s very hard to compare the cranial capacity of two people just from looking at photos because as commenter pumpkinhead has noted, small differences in closeness to the camera can distort the relative sizes. Nonetheless when two people are sitting behind the same desk, you might get more reasonable results.
Putting a ruler on my computer screen, it seems that Oprah’s cranium is 1.205 as long as Ellen’s.
And 1.26 times as high.
To determine head breadth, we need a photo where they’re both facing the camera.
From here it seems Oprah’s head breadth is 1.017 times as great as Ellen’s.
The following are actual head dimensions from the U.S. military.
If we conservatively assume a woman as intelligent as Ellen has the head dimensions of just the average white woman (L: 186 B: 144 H: 124:) then Oprah should have the following dimensions: L: 224 B: 146 H: 156
This gives Oprah a cranial capacity of 1874 cc (1.48 times as big as the average white woman’s) using the Lee and Pearson formula, but given the huge error that can occur from trying to measure photographs, I could be off by as much as 100 cc. Commenter pumpkinhead doubts she is beyond the mid 1700s.
Pumpkin Person 
I would say that the Lee Pearson formula is good for getting population averages but can give wildly inaccurate results when measuring individuals. This can be gleaned from the fact that the formula essentially amounts to the following:
It is based on the formula for a volume of an ellipsoids
http://www.web-formulas.com/displayImage.aspx?imageid=479
Adapted for the cranial vault it basically amounts to the following,
Cranial Capacity = 64% of the volume of an ellipsoid(Length x Breadth x Height) + a fixed constant of 406 for men.
Now once you examine the human brain this will start to make sense as it basically looks like half an ellipsoid(elongated sphere) with a little bit sticking out at the bottom rear end of it(this would be the added constant).
This is great as a rough estimate and when testing large populations things do tend to average out, that is those that are under predicted are cancelled out by those that are over predicted. Problems arise on an individual basis when we try to take measurements of a-typical heads, namely non spheroid heads. Those that have a high cranial vault with straight vertical foreheads flat tops and straight vertical rear of the head would be massively under-predicted while those with slanted foreheads and overly rounded rears would be greatly over-predicted. What’s more the constant that is added basically assumes that we all have roughly the same size cerebellum and brain stem but that is far from the truth. Naturally one would expect to have a cerebellum + brain stem that was proportional to the rest of the brain. In other words they would increase or decrease in size as the brain deviates from the average. CSF volume and skull thickness tend to mitigate this discrepancy but in my view they do not do a good enough job on average.
It is perfectly feasibly however for an astonishingly big headed person to have an unimpressive brain assuming they are big boned(thick skull) and have a lot of CSF they may have a brain that is just above average in size. Conversely a small headed person might have low CSF be thin boned(tends to add 20- 70 cc in volume) and have a brain just as big. Throw in the fact that they have a smaller body to manage then they have the upper cognitive hand so to speak. We see this quite often with small headed people having incredible wit(of course there are other qualitative reasons that this might be the case but lets not delve that deep, for now).
These two would be massively under predicted by the formula especially the one on the right(by as much as 200 cc).
and this person would be massively over-predicted by the formula(100-200 cc).
That upper-crossed syndrome (UCS) in picture 2… ouch. I’ve seen worse, he could stand to fix his posture. Pic 1 looks a bit better, mostly because he’s probably posing for the camera better, but you can clearly see it in pic 2.
In UCS, the back muscles are weak (underactive) while the chest/deltoids/neck muscles are overactive, causing that head tilt; though, since he’s posing for the camera his shoulders are back, his UCS peeks through in his neck.To fix, one needs to stretch the overactive muscles and strengthen the underactive (weak, in this case back) muscles.
A major cause of this is sitting at a computer for long hours; working in factories (holding things; moving forward in a fast-paced environment). It’s becoming increasingly more common due to how much more sedentary we are becoming as a society.
Yes I think this is a problem that is quite prevalent these days given our lifestyle. We were designed to take down wild game, not game wildly(on XBox) LOL
Yea computer nerds get it too because they push their head forward a lot along with their shoulders. It’s easily fixable if you know what you’re doing. (I wonder how many commenters here have UCS.)
You might have to count me in, though it is minimal I see it getting worse if I don’t do something about it soon(gym etc). Would you say that simply minding your posture along with some exercise/stretching is good enough to fix the problem?
See my first comment on how to fix it. If recommend talking to a personal trainer that specializes in corrective exercise.
Minding your posture is a good idea, but the overall postural imbalance arises from overactive and underactive muscles.
Oprah sits somewhere in the middle, with a typical head shape for a woman meaning the formula would be quite accurate with her.
I suspect the Lee & Pearson formula underestimates modern cranial capacity, at least in whites. If you look at Morton’s 19th century data (even as revised by Gould) on cranial capacity (directly measured by filling the skull), you get cranial capacities that are as high or higher than Rushton’s army data from 1989. So either there’s been no increase in head size over the 20th century (which seems unlikely) or the Lee & Pearson formula is underestimating people today. Just as he required different formulas for different sexes, one may need different formulas for different generations.
That could be the case but to be honest I don’t think it would make that much of a difference. I think that formula was created as a happy mean between Asians, whites and blacks. Now we may have increased slightly in cranial capacity(nutrition and lifestyle changes) but short of some radical child rearing techniques(there is some evidence for moderate changes) I don’t see how the skull shape would change that dramatically. As far as I can tell Europeans have a pretty good fit for the formula on average though from individual to individual this can be dramatically different while some European sub-populations may indeed be under predicted by the formula.
Given the fact that invariably big brained individuals find themselves at the peak of success(particularly in the show biz world) our perception of population averages gets skewed upwards when the reality is quite different.
In any case the final arbiter at this point are MRI scans and on the whole they seem to be fairly close to the figures produced by Rushton. According to my research MRI control group scans average around 1490 cc for white males while Rushton’s figures were between 1440-1460. That is a difference of 40 cc, not anything to write home about while it could very well be explained by screening. You wouldn’t expect a homeless or low income person to be included in an MRI study control group(by definition screened for illnesses) while all too often low income males enter the military(albeit healthy ones).
That could be the case but to be honest I don’t think it would make that much of a difference. I think that formula was created as a happy mean between Asians, whites and blacks. Now we may have increased slightly in cranial capacity(nutrition and lifestyle changes) but short of some radical child rearing techniques(there is some evidence for moderate changes) I don’t see how the skull shape would change that dramatically.
IMHO the shape doesn’t need to change. The formula is not directly calculating the volume of a shape from its length, breadth and height, it’s a regression equation predicting volume using the product of length, breadth and height as its one and only independent variable. So even if the correlation between X (LxBxH) and Y(volume) stays the same, an increase in mean volume will cause the regression line to move higher along the Y axis, which means the same head dimensions that predicted a 1300 cc in 1901 might predict a 1400 cc in 2001. Put simply, we may be regressing to a higher mean so the constant value in the formula may need increasing. Only if there were a near perfect correlation between head dimensions and volume would this be avoided, but because the part of volume not captured by the product of length, breadth and height may have increased, then the formula may underpredict.
Given the fact that invariably big brained individuals find themselves at the peak of success(particularly in the show biz world) our perception of population averages gets skewed upwards when the reality is quite different.
True
In any case the final arbiter at this point are MRI scans and on the whole they seem to be fairly close to the figures produced by Rushton. According to my research MRI control group scans average around 1490 cc for white males while Rushton’s figures were between 1440-1460. That is a difference of 40 cc, not anything to write home about while it could very well be explained by screening.
Most MRI scans seem to support Rushton I agree, but the Linden one is a glaring exception & it’s the most recent one I’m aware of. MRI scans are extremely reliable so they’re the final arbiter of which volume is bigger than which, but I don’t know how well scaled they are to actual 3-dimensional reality. I would love to see a study comparing volume directly measured by putting beads in skulls with volume calculated by MRI.
You wouldn’t expect a homeless or low income person to be included in an MRI study control group(by definition screened for illnesses) while all too often low income males enter the military(albeit healthy ones).
True, which is why I like to look at the average height and education level of the study participants, to see how elite the sample is, though that’s not always available.
Gould’s reanalysis of Morton’s measures were nowhere near as bad as Rushton, Jensen et al made it out to be:
Although Gould made some errors and overstated his case in a number of places, he provided prima facia evidence, as yet unrefuted, that Morton mismeasured his skulls in ways that conformed to 19th century racial biases. (Weisberg, 2014)
Click to access remeasuring-man.pdf
Kaplan, Pigliucci, and Banta (2014) are more critical of all three (Gould, Lewis et al (2011) and Morton), but Kaplan, Pigliucci, and Banta (2014: 8) write::
In the end, the question “Whose statistical approach to summarizing the skull volume data was right? Morton or Gould?” is the wrong question to ask. It is hard to see how a set of skulls,collected unsystematically, often of uncertain provenance (how far should we trust the descriptions of where the skulls came from that were sent to Morton along with the skulls?), and identified in pre-modern fashion with no way to tie them back to meaningful biological groups, could be usefully deployed to answer any meaningful question about the larger populations from which they were drawn. Neither Gould’s nor Lewis et al.’s analysis is appropriate for answering many questions that a reasonable person might want answered, in a modern context where biological definitions of “race” and “population” are used instead of arbitrary pre-modern delineations. Debates about how best to summarize measurements of those skulls should be seen as hopelessly misguided. That Gould permitted himself to get
sucked into such a debate is telling the availability of another way of analyzing the data clearly made doing so tempting to him. Lewis et al. were right to call Gould out on this failure, but in the end, they followed the same garden path, refusing to see that trying to make use of Morton’s skulls for any interesting purposes is just pointless.
Click to access KAPGOM.pdf
Finally, a more recent commentary by Weisberg and Paul (2016):
Gould never made, nor did he ever claim to make, nor did he have any reason to make any measurements himself. Gould’s argument depends on the difference between the two sets of measurements. Thus, as a matter of logic, there is no way that the results of Lewis et al.’s remeasurement program could be used to adjudicate the issue of who was biased. The many commentators who cite as a major failing of Gould’s that he “never bothered to measure the skulls himself” [6] have also, though perhaps more understandably, missed the point.
[…]
Lewis et al. have charged that Gould’s “own analysis of Morton is likely the stronger example of bias influencing results” [3]. We maintain that this accusation, which continues to reverberate, is undeserved …
https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1002444
So what are the correct numbers?
“IMHO the shape doesn’t need to change. The formula is not directly calculating the volume of a shape from its length, breadth and height, it’s a regression equation predicting volume using the product of length, breadth and height as its one and only independent variable.”
It is true that the shape doesn’t need to necessarily change in order to increase volume, increase in the dimensions is all that is needed. However it is possible to change the shape of the head and produce a greater volume with the same dimensions. I’ve tried to articulate this in my post above, but I’m not sure I did a good enough job. The truth is we are essentially saying the same thing however you are using regression formula language while I am using geometric language. Being an engineer I like to understand a formula in how it is applied to real world variables. The actual regression equation is as follows:
CC = 0.000337x(L-11)x(B-11)x(H-11) + 406
The dimensions are measured in mm and subtracting 11 is necessary to account for the thickness of the skull and skin. Even though the units input is in mm the units output is in cm.
The equation of the volume of an ellipsoid is:
V=4/3πabc where if we apply it to ICV a=(L-11)/2, b=(B-11)/2, and c=(H-11)/2
0.6436 x 4/3π(1/2)(1/2)(1/2)/1000 = 0.000337 or in other words about 64% of the volume of an ellipsoid. Note that I am dividing by 1000 to convert the units back into cm.
At this point it should become clearer how in fact even though this is a regression formula it actually accurately fits the description of the shape of a brain. Essentially 64% of the volume of an ellipsoid plus a fixed constant(roughly corresponding to the cerebellum and brain stem).
It was probably fitted for the average cranial vault(which takes roughly speaking the shape of a brain). The problem arises when the cranial vault increases in size. The first part of the equation perfectly captures that increase however it does not account for the possible increase in size of cerebellum and brain stem. Things get even more tricky when we alter the shape of the skull a little, akin to the photo I posted of the two guys standing back to back. The outline of their skull from the profile is not a perfect ellipsoid, in fact it starts to resemble a rectangle. So this formula is bad for those people. Now if a group is predominantly populated by people like that then we would have to alter our regression equation slightly, ie increase our constant. If however the change in volume is due to simple increase in dimensions then the formula is still more or less as accurate as it used to be. So IMO what would require a dramatic change in the formula would be a change in the shape of the skull(what I like to refer to as box or block headed). This would be necessary to account for the bits the ellipsoid would not include in the measurement(the cerebellum, brain stem and the edges of a more rectangular head).
The reason I’m happy with Rushton’s figures is because they include large population samples which is what the Lee Pearson equation was designed for. It captures quite accurately the mean of a population when measuring a large number of people(the outliers cancel each other out). However things get tricky when we apply it on an individual basis with people that are more than two standard deviations away from the mean. Add to that the complications due to skull shape you can see how it can be highly problematic assuming you do not know how to account for these changes.
So while a slight uptick in general population CC could effect the accuracy of the equation IMO what would dramatically effect it would be a change in the shape of the skull. Which is why at one point they devised equations specific to racial groups given the difference in the shape of the skull, if I am not mistaken.
I kind of see what you’re saying, but if you look at photos of actual cranial capacity shape, instead of brain shape, it seems more like 90% of an ellipsoid, though maybe the Lee & Pearson formula works out to about the same when you add the constant, but why not just use 90% from the outset and skip the constant?
So the average white army man is L: 197 B:151 C:132. Subtracting for fat and skin, these become L:186 B:140 C:121.
Entering them into the 4/3(pi)(L/2)(B/2)(H/2) = 1648,9340
But since cranial capacity is only 90% of an elipsoid we multiply by 0.9 which gives 1484046 or 1484 cc. Very similar to the 1468 cc you get from the Lee & Pearson formula.
Fascinating!
“MRI scans are extremely reliable so they’re the final arbiter of which volume is bigger than which, but I don’t know how well scaled they are to actual 3-dimensional reality. I would love to see a study comparing volume directly measured by putting beads in skulls with volume calculated by MRI.”
I share your concern regarding MRI scans, however it seems that their error is down to 1% which to be fair is better than anyone could hope for. Your bead idea sounds pretty good to me, it would be interesting to see if they have done something to that effect already.
“So what are the correct numbers?”
See the discussion in Weisberg (2014).
“Fascinating!”
Yes, I find it quite interesting as well. To be honest I actually thought that the constant they used was unnecessary, just use a slightly different multiplier. In any case until you actually start stuffing brain cases with beads you wouldn’t know which formula works best in the full range of the normal distribution. As for 90%, I would say that is a little too high(it gives wildly different results at higher brain volumes). Given that the cranial height is measured from the upper margin of the ear canal and that it tends to be just above the base of the cranial vault, this means that the cerebrum lies a fair bit above that point. Which to me makes it look more like half(or just over half) an ellipsoid which curves slightly downward at the back where the cerebellum and brain stem are attached. An MRI scan can give you a good idea of what I mean.
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSsS7e5pvKXGl_qX-_HhUBjBxj3IcS22Gdh46pp_Hk3kQSGbCKKaA
Note that the ear canal would be just where the brain stem starts to bulge.
However I will agree with you that perhaps a better formula is necessary in order to eliminate error. An idea had occurred to me a while back, basically take tape measures(akin to head circumference) but all taken from ear canal to ear canal. 3-5 might be necessary, one going round the base of the forehead, one from the top of the forehead, another round the mid-point at the top of the head, another round the top of the back of the head, and a final one going round the back of the head, maybe throw in HC for good measure. Not sure how to put these into an equation but I can’t imagine it would be that hard. This should account for size and skull shape and perhaps give us much more accurate results. One thing it doesn’t account for is that rounder(more brachycephalic) heads tend to pack in more volume per given circumference up to 4% more but that is from absolute extreme(perfectly round) to absolute extreme(extremely narrow). However this would account for a really small percentage of the population. I imagine the error would be of the order of 1 – 2%.
If AK’s iq is 18 points above 100, PP iq is 17 points above AK or twice AK’s iq points. This makes more sense than 113 since the middle of 18 and 35 is about 27. And a difference of 9 points is significantly noticeable by comparison in what intelligence can do. What PP can do is significantly above what 127 can do. It is noticeable.
The capacity of intelligence comes from a control system where memory is wired up to handle more pathways for information. So even if say 7 bundles can handle 7 digits span, the brain matter stays the same but now 14 bundles can handle 14 digits. Each bundle splits into two new strands or cables.
The number of stands or cables is important because a larger number of them and their arrangement allows the control mechanism to process more as complex problem-solving. More can be kept track of and held in mind, with a greater number of steps as well.
Being around a person long enough it is noticeable how much information they can keep track of. You can make a general guess their IQ this way.
Ellen looks like an alcoholic. Her skin and face remind me of it anyway.