Head growth

At reference 1, I noted the suggestion in my phrenology book, reference 3, that the heads of adults could change their size and shape over the years, reflecting the changing character of the owner. Thinking that bones, including skulls, did not change much at all once one makes adult, this was surprising and I have now got around to checking, or at least attempting to check.

A check which revealed a lot of measuring with tape measures, in much the same way as Severn of reference 3, some work with skulls and some work with scanners. Lots of population studies and analyses. But none of the expensive, long-term, longitudinal work needed to truly put the matter to rest. No-one has thought it worth their while.

The growth of fishes

 

Figure 1: The growth of fishes?

But I start with fishes, with the thought that some fishes never stop growing, although they may have accidents of one sort or another, and that one sometimes comes across very large individuals. I remember once, for example, seeing a very large plaice, on its own barrow, at a fish dock, a yard or more long. Turning to Bing (with Google in support), the first thing I turned up was reference 4, the abstract of which said ‘Fishes exhibit a ‘determinate’ type of growth in short-lived species of warmer regions and an ‘indeterminate’ type in long-lived species of colder regions’ – which seemed to corroborate my thought. Sadly, this paper did not seem to have leaked out into the public domain from behind its rather expensive paywall. After that, it was all talk of exponential growth towards an explicit maximum, with fish continuing to grow with age, but at rates which get very small in adults.

That said, it only takes a very modest tweak to the albeit very simple model, to allow steady adult growth after the first spurt – as illustrated above. No doubt some resourceful biologist could fix up a plausible scenario which delivered such a tweaked model.

Human height
 

Figure 2: An army sample of male heights

However, most land animals, including humans, more or less stop growing once they are adults. In their version of Figure 1 above, the right hand part of the blue line is horizontal. Furthermore, the heights of human populations are a very good example of a normal distribution and the probability of extreme heights is vanishingly small – with the proviso that the parameters of that distribution vary with time and place. That said, while different people might have different heights, there is not much to be done about it. Once adult, you are the height you are, give or take a bit of curvature of the spine. While Severn claims that exceptional people can do something about their heads.

A sample distribution is given above, with heights varying from left to right from 150cm to 200cm. Presented as it is on account of the vagaries of (my use of) Microsoft Excel pivot tables. The orange line uses the left hand scale of frequency counts, while blue line uses the right hand scale which give the size (band) in centimetres. The numbers along the bottom are the bin numbers – with bins and binning being the subject of the excursion at reference 12. Note that the lower limit of 150cm is 4 feet and 11 inches and the upper limit of 200cm is 6 feet and 7 inches.

Human head growth

Severn tells us that healthy heads vary between around 18 and 25 inches in circumference. Less than that and you are likely to be an idiot, more than that and you are likely to be insane. Or, put another way, the balance of your mind, of your phrenological bumps, is likely to have been disturbed. And while, within limits, bigger is better, Severn also allows for brain quality, although I have no idea how he made any assessment of that quality.

But the evidence for growth given in reference 3 is pretty thin. Despite having measured hundreds of thousands of heads over the years and measured quite a few more than once, Severn does not offer many facts. Just several heads, including both that of his own and that of past PM Lloyd George, which grew between half an inch and an inch over a decade or more – enough, one supposes, to give some bumps room to grow. Severn was indeed confident that some individuals, by dint of effort, could grow both their character and the phrenological bumps which evidence that character. With more bumps generally making more circumference – as well as more of whatever character traits those bumps covered.

Figure 3: The head of a criminal

A colleague whom Severn does not seem to mention is the slightly older criminologist, Cesare Lombroso, who claimed, very roughly speaking, to be able to detect a criminal from the appearance and measurements of his or her face and head. He was rather keen on criminal ears. See, for example, reference 10, from which the figure above is taken.

Anthropometry

 

Figure 4: Invitation to the ball

Next, following on from the work of the likes of  the S. M. Morton noticed at reference 2, we have anthropometry, inter alia, a department in the Police Judiciare of Maigret and Simenon. A department which took in the people who had been taken in overnight and stripped them for the purposes of anthropometric measurement; all rather humiliating for the novice in crime. And following Lombroso, the Police Judiciare worked a system of identification, later made obsolete by finger prints, using ears. While Simenon chose to publicise his first Maigret stories by holding something called the Anthropometric Ball, properly the Bal de l'Anthropométrie, presumably in some sort of fancy undress.

 

Figure 5: Measuring the circumference

It turns out that despite the bad name that this sort of thing has acquired from a race relations point of view, the US Army does a lot of it, producing, for example, reference 4. A report which is thorough and accessible. It explains what it is doing in a way which many of the products of universities do not. You get, for example, colour pictures of all the apparatus. A report based on measurements – including head circumference - taken over a year or more of some 4,000 male soldiers and 2,000 female soldiers. With head circumference apt to be slightly disturbed by the style of hair worn by some female soldiers – not thought to matter to the army as their main point of interest was helmet size.

But it would be interesting to know how reproducible measurements of this sort are. One might have thought that they might easily vary by a small number of millimetres, without there having been any change to the ‘facts on the ground’.

Figure 6: Distribution of the circumferences of some non-civilian heads

Among the large amount of data presented, we have the distribution of head circumference, by sex. Not evidence of change in circumference in individuals over time, but a distribution which is consistent with the figures given by Severn. With females showing a slightly bigger range and a slightly flatter distribution.

The figure is in the same format as Figure 2 above. Note that the lower limit of 50cm is 19.7 inches and the upper limit of 65cm is 25.6 inches.

Other sources

 

Figure 7: Forbidden fruit

There is something called the National Health and Nutrition Examination Survey in the US (reference 11), an annual survey of around 5,000 people which includes a good range of body measurements, as suggested in the figure above, including head circumference. There is even a longitudinal component, but I think that most of the body measurements are missing from that. The data is published and freely available – but sadly in something called XPT format, an export from the rather elderly SAS statistical analysis package. And I have no way of converting that to an Excel format. That apart there are plenty of tabulations published – for example detailed analyses of infant head circumference. But I did not find quite what I wanted. All put aside until next time.

Perhaps the US is more into anthropometry than the UK: I don’t recall ever seeing anything of the sort over here.

Next we have the trauma surgeons – the people who, inter alia, deal with the results of motor traffic accidents – who are interested in the strength of skulls and how that might change with time. From I can make of reference 6, the gross thickness does not change very much, but the thickness of the two bony layers making the two outer layers of the three-ply sandwich which makes the flat bones of the skull, does decline significantly with age in the case of women, making them more liable to serious head injury. But no mention of any change with age of the gross dimensions of crania.

Next we have the dentists and the plastic surgeons interested in the changes of the facial skeleton with age, with a sample of their work to be found at reference 7. With most of the plastic surgeons being into attempting to reverse the effects of aging on the faces of ladies rather than of trauma. The story here seems to be that there are changes in the facial skeleton over the years, mainly the result of bone being reabsorbed, in a word, shrinking. But this is the face not the cranium and, again, there is no mention of any change with age of the gross dimensions of crania.

I associate to an orthodontist colleague of my father – a chap who pulled four of my own premolars to make space for the others, an intervention which was entirely successful but which leaves me a bit short on lower chewing machinery now – who spent quality time thinking about how to map growing faces, how to measure the movement of landmarks. I think his answer was to use some of the landmarks to impute a centroid, a centroid which could be used as the fixed origin of a two dimensional coordinate system.

The only other reference to change over time that I found was the article at reference 8 from 1956, a reference which I have failed to convert into a paper, although I did manage a three page review. What we look to have is another US Army survey of heads, but looked at this time from the point of view of change during the third decade of life. The answer seemed to be that while there were changes to the face, there was no significant change in circumference, at least not in males.

My last port of call, having failed to find any longitudinal work on skulls, was reference 9. From which I had two takeaways. First, the bone is a living tissue, with bone being laid down and bone being taken up, resorbed, through life. In adults, the laying down and taking up are usually more or less in balance, with no net change. Second, people studying skulls have moved away from taking measurements on the surface with tape measures, to mapping landmarks in three dimensions using scanners. A business which Lieberman calls geometric morphometrics.

Conclusions

Quite a lot of skulls have been measured over the years. There has been some interest how the skull changes over the years, but only average changes. The average circumference of the heads of 6 month old males has increased from X to Y over the period A to B. But no-one seems to have made a longitudinal survey of a population of living skulls to trace their changes over a period of years, let alone over lifetimes.

Figure 8: Head size and race

Perhaps the interest in superior races which seems to have been triggered by tables like that snapped above, from the big S. G. Morton book noticed at reference 2, has resulted in something of a backlash, with the systematic measuring of skulls being ruled out of order by university ethics committees.

From all of which I conclude that, leaving aside the face, maybe there is a bit of growth, a bit of change in adult skulls, but not much.

It is a pity that Severn did not keep better records, records which might have survived to be turned up on the Internet.

But it has been a useful reminder of the limits of knowledge, even in this day of armchair research with a laptop and the Internet. There does not seem to be a clear and simple answer to what seemed like a clear and simple question: ‘do human skulls continue to grow and move about during adult life’. From where I associate to the fact that in first order logic and following the near century old work of Gödel, there are a lot more questions that you can’t answer than there are questions that you can answer. If memory serves, the former is uncountable, the latter is countable.

References

Reference 1: http://psmv4.blogspot.com/2020/06/phrenology-redux.html.

Reference 2: http://psmv4.blogspot.com/2020/06/why-bother-with-real-libraries.html.

Reference 3: The life story and experiences of a phrenologist – J. Millott Severn, fellow and past president BPS – 1929.

Reference 4: Growth in Fishes - Dutta H – 1994.

Reference 5: 2012 Anthropometric Survey of U.S. Army Personnel: methods and summary statistics - Claire C. Gordon, Cynthia L. Blackwell, Bruce Bradtmille and others – 2014.

Reference 6: Evaluation of Skull Cortical Thickness Changes With Age and Sex From Computed Tomography Scans - Elizabeth M Lillie, Jillian E Urban, Sarah K Lynch, Ashley A Weaver and Joel D Stitzel – 2015.

Reference 7: Changes in the facial skeleton with aging: implications and clinical applications in facial rejuvenation - Mendelson B, Wong CH – 2012.

Reference 8: Dimensional changes in the human head and face in the third decade of life - Melvyn J. Baer – 1956.

Reference 9: The evolution of the human head – Daniel Lieberman – 2011.

Reference 10: Criminal Man according to the Classification of Cesare Lombroso – briefly summarised by his daughter Gina Lombroso Ferrero, with an introduction by Cesare Lombroso – 1911. G. P. Putnam's Sons New York and London. The Knickerbocker Press.

Reference 11: https://www.cdc.gov/nchs/nhanes/.

Reference 12: https://psmv3.blogspot.com/2017/10/on-multi-dimensional-binning.html.