June 24, 2010

I was saddened to hear of the recent death of Manute Bol.  As you know, he was a 7’7″ member of the Dinka tribe who played for several years in the NBA.  He devoted nearly all of his resources in trying to help his native Sudan (perhaps in a misdirected way, but that is a discussion for another forum) and died essentially in poverty.  As you may recall, there was a life-size poster of Bol in the gym at our elementary school.  Although he was the tallest professional hockey player of all time, he was not close to being the tallest person ever.

I think we both saw the episode of The Amazing Race that featured He Pingping and Bao Xishun, at the time the world’s shortest and tallest men.  He was 2’5″ whereas Bao is 7’9″, a difference of 5’4″.  (He also recently died, whereas Bao lost the title to Sultan Kösen.)

The range of human dimensions is just amazing, isn’t it?  And that isn’t even considering the possibility of other hominid species like the hobbits I had mentioned previously.  As noted on p. 358 of A Short History of Nearly Everything by Bill Bryson, Linnaeus “made room for mythical beasts and ‘monstrous humans’ whose descriptions he gullibly accepted from seamen and other imaginative travelers.  Among these were a wild man, Homo ferus, who walked on all fours and had not yet mastered the art of speech, and Homo caudatus, ‘man with a tail.'”  Bryson goes on to say on p. 368 that the world “is actually enormous—enormous enough to be full of surprises.  The okapi, the nearest living relative of the giraffe, is now known to exist in substantial numbers in the rain forests of Zaire—the total population is estimated at perhaps thirty thousand—yet its existence wasn’t even suspected until the twentieth century” going on to further describe the large flightless bird from New Zealand called the takahe and the Tibetan breed of horse called the Riwoche.  I do wonder if there are other hominid species around, but we just don’t know about them.

Coming back to our own species, there are whole books on the topic of human body size variation and the advantages of being short and the advantages of being tall.  The principle of allometric scaling, which we previously discussed here, is used in many of the arguments.  The most easily accessible examples are in sports.  For example, wikipedia argues that different positions in soccer have different optimal heights.  Since the World Cup is going on these days, there is an interesting opportunity to see if the height distribution of a team is predictive of performance.  Squad lists for each of the 32 teams, including the heights of each player, are provided on the FIFA website.  For example, the 23 players on the American side have the following heights (in cm): [187, 183, 184, 185, 192, 168, 170, 185, 178, 173, 178, 175, 178, 185, 180, 168, 185, 193, 183, 175, 193, 175, 192].  Even if the height distribution turns out not to be predictive of much, I think just the mapping of the height distributions would be very interesting.  I know you have some interest in information geometry, so this would be a kind of “demographic information geometry.”  It might also play well into your interests in dimensionality reduction since the map would hopefully not be in a high-dimensional space.  Also, the height distribution should probably be treated as a multiset rather than as a sequence (or perhaps a partially ordered set, using the players’ positions).

Readers of this blog might wonder why such fascination with anthropometry.  Besides the fact that is just generally interesting, that it may have applications in medicine, that it may be useful in determining genotype-phenotype relationships from genome wide association studies, and that it is useful in an engineering sense for the clothing industry, it is actually historically a topic that led to foundational developments in statistics (for estimation rather than detection as you detailed previously).  You had mentioned the work of Mahalanobis, but it seems that Galton was previously inspired to come up with the concept of correlation due to his anthropometric studies.

The traditional approach to anthropometric surveys has been to make some number of physical measurements on a large number of people.  For example, 240 body part measurements on the United States Army.  A more modern approach is to use three-dimensional whole-body scanners; this was used in two large scale surveys in Britain and the US, both sponsored by industry.  There seem to be all kinds of sampling questions though.  The first is the sampling of subjects and is a classic topic in statistics.  The second more interesting one, however is the sampling in the scan itself, a signal processing topic.  Is there a Nyquist-like or FRI-like sampling theorem for the signal class of human bodies?  How many measurements are needed to be able to reconstruct a human’s physical dimensions?  Slightly more easily than a full sampling theorem, due to scaling, is it possible to recover certain body measurement functionals from a set of other body measurement functionals?  There have actually been several weird studies along these lines, using simple correlation statistics that even Galton would recognize.

One use of all this anthropmetric data is to come up with standardized clothing sizes, a problem of categorization and quantization.  In men’s clothing, the names of the sizes often correspond to some physical measurement such as the lengths of the waistband and inseam for pants.  In women’s clothing, however, the names of the sizes are on an arbitrary numerical scale, which leads to all kinds of problems like vanity sizing.  In either of these cases, however, one or two numbers cannot be enough to describe the cut.  Perhaps a sampling and quantization theory of anthropometry will allow us all to have tailor-made clothes.

As a closing thought, let me congratulate someone who recently had a son that was 7 lbs. even and 1’9″ tall at birth.  Apparently an average North American newborn baby is 7.5 lbs. and 1’8″ tall, with 95 percent of full-term newborns being 1’6″ to 1’10” inches tall and weighing 5.5 to 10 lbs, so right on.


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