Thursday, August 26, 2010

Mediocre regression

Our year were the first to do General Studies in the Sixth Form. There was an external exam, but it did not count formally for anything, was just one of the early steps in the various efforts that have been made to broaden out the curriculum, which was even tighter, & started to be so at an earlier age back then, not least because of the need to do Latin.

Latin O level was a condition of entry for those aiming to study for a BA in virtually any subject at most English universities, & in the days when 8 'O' levels were regarded as plenty, keeping up Latin usually meant dropping at least one of your science subjects from the mix.

At our school the teaching load for general studies was shared between different teachers. I especially remember one term being taught by the RE teacher, who was also the parish priest, who had us discussing what ‘being normal’ means & introduced us to Galton’s study of the heights of parents & children. When I said that I was exactly half way between my parents in height, he told me that meant I was the perfect regression. I think he meant it to sting – we didn’t really get on for some reason, perhaps because he was a very short (and rotund) man - & until that lesson we thought of regression as a going backwards, back to animal nature, the opposite of progress & civilisation.

Edna Healey says in her biography of Emma Darwin that her husband Charles was, like his father Robert & grandfather Erasmus, ‘well over’ 6 feet tall’ (various internet sources say 5’ 11½”). That surprised me because for whatever reason I have always thought Darwin was quite short, as were many Victorians; thinking of him on the Beagle meant he was always, in my mind, associated in some way with the short-of-stature Admiral Nelson. Darwin’s height can only have added to the discomforts of that voyage – it’s no wonder he liked to spend long hours riding & roaming free when he was on dry land.

Francis Galton was of course a cousin of Charles Darwin (his mother was Charles’s father's half sister by Erasmus’ second wife). It occurred to me to wonder if Galton had a particular family reason for investigating the relation between the heights of parents & children – perhaps a little cousinly jealousy at Charles’s superiority? I haven’t been able to find any information on Galton’s height but the explanation for his choosing height shows that my suspicion was unworthy – there were good technical reasons for his choice. Still, by deciding to call it ‘regression to mediocrity’ Galton leaves a suspicion in the modern mind which regards the mediocre as simply not good enough.

Galton deploys a nice clear argument from first principles about why height should follow ‘the beautiful regularity’ of what we now call the Normal curve.

The Normal curve, or Law of Error, depends first upon there being many separate sources or causes of difference between individuals & then that these differences add together (rather than, for instance, multiplying up) to produce the overall difference from the mean. Finally positive differences must be just as likely to occur as negative ones, & small differences must be more likely than large ones.

For Galton height depends on many elements all of which vary between individuals – the lengths or thicknesses of more than a hundred parts of the body ‘each so distinct from the rest as to have earned a name by which it can be specified’. These include fifty separate bones, two cartilages at each joint, the thickness of the scalp & the soles of the feet.

A long way from current popular ideas of a gene ‘for’ everything, & one that we would do well to remember, particularly when thinking about why some people are fatter than others.

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