[발췌] 정규 분포에 대한 골턴의 묘사

※ 발췌 (excerpts):


출처 1: http://www-history.mcs.st-andrews.ac.uk/Quotations/Galton.html

I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the "Law of Frequency of Error." The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand and marshaled in the order of magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.

... Quoted in J.R. Newman, The World of Mathematics, 1956.


출처 2: Francis Galton: Pioneer of Heredity and Biometry (M. G. Bulmer 지음. JHU Press, 2003) 구글도서

Three reasons underpinned Galton's enthusiasm for the normal distribution. The first was his scientific delight, expressed in this quotation from ^Natural Inheritance^, that such a simple law was so widely exemplified:

^Order in Apparent Chaos.^--I know scarecely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the "Law of Frequency of Error." The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. (Galton, 1889, 66)

But he regarded the law as an approximation, and his psychological investigations led him to think that physiological and psychological variables obeyig the Weber-Fechner law should follow a lognormal distribution; that is to say, they should be normally distributed after a logarithmic transformation (Galton 1879, McAlister 1879). He recognized that it would not apply to weight, which was, he thought, approximately proportional to the square (not the cube) of height (Galton 1874b).

Galton's second reason for emphasizing the normal distribution was his mistaken adherence to Quetelet's idea that it had a priviledged position, and that is mean had a special importance as an indicator of the racial type. Quetelet thought that only the mean value of an approximately normal biological variable, such as chest circumference, is important, and that deviations from the mean are meaningless errors, similar to errors of measurement, to be eliminated from the analysis as far as possible. Mayr (1982) has characterized this style of thinking in biology as essentialist or typological, as opposed to population thinking. In population thinking it is recognized that differences between individuals are real and often reveal the hereditary variability on which evolution depends, while mean values are only man-made constructs. It was necessary to progress from typological to population thinking to understand how natural selection worked. Mayr continued: "Francis Galton was perhaps the first to realize fully that the mean value of variable populations is a construct. Differences in height among a group of people are real and not the result of inaccuracies of measurement. ( ... ... )" (1982, 47)

This assessment exaggerates Galton's progress from typological to population thinking. ( ... ... )

The third reason for Galton's dependence on the normal distribution was technical reason, that its theoretical properties were well understood. ( ... ... )

Galton's Quincunx

( ... ... )


출처 3: Biology, Medicine and Society 1840-1940 (Charles Webster 지음. Cambridge University Press, 2003) 구글도서

Galton himself did not speak of 'intelligence,' but of vaguer entities, such as 'natural ability' and 'civic worth'. He was, however, in no doubt that these qualities would follow a normal or Gaussian distribution in the population, arguing from analogy with stature, which could be empirically proven to be thus. Equally important, one supposes, was Galton's long devotion to the normal curve, which he saw as the 'supreme law of unreason', as something which the Greeks would have deified ha they known of it. What precisely Galton meant by 'natural ability' was never made entirely clear, though it was, in one account, characterized by the trio of zeal, capacity, and power of work. Thus in ^Hereditary Genius^, he wrote as follows. ( ... ... )


출처 4: The Rise of Statistical Thinking, 1820-1900 (Theodore M. Porter 지음. Princeton University Press, 1986) 구글도서
https://books.google.co.kr/books?id=5a2a3jlBNb0C&dq=%EA%B3%A8%ED%84%B4+%22unreason%22&hl=ko&source=gbs_navlinks_s


출처 5: Against the Gods: The Remarkable Story of Risk (Peter L. Bernstein 지음. John Wiley & Sons, 2012) 구글도서

As Galton suggested, two conditions are necessary for observations to be distributed normally, or symmetrically, around their average. First, there must be as large a number of observations as possible. Second, the observations must be independent, like rolls of the ice. ^Order is impossible to find unless disorder is there first.^.


출처 6: 신은 주사위 놀이를 하지 않는다: 로또부터 진화까지, 우연한 일들의 법칙 (데이비드 핸드 지음. 도서출판길벗, 2016) 구글도서

"'오차의 빈도에 관한 법칙'이 표현하는 우주적 질서의 놀라운 형태만큼 상상력을 적절하게 자극시키는 것은 거의 없다. 만약에 그리스인들이 이 법칙을 알았다면 그들은 이것을 의인화하고 신격화했을 것이다. 이 법칙은 더없는 혼란의 한복판에서 자신을 전혀 내세우지 않고 평온하게 지배력을 발휘한다. 군중의 규모가 거대해지고 외견상의 무질서가 커질수록, 이 법칙의 지배력은 더 완벽해진다. 이 법칙은 비이성에 관한 지고의 법칙이다. 카오적인 요소들로 이루어진 큰 규모의 표본이 다수 집적될 때면 뜻밖으로 가장 아름다운 형태의 규칙성이 잠재해 있었음이 어김없이 드러난다."