- STATISTICS 525
useful. An early example was an argument intended to prove that the world was
designed for human habitation based on the ratio of male to female births. In 1710
Queen Anne's physician John Arbuthnott (1667-1735) published in the Philosoph-
ical Transactions of the Royal Society a paper with the title, "An argument for
Divine Providence, taken from the constant regularity observ'd in the births of
both sexes." In that paper Arbuthnott presented baptismal records from the years
1629 through 1710 giving the number of boys and girls baptized during those years.
In each of the 82 years, without exception, the number of boys exceeded the num-
ber of girls by amounts varying from less than 3% in 1644 (4107 boys, 3997 girls)
to more than 15% in 1659 (3209 boys, 2781 girls). Arbuthnott inferred correctly
that the hypothesis that births of boys and girls were equally likely was not plau-
sible, since it implied that an event with probability 2~^82 had occurred. He even
consulted a table of logarithms to write this number out in decimal form, so as to
impress his readers:
1
4 8360 0000 0000 0000 0000 0000 '
Exhibiting the usual haste to reach conclusions in such matters, Arbuthnott con-
cluded that this constant imbalance must be the result of a divine plan to offset the
higher mortality of males due to violence and accidents.^15 He did not, for example,
consider the possibility that more girls than boys were simply abandoned by moth-
ers and fathers unable to support them. His final conclusion was that polygamy
was against nature.
2.1. Quetelet. The first work on statistics proper was a treatise of 1835 entitled
Physique social, written by the Belgian scientist Lambert Quetelet (1796-1874).
Quetelet had been trained in both mathematics and astronomy, and he was famil-
iar with the normal curve. He was the first to use it to describe variables other
than those representing observational errors. He noticed certain analogies between
probabilistic concepts and physical concepts, and he introduced them into social
analysis. The most famous of these concepts was the "average person" (I'homme
moyen), which he hoped could play a mathematical role similar to its physical
analog, the center of gravity of a physical body.2.2. Statistics in physics. One of the places in which individual phenomena
are too numerous and too chaotic for analysis is in physics at the molecular level
and below. Statistics has become an important tool in analyzing such systems. A
very good example is thermodynamics, in which thermal energy is considered to
be stored in a hypothetical (unobserved) translational and/or rotational motion of
molecules against resisting forces that are equally hypothetical. In the simplest
case, that of an ideal gas, there are no resisting forces and there is no rotational
motion of molecules. All the thermal energy is stored as the translational kinetic
energy of the molecules, which determine its temperature. At room temperature
helium, which is monatomic, is the best approximation to an ideal gas.
In a way, thermodynamics, and in particular its famous second law, is only
common sense, but physics needs to explain that common sense. Why can heat
flow only from higher temperature to lower, just as water can flow only downhill? If
temperature is determined by the translational kinetic energy of molecules, objects
(^15) In his day, death from contagious disease was at least as common in women as in men, perhaps
even more common, due to the dangers of childbirth. Death from the debilities associated with
old age was relatively uncommon.