Continued from Part 1

In his book *Hereditary Genius*, Francis Galton provides an excellent illustration of this phenomenon with data from the Cambridge Mathematical Tripos.
There were two degrees in the old Cambridge system, an honours degree
and a pass degree. In the original Tripos, which ran from 1748 - 1909,
the honours students were ranked based on how many points they scored on
the exam. The highest scorers were called Wranglers and those below
them Optimes, while the very highest scorer was called the Senior Wrangler. The candidate who scored lowest, but still managed to perform at the honours level was called the Wooden Spoon. Here is what Galton has to say about the matter:

"*There can hardly be a surer evidence
of the enormous difference between the intellectual capacity of men,
than the prodigious differences in the numbers of marks obtained by
those who gain mathematical honours at Cambridge. I therefore crave
permission to speak at some length upon this subject, although the
details are dry and of little general interest. There are between 400
and 450 students who take their degrees in each year, and of these,
about 100 succeed in gaining honours in mathematics, and are ranged
by the examiners in strict order of merit.*

*About the first forty of those who take mathematical honours
are distinguished by the title of wranglers, and it is a decidedly
creditable thing to be even a low wrangler; it will secure a
fellowship in a small college. It must be carefully borne in mind
that the distinction of being the first in this list of honours, or
what is called the senior wrangler of the year, means a vast deal
more than being the foremost mathematician of 400 or 450 men taken at
hap-hazard. No doubt the large bulk of Cambridge men are taken almost
at hap-hazard. A boy is intended by his parents for some profession;
if that profession be either the Church or the Bar, it used to be
almost requisite, and it is still important, that he should be sent
to Cambridge or Oxford. These youths may justly be considered as
having been taken at hap-hazard. But there are many others who have
fairly won their way to the Universities, and are therefore selected
from an enormous area. Fully one-half of the wranglers have been boys
of note at their respective schools, and, conversely, almost all boys
of note at schools find their way to the Universities. Hence it is
that among their comparatively small number of students, the
Universities include the highest youthful scholastic ability of all
England. The senior wrangler, in each successive year, is the chief
of these as regards mathematics, and this, the highest distinction,
is, or was, continually won by youths who had no mathematical
training of importance before they went to Cambridge.*

*... *

*The examination lasts five and a half hours a day for eight
days. All the answers are carefully marked by the examiners, who add
up the marks at the end and range the candidates in strict order of
merit. The fairness and thoroughness of Cambridge examinations have
never had a breath of suspicion cast upon them.*

*Unfortunately for my purposes, the marks are not published.
They are not even assigned on a uniform system, since each examiner
is permitted to employ his own scale of marks; but whatever scale he
uses, the results as to proportional merit are the same. I am
indebted to a Cambridge examiner for a copy of his marks in respect
to two examinations, in which the scales of marks were so alike as to
make it easy, by a slight proportional adjustment, to compare the two
together. This was, to a certain degree, a confidential
communication, so that it would be improper for me to publish
anything that would identify the years to which these marks refer. I
simply give them as groups of figures, sufficient to show the
enormous differences of merit. The lowest man in the list of honours
gains less than 300 marks; the lowest wrangler gains about 1,500
marks; and the senior wrangler, in one of the lists now before me,
gained more than 7,500 marks. Consequently, the lowest wrangler has
more than five times the merit of the lowest junior optime, and less
than one-fifth the merit of the senior wrangler.*

*The results of two years are thrown into a single table. *

*The total number of marks obtainable in each year was 17,000.*

* *

*The
precise number of marks obtained by the senior wrangler in the more
remarkable of these two years was 7,634; by the second wrangler in
the same year, 4,123; and by the lowest man in the list of honours,
only 237. Consequently, the senior wrangler obtained nearly twice as
many marks as the second wrangler, and more than thirty-two times as
many as the lowest man. I have received from another examiner the
marks of a year in which the senior wrangler was conspicuously
eminent.*

*He
obtained 9,422 marks, whilst the second in the same year—whose
merits were by no means inferior to those of second wranglers in
general—obtained only 5,642. The man at the bottom of the same
honour list had only 309 marks, or one-thirtieth the number of the
senior wrangler.*

*...*

*The
mathematical powers of the last man on the list of honours, which are
so low when compared with those of a senior wrangler, are mediocre,
or even above mediocrity, when compared with the gifts of Englishmen
generally. Though the examination places 100 honour men above him, it
puts no less than 300 “poll men” below him. Even if we go so far
as to allow that 200 out of the 300 refuse to work hard enough to get
honours, there will remain 100 who, even if they worked hard, could
not get them. *"

From the table, we see that the scores are indeed positively skewed. One amusing story about the Tripos is that William Thompson, later Lord Kelvin was universally acknowledged as the best in his year at Cambridge, so when the Tripos results were posted, he asked one of the college servants, "Go see who is the second Wrangler." The servant did so and then responded, "You are, sir." Someone else had beaten him.

* *

Good illustration!

ReplyDelete(As an ex-uni examiner - I assume that each examiner's mark was scaled and given the same proportionate weight, before adding the marks!)

I don't know if you know an interesting bit of folklore concerning the Mathematical Tripos, which is that the Second Wrangler lists seem to contain more men of genius than the First Wrangler does! Like Lord Kelvin and James Clerk Maxwell.

I don't know if this is a real fact, but there certainly are several genius Second Wranglers. https://en.wikipedia.org/wiki/Category:Second_Wranglers

I tend to assume that this is because the best people at examinations (esepcially the Mathematical Tripos, which required a vast amount of study and slog) are those who are very high in Conscientiousness, as well as Intelligence - and (beyond a moderate degree) conscientiousness is inversely correlated with genius.

(Because geniuses need to be inner motivated, and conscientiousness includes high responsivity to external, societal, norms.)