csc@watmath.UUCP (Computer Sci Club) (05/20/84)
My article on concerning the cause of observed differences between men and
women has generated much (sometimes heated) comment. First note that what
I said was that; 1: We have no strong evidence that differences between
men and women in mathematical ability (this was singled out because this
differeces are large and I know about them, not for any other reason) are
purely (or even predominantly) enviornmental. 2: No one doing research in
this area should be critisized for being sexist.
A seperate question is "should such research be done?" I touched upon
this question but did not treat it in much detail. Many of the replies
(esp. those of Mario Vietri) have centered on this question. Many of the
arguments I consider to be falacious. This is best illustrated by the sad
case of the TQ (tallness quotient).
Dr Jones: I have been studying basketball players and have come up with
a new scale I call tallness. It is easy to determine the tallness of any
person (appendix A), and test, retest correllation is excellent. To each
person we assign a tallness quotient,TQ, the ration of this persons tallness
to the average. I have noted that professional basketball players have an
average TQ far above that of the population at large (significant at the .0001
level). I propose to study the TQ further. I wish to study the wide variation
of TQ among races, and between sexes. I wish to try and find out what causes
the variations in the TQ with possible future benefits in helping those with
esp. low TQ. I would also like to study the relationship between TQ and
playing basketball, but I fear the relationships may be too complicated (it may
be that TQ has no direct effect on playing ability but that both are related
by some common cause). I submit that TQ is interesting in itself.
The critics were swift to reply:
Dr Jones is an idiot. It is clear that there are many factors which go into
making up a good basketball player. Speed, coordination, stamina, intelligence,
ability to cooperate with other players and with the coach. Seperating out
this "Tallness Quotient" is meaningless.
Dr. Jones is an idiot. Take the cases of A,B,C and D, all of whom had
relatively low tallness quotient and yet all were excellent basketball
players. But E,F,G and H and myself all have high tallness quotient and
we can't play basketball worth a damn. This TQ doesn't mean a thing.
Questions as to whether one group or another is higher in average TQ are
irrelevent. There is always wide variation inside the groups. There are
much better ways to test basketball playing ability, and people should
be treated as individuals not as members of some group. It is a waste
of effort to study this TQ.
Dr. Jones is racist. He knows that other races, notably some African
races, have lower TQ than the North Americans. This is but another
scheme to subvert science into proving racial "superiority". If
Generic University has any ethical backbone they will fire Dr. Jones
immediately.
Dr. Jones is sexist...
Tallness is caused by many enviornmental factors. Consider the case
of H who was starved when young and hence has a low TQ. Open your
eyes to the real world Dr. Jones, you blind idiot, this happens all
the time. We should direct our efforts to eliminating malnutrition
not waste them studying differences in TQ.
The TQ score can be increased easily, for instance I can raise my
TQ substatially by putting wedges is my shoes. This does not make
me a better basketball player. TQ is obviously meaningless.
Dr. Jones was dismissed due to widespread protest. He was later
found dead in his apartment (it appeared he had been killed by a
poison dart fired from a blowpipe).
Note that many of the above points are valid, it is the conclusions that
are falacious. In particular, height is not the only factor in basketball
ability, people be judged on their ability to play basketball not on
their height, differences in average height are no basis for racial
or sexual "superiority", malnutrition can cause stunted growth and
should be combatted whatever the results of Dr. Jones studies. However,
height is an important property of human beings and studies of it
have lead to greater understanding of the way our bodies work and even
cures for cetain types of dwarfism.
Now substitute mathematics for basketball, and some suitable test
(even IQ though there are better ones) for the TQ. The analogy
is not exact. The test, retest correlation will only be good, not
excellent. The relation between the score and the pratice of mathematics
will not be clear at all (though note above I made the assumption that
no one knew why taller people play better basketball). The causes of
variations in the score will be more complicated (in particular
cultural differences and training will effect the score). But the
score remains interesting, IN ITSELF. It may be that the problems
involved in studying it will be too intractable and no progress will
be made. Decisions will have to be made by those who allocate
resources to scientific study (only they will have the information
and the experience to judge). The results will have no bearing on
"superiority", and the score is of limited use in studying individuals.
But the results of the study may still be very interesting. (Of what
use is a coil of wire and a magnet Mr. Faraday. "Of what use is
a newborn baby?")
William Hughes