There have been some good points made in this thread,
and a lot of platitudes.
Below, I do not know what Murray Eisenberg intended by "the specific analogy" --
there is no analogy evident in the example immediately following,
about whether athletes should warm up; I suppose the writer
intended the analogy between doing math to improve reasoning skills,
and doing tire-stepping to prepare for football.
Actually the example immediately following is not well stated,
because the serious question is not whether one should warm up
before exercise, but whether one should warm up before stretching.
I speak as a former college athlete who continues
to compete in track & field, and to take ballet lessons (possibly,
at its best, the most scientific of all exercise programs), and
currently getting therapy to stretch my fingers.
If there are serious people arguing against warming up
before exercise, I'd like to see some citations.
But stretching without first warming up
is quite well understood to be dangerous.
Jonathan Groves and Raymond Greenwell
bring up the obvious point that there are different kinds
of thinking, in fact different kinds of intelligence.
Mathematics surely is usefully related to grammar
rather more than to literature, and to law
rather more than to sociology.
I worked with a very thoughtful lawyer for several years
(in historic preservation) and we both were struck by
how similarly our minds worked.
I gather that to diagram a sentence was not a standard
grammatical exercise in the UK as it used to be in the US,
but it is a way to bring geometrical intuition to bear
on the parsing exercise. Thus it is even closer to mathematics
than most grammatical work, because it is not only
a matter of understanding rules and applying them,
but of displaying patterns in space.
However, it is just arrogance for mathematicians to believe
that only they have the key to real thinking. I used to
suffer from that form of arrogance, but later in life
I had the good fortune to meet many persons of striking
intelligence, who were weak in mathematics, but who could
solve problems of other kinds with infinitely more speed,
skill, and grace than I ever could.
At 08:01 AM 5/19/2010, Murray Eisenberg wrote:
>Why?
>
>Reasoning by analogy can be treacherous. And the specific analogy is dubious (unless there is specific evidence to back up the claim).
>
>For example, trainers typically insist how important it is to warm up, even perhaps stretch, before exercise. But lately quite a few doubts have been raised about that by medical and exercise scientists.
>
>Sometimes common sense and the self-evident is correct; often they are not.
>
>On 5/18/2010 5:49 PM, Martin C. Tangora wrote:
>>(1) I think that the burden of proof
>>that learning mathematics *does not* train the mind
>>belongs with those who make that (negative) claim.
>>Similarly the claim that learning Latin grammar
>>*does not* make one a better speaker and writer of English
>>is so dubious that it hardly deserves our attention.
>>
>>Nobody in the athletics department questions
>>the value of football players high-stepping through
>>automobile tires. It is self-evident that this exercise
>>improves strength and coordination. The fact that
>>the tires are removed from the field of play
>>before the opening kickoff does not detract from
>>the value of the exercise.
Martin C. Tangora
University of Illinois at Chicago
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