Re: How much can science tell us about sculling?


"Charles Carroll" <charles_carroll@xxxxxxxxxxx> wrote in message
news:78al7gF1kqkvhU1@xxxxxxxxxxxxxxxxxxxxx

Charles

I have now skimmed the book "A=B" and I don't think it can bear any of the
ideas you try to draw from it. It is not about science, it is pure
mathematics. In broad outline it sets out to describe some computer based
methods for representing certain algebraic expressions in a different form.
This absolutely has no bearing on the nature of science.

By the way, unless you are a professional mathematician, and are interested
in the subject, don't try to read the book. It consists largely of algebra,
interspersed with packets of computer code. It is extremely heavy going.


Alexander,

You write that "anecdote is not science," and I instantly think, Post hoc
ergo propter hoc! Not only does Anecdote not help us understand why
something happens, it also may lead to logical fallacy.

Having said this, I am playing with a new definition of Science. Could it
be that Science may be understood very simply as the search for proof?

What inspires me to ask this are two sentences from "A=B," the book I just
mentioned to Pete.

"As civilization grew older and (hopefully) wiser, it became not enough to
know the facts, but instead it became necessary to understand them as
well, and to know for sure. Thus was born, more than 2300 years ago, the
notion of proof." ("A=B," p. 4)


A closer reading of this, in context, makes it clear that this about
mathematical proof, not science.


Didn't Descartes take a huge leap into the modern world with his phrase
"mathematical certainty?" "The notion of proof," of being able to
demonstrate something with "mathematical certainty," became the decisive
factor in our claims to have understood a subject - be it how objects move
through fluid mediums, the motions of heavenly bodies, a rowing stroke,
etc.

Conversely, if we are unable to demonstrate our understanding of a subject
with "mathematical certainty," can we really claim to know it?

This is why Donald Knuth's statement is so intriguing to me. "Science is
what we understand well enough to explain to a computer." When I read this
sentence I instantly saw it as ultimately Cartesian, that is, we can only
explain to a computer what we can demonstrate to ourselves with
mathematical certainty.


I have already commented on this statement. Now, seeing it in context, in
the Forward to the book:

"Science is what we understand well enough to explain to a computer. Art is

everything else we do. During the past several years an important part of
mathematics

has been transformed from an Art to a Science: No longer do we need to get a
brilliant

insight in order to evaluate sums of binomial coefficients, and many similar
formulas

that arise frequently in practice; we can now follow a mechanical procedure
and

discover the answers quite systematically."


it is clear that Knuth is including mathematics in "science". What he is
saying is that some mathematical proofs, which were produced with great
labour by human mathematicians (Artists) can now be done by computer
programs ("Science").

Of course anyone can, if they wish, like Humpty Dumpty, use a word to mean
"just what I choose it to mean - neither more nor less", but it doesn't help
understanding to call pure mathematics "science".

When I think about it, it seems to me that this is a much more inclusive
notion of science than anything that has so far been proposed. You don't
need to arrive at first principles, at unvarying and immutable laws upon
which the facts depend. Science is only understanding something well
enough to explain it to a computer.

Cordially,

Charles

Sorry to be so negative.

Alexander


.

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