FOM: Re:

Martin Davis martind at
Sun Mar 22 14:38:12 EST 1998

At 04:53 PM 3/21/98 -0700, Reuben Hersh wrote:

>What about the different mathematical models, (none of which
>is perfect!) the different computational tricks to solve a
>system of nonlinear o.d.e.s, the non-well-posed inverse problems
>to try and guess about the density distribution of earth, moon ,
>or any relevant planets, and all the codes, languages and software?
>Do you say that's all out there in space?

Dear Reuben,

I have urging the need for civil discourse in this forum. But I have to
admit that I'm getting increasingly annoyed by your putting words in my
mouth. Why not use the computer to display and reply to what I actually said?

>Of course if you believe any and all math is celestial and
>timeless, than that would apply to the whole big deal to
>track and control a satellite.

Where did I suggest that "Math is celestial"?

>But keep in mind this isn't math as you all talk about it.
>Damn few definitions or theorems.  A lot of guesswork, trial
>and error, seat-of-the-pants know-how.
>You could just say, that isn't math, that's plumbing.  But
>then how do you use astronomy to prove the divinity of math?

Of course, it's math. Embedded in it are logical inferences, calculations
based on theorems or hoped-for-theorems.

I purposely used a theorem from elementary number theory (LT) just to make
it impossible for you to use just this rhetorical dodge. 

>If you think math as it's really done (both pure and applied)
>might really be relevant, then you have to pay attention
>to what's really going on.

Paying "attention to what's really going on" is where you have been making a
real contribution. But the question you have evaded over and over again
although it has been brought up by a number of people on the list: What is
the basis for whatever validity the work of mathematicians has?

As a member of the Courant Institute, I certainly was made aware of
methodological difficulties in applied mathematics. Often there was just
computations and no real theorems. Guess what? When that occurred,
"consensus" disappeared. I witnessed the work of eminent mathematicians
being criticized severely as producing meaningless numbers.


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