🚀 go-pugleaf

In article <Bv53wy.L9r@news.cso.uiuc.edu> jjt@uihepa.hep.uiuc.edu writes:
>In article <1992Sep25.065628.25017@CSD-NewsHost.Stanford.EDU>, pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>
>   (...stuff deleted for brevity...)
>
>> We constructed several hypotheses about what the coefficients of a
>> formula might be, and tested them against the data to get some idea of
>> the robustness of the different formulae being used to model the
>> sequence.
>
>This sounds to me like the caterpillar in "Alice in Wonderland."  Webster
>notwithstanding, in scientific research "experiment" implies observation of 
>the external world, not computation of the results of a mathematical model.  
>
>Suppose you are trying to determine the roots of x**2 +x -2 , and  you use
>an approximation method to determine that one root is about 0.997. Is that
>an experimentally determined quantity?  Not in the scientific sense.

By this argument Mandelbrot's preliminary exploration of the shape of
the Mandelbrot set could not be considered "experimental."  Sounds like
you've defined "experiment" so as to rule out altogether the
possibility of experimental math.

I can think of one reason you might want to do so, namely because it is
"clear" that physics and math are about different worlds, natural and
Platonic.  But that would mean that your argument, that math and
physics are as different as you say, is circular, mediated by what you
and not the dictionary believe a word *should* mean, with your belief
in turn based on a premise you are now trying to prove.

Does the term "experimental math" create any problem for you besides
conflict with an old prejudice about the meaning of "experiment" that
has now been outdated by the advent of the computer?

Neither mathematics nor physics will ever be fully understood, and for
the same reason: they are both too complicated.  Moreover the
complexity has the same basic roots:  in mathematics there are too many
things that can happen when theorems interact, and dually when
structures interact, for us ever to know them all.   Likewise in
physics when particles interact, and dually when waves interact, the
full consequences are unknowable.  Anyone who doubts either of these is
seriously confused about that subject.

It follows that we should respect both the theoreticians and the
experimentalists in both subjects.  Backing one kind to the exclusion
of the other would greatly impede the progress of science.

-- 
=================================================== In short, I am floundering
Vaughan Pratt   pratt@cs.Stanford.EDU  415-494-2545 around and don't take what
=================================================== I say seriously.