Science And Math Was: Python's Lisp heritage

[Tim Daneliuk]

Carl Banks wrote:
> 
<SNIP>

> 
> Sorry, but I don't agree that algorithms, or any mathematical concept,
> is an invention of the human mind.  The algorithms have existed since
> the beginning of time.  The quicksort had the property of requiring ~
> n^2 comparisons in the worst case before it had ever been used or
> applied.  We merely discovered this algorithm; we didn't create it.
> 
> So I say mathematics, including the study of algorithms, is a natural
> science.  And, for now, that's all I have to say about it.

I disagree strongly (but am willing to be convinced otherwise).  All of
mathematics is a formal construct of the human mind created with the
intent of removing ambiguity and enhancing our ability to describe what
we *think* and what we *observe*.  We can (and do) create all kinds of new
calculi that are problem- or domain-specific.  That is, we *invent*
mathematics to suit our needs - mathematics is not one-for-one
correspondent to the natural universe.

e.g., Calling the upper-bound of Quicksort N^2 is merely one way of looking at 
the time complexity of this "idea".  There is not some hardwired constant
in the universe that declares heapsort to be O*(N^2) - this is merely an
artifact of the calculus used for Big-O analysis.

The reason I take this position is pretty simple.  We are able to construct
mathematical systems which describe intellectual abstractions for which
there is no natural analog.   That is, mathematics can embrace way more than
just the natural world and its workings.  (Theoretical mathematicians are famous
for their contempt of "mere" Applied mathematicians whom they view as operating in a
very limited, mechanical intellectual domain.)  For instance, even the theoretical
physicists only need about 5 dimensions to describe Life, The Universe, and
Everything, but mathematicians routinely work in arbitrary "n-space" for which
there is not physical/natural correspondent.  Similarly, a mathematician
can introduce ideas like an "Incompleteness Theorem" which is a meta-mathematical
commentary on mathematics itself - something far beyond the domain and range of
mere natural science.

I'm not choosing sides here on the math vs. science debate - both are important
artifacts of the human intellect.  I merely take umbrage with the notion that
mathematics is innately wired into the universe somehow.  


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Tim Daneliuk
tundra at tundraware.com