Python's Lisp heritage

[Huaiyu Zhu]

John Roth <johnroth at ameritech.net> wrote:
>
> The study of algorithms may very well
>be a branch of mathematics, but mathematics is not science.
>
>Science is, among other parts, the study of the natural universe
>and things in it. The study of algorithms is a study of things
>that have been created by the human mind.
	  
I hope the following terminology might be better:

Science is the study of objective descriptions of interesting phenomena.
Natural science is concerned with phenomena independent of human mind.
Mathematics is concerned with formal structures.  Science generally consists
of mathematics and natural sciences (ignoring social sciences here).

Before the invention of computers, the best device for generating
interesting formal structures is a live human with books, pens and lots of
scratch paper.  But mathematics is not about the peculiarities of specific
human thinking.  The word "formal" meant that two reasonably knowledgeable
mathematician would essentially agree on a conclusion if sufficient details
are spelt out.  Nowadays computers themselves generate sufficiently complex
and interesting formal structures that could not be generated by human brain
alone.  Study of algorithms is part of mathematics.

Objectivity is defined by observability, verifiability, refutability, etc.
That applies to mathematics as well as other branches of science.
Mathematicians work by making observations, conducting experiments,
proposing theories, exploring consequences and verifying results, just like
natural scientists do, except that their objects are formal structures.

The structures mathematicians study are discovered.  The symbolic languages
used to describe them are invented, but such inventions are guided by the
structures.

(The natural laws physicists study are discovered.  The instruments used to
observe and experiment are invented, but such inventions are guided by the
physical laws.)

The "unreasonably good applicability" of mathematics in natural sciences is
partly due to the fact that actual structures in the physical world often
give hints of interesting formal structures, partly due to the fact that
problems in natural sciences often influence mathematicians' sense of
"interesting".  However, this does not mean that mathematics is itself part
of natural sciences.

None of the above was intended to _define_ any term.  The intention is to
constrast various terms.

Huaiyu