Science And Math Was: Python's Lisp heritage

[Bengt Richter]

On Mon, 22 Apr 2002 14:50:20 GMT, grante at visi.com (Grant Edwards) wrote:

>In article <mailman.1019483442.32389.python-list at python.org>, brueckd at tbye.com wrote:
>>
>>> > You should understand that this is a philosophical viewpoint. The
>> [snip]
>>> To put this another way, ask yourself where you stand on this
>>> question: is mathematics discovered or invented?
>
Too big a question ;-) Was pi discovered or invented? I'd say discovered ;-)
I.e., I think there are fundamental things, and there are compositions. I would
tend to say that we discover fundamental things, but that we can make/invent endless
compositions. However, when we notice that one of our inventions has an interesting
property, that is a discovery ;-) Or perhaps a re-cognition.

>Very well put.
>
>> Is there a difference?
>
>Yes.  Science verifies it's theories by comparing them to the
Who is that anthropomorphized "Science" ?
>physical world which they are attempting to describe.  It
IMO, when you get to implementation details, comparing theories
to the physical world involves representing both in some medium
where they can be "inspected" for correspondence. This inspection
involves either a programmed process operating on representations
and yielding a true/false indication, or a careful mental version
of the same with associated consciousness of the process.

>doesn't matter how elegant, or internally consistent Science
>is.  If it doesn't successfully describe the physical world,
>it's wrong.
What "physical world" though? And what is a successful description?

IMHO describing the physical world is putting your description into
correspondence with some representation of observations of the physical
world. Those observation representations are not the physical world itself.
They are a product of a special relationship between observer, observation process
and world.

My point is that convincing yourself that something is true "about the world"
is really an operation with representations, and so is convincing yourself
that something is true in mathematics.

It is interesting to speculate on how our ability operate with mental
representations is implemented, and how consciousness arises in conjunction
with some of it, but that would make for a long thread ;-)

>
>Science has an external reference point. Mathematics does not.
How is a cup more like a donut than a bowl? IOW, ISTM many mathematical
concepts owe a lot to relationships we abstract from our perceptions of
the world. Indeed, it would not surprise me if we are hardwired for some
abstract operations, and that the hard-wiring depends on a mapping between
laws of the physical world and laws of thinking. E.g., I suspect that the continuity
of fields under the influence of discrete particles/effects is fundamental
to our unified conscious experience of discretely sensed world and body elements.

>Internal consistency is the only thing which mathematics can
>attempt to verify.  Mathematics is not an attempt to describe
>the physical world.
>
>> One could argue that the only difference between discovery and
>> invention is the arrogance of the person reporting it.
>
>One could.  But one would be missing the point.
>
One could also be missing _a_ point by dismissing a thought ;-)

IOW, when I invent something, I don't know how I do it, any more than
I know how "I" select and activate the muscles it takes for me to walk
or circulate my blood[1]. So, to say that "I" invent something is a kind of
foolish arrogance. It's more like a happy privilege to discover that my
mind/brain has produced a (to me) new combination of thought elements.
Of course, if someone else is playing with similar mental Lego pieces,
it's not unlikely that they will have a similar experience. (USPTO take note ;-)

[1] That's not to say they can't be identified objectively and scientifically
investigated. It's saying that I don't consciously know how "I" control my
body (if and when I do ;-)

Regards,
Bengt Richter