Re: Programming is the Engineering Discipline of the Science that is Mathematics

Cimode wrote:
> Marshall wrote:
> > Cimode wrote:
> > > Marshall wrote:
> > > >
> > > > Hrm, well, I wrestled with what word to use there, and settled
> > > > on the bland "useful". My understanding (I'm not a scientist) is
> > > > that one determines the utility of a hypothesis by testing its
> > > > predictive ability. Hypotheses with strong predictive ability
> > > > give us information about how the universe works, which I
> > > > would propose is interesting and useful regardless of social
> > > > context. I did not intend a narrow meaning such as "what will
> > > > make our stock price go up."
> > >
> > > I see...you mean *useful* as a charateristics of hypothesis tthat can
> > > represent nature in a thrustworthy and reasonnable manner. Don't you
> > > think *reasonnable* would be a good substitute to *useful* which would
> > > then become a consequence and not a characteristics of science?
> >
> > Well, I want a term that's as generic as possible. "Reasonable"
> > seems less generic that "useful." Also, the connotation of
> > reasonable is that it would appeal to the intuition of an
> > ordinary man, and in that sense, I would not say that
> > e.g., relativity is reasonable.
>
> I see your point, *reasonnable* seems to be unsufficient. *useful*
> bothers me as it is a consequence rather than a describing
> characteritics of what may be a good hypothesis.
>
> Your example about relativity is interresting. Is hypothesis behind
> relativity useful? I prefer *sound*. I understand now why this
> question bothered you.

It's clear I don't have le mot juste yet.

> > > > One never tests a mathematical idea by conducting an
> > > > experiment. One tests a mathematical idea by doing more
> > > > math. It is self-contained in a way that chemistry is not.
> > > > Chemistry has beakers and flasks and huge vats of
> > > > bubbling chemicals, and also symbols on the chalkboard.
> > > > Math has the symbols on the chalkboard, but no beakers
> > > > or anything like them.
> > > I see...
> > > What about mathematical ideas that are generated or invalidated from
> > > observation of computing?
> >
> Hmmm. I see your point: since the computer exists in the natural
> world, we could sort of call something we did with the computer
> an experiment. It's not entirely clear to me, though; the computer
> merely moves around symbols; it is our interpretation of these
> that gives the process meaning, is it not? Can math be reduced
> to purely syntactic issues?
>
> No but math can be reduced to numbers and math are based on a direct
> equation of meaning between numbers and the symbols that represent them
> . Else it is not math.
>
> >
> > > > Above I noted the example of hyperbolic geometry. Can
> > > > one conduct an experiment to determine whether hyperbolic
> > > > or Euclidean geometry is more "true?"
> > >
> > > I do not know. But above is an example that demonstrate the influence
> > > of observation over math. I think there is at least a bidirectional
> > > relationship between math and nature.
> > > [...]
> > > Very interresting indeed...But don't you think that this relationship
> > > is not as unidirectional as you imply?
> >
> //I'm not sure. I'm not sure it's any-directional. I think of math's
> relevance to the real world is as by-analogy. //
> I think the structural relationship between math and nature is
> bidirectional as math is dynamic concept.
>
> The example provided proves that mathematics is subjected to
> observation of nature.
>
> //I have never seen any mathematical construct in the real world//
> Well here is one for you: take a microsope and observe an snowflake.
> You will see a perfect example of Fractal Mathematics .

I agree that there are many things that are well-described by mathematics in the natural world. I disagree that there are mathematical objects directly present in the real world.

I might have a basket with 3 oranges, but I can never have a basket with just 3 in it.

I might be able to accurately predict the volume of a soccer ball using equations about spheres, but I'll never directly see a sphere in the real world; a sphere is made up of points, and the real world has no points in it. At least, not with the instruments I've used to go looking for them.

> , although
> I *can* use math to make predictions about the real world.
> (Likewise, I have never seen any real-world object in math.)//
>
> //Is 3 a real thing? I used to wonder about that. And in fact I
> have put the question directly to a few of the best minds in
> computer science. They mostly shrug. I now see why: it's
> not that interesting a question.//
>
> I do not quite understand what you are getting at...3 is the
> mathematical symbol representing a number value extracted from an
> ensemble of both reals and integer subset.

In strict English grammar, we would say "3" is the mathematical symbol representing a number value. But 3 is not the same thing as "3". 3 is the actual number; the successor to 2, *not* the glyph. "3" is a real thing, because symbols *do* appear in the natural world. You see them on pages of math books all the time. But is 3 a real thing, the way horses are real and unicorns are not real?

I rather think 3 has more in common with unicorns than with horses. (This is of course a metaphoric statement rather than a literal one.) But I find 3 to be ... useful nonetheless.

Marshall

PS. 5 is right out. Received on Wed Jun 07 2006 - 22:08:48 CEST