Re: Programming is the Engineering Discipline of the Science that is Mathematics
Date: 7 Jun 2006 13:25:51 -0700
> 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.
Yep. Lets' give it a few years...
> > > > > 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.
Mathematics is abstract concept and can not be incarnated therefore you can not really have math *objects*. In nature, "Seeing" math can only mean seeing representation of that absract. By definition math are incarnated by how and why they represent the universe.
> 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.
Yes we agree on that.
> 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?
Interresting theory.. Just do not tell that to mathematician (they would burn you in public place for heresy) ;).
> 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
I guess we have reached the end of discussing your theory...I can not really follow you onto unicorns and horses starting from relationship between math and science.. Nice exchaning with you though...
> PS. 5 is right out.
Just do not bring 0, just do not bring 0 , just do not bring 0 LOL Received on Wed Jun 07 2006 - 22:25:51 CEST