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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.
> > > 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 .
, 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. Maybe in 27th century mathematics it may mean something else but for the moment it precisely mean.one thing..well '3' ..Else it is not mathematics at least not known mathematics. This illustrates the dynamic nature of math once again.
> Marshall
>
// PS. For some reason, the canonical generic example value
lately is 3. In college it was always 7.//
That's because some numbers are more important to some cultures than others.
For instance, 3 (trinity based heritage) and 7 has strong meaning in
Christian cultures.
On the other hand, 1, 5 have strong meaning to Islamic cultures.
Received on Wed Jun 07 2006 - 14:13:12 CDT