I am taking the liberty of forwarding this to the FRIAM group because I think
it is such a great opportunity. It is the kind of thing large numbers of
people pay big money to go here in some hotel ball room somewhere and it is
happening right here in Santa Fe.Please see below.
Hope to
Glen,
You have made some interesting points. I don't deny that forming a proof
involves invention and symbol manipulation. I also agree that mathematical
truth is different from scientific truth. I now think the core question is
whether a proof, according to the usual rules of symbol manipulat
Thus spake Phil Henshaw circa 10/07/2008 12:15 PM:
> Well, the reliance on competence is relative to the difficulty of the task.
> As our world explodes with new connections and complexity that's sort of in
> doubt, isn't it? Isn't Taleb's observation that when you have increasingly
> complex pro
Or. another angle. Proofs represent discoveries about the invented grammar
they use, with the proviso of "so far as we can see"? The way we define
grammars changes to suite our intentions occasionally, but we're generally
trying to identify things inherent in nature, for grammars drawn as
con
Well, the reliance on competence is relative to the difficulty of the task.
As our world explodes with new connections and complexity that's sort of in
doubt, isn't it? Isn't Taleb's observation that when you have increasingly
complex problems with increasingly 'fat tailed' distributions of corre
Russ,
Oh, just that scientists appear to be one of the main violators of your
self-awareness principle. Scientists tend to describe the physical world
as if they are unaware that science constructs descriptive models of things
far too complex to model, that might behave differently from any ki
Thus spake John F. Kennison circa 10/07/2008 10:53 AM:
> Okay, suppose someone else simply entered some numbers in a Suduko
> grid and said, "I wonder whether there is any solution that
> incorporates these numbers, and, if there is a solution, is it
> unique?" I concede that the person who did thi
Okay, suppose someone else simply entered some numbers in a Suduko grid and
said, "I wonder whether there is any solution that incorporates these numbers,
and, if there is a solution, is it unique?" I concede that the person who did
this invented the problem. But if I prove that there is a solut
Thus spake John F. Kennison circa 10/07/2008 10:01 AM:
> I would like to respond to Wittgenstein's idea that a mathematical
> proof should be called an invention rather than a discovery. When
> solving a Suduko puzzle, I often produce a logical deduction that the
> solution is unique. It seems clea
I would like to respond to Wittgenstein's idea that a mathematical proof should
be called an invention rather than a discovery. When solving a Suduko puzzle, I
often produce a logical deduction that the solution is unique. It seems clear
to me that I discovered that there is only one soluti
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