Re: "The map is not the Territory"...

From: stan (stan_at_invalid.com)
Date: 07/31/04 

Date: Fri, 30 Jul 2004 19:51:22 -0500

"Bill Hobba" <bhobba@rubbish.net.au> wrote in message
news:HlBOc.24201$K53.5260@news-server.bigpond.net.au...
>
> "stan" <stan@stan.stan.com> wrote in message
> news:2msjotFqc6itU1@uni-berlin.de...
> >
> > "Robert J. Kolker" <robert_kolker@nospam.hotmail.com> wrote in message
> > news:yA5Oc.208428$XM6.198706@attbi_s53...
> > >
> > >
> > > stan wrote:
> > >
> > > >
> > > > Quite true - math is a tool that helps us understand and can
predict,
> > but
> > > > our math fails us (in many areas) in understanding physical things,
> One
> > > > glaring example: the singularity, black hole and the sqrt(-1)
issue.
> > >
> > > The square root of -1 is perfectly understandable. Take the ring of
> > > polynomials with real co-efficients mod the irreducible polynomial
> > > x^2 + 1 = 0. You get a field in which the root of the polynomial
exists.
> > > The only reason why the square root of -1 is called imaginary is that
> > > mathematicians did not fully understand its nature at firt. But
> > > sophisticaion increased and algebraic concepts were sharpened up.
> > >
> > > Also one can define a commutative division alebra on a vector space
> > > real x real. Goood old i is the unit vectory in the y direction.
> > >
> > > Bob Kolker
> > >
> > I agree with you from a Mathematical point of view, I can throw it
around
> > with the best of them, but if you look at the equations that define a
> black
> > hole or singularity, we run right into i, and trying to relate that to
the
> > physical nature of what a black hole really is - here the imagination
> > starts in.
>
> So you can throw it around with the best of them can you? Just a little
> challenge then please explain to me contour integration, the residue
> theorem, and its application to Wick Rotation? And after that you might
> like to detail exactly where imaginary numbers and GR fits in? Or are you
> simply using one of these buzzard generators based on where Steven Hawking
> takes about imaginary time in his A brief history of Time? Hence my query
> about Wick Rotation.
>
> Bill
>
>

Take your mapping function of Euclidean space and transform it!
Then try transforming n-dimensional Euclidean space and see what happens.