Re: [Phys-l] Another t trivial question

[ludwik kowalski <kowalskil@mail.montclair.edu>]

On Jan 4, 2011, at 2:20 PM, John Denker wrote:

> On 01/04/2011 12:10 PM, ludwik kowalski wrote:
> > Suppose I create a 2D coordinates system that has three axes, at 60
> > degrees with respect to each other. It has three triants (what is a
> > better name three regions in such space?). Suppose I use this system
> > to describe rooms. Suppose the axes are labeled (a) for the absolute
> > pressure, (b) for the absolute temperature, and (c) for the floor  
> > area. Is
> > there anything heretical in doing this?
>
> Yes (in almost all cases).
>
> There is a theorem that says you cannot map 3 dimensions onto
> 2 dimensions in a way that is one-to-one and continuous.
>
> So ... except for the unusual case where your data was somehow
> confined to a 2-dimensional subspace of the nominally 3-dimensional
> space (pressure, temperature, area) ... something bad is going to
> happen if you try to plot 3 axes in the plane.

I deliberately selected a case in which three coordinates are always  
positive. Each positive axis begins at the origin, not at infinity.  
Plotting three positive axes in 2D space is actually easier than in  
plotting three positive perpendicular axes in 3 D space.

Ludwik

http://csam.montclair.edu/~kowalski/life/intro.html