Re: are Real Numbers evil?

I don't see any relationship between Perspex and the polysigned
numbers.
The Perspex seems to be an errant system that will still have some
decent behaviors.
The polysigned numbers are strict though they do have multiple
representations via nonorthogonality.

The geometrical interpretation of the polysigned numbers just falls out
of the construction.
The symmetry that they possess is a unique feature as far as coordinate
systems go.
You can find others who will espouse 'quadrays' as superior to the
cartesian alternative:

http://euch3i.chem.emory.edu/proposal/www.teleport.com/~pdx4d/quadphil.html
http://groups-beta.google.com/group/sci.physics.fusion/browse_frm/thread/ac35cde89ed5f6c0/7e797cbb721e722f?q=quadray+symmetry&rnum=2&hl=en#7e797cbb721e722f
http://www.grunch.net/synergetics/quadrays.html

The four-signed numbers happen to match this representation but also
have a product defined. The cartesian coordinate system is inherently
less symmetrical than are the triangulated systems.

We can avoid traditional vectors by composing values with unit vectors
in their product. This then allows algebraic representations such as:
a + bi, (a complex number, 2D)
2 i + 3 j - 4 k, (a 3D cartesian value)
- 1 + 2 # 4 . ( a four-signed value )
Whereas the first and the third have algebraic product rules, the
second does not.
This is a weakness of the second form. There are the unit vectors being
taken as products with a signed value but they can't be used generally.

I argue that the space we live in is
P1 x P2 x P3 .
But you can also use P4 to represent 3D space.
That might be a source of confusion.
The first construction includes a time component, a linear axis
component, and a rotational plane component, all orthogonal to each
other.

It may be that you are seeking too fundamental a solution for your
problem.
I'm not really sure exactly what the problem is.
I am picturing things which are connected but can rotate and translate
and so are composed of a myriad of component parts. At that structural
level the basis need not be anything new. It is what you build with
that basis that should form the complexity.

-Tim

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