# Building a hybrid and dynamic mathematical space

1. Apr 13, 2006

### Alvaro.Castro.Castilla@gmail.com

building a "hybrid" and dynamic mathematical space

Hello,

Maybe I'm going to say very stupid or crazy thing for real
mathematicians (I'm an architect):

I want to build a concept that I call "dynamic abstract space" ("das"
from now) for a digital architecture project. I would like to be able
to say the idea I have in mind with mathematics.

This is the essence of the idea:
1) I have a n-dimensional space (the "das") which is built from gluing
together ANY number of ANY type of spaces:
A boolea algebra, a Minkowski space, a ring, R=B3, N, C...

2) Then I introduce particles in my space which are m-dimensional
spaces. If the particles are cointained in the space, then there is no
dynamic reconfiguration of the space, but if the particles are not
contained, the space grows until is able to contain them (for example
in a R=B2 space if we want to insert a R=B3 particle, we have to expand
the space up to R=B3, in a very simple situation). That is the reason I
call it "dynamic".

How to mathematically define that space and that particles?
What do you think of explaining programmable objects and their
variables through this "spaces" and "particles"?

-----

The second thing I would ask is:
Is it correct to say that inside a computer simulation we are inside a
mathematical space of, for example:
R=B3 * R+
for a 3-d space running in a continuous time, or:
R=B3 * N
for a 3-d space running in a step by step basis.
?