being on a manifold.

Descartes said, 'I think, therefore I am.'

How can we reach to 'therefore I am' from 'I think'. 
To present data points, we need data space. Likewise, in order to reach the
conclusion 'therefore I am' we need to find the space for the existence.
Moreover, the 'being' should have any relationship with the space as in set theory. 

Thinking is not enough to be 'being' without any relationship with space
(or at least with other data points which makes the relationship with space.)

A data point is in a data space and the manifold gives more meaning to it. 
Descartes said, 'I think, therefore I am,' but God said, 'I am who I am.'

Dec. 03, 2006
- H. Choi