Turing completeness of the functional paradigm?

Hello,
It seems to be the case that _on the absolute scale of things_
temporality is entirely eliminable within the functional paradigm (with
the ideas of state / assignment being merely abstractions, and a state
machine simply a set of spatial, and atemporal sequences).

(This is hinted by Prof. Abelson in a lecture on streams (L6b):
http://swiss.csail.mit.edu/classes/6.001/abelson-sussman-lectures/
with a remark on the nonplausibility of such an approach
implementationally. Still, it is the absolute case that I am after.)

Actually, having pondered Peano's axioms a little more carefully, I
have concluded that there seem to be no nospatial relations whatsoever.

Please, is my thinking erroneous (again, on the absolute scale of
things, and not implementationally)?

Thank you.
Tom

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