> That is a fascinating claim! "...we could argue the UD is 0
> dimensional: it computes an undefined function with 0 arguments."
> What is the quantity of computational resources required for such
> a computation?
Probably null. Provably so with the QM hypothesis or the comp hyp.
>
> A new question is born from your comment: Is your notion of a
> "dimension" flow from linear independence, like that of vectors? How
> does one define the notion of a "basis" in this computational
> dimension?
Yes, it is. Actually in computer science the notion of dimension is not
globally relevant.
See the "parametrisation theorem" or the "SMN theorem" in my "amoeba,
planaria and dreaming machines", or see a textbook like Cutland's one
(ref in my thesis). Such theorems make it possible to code m-variable
function by effective collection of n-variables function.
The combinators exploit this at the start(*)