If mathematics is computing, and all computing is physical, then …

the issues of infinities (of any level and type) reduce to questions about the existence of various kinds of computers (“machines”) in nature: **Z(**eno)-machines and **U**-machines and so on.

The U-Machine: A Model of Generalized Computation

Bruce J. MacLennan

web.eecs.utk.edu/~mclennan/papers/U-Machine.pdf

*Other physical realizations of the U-machine will operate on fields, that is, on continuous distributions of continuous data, which are, in mathematical terms, the elements of an appropriate Hilbert function space. This kind of computation is called field computation.*

(The “U” is for Pavel Samuilovich Urysohn.)

Physico-formalist philosophy of mathematics (lecture course)

László E. Szabó

(2015-05-31)

Mathematics Is Physics (arXiv)

M. S. Leifer

(Submitted on 11 Aug 2015)

Mathematics can be seen as a collection of *machines*, or as a collection of (domain-specific) *languages*: DSLs.

e.g.,