[FOM] Regarding Integer/Real Multiplication

[Harvey Friedman]

This is a very brief response to
http://www.cs.nyu.edu/pipermail/fom/2015-September/019003.html

I said that multiplication of nonnegative REALS is grounded in the
idea of areas. That multiplication of nonnegative INTEGERS is grounded
in the idea of counting.

I got the impression that Mark Steiner was under the impression that I
was saying something else.

Both addition and multiplication can be viewed as special cases of
many mutually different and diverse general theories, especially ones
involving abstract nonsense (in the technical sense with commutative
diagrams). At least superficially, this is an in house mathematical
development, perhaps of great mathematical importance. Although there
is no question as to the great general importance of measuring
(counting and areas and volumes, etc.), for practically the entire
science/engineering world outside of mathematics, it remains to be
seen just how universally fundamental the abstract nonsense setups
are.

Harvey Friedman