If this is what at issue, I note that for one, Erwin Schro"dinger
questioned whether or not real numbers were suitable for use by physicists
to represent physical phenomena, presumably on account of his thoughts
about quanta. If I recall correctly, he suggested that perhaps people had
taken a wrong turn in ancient Greece when they went the way of Eudoxus as
found in Euclid, and eventually came up with what we call the real numbers.
He evidently had hopes that some of the puzzles of quantum theory would be
relieved by the introduction of some new kind of numbers for use in
physical measurement. A number of physicists tried to do something along
these lines. I believe one of these was Philip Bridgman (if Philip was his
first name -- Bridgman, anyway).
I don't know exact references for this. Schro"dinger's speculations on
this topic may have been published in a book called "What Is Life?".
I also recall over the years dipping into treatises and articles on the
nature of physical measurement both by physicists and by philosophers of
science. I expect a subject search in some good library catalog would
yield something. An online catalog which I often use is the MELVYL system
at the University of California at Berkeley. I get to this through a
university computing system, and I don't know if it, or something like it,
can be accessed on the internet. I wonder what would happen if you ran
"physical measurement" through a number of internet search engines?
Gordon Fisher gfisher@shentel.net