In a message dated 04-25-03, Herman Trivilino said to Fred Kantor:

 FK> PMFBI... I'm interested in the foundations of physics;
 FK> especially, re amount and representation of information in
 FK> physical systems.

HT> Would that be information theory?

No. The area of work is called 'information mechanics'.

IMHO, what is called 'information theory' would seem to be based on 
a set of assumptions which does not seem able to support formal, 
quantitative treatment of amount and representation of information,
i.e., 'information bookkeeping'.  Let's go into that a little,
here:

Amount of information equals log base 2 of the number of
possibilities from which one is designated. That amount of
information does not depend on which one of the possibilities was
designated.

Built into the definition of 'the real numbers' and the definition
of 'the integers', is the idea that you can always add another; if
I understand correctly, that assumption traces back at least to the
Pythagorean school, ca 2500 years ago.

That assumption that you can always add another point, means that
one element out of such a set is assumed to be one out of
arbitrarily many possibilities.  For this reason, the amount of
information assumed to be represented by the designation of any one
specific such value appears as log_2(arbitrarily many), which, in
their mathematical picture, can be made bigger than any particular
value.

'Information theory' was based on such mathematics.

IIUC, the axiomatization of information mechanics, in the 1970's,
provided tools for information bookkeeping.

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