Rob,
You are missing my point. He is still using a single base number system - than of logs. It doesn't matter which base he uses, as they are inter-convertible.
We all use a single base number system, be it decimal or binary. We don't really know of any other one as we have been using decimals and logs for a few hundred years.
Is that system the best one that can be built? Or can a better one, say using multiple bases in the same number representation, be devised? Such a system might be able to represent numbers we cannot today. If so, then these calculations MAY need to be revised (as well most other ones).
A (poor) analogy is the Romans attempting to build space ships using their Roman numeral system. The calculations would be much too hard and many measurements could not be performed (as they could not properly represent Real numbers). They would not be able to make certain measurements we can today, without proper scaling of numbers.
Might we be in a (somewhat) similar situation, where a more powerful numeric system could be devised that would alter what and how we measure and/or calculate?
Then a different value, inexpressible today, would change what a bit can represent.
As I understand things, Shannon is saying this is the absolute limit regardless of mathematical tools. I am suggesting his statement needs to be limited to the tools we are currently using and there might be a different way, since there might be better mathematical tools.
Don