Science is countable.
Something cannot really be said to be science unless
there is a representation which can be communicated
between scientists. (If there's an idea in one person's
brain, but that person can't transmit it to someone
else's brain - you can't call that scientific.)
Scientific representations are countable, because every
scientific representation can be mapped to a finite list
whose elements come from a finite set of symbols.
Mathematics is countable. The set of real numbers is
uncountable - but the numbers which can be represented
by mathematics is countable. So, there are real numbers
which are unrepresentable (and in fact, most of them are unrepresentable).
Um, Wow. In response to Gorgonzola's writeup:
If I had wanted to say that all the science that will be achieved within the (useful) lifetime of this universe is finite, I would have made a node with an appropriate title. If I had wanted to say that all the representations that can be practically made within this entropy-ruled universe is finite, I would have chosen a different node title. I have known these things for quite some time, and I don't think they are really interesting enough to make nodes out of. So I didn't. That's not what I wrote about.
There is one thing I did not make clear in the original post. When I wrote about a "scientist", and a "person"'s "brain", I was using these words in a much more general sense than is normal. I meant to include a hypothetical "person" who is immortal and who has infinite writing supplies which never decay. This person could even have an infinite capacity "brain". The relevant limitations of this person/scientist is that it starts with only a finite amount of information and can only do a finite amount of computation in a finite time. This lack of detail on my part is the only way I can see how Gorgonzola could think that proton decay was in any way related to the content of the writeup, so I apologise for the omission.
I wrote about science in a more abstract sense, not just the science that will be achieved in this limited universe - not even just the science that can be achieved in this universe. The idea is not that narrow, it applies to immortals. Yes, there are no immortals in this universe, yes, the idea is irrelavent in the limited context of this universe. The idea is not about this universe, it's about science.
About confusing "statements about a field derived from a particular meticulous method, with the field itself", the only field of which I speak is science - which is ruled by "meticulous method" (scientific methods, which, by nature of being scientific, can be represented by a finite list of elements from a finite symbol set, - i.e. countable methods). Not to say that there are not other fields, and not to say that science can cover all of any other field... but, science was the only field to which I referred. The idea is not about all fields to which the scientific method may or may not apply, it is about the particular field of science and the parts of other fields which can be embraced by science.
Applying the idea to our limited universe, it's irrelavent. Applying the idea beyond the limits of science, it doesn't hold up. I know that. I was doing neither.