We dont know necessarily how long a string in proof will get, nor do we know how many steps we
are going to use. How many times we will infer from axioms.
How could self referentially systems come up in statements only talking about integers and
their properties?
Well formed vs theorems Theres no unpredictability to whether a formula is well
formed. Via recursive breakdown into simpler parts
Some properties of numbers can be tested quickly, like is x a fibonacci number, you could
calculate fibonacci sequence up to around x and check. Same with checking if x is prime.
Collatz number involves going along a path to check by a set of rules
Integers could simulate things that weren’t mathematical objects. The process of creating
a proof being a mathematical process. Manipulation of symbols is a mathematical process
For instance if you encoded a piece of music as a large integer, what kind of questions
could you ask about the piece of music/the integer? could you answer qusetions like who
wrote it? etc., or something trivial like, how many notes are in the piece would be easier
If you encoded a string of symbols (like the golbach conjecture) as a large integer. If we
asked questions like, is it true or false, is it trying to say this or that.
Is this string a theorem. With numbering acting isomorphically to statements. A theorem is
a mathematical notion. A property of one of these isomorphic numbers