geb chapter 3 (figure and ground)
Tags: Hofstadter  Godel, Escher, Bach

What is a typographical system?
 Reading & recongizing any set of finite symbols
 Writing down any symbols that belong to that set
 Copying any of those symbols from one place to another
 Erasing any of those symbols
 Checking to see if symbols are the same
 Keeping a list of the symbols already made

We can define primes by defining the negative of the composite, but this comes with a problem
there eixst formal systems whose negative space is not the positive space.

If we define the space of all composite numbers, prime numbers are recursively enumerable, but they are not recursive derivable. We cannot compute primes without checking all the numbers that lead up to it, this is a one way function.
 This allows the embedding of information, such as crypto (for cryptography)
 halting problem
 godel’s incompleteness theorem