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> Mathematics are more limited The fundamental point of the Church-Turing thesis is to show that everything computers can do can be described by mathematics, s
by kd5bjo 7y ago
> Mathematics are more limited
The fundamental point of the Church-Turing thesis is to show that everything computers can do can be described by mathematics, so any programing language has either the same or less power than math. They are certainly easier to use for many problems, though.
Additionally, Gödel showed that there are true statements that can be described but not proven by math, ao it can never be a perfect model of the real world.
- progval 7y ago> Additionally, Gödel showed that there are true statements that can be described but not proven by math, ao it can never be a perfect model of the real world. I assume you are refering to Gödel's incompleteness theorems; but this is not what they "say". What they say is that any formal system powerful enough to contain basic arithmetic is either inconsistent (ie. it can both prove and disprove a particular theorem) or incomplete (ie. cannot either prove or disprove all theorems). If you take the ZF set theory, for example, it is incomplete, because some statements cannot be either proved or disproved within ZF, such as the Axiom of Choice (AC) or Zorn's Lemma. However, that doesn't imply that ZF cannot be "a perfect model of the real world", because the AC is irrelevant in a the real world, because the AC only applies to infinite sets, which do not exist in the real world.
- The_rationalist 7y agoGödel theorem does not say anything about the real world. Mathematics are a superset of physics as they allow to explain all possible universes not just our. I've yet to see one concrete statement that ZFC can't explain. There's a list of such statements on wiki if I remember well.