4 ms·
Godel has nothing to do with it. Godel’s Incompleteness is just the math version of the Halting Problem, which is just a fancy version of the classic paradox “T
by BreakfastB0b 5y ago
Godel has nothing to do with it. Godel’s Incompleteness is just the math version of the Halting Problem, which is just a fancy version of the classic paradox “This statement is false”. Godel showed that even if you outlaw self referential definitions e.g. “This statement is false”, math is rich enough in complexity to simulate itself and thus end up with self referential paradoxes anyway.
It’s not this mystical thing that people make it out to be online.
- jychang 5y agoUndecidability is not tied to only self referential definitions, though.
- BreakfastB0b 5y agoThe only ones I’m aware of are. Can you link me some examples? I’d like to read up on it.
- jychang 5y agohttps://xorshammer.com/2008/09/04/a-geometrically-natural-uncomputable-function/ https://xorshammer.com/2008/09/04/a-geometrically-natural-un...
- BreakfastB0b 5y agoVery cool! Thanks for the link! Got a lot of reading to do. However I do wonder if it’ll turn out that these higher dimensional geometric problems turn out to have the same structure as Godel’s proof. That the higher dimensional geometric structure is complex enough to represent their own foundation. Although now I’m committing the same fallacy I was arguing against i.e. an equivalence between unknowns
- mensetmanusman 5y agoExcellent insight.