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"Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effecti
by snarfy 12y ago
"Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory" - Gödel (Kleene)
- k__ 12y agoSome CS prof. told us this in first semester. After that, Physics was over for me. And I felt that the Planck-scale was somehow a proof for this.
- deeviant 12y agoThe thing is, the universe and mathematics are totally separate entities. The universe did not start off "as math", nor is it defined by it. We, as clever little beings found similarities and analogies between the universe and mathematics and leverage those to make conjecture regarding the form and nature of the universe. However, having a "complete" knowledge of either mathematics or the physical universe does not confer complete knowledge of the other.
- s_baby 12y agoYou don't experience the universe directly. You experience it through cognitive constructs and all the limitations that entails.
- xenophonf 12y agoPhysics (and science in general) isn't about searching for the Truth. Instead it's about reducing the amount of error in the mental models we use to approximate reality. Like, when a scientist says "the Law of Gravity", they actually mean "our best current guess as to how gravity works, which seems to make accurate predictions in what we consider a statistically significant number of different scenarios, but which is incomplete and perhaps even completely wrong in several other interesting scenarios or edge cases". Only _everything_ in science has a confidence interval, and prefacing every description of some phenomena with the phrase "we're pretty sure this is how this works, but to be perfectly honest, it's only an approximation to some X degrees of accuracy" gets really exhausting, so for stuff we're really, really sure of, like 99.9999% sure, we call it a "Law" (even though it isn't) and move on with our lives.
- pfortuny 12y agoIt is funny because if nature is discrete then Gödel has nothing to say about it. Only our present MODELS fail to deal with finiteness properly.