@progressivepb To me, any proof that is too big to be written on 2 pages isn't a proof, because nobody can freakin' understand it. Proof among elites isn't proof among commons. Proof among commons is REAL proof.
@theboombody That only makes sense if the only "true" theorems are simple enough to be done in two pages. Or each sentence of the proof is actually code for pages of other proofs, like when a theorem is cited. That theorem has to be proven too. So...if you allow us to make each sentence a reference to another theorem, we probably could keep each proof under two pages. There just would be 150 different proofs.
@jamesblackburnlynch I see your point. But I desire a way to increase the power of intuition so that such complexity is automatic and much more complex information can be thought of as an axiom. That would be the best way to reduce the length of such huge proofs.
@theboombody But perhaps that just isn't the case. That is, perhaps many truths are complicated and require more than just quick intuition. Of course, we can choose anything we want as an axiom. An old friend long ago suggested the single axiom: "All theorems are true." With that axiom there are no two page proofs. But I find the statements that can be proven with that axiom a bit disturbing. So I prefer to accept that some ideas are just complicated and require deep thought.
@jamesblackburnlynch I think of an axiom as something generally and automatically accepted by the general population though. I just don't think it has to be true. Just universally accepted.
You can make things overly simple, or overly complicated. It's nice to find a happy and accepted medium. I like leaning towards the simple myself. The world of Winnie the Pooh was so interesting to me because the population of the world never exceeded the single-digit numbers. So little legalism.
@theboombody I guess I'm the other way around. I love the complexity. If the most difficult ideas were comprehensible in two pages, I'd be saddened. I love that so much of what is happening is beyond my understanding.
But more than that, single digit numbers just won't do. We need more. I guess the main difference is that I like that and celebrate it. I gather you don't care for it.
this reminds me of a documentary i saw i think on pbs that had something to do with x^x + y^y = z^z or something like that. someone killed themself over it but was eventually solved by some elliptic modular function. don't ask me what the hell that is.
Ten years later of this documentary, Wiles discover a proof for the Last Fermat Theorem. Thank you very much for this videos.
progressivepb 2 years ago
@progressivepb To me, any proof that is too big to be written on 2 pages isn't a proof, because nobody can freakin' understand it. Proof among elites isn't proof among commons. Proof among commons is REAL proof.
theboombody 1 year ago
@theboombody That only makes sense if the only "true" theorems are simple enough to be done in two pages. Or each sentence of the proof is actually code for pages of other proofs, like when a theorem is cited. That theorem has to be proven too. So...if you allow us to make each sentence a reference to another theorem, we probably could keep each proof under two pages. There just would be 150 different proofs.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch I see your point. But I desire a way to increase the power of intuition so that such complexity is automatic and much more complex information can be thought of as an axiom. That would be the best way to reduce the length of such huge proofs.
theboombody 1 year ago
@theboombody But perhaps that just isn't the case. That is, perhaps many truths are complicated and require more than just quick intuition. Of course, we can choose anything we want as an axiom. An old friend long ago suggested the single axiom: "All theorems are true." With that axiom there are no two page proofs. But I find the statements that can be proven with that axiom a bit disturbing. So I prefer to accept that some ideas are just complicated and require deep thought.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch I think of an axiom as something generally and automatically accepted by the general population though. I just don't think it has to be true. Just universally accepted.
You can make things overly simple, or overly complicated. It's nice to find a happy and accepted medium. I like leaning towards the simple myself. The world of Winnie the Pooh was so interesting to me because the population of the world never exceeded the single-digit numbers. So little legalism.
theboombody 1 year ago
@theboombody I guess I'm the other way around. I love the complexity. If the most difficult ideas were comprehensible in two pages, I'd be saddened. I love that so much of what is happening is beyond my understanding.
But more than that, single digit numbers just won't do. We need more. I guess the main difference is that I like that and celebrate it. I gather you don't care for it.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch To each his own. In life there are no rules. Which makes me wonder why so much effort is put into constructing and obeying them.
theboombody 1 year ago
this reminds me of a documentary i saw i think on pbs that had something to do with x^x + y^y = z^z or something like that. someone killed themself over it but was eventually solved by some elliptic modular function. don't ask me what the hell that is.
slappy480ic3f4 3 years ago