for x,y > 7 twins(x+y) <= twins(x) + twins(y)
in [Math]
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From: James Burns on 10 May 2010 13:09 Transfer Principle wrote: > -- I _resolve_ not be the first poster in any thread to > use the word "crank." I shall only use the word "crank" > if someone else has already used the word earlier in > that thread. The same goes for any other five-letter > insult that commonly appears on sci.math., as well as > phrases such as "crank"-buster, "standard theorist," or > similar grouping phrase. Thank you for your resolution. If I had any wit, I would shut up at this point, and let you see how that works out. Alas, I apparently have no wit. Right now, you are trying to be more careful about how you group different posters together, and I appreciate that. There is another kind of grouping that I would like to call your attention to. You seem to feel that any particular poster is "for" ZFC (or ZF, or NFU, ...) in a permanent to semi-permanent way. From what I have seen, this is as mistaken as assuming that a particular writer of travelogues writes only about one place on Earth. That sort of thing could lead you to try to make sense of stories about an unpopulated coral atoll in the South Pacific, to which crowds flock to enjoy the downhill skiing. [...] > What might actually have an effect on opinions about the > irrationality of another poster is if I could post a > _rational_ theory in which the poster's claims are in > fact provable. This brings up a question that I have wondered about for a while, pretty much ever since you started posting in defense of cranks. It could be that you have explained this before, but, if you have, I have missed the explanation. Would you mind explaining /why/ you think that, if /you/ came up with a theory in which some other poster's claims are provable, that would affect opinions of that /other/ poster? Imagine that Poster X posts that the number sqrt(2) is irrational because his cat told him so. In response, he is called a crank (among other things). Let us suppose that you triumphantly display the well-known proof that sqrt(2) is irrational. Would you expect this to change anyone's mind about Poster X (and his cat)? Instead, suppose that Poster Y asserts that 1 > 0.999... and it is clear he means to use those symbols in the standard way. People tell him he is mistaken. People go on at great length explaining why he is mistaken, all to no avail. Eventually, he convinces people that he is not merely mistaken but a crank. Suppose that you find another mathematical system, another interpretation of "1 > 0.999..." in which it is true. Your use of "1 > 0.999..." is, in an important sense, not even the same thing Poster Y is saying. Why would you expect your newly introduced system to change anyone's mind about Poster Y's crankhood? Jim Burns
From: James Waldby on 10 May 2010 15:33 On Mon, 10 May 2010 13:09:48 -0400, James Burns wrote: > Transfer Principle wrote: [stuff] > This brings up a question that I have wondered about for a while, pretty > much ever since you started posting in defense of cranks. It could be > that you have explained this before, but, if you have, I have missed the > explanation. > > Would you mind explaining /why/ you think that, if /you/ came up with a > theory in which some other poster's claims are provable, that would > affect opinions of that /other/ poster? > > Imagine that Poster X posts that the number sqrt(2) is irrational > because his cat told him so. In response, he is called a crank (among > other things). Let us suppose that you triumphantly display the > well-known proof that sqrt(2) is irrational. Would you expect this to > change anyone's mind about Poster X (and his cat)? Clearly, not enough information has been supplied to allow us to form a definite opinion about the cat. Perhaps you could add a few more details to your hypothetical case? For example, if you posit that Transfer Principle has really shown that the cat has really proved irrationality of sqrt(2), then we can reach a conclusion. -- jiw
From: James Burns on 10 May 2010 15:47 James Waldby wrote: > On Mon, 10 May 2010 13:09:48 -0400, James Burns wrote: >>Transfer Principle wrote: > > [stuff] > >>This brings up a question that I have wondered about for a while, pretty >>much ever since you started posting in defense of cranks. It could be >>that you have explained this before, but, if you have, I have missed the >>explanation. >> >>Would you mind explaining /why/ you think that, if /you/ came up with a >>theory in which some other poster's claims are provable, that would >>affect opinions of that /other/ poster? >> >>Imagine that Poster X posts that the number sqrt(2) is irrational >>because his cat told him so. In response, he is called a crank (among >>other things). Let us suppose that you triumphantly display the >>well-known proof that sqrt(2) is irrational. Would you expect this to >>change anyone's mind about Poster X (and his cat)? > > Clearly, not enough information has been supplied to allow us to > form a definite opinion about the cat. Perhaps you could add a few > more details to your hypothetical case? For example, if you posit > that Transfer Principle has really shown that the cat has really > proved irrationality of sqrt(2), then we can reach a conclusion. This is unfortunate, since I fear that my releasing more information about the cat could lead to suspicion that I, myself, am Poster X. I am /not/ Poster X. I am not Poster X -- and I have the cat to prove it. -- James "Not Poster X" Burns
From: master1729 on 10 May 2010 13:22 > On Mon, 10 May 2010 13:09:48 -0400, James Burns > wrote: > > Transfer Principle wrote: > [stuff] > > > This brings up a question that I have wondered > about for a while, pretty > > much ever since you started posting in defense of > cranks. It could be > > that you have explained this before, but, if you > have, I have missed the > > explanation. > > > > Would you mind explaining /why/ you think that, if > /you/ came up with a > > theory in which some other poster's claims are > provable, that would > > affect opinions of that /other/ poster? > > > > Imagine that Poster X posts that the number sqrt(2) > is irrational > > because his cat told him so. In response, he is > called a crank (among > > other things). Let us suppose that you triumphantly > display the > > well-known proof that sqrt(2) is irrational. Would > you expect this to > > change anyone's mind about Poster X (and his cat)? > > Clearly, not enough information has been supplied to > allow us to > form a definite opinion about the cat. Perhaps you > could add a few > more details to your hypothetical case? For example, > if you posit > that Transfer Principle has really shown that the cat > has really > proved irrationality of sqrt(2), then we can reach a > conclusion. > > -- > jiw my cat is very well trained by me.
From: master1729 on 10 May 2010 14:40
> > Instead, suppose that Poster Y asserts that 1 > > 0.999... > and it is clear he means to use those symbols in the > standard way. People tell him he is mistaken. People > go on at great length explaining why he is mistaken, > all to no avail. Eventually, he convinces people that > he is not merely mistaken but a crank. Suppose that > you find another mathematical system, another > interpretation of "1 > 0.999..." in which it is > true. > Your use of "1 > 0.999..." is, in an important > sense, > not even the same thing Poster Y is saying. Why > would you expect your newly introduced system to > change anyone's mind about Poster Y's crankhood? > > Jim Burns > > he convinces people that he is not merely mistaken but a crank ... thats an intresting sentense. what would it mean actually ? that he is shown wrong but not willing to admit it ? so suppose the thread has 100 posts and he is called crank after 10 posts. in other words , by the above , he is not willing to admit he is wrong -> "crank" ( sidenote , even cranks who admitted mistakes are often still called cranks , whereas others are just people who where wrong/mistaken ... weird ... so crank is probably just a description and insult to people you dont like , justified by somewhat controversial , wrong in some theory , or 'annoying' ( not objective ! ) behaviour.(e.g. caps) ) but - and now i make some sort of point - if he later mentions that 1 > 0.99999999 is true because LH is an infinitesimal larger , he could be considered correct. and if he said so in the first post , he might not be called crank , and some might even agree with him. but then something strange happens , since he didnt talk about infinitesimals from the beginning , he became " crank " and whatever he says is wrong !! people will then disagree more often and respond by things like : idiot (in caps) or there are only reals on my real number line , no infinitesimals !! stupid ! which is not fair. this kind of follow-ups to crank-threads and 1>0.9999 threads are very common. the reason i dont like 1>0.9999 is that i know it will be like that. both the "crank" and the others are " wrong " , not in their math but their behaviour. i explained why the ones who call him crank and continue to do so , after the infinitesimal remark , are dishonest. but in case of 1>0.9999... the "crank" should have posted about infinitesimals in the OP to avoid such flamewars and long threads !! on the other hand confusion and incompleteness is not always the fault of the "crank" nor should it 'make' someone a "crank". when posting to a math form about math , there are just 3 ways : you post classical student question. ( e.g. need help with galois ) you post already known proofs. ( sometimes called crank sometimes not ) you post like a "crank". ( conj / proof / question / general idea ) and clearly , when you think about it , only the last is a meaningfull contribution to the forum. all the rest is old hat. but new things require new things. new ideas require new concepts. almost anything new will label you crank. *end point* i did not mention - in the 3 ways to post - objecting to already accepted things. that can be wrong(e.g. cantor diagonal or monty hall misunderstood ) or quite meaningless ( 1 > 0.9999999) but it can also be part of the new idea , the 3rd way of posting and thus be potentially meaningfull.( 3 valued logic ) in the case of wrong or meaningless as described above , i dont mind if these people are not taken seriously. but the other kind of " cranks " are intresting. but rare. rare and unrespected. even if they have phd. sigh. even if they are wrong , it would often be hard to show and intresting to talk about their ideas. disproving them often is non-constructive , probabilistic and highly axiomatic rather than convincing. and the funny thing is , such disproofs make the " intelligent cranks" feel like the other ones are the " real cranks " not concerned with rigor and formal good proof. since i have degrees and yet still post controversial things , unlike " real cranks " with no education misunderstanding the diagonal argument , at a rate nobody has ever done before , in the 3rd way(!) (as described above ) and i have proofs of many important open problems ( andrica , RH , ... ) i am in a sense , the new king of amateurs (like fermat) , but even stronger , with degrees and also proofs. in fact a lot stronger ( multiple degrees and important proofs ). a strenght other controversials could only dream of. and therefore , i am the master |