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Math Forum / Mathematics / Recreational Math / October 2008JSH: How can I top that?
I'm kicking back now kind of wondering to myself as I try to get some sense of the feeling of accomplishment with the discovery of my own infinite series, and the wild thing to me is the feeling that, hey, good thing I didn't find this thing years ago as I can't see how I'd have done anything else, as how can I top it? And what's really wacky wild is that years ago I thought it'd be this great thing to find a simple proof of Fermat's Last Theorem, and got that, and it was like nothing as the math world wouldn't accept it, and it didn't feel satisfying anyway, and I had to use this weird new analysis technique I'd invented called tautological spaces, when I wanted something that felt CONCRETE. So I kept at it. Found my prime counting function. Non-polynomial factorization. The object ring, and nothing really had that truly solid feeling to it, no matter what I could prove, and people kept ripping on me, so I kept going. It's so ironic. But it does go back to when I was a kid and I'd read about series like the Taylor series and wonder about that and it didn't sink in to me until now that I really wanted my own. So, ok, proving FLT is cool. Discovering the object ring is cooler. Inventing my own analysis technique with tautological spaces is rather awesome. But NOTHING beats having my own infinite series which is an infinite series of equations! So it's better yet!!! 1. x^2 + Dy^2 = F 2. (x-Dy)^2 + D(x+y)^2 = F*(D+1) 3. ((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F*(D+1)^2 4. ((1-3D)x + (2D^2 - 4D)y)^2 + D((3-D)x + (1-3D)y)^2 = F*(D+1)^3 and that goes out to infinity. To get successive terms in the series you use the algebraic result that given: u^2 + Dv^2 = C it must be true that (u-Dv)^2 + D(u+v)^2 = C*(D+1). And where whenever the exponent of (D+1) is even, you can have a case where you just have a multiple of x and y, so you can solve for D, which defines possible values for F in terms of x or y. An infinite series of equations that I like to call a huge number theoretic super structure. My own infinite series. Finally, something I really FEEL is concrete. Can't see how I can top that. So I'm done. Time to kick back and rest on my laurels, drink more and chase more women. James Harris In article <fbe9e602-26fc-431c-b0c6-4eb7643a7c53@b2g2000prf.googlegroups.com>, > I'm kicking back now kind of wondering to myself as I try to get some > sense of the feeling of accomplishment with the discovery of my own [quoted text clipped - 57 lines] > Time to kick back and rest on my laurels, drink more and chase more > women. JSH, you are a very funny guy. Let us know how the drinking and chasing goes. > I'm kicking back now kind of wondering to myself as I try to get some > sense of the feeling of accomplishment with the discovery of my own [quoted text clipped - 59 lines] > > James Harris It'll be known as the JSH series. > > I'm kicking back now kind of wondering to myself as I try to get some > > sense of the feeling of accomplishment with the discovery of my own [quoted text clipped - 61 lines] > > It'll be known as the JSH series.- Hide quoted text - You mean like that other infinite series ? ***MASH*** ? In article <fbe9e602-26fc-431c-b0c6-4eb7643a7c53@b2g2000prf.googlegroups.com>, > I'm kicking back now kind of wondering to myself as I try to get some > sense of the feeling of accomplishment with the discovery of my own > infinite series, and the wild thing to me is the feeling that, hey, > good thing I didn't find this thing years ago as I can't see how I'd > have done anything else, as how can I top it? You could top it by actually solving some real equations using your "infinite series". And after that fails, you could then go back and try to fix your theory so that it actually works. ... > But NOTHING beats having my own infinite series which is an infinite > series of equations! So it's better yet!!! [quoted text clipped - 15 lines] > > (u-Dv)^2 + D(u+v)^2 = C*(D+1). Brahmagupta beat you by ~1300 years, except his results were more general than yours: Given x^2-Ny^2 = z and u^2-Nv^2 = w Then (xu+Nyv)^2-N(xv+yu)^2 = zw You have discovered the special case u=1, v=1, N=-D. And yes, James, not only did he have the basic formula, he had the idea of using solutions of x^2-Ny^2=k to find solutions of x^2-Ny^2=1. He was able to show, for instance, the solutions of x^2-Ny^2=4 can be used to find solutions of x^2-Ny^2=1. In other words, he had chains. Maybe you should give up on mathematics, and take a stab at physics. If you can build a time machine and go back 1300 years, you can find a world where your trivial (by today's standards) algebraic manipulations will be new and impressive, and well received. ... > Can't see how I can top that. So I'm done. There's been a lot of interesting developments in number theory since Brahmagupta's day. One way you could top having discovered a minor special case of his work, would be to rediscover minor special cases of the work of later mathematicians.  Signature--Tim Smith >> [...] But NOTHING beats having my own infinite series which >> is an infinite series of equations! So it's better yet!!! [quoted text clipped - 24 lines] > > You have discovered the special case u=1, v=1, N=-D. [...] To be fair, probably most students of elementary number theory would not discover this composition law on their own - at least without some prior exposure to norm maps in quadratic fields. Indeed, it appears that even you were not aware of this viewpoint till I pointed it out to you on Sept. 28 in [1]. But I've been emphasizing that point to James since Sept. 7 in [2]. Alas, he doesn't seem to want to acknowledge how this viewpoint makes all his observations completely trivial. More generally, the ideal-theoretic viewpoint, by _linearizing_ what was before _nonlinear_ phenomena in the theory of quadratic forms, has led to great simplifications in the number theory of quadratic number fields. Strong evidence in support of this claim is easily found by comparing many of the proofs from the time of Euler, Lagrange, Legendre, etc (e.g. see Weil: Number Theory) to their modern counterparts using notions of ideals (or divisors). As a simple analogy of the power of such linearization, consider the extension from real to complex numbers. This allows us to factor polynomials completely into linear factors (vs. quadratic over R), and, e.g., greatly simplifies the integration of rational functions, since now partial fractions involve at most linear (vs. quadratic) factors. In an analogous manner, the injection of linear notions into number theory by Dedekind, who essentially discovered all of the important foundational abstract structures (ideals, modules, rings, fields etc), was nothing short of a revolution in the development of number theory. --Bill Dubuque [1] http://google.com/groups?selm=y8z4p40z8g3.fsf%40nestle.csail.mit.edu [2] http://google.com/groups?selm=y8zhc8r51pb.fsf%40nestle.csail.mit.edu > >> [...] But NOTHING beats having my own infinite series which > >> is an infinite series of equations! So it's better yet!!! [quoted text clipped - 30 lines] > Indeed, it appears that even you were not aware of this viewpoint > till I pointed it out to you on Sept. 28 in [1]. But I've been I believe I was aware of these kinds of relationships. I'd completely forgotten the stuff about numbers of the form a+b*sqrt(N), and how you can defined a norm on them such that the norm of one of those numbers is a^2-Nb^2, however. > emphasizing that point to James since Sept. 7 in [2]. Alas, he > doesn't seem to want to acknowledge how this viewpoint makes [quoted text clipped - 6 lines] > Euler, Lagrange, Legendre, etc (e.g. see Weil: Number Theory) > to their modern counterparts using notions of ideals (or divisors). This probably falls under what he considers to be "complexity", which he accuses mathematicians of preferring over simple approaches. Signature--Tim Smith > I'm kicking back now kind of wondering to myself as I try to get some > sense of the feeling of accomplishment with the discovery of my own > infinite series, trivial. > and the wild thing to me is the feeling that, hey, > good thing I didn't find this thing years ago as I can't see how I'd [quoted text clipped - 5 lines] > and it didn't feel satisfying anyway, and I had to use this weird new > analysis technique I'd invented called tautological spaces, tautological spaces => crap spaces > when I > wanted something that felt CONCRETE. [quoted text clipped - 9 lines] > the Taylor series and wonder about that and it didn't sink in to me > until now that I really wanted my own. took a very long time, most only take a day or two. > So, ok, proving FLT is cool. Discovering the object ring is cooler. > Inventing my own analysis technique with tautological spaces is rather > awesome. yawn, a lost mouse in the maze of life. > But NOTHING beats having my own infinite series which is an infinite > series of equations! So it's better yet!!! yawn, go get a book on infinite series. <snip math> > An infinite series of equations that I like to call a huge number > theoretic super structure. > > My own infinite series. Finally, something I really FEEL is concrete. > > Can't see how I can top that. So I'm done. you were done a while back > Time to kick back and rest on my laurels, drink more and chase more > women. yes! Tell da womens bout your big infinite series you feel is concrete > James Harris > I'm kicking back now kind of wondering to myself as I try to get some > sense of the feeling of accomplishment with the discovery of my own > infinite series, and the wild thing to me is the feeling that, hey, > good thing I didn't find this thing years ago as I can't see how I'd > have done anything else, as how can I top it? You've actually discovered two infinite series. The second is your infinite series of newsgroup posts. <SNIP> Every result you've posted is either one of 1. WRONG, or 2. TRIVIAL. If you can get something that is neither of those that would be much, much more impressive. > <SNIP> > [quoted text clipped - 7 lines] > much more > impressive. It's a personal accomplishment. Something I'd always wanted but didn't know if I'd ever achieve, to discover my own infinite series. You can call it trivial if you wish, but it's not for you. It's a goal of mine from childhood that I reached. Feels weird though. Not how I expected. James Harris On Oct 5, 7:37 pm, mike3 <mike4...@yahoo.com> wrote: > On Oct 4, 1:05 pm, JSH <jst...@gmail.com> wrote: > <SNIP> [quoted text clipped - 8 lines] > much more > impressive. It's a personal accomplishment. Something I'd always wanted but didn't know if I'd ever achieve, to discover my own infinite series. You can call it trivial if you wish, but it's not for you. It's a goal of mine from childhood that I reached. Feels weird though. Not how I expected. James Harris *** they call that a personal discovery, feels good too. Try some more, there are an infinite number out there. I discovered a few, too complicated to put in ASCII. The best are the closed form ones, where the series adds up to a sum that is defined by a formula. > > <SNIP> > [quoted text clipped - 18 lines] > > James Harris If you are just doing it to feel good, to do something _you_ like, that's fine, but please don't pass it off as new and revolutionary when it's really just a reinvented wheel, and when this fact is brought up to you, you should drop the grandiose claims about the thing. > > > <SNIP> > [quoted text clipped - 25 lines] > reinvented wheel, and when this fact is brought up to you, you should > drop the grandiose claims about the thing. You mean like noting that it is the reason for the behavior of Diophantine binary quadratic equations? And explains their behavior perfectly? Your obvious anger does not surprise me, nor does the denial. I've faced that before with my prime counting function--exact same objection to it. Posters would protest that it was nothing new when I could explain the prime distribution, show how it connected to continuous functions, and explain why there was a gap between continuous functions and the discrete count. And that was YEARS ago. The math world has preferred to remain in ignorance with the answer to the prime distribution right out there. But, I'm not surprised. Plenty of people prefer ignorance. Stupidity rules our world. James Harris <snip> > > If you are just doing it to feel good, to do something _you_ like, > > that's fine, [quoted text clipped - 6 lines] > Diophantine binary quadratic equations? And explains their behavior > perfectly? If it's been discovered before, it's not new. 'Nuff said. <SNIP!> > <snip> > > > If you are just doing it to feel good, to do something _you_ like, [quoted text clipped - 9 lines] > > If it's been discovered before, it's not new. Duh. > 'Nuff said. You didn't even start. > <SNIP!> Ok so run away. For people who claim to like mathematics so many of you really do talk a lot. The old explanations for x^2 - Dy^2 = N, sell more papers, give room for more research, so there can be more public funding for more "mathematicians", which is why I call the current system white collar welfare. The problem is that too few of you are intellectually capable of doing real mathematical research. Your mental abilities are not up to the task, so you make things up. THAT is really all there is to it. You just are not smart enough to do real mathematics. Period. James Harris > > <snip> > > > > If you are just doing it to feel good, to do something _you_ like, [quoted text clipped - 34 lines] > > You just are not smart enough to do real mathematics. Period. And looking back all that sounded kind of mean. I WAS angry but maybe I could have been less harsh. Funny thing is though I do, however, feel like the modern system is white collar welfare. So I wouldn't want to take that back, but maybe I could have said it all a bit better. It is so frustrating though when I know the problem here isn't mathematical proof as that's the easy part. I have the proofs. The problem is a society which shut the door. And you know and I know that if a bloc of math people keep chanting I'm wrong it doesn't matter what I can prove, unless I go over to the dark side and destabilize the world with a solution to the factoring problem. So part of me feels even madder that I feel like I'm forced to ALLOW this situation to continue. Reality though has for whatever reason given you some grasp of what I was concerned about, and why, as it befuddled me how stupidly none of you seemed to comprehend what a global financial situation would look like, what I was pondering, and this isn't as bad as it could be. Not yet. Quite simply if I'd crashed the financial system, some of you would not have survived it, and I probably wouldn't have either, as in most scenarios I saw mathematicians torn apart by angry mobs of enraged people. Oh yeah, I run scenarios as I model the world. I tend to try to avoid those that end with mass death. James Harris > > > <snip> > > > > > If you are just doing it to feel good, to do something _you_ like, [quoted text clipped - 54 lines] > So part of me feels even madder that I feel like I'm forced to ALLOW > this situation to continue. But what if I couldn't have finished the research? I'm bugging myself about something I'm not certain I could do. > Reality though has for whatever reason given you some grasp of what I > was concerned about, and why, as it befuddled me how stupidly none of [quoted text clipped - 9 lines] > Oh yeah, I run scenarios as I model the world. I tend to try to avoid > those that end with mass death. But I'm still just guessing. The problem is that if my best guess is mass death, and I continue anyway saying it's just a guess then I'd feel guilty, but if I just don't go down that path. I don't feel guilty, I just feel annoyed. Decision was made. I left that research to do other. Maybe I could have finished it, I don't know, and I didn't so it's past history. After all, so much of what I do is guess. And your fates are your own. I won't feel like I'm the source of what befalls you. Reality doesn't need my help at all. For whatever that's worth. Ok, time for me to take a nice long break! Math research is done. I didn't destabilize the world, and things are going bonkers anyway, but at least I don't feel guilty! James Harris > > > <snip> > > > > > If you are just doing it to feel good, to do something _you_ like, [quoted text clipped - 68 lines] > Oh yeah, I run scenarios as I model the world. �I tend to try to avoid > those that end with mass death. Making death threats again, eh? Sooner or later they're going to wise up about people like you and that kid in Finland. I'd love to see you explain to a judge how his job is white collar welfare. > James Harris- Hide quoted text - > > - Show quoted text - James "Google SWJPAM" Harris wrote: > I WAS angry but maybe I could have been less harsh. You're beautiful when you're angry. > Quite simply if I'd crashed the financial system, some of you would > not have survived it, and I probably wouldn't have either, as in most [quoted text clipped - 3 lines] > Oh yeah, I run scenarios as I model the world. I tend to try to avoid > those that end with mass death. Is this an example of you lying to be entertaining and attract readers? Or is this just more of you being a genuine crackpot? > Ok, time for me to take a nice long break! Five buck says your "nice long break" won't last to the end of the week. -- "The evidence is in: Google search results are b.s. and it's more for the conspiracy theorists who realize that aliens really run the world, or maybe babies. Or maybe baby aliens?" -- James Harris In article <daf8257d-b405-4763-9ef7-0c38fb8e8a56@r38g2000prr.googlegroups.com>, > I've faced that before with my prime counting function--exact same > objection to it. [quoted text clipped - 3 lines] > explain why there was a gap between continuous functions and the > discrete count. Are you going to publish any of that? All I see on your website are a bunch of articles where you've rediscovered well known fuzzy probabilistic arguments about prime distribution. These have been known for a very long time. The hard part is actually getting rid of the fuzz. Why don't you pick one particular result and try to actually make it rigorous? A good one might be the one where you claim that if the twin prime conjecture is true, then Polignac's conjecture (every even integer can be expressed as the difference between two primes) is true. As far as I can tell from what I've found on the net, showing that this follows from the twin prime conjecture would be new. Signature--Tim Smith > In article > <daf8257d-b405-4763-9ef7-0c38fb8e8a56@r38g2000prr.googlegroups.com>, [quoted text clipped - 17 lines] > as I can tell from what I've found on the net, showing that this follows > from the twin prime conjecture would be new. that stuff is much too hard for JSH, his is math challanged. ......better to start with the distribuitive property, or negitive square roots.... In article <daf8257d-b405-4763-9ef7-0c38fb8e8a56@r38g2000prr.googlegroups.com>, > > > > <SNIP> > > [quoted text clipped - 41 lines] > ignorance with the answer to the prime distribution right out there. > But, I'm not surprised. I know three things about the prime distribution, and for none of them are you the first to publish it. What is your answer to the prime distribution? I confess that I am ignorant of it and would like to know a fourth. > Plenty of people prefer ignorance. Stupidity rules our world. SignatureMichael Press |
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