Sunday, August 29, 2010


JSH: Not a bad place to be

Often in arguments with Usenet posters on math newsgroups I've seen an attitude like I should be looking to be celebrated, seek consensus at any cost, or just be NICER, where I should think of group impact, how other people feel, and believe that I NEED something from them, like approval, which surprised me.

After all, the public perception I'd think of math people would be none of the above, pursuit of truth above all else, and a disdain for social approval with a contempt for the idea of accepting ideas because someone tells you they're good.

As in mathematics, who needs someone to tell you what is correct?

In mathematics, unlike in most areas of human endeavor there is mathematical proof!

And I got to define it.

I am in an incredible position at this point. And I talk about being able to search for my definition of mathematical proof on the web, where posters replying seem to think, still, that I want something from them!!! I'm just still amazed about it, in shock to some extent, and yes, awe.

Today I can search across number theory on various topics from primes to Diophantine equations and get my ideas reflected back at me.

That is not a bad place to be.

Our new tool of advancement, the hot thing of today, the Internet, reflects my research back at me. My ideas reflected back to me by the mirror of the greatest technologies of human advancement.

To the extent that I am still subject to ridicule from this modern mathematical community, I think you learn more about them than about me, about how they work, what is important to them, what they know.

And I know they don't know this feeling. Yes, I do stand on the shoulders of giants, as Sir Isaac said of himself, but I'm luckier, because I can see so much further than any others before could ever have imagined because I live in the world they helped create, which is so much greater than I'm sure they ever imagined.

Those who dream to learn, who love the excitement and daring of a great adventure we did not choose for ourselves—we were born into it—cherish the opportunity to learn about it. To find a way. To forge new paths.

To be the ones who themselves, like those before us, help make a better distant future which should hopefully be as unimaginably better as ours was—as if not me, or you? Who?

Tuesday, August 24, 2010


JSH: Having your own "team", more on using Usenet

Some of you may notice that I post various mathematical issues and then people help me. Often while delivering insults. Seem odd? Welcome to yet another class on using Usenet.

Arguments drive Usenet. If you're not arguing with someone over math then you're probably not really doing anything.

As you argue with people, something odd can happen, they end up helping you critique your ideas and then seem to ENJOY it, even if they have to hurl insults at you along the way, just for denial purposes. Why? Who knows…

At the upper levels when you've gained a lot of mastery, you can then acknowledge the help. It doesn't seem to matter!

Often at times it's like I have this world-wide team of people who go about helping me at the drop of a hat on various mathematical issues, often while insulting me, attacking my ideas, and thereby removing any hope for themselves of credit for anything.

Bizarre, eh?


JSH: Expression blocking by ring of algebraic integers

A simple way to see a problem with the ring of algebraic integers is by compare and contrast, as consider:

7(g_1(x) + 1)(g_2(x) + 1) = (f_1(x) + 7)(f_2(x) + 7) = 7*P(x)

where P(x) is a quadratic irreducible over Q, P(0)=1, and none of the functions are constants. That is ALWAYS available in the ring of algebraic integers without restrictions. Now in contrast consider:

7(g_1(x) + 1)(g_2(x) + 2) = (f_1(x) + 7)(f_2(x) + 7) = 7*P(x)

where also P(x) is a quadratic irreducible over Q, but P(0) = 2, but still none of the functions are constants. That is NOT available in the ring of algebraic integers.

That expression blocking is peculiar because one wonders, why did changing a 1 to a 2, blow an expression out of the ring of algebraic integers for certain cases? Answer: symmetry breaking

If one considers those expressions carefully you DO find that in BOTH cases the f's can be algebraic integer functions. And it turns out that one of the g's can always be an algebraic integer function as well, but one cannot in the second example, while BOTH can in the first example.

What is happening is that the rules of the ring of algebraic integers do not allow it to allow the second example in certain particular circumstances, so it blocks it. It doesn't allow those particular expressions to exist as given.

And all it takes is changing a 1 to a 2.

One way to look at the issue is that the ring of algebraic integers has symmetry requirements that allow it to specify to algebra itself that certain algebraic expressions are not allowed within that ring, under highly particular circumstances, unlike any other ring known.

Monday, August 23, 2010


JSH: Weirdness with ring of algebraic integers

Oddly enough I've found a simpler demonstration of the weirdness of algebraic integers, as consider the following is NOT valid in that ring:

7(g_1(x) + 1)(g_2(x) + 2) = (f_1(x) + 7)(f_2(x) + 7) = 7*P(x)

if P(x) is a polynomial irreducible over Q. Here note the f's and g's are blocked from being algebraic integer functions!!!

When I trotted this out a couple of days ago I also thought you needed g_1(0)=g_2(0)=0, but now don't think that is the case.

So bizarrely enough that seemingly simple algebraic expression is not available in the ring of algebraic integers.

Here arguments are unnecessary, as all anyone has to do is give valid algebraic integer functions for the f's and g's.

It's a stunning demonstration: the ring of algebraic integers actually stops algebra itself in this peculiar way.

It tells Mother Algebra—thou shalt not do that here.

Saturday, August 21, 2010


JSH: Stacking threads

Oh, one cool technique for advanced Usenet users is stacking threads where you'll have about 3 threads stacked one after the other by the timing of your replies! The most advanced users can do that to guide people along subjects quite deliberately.

It's kind of a hard trick to do and requires a bit of luck, but it's one I play at often enough.

Oh, so yeah, if you reach a certain level you need multiple threads for many reasons, like when your competition tries to drown out your original thread with nonsense replies, or when you need to do stacking!!!

I like to stack.

You should keep threads down to a minimum though because you get diminishing returns with too many and begin to liquidate your own message. You spam yourself!!! Lately I like to keep no more than 5 at a time, but feel most comfortable with 2.

Friday, August 20, 2010


JSH: But is it funny too?

I can put out evidence that SHOULD be overwhelming to at least say that I'm not just some loser who has no valid or interesting mathematics at all. But none of it seems to work with math people!!! They're like, immune or something to evidence, including mathematical proof, or my having defined mathematical proof.

So yeah, you can search in Google: definition of mathematical proof

It gets MUCH weirder. I DID get published. Some person posted that on sci.math which infuriated some people and a few of them decided to write letters to the editors claiming—falsely—that I was wrong. They used the error I found to claim that my paper was in error. Amazing. So the editors freak, yank my paper after publication. The chief editor actually went on sabbatical—though maybe that was already planned? The journal managed one more edition, then SHUT- DOWN. Its hosting university SCRUBBED ALL MENTION of it from their webpages!!! It had been around for somewhere around TEN YEARS!!!

Search in Google is: SWJPAM

And here it's also wacky!!! That should give you a link to a European organization that archives mathematical journals from all over the world. Despite the American universities attempts to pretend the journal never existed EMIS kept it archived and did something more interesting in my opinion: they also restored my original paper with a link to it separately.

Oh, on a sidenote, I think it remarkable that an American university showed a dismal set of values, but a European group over-rode them to some extent. I think that is sadly telling about the state of my country. The United States tries hard. It talks a great game, but its actuality is often way, way, way below even minimal standards.

There is no way the United States of America gains prestige with this story. I have found myself recently noting that I'm a "black guy" in this country. Given the history of the United States when it comes to racial issues, I think it telling that certain elements in this country would maybe not like it so much to hear that there was a black major discoverer.

And so far, notice, they haven't had to be so bothered. Oh dear, don't want to DARE trouble them, eh?

No one wants to trouble the racists!!!

Greatness is as greatness does?

The Google search results are beyond belief at this point. Like recently I gave the world an idea for postal services. Not a random thing as the US Postal service is hurting as the web changes how people communicate and drops mail volume, so I'm trying to help them out. Google search: scan post office idea

I've also found it with just: post office idea

I like to give. But also what else can I do? If US citizens can just pretend that I don't have valuable research, then what should I do, mope? I have a duty to the world. Just because there are small- minded people who try to block me, I can't just shrug that responsibility off! The future demands certain things of me. I have a role to play.

So what could be funny about any of these things?

Well, the US DOES have a certain history, and some people within it seem to think that some races are better than others.

What if?

What if to prove that belief they'd rather stop human progress entirely? Isn't that funny?

As, how can you prove one race superior by having it try to destroy the future of the entire human race?

American racism is an odd animal. It is hard to kill. But oh does it like to make history.

I don't think anything like this situation has EVER happened in world history before—that a people tried to pretend that the next major discoverer had not arrived.

God has a sense of humor. If Americans had thought about it carefully, they'd have realized: of course the next major discoverer if he or she arrived in the United States of America, would be "black".

God. So cool. You gotta laugh, if you think it's funny.


JSH: Upheavals in mathematics

One of the weirder things mathematicians reportedly pride themselves on, is the lack of upheavals in their discipline like those in physics, which is the discipline I was trained in, as I got a B.Sc. in physics from Vanderbilt University.

Now on the surface that can seem like a reasonable claim: mathematicians purportedly rely on mathematical proof. Mathematical ideas if correct often have a concrete reality that is as obvious as 2+2 = 4, a simple example of that type of reality.

(I DEFINED mathematical proof. Search in Google: definition of mathematical proof )

Yet I, a physics graduate, claim that there is a HUGE error in established number theory i.e. a major upheaval in the field, which is being ignored.

What gives?

Well it's "pure math" which is a perfect way to be perfectly wrong— and hide it. But with a dogmatic field that claims it can DO NO WRONG years have passed by while I slog forward pushing the argument forward year after year.

The error is so easy to show it actually violates the distributive property, and has the field of complex numbers in contradiction with the ring of algebraic integers.

Yup, the field of complex numbers contradicting the ring of algebraic integers.

They fight. Guess who wins?

Search for it on Google: algebraic integers vs complex numbers

That is a demonstration of world interest that is dismissed by posters who reply that being #1 in Google search results is "meaningless". So why is Google suddenly crap? Because I'm right. If they acknowledge that Google is not crap then they are forced down the path of admitting that the mathematics is correct, which forces them down the path to admitting that there is an upheaval in the field of mathematics—but dogmatically the field of mathematics has no major upheavals!!!

Human beings are kind of simple in their ability to be deluded. They can lie themselves into any particular belief that suits them.

As a person with physics training I'll admit I find it fascinating. A value taught to physics students is NOT taught to math students, clearly, from this ongoing refusal to accept all evidence.

Years ago I'd point out over and over again the fight with the distributive property. Posters would just reply over and over again that the distributive property wasn't being violated. So I'd show it being violated. They'd just say it wasn't! Round and round it'd go.

If mathematicians have as a firm belief that their field cannot have a major error then they just refuse all evidence.

It's REALLY HARD to imagine a greater demonstration than an error that has the ring of algebraic integers contradicting the field of complex numbers!!! It's easy to show that contradiction. Google itself will pull that contradiction up to #1 for you, indicating there are people who seem to know it exists!!!

So how do they continue in error? How does anybody?

After all, did Jesus actually walk on water?

Thursday, August 19, 2010


JSH: More about using Usenet

Usenet is a great tool for you to be international. If you're NOT part of the math establishment, with papers published in mainstream journals, and a lot of connections to the mathematicians that matter, then Usenet may be the ONLY really viable means for you to push your ideas to the world.

But it is competitive. Have some common sense. You're not the first person to see value in Usenet! And you can see posters who've been using it for DECADES, but where are they really now? Do you think some person who has been working at Usenet, digging for gold as it were, for DECADES is really here to help YOU?

Check posting histories. The longer that string of posts, the less likely you're dealing with a happy camper. That guy—it's usually a guy—has been dreaming for a long time, and his dreams have probably not been realized. I should know! I have a long history myself! I'm still mostly frustrated in my efforts, but then again, I'm not replying to other people's ideas pretending I want to help them.

Surface reality on Usenet can be VERY distracting. One or two posters who reply to you day and night can seem very big, like really hairy scary monsters that will not let go! And they won't! If you reply to them they will reply to you!!!

But it's not the replies that matter—it's the readers.

I have nincompoops who will reply to me now, who have nothing, who have done nothing, who will tell me I have nothing and that I have done nothing, oh, while they rip on Google saying search results mean nothing! Why? Because I'm #1 in the freaking world on some of those search results. So they'll tell you that being #1 in the world means nothing.

They are not here to help you. If you think posters are here to help you deliberately, then you are playing in the wrong zone.

They are your competition. If people are posting they are trying to get attention. The more attention YOU get, the less satisfied they feel about their own.

No one posts on Usenet to be ignored.

EVERYBODY who posts is trying to get attention. In that sense EVERY POSTER is a troll.

But substance does matter. I have #1 for the definition of mathematical proof I say because it's a goddamn good definition!!!

I have binary quadratic Diophantine equations because my equations generally reduce ALL binary quadratic Diophantine equations!!!

You have to have substance, but if you're worth anything you WANT YOUR MATH TO BE RIGHT so that's the easy part.

But never trust that people can't lie about mathematics!!! People can lie about anything.

So yes. You will have posters who will calmly tell you your math is wrong, especially if it's actually right!!! If they can't get away with saying it's not right—like you can demonstrate it with numbers— they will tell you it's "not important". Or "not of interest".

Those are code phrases for—curse you, you bastard I will not help you!!!

The most important role I can play now on Usenet is to note that those seemingly scary monsters who will stalk you in posts ultimately can't prevent the world from noticing if you have something. These people still stalk MY posts, but now they have to rant against Google. And they do.

Because they do not matter. It is the hardest lesson for you to learn: the angry idiots as I sometimes call them, DO NOT MATTER.

They will tell you day and night they DO. They will tell you day and night no one will listen to you. They will tell you day and night that no one in the world cares what you say.

And you can read all of that in my threads over a decades worth.

Check those posting histories!!! These people leave a trail a mile long. When some person you don't really know starts critiquing your math, see their history.

Because it's YOUR math. The hatred flows most against you when you're right! Like it did for me, with my math.

I can't emphasize enough that you should not trust your competitors. Mathematics is a singular discipline. You hear about Gauss, right? Not Gauss and his buddies. It's about Euler, right? Not Euler and the crew.

The name Archimedes has moved through time for over two thousand years, but you don't hear about Archimedes and his best friend.

If you get nothing else, get that: mathematics is not a group activity. Not at the highest levels. You will rise alone, and the posters around you want to rise above you, not lift you.

History notes: Sir Isaac Newton. NOT Sir Isaac and the gang of really rocking dudes.

You will rise alone if you rise. And it will be your name alone.

Wednesday, August 18, 2010


JSH: Usenet's world spanning reality

To me it's a good working hypothesis to strongly suggest that all those years of posting on Usenet, mostly in math newsgroups, have a good bit to do with some of the oddities of a peculiar popularity(?) that I now have, where I noted yesterday that so far THIS YEAR I have hits to my math blog according to Google Analytics from 94 countries/territories as Google puts it. Along with that information which people might doubt, most can do various web searches to get their own sense of it, like on: mymath

That Usenet still has a role to play is interesting in and of itself, as for years now in readings I've done I've repeatedly seen it considered to be a dark corner of the Information Superhighway whose time had long passed. And often the newsgroups seem to be just a hopeless jumble of bizarre conversations—many nonsensical—juxtaposed with ads, and various other spam which can be very bizarre.

But people CAN cut through the noise. I do.

In my case I can at times oddly enough sort of dominate the newsgroup enough to get howls of complaints from posters, posting, to decry all the attention around MY posting, which always strikes me as rather odd…

So how was it done? That is the question which is intriguing me more and more and a lot probably has to do with Google Groups, and the indexing by search engines, which means that Usenet can get pulled onto the Internet, but selectively. Very selectively.

But the exact mechanisms do puzzle me, though I would think that the worldwide nature of Usenet itself, and the ability to push out information through posting, allows the growth of familiarity that is necessary to become in any way "established" in just about any social arena, while intriguingly, the negatives pushed out against me, seem to have made my ideas the real stars here—not me!!!

My own position, not surprisingly, is that my ideas are valuable, so the world is picking up on them regardless of what people might say on Usenet against them. While even those who might disagree, must be somewhat taken aback if they do a search like: algebraic integers vs complex numbers

Or: binary quadratic Diophantine equations

Today with hits from so many countries to my math blog I no longer feel much of a compulsion to get published through traditional means—though I do try at times but now only send to the Annals of Mathematics which has a paper currently under review—as why bother?

Search results on my ideas now routinely eclipse those of established mathematicians, or even entire institutions with one of my favorite topics being the ongoing competition of my definition of mathematical proof with the Wikipedia.

THE Wikipedia. Of course the Wikipedia has a LOT more information than just its page on mathematical proof, but the ability of users around the world to do a simple search and see my ideas in direct competition with it, still floors me:

Search: definition of mathematical proof

That Usenet and the Internet are about the new, and that the new always brings in surprises doesn't quite seem fulfilling just yet, though it is odd to possibly be a part of history in this way, where a transitioning world may move away from mathematical journals and the processes that have been in place for generations.

After all, if when people do a search on binary quadratic Diophantine equations, and one of the top links is mine, it stands to reason that the simple reality of that availability is a potency far greater than that of researchers who just have a journal article, somewhere, out there.

That my work now outshines that of mathematical professors all over the world—at least by web searches—is a reality so disturbing to some that posters have routinely made posts in reply when I bring this subject up--attacking the value of Google searches themselves.

So back to Usenet, what lessons may there be for others who are trying to get their ideas known in our possibly wacky world, where a "crank" or "crackpot" can beat top ranked math professors, mathematical journals, and entire organizations like the Wikipedia in search results?
  1. Argue effectively, argue honestly, and for God's sake—argue!!!

    I call it the battle of ideas. If no one is arguing with you about your ideas, then in my opinion, you're not getting anywhere. But personal attacks don't seem to do much. I've tried them. And I've been on the receiving end of quite a few! Notice that didn't stop me from getting 94 "countries/territories" so far this year. The personal attacks my have hurt my personal fame, but my ideas don't appear to have been impacted at all as their continued dominance is just a web search away at any given moment to be seen.

  2. Try to stay away from personal attacks!

    With all of the above said, it IS a rather stunning reality that my personal fame level is clearly a trickle compared to the apparent domination of some of my ideas. A search on my name in Google still brings up a link to, where I'm ripped on as a crank. Clearly then my story is not an unequivocal success at this point! As presumably most would prefer not just that their ideas dominate, but that they themselves get some popularity as well.

  3. Practice. Practice. Practice.

    The situation I have today was over a decade in the making and I also had the luck of coming in with a transition in the world, as the web takes over in so many ways, and so much transformation is occurring. But also for years I've had the idea firmly in mind that practice is an essential part of any strategy that is meant to be successful in the long-run.
Through years of posting I have a practiced sense of how to do it. Feel confident doing it, and developed a personal style so distinctive that when posters try to imitate it, they are often immediately called out as frauds. That takes a lot of practice and a lot of thinking of writing as an art. Communication isn't easy. Whether you hate my style or not, the reality is that my writing has driven quite a bit of activity over the years, and that cannot happen without working for it.

After all, today grabbing your attention is something lots of people are trying to do ALL THE TIME. If it were easy, everybody would get more than just the supposed 15 minutes of fame. But you see, not everybody CAN get a lot of attention as then I guess all people would be doing would be staring at each other as everybody caught everybody else's attention and then what could actually get done?

Reality is a few people grab attention because it's hard to do, and should be hard. Otherwise, how could we possibly get any work done?

Usenet can be your ticket to worldwide attention for your ideas. But it is your ideas first, last, and foremost. They can take you on electronic wings around the world, so there I will end it, as you still have to THINK.


JSH: Attention burns you

People don't tell you, but all that attention sears your soul. It burns itself into you.

I live in an odd world of attention. My ideas travel the world and protect me. But they also force me to think, and as I think, I feel like I touch ice. It's the ice that burns. The coldness burns you.

I have ideas traveling the world now. I call them super memes. They work to protect me. I love my ideas.

The super memes have been working to help the human race. To help the human species.

And they are my friends. My super friends. The super memes are tireless. They are brilliant. They cannot be stopped.

Super memes. Super memes. Super memes. So like dreams the super memes.

Unlike human beings the super memes will fight for me without question without qualm. Without hesitation.

They are my angels. My beautiful ideas.

Currently the super memes are engaged in various missions around the world. They report back at times, but more and more I kind of just drift, as I consider that maybe it all isn't that big of a deal anyway.

It's all maybe just a dream. A silly dream. A really wacky silly dream. Of my super memes.

My most powerful agents wreaking their way across the world stage. Unstoppable. Immortal. With absolute power.

The dreams. The super memes.

I wish I had their faith.

Tuesday, August 17, 2010


JSH: Practice makes better

There are times I practice in posts. Actually a lot of times I practice in posts. It'd infuriate other posters at times, asking me, who are you talking to? What is this audience you're addressing?

I don't know how to talk to world leaders. It's outside my experience zone.

Without practice, if I get in a position to talk to them, how would I proceed?

Posters reply to me with absolute confidence that my ideas are junk and that no one listens to me, which they tell me a lot, or have told me a lot over the years. Easy for them to say. But I have to live my life. If I'm talking to a world leader down the line despite what some Usenet poster says today, how can I do so without practice?

And you're seeing what I might say.

And regardless of what some Usenet poster says in reply to me, I do have those hits according to Google Analytics and my message is a very negative one for academics. It is: do not just trust them. They can lie.

Practice makes better.

What you see on Usenet is practice.

I'm practicing talking to the world.

That audience that befuddled posters arguing with me for years is getting closer and closer.

The future is getting here. And that audience simply enough, will be the entire world.


JSH: May be serious this time

To world leaders, I'm wondering more and more if it wouldn't be simpler despite the fear of disruption to just fire the research side of professors across the world. Leave them to teach, but nothing more. It may seem harsh, or impossible, but what we've been seeing from mathematicians shows how deep the problem has gone.

The academic system is a medieval artifact. Our position today is undermined repeatedly by failures from that system.

I suggest we all consider carefully how it might be done.

There isn't a big hurry here. I'm thinking within two years is fast enough. They will howl, of course, but they've already done so for the marginal moves already made.

These people create their own reality and cannot be moved in THEIR OWN discipline to accept the truth if they decide it doesn't suit them.

This archaic system has passed its obsolescence date.

My position then is to move forward with plans to end the research arms of most universities worldwide.

Leave them to teach. But don't pretend that their research matters any more.

Our world has advanced beyond the academic system for research.

It is, of course, not my decision alone. You have time to consider.


JSH: But what does 94 countries really mean?

One argument on Usenet has been about the meaning of country counts from Google Analytics to my math blog, and I just checked now—gotta love technology!—and according to Google Analytics so far this year, starting from January 1st, I have visits from 94 countries/territories as Google puts it, from 1659 cities. Last year for the entire year the count was 121 countries/territories from 2486 cities, and maybe I'm less popular this year for some reason or other but 94 countries/territories is still a lot, I'd think.

One thing I get back from posters then is: why bother posting on Usenet if I have a math blog that gets hits from all over?

Simple answer is I USE Usenet, often to puzzle out problems. I talk out math problems as part of extreme mathematics and naturally turn to that method to try to understand people problems as this one is rather odd.

YEARS ago, long before those high country counts, I'd tell myself that my job was to convince one person. I had this strong feeling that if I could convince one person of the importance of my mathematical research then that could be the start, but years later I have THOUSANDS of visits to my math blog from all over the world!!! Where is that one person now?

Some posters have claimed that people go to my blog to laugh at me. That theory could explain the lack of impact of those high country counts, or the apparent lack of impact.

I mean to put it all in perspective, I don't need to go to a media outlet to send a message that will cross the world. In the last 30 days I've had hits from 46 countries/territories. That's typical. If I want to say something to the world—I can just put it on my math blog. It would seem.

But I DO put things on there and things don't seem to change much.

Another claim by posters is that all websites get that kind of traffic. One poster persistently claimed that it was robot traffic. That is, robot programs from all over the world checking my math blog and that it didn't represent humans at all.

So it's an interesting problem.

How would someone test influence on that level? Conceivably I could push just about anything I thought important across country boundaries all over the world, at will.

So far I've mostly been pushing the idea that academics lie. That math people can't be convinced all the time by mathematical proof. And that there is this big error in their field that they're hiding.

The possibility that I do have some influence is seen by Google searches, like: algebraic integers vs complex numbers

If I AM right, and the world is listening, then it hasn't figured out what to do with its academics yet.

My own suggestion has been simple: fire them.

Fire them all. Start over. The best people will rise to the top.

Leave enough professors to teach, but shut down their research completely.

It's a waste of the world's time.

And yup, I'm not just talking about mathematicians any more.

I no longer trust the entire academic system.

I'm ready to fire most professors across disciplines, worldwide—and start over.

Sunday, August 15, 2010


JSH: Parameterizing conics with Pell's Equation

One result I find interesting for trying to understand the psychology of the modern mathematical community is a parameterization of conics using "Pell's Equation" which is kind of wrong you can say because it's a result over rationals! While "Pell's Equation" is traditionally considered with integers:

Given x^2 - Dy^2 = 1, in rationals:

y = 2t/(D - t^2)


x = (D + t^2)/(D - t^2)

You get hyperbolas with D>0, the circle with D=-1, and ellipses with D<0.

You can see the D=-1 case from a well-known mainstream source at the following link:
See: eqns. 16 & 17

Now what's fascinating to me is that the result was known to Fermat, so I've never said it was new to me, and I'm happy to note I re-derived it. It's actually kind of a funny story as I was still playing with what I call surrogate factoring, trying to solve the factoring problem, and came up with this result I terrified myself was close.

So I wouldn't finish deriving the result.

And I ended up in these arguments on the newsgroups about it's importance with me saying dire consequences for the world if it weren't acknowledged and posters arguing with me about it being this trivial thing that did NOT solve the factoring problem, and finally I relented and finished my own derivation and found this nifty thing.

So I have the pleasure of having re-derived this result, which I think is way cool.

What's fascinating to me is that you can use it to replace the Kepler favored style of equations for ellipses and consider orbits with just this D number, which then is directly related to the eccentricity, and I've pondered it for a while and the BEST explanation I think for why mathematicians don't just note this result along with so many others is that it uses "Pell's Equation".

So because to math society, x^2 - Dy^2 = 1 is a Diophantine equation, then you aren't supposed to use it with rationals is my theory, which while wacky, can give you insight into that community!!!

Math society can be very weird.

So it turns out that you can re-do stellar mechanics using "Pell's Equation" and use D instead of the eccentricity. But don't expect to read about it in a standard mathematical text!

It's a buried result. Those who wish to argue that point: cite!!!

Sunday, August 01, 2010


JSH: So why my initials at the start?

Every once in a while I like to remind why my threads start with my initials "JSH" in front, as I'm sure the why gets forgotten, and the answer is that years ago—like now as some things just don't change—posters would complain about my posts, and look for ways to avoid them.

So I'm reading these complaints and I don't care, if you don't want to read my posts that's fine with me and preferable to all the verbal abuse anyway, so one of these guys complaining is talking about how hard it is to figure out which threads are mine, and asked that I do something to make it easier!!!

So I added my initials to help people on the newsgroup avoid my threads.

And that is why I put my initials at the start of threads I create though at times I may for my own reasons drop that usage and will not always do it on other newsgroups.

So the "JSH" is there to help people who wish to avoid threads that I create.

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