Having been a big comic book fan in the past I feel gratified by a lot of movie-making which has finally done the job needed for handling a fantasy reality where superpowers rule.
With that said it occurred to me that I have not seen a movie with the lead from one particular superhero who could, I think, handle the massive weight of a major motion picture all on her super-powered shoulders and that is Rogue.
Movies with female leads have been showing their box office clout, while Wolverine has shown that there is still room for other often singleton superheroes along with the perennial favorite Spiderman.
As a female lead superhero few are in the range of Rogue.
So should Marvel--or someone who has the insight and power--go a movie about Rogue?
(Assumed they have the rights to do so, and finally stumbled across indications they do not. Shows what I know about licensing issues around these characters which is admittedly not much! Will leave the post up though as, why not?)
I think they should.
Rogue can hang with the best of them at her maximum, while she has the vulnerability in character and in her story that can make her appealing to a wide audience. She can not only fly, punch, and hurl cars with the best of them, but she also has to deal with her root ability to steal superpower or memories or life energy.
Of course modern movies are massive investments, but hey, it's the web so I can express my opinion. And maybe some people with clout have already realized the above and there is something in the works.
If so, great thanking you unknown people who help bring the Marvel Universe to life on the big screen!!!
You continue to impress me.
If not?
Go Rogue.
And give us more. And it better be great. Her character deserves nothing less.
I am a HUGE fan of the Rogue character. I am certain there is a lot of strength and power there which is the raw material needed. Getting it right is the job of others.
There are few if any minor heroes in the Marvel Universe.
There may be too many writers and directors not up to the challenge.
Get the best, and make them deliver.
Thank you for your time and attention. And, um, that's it.
James Harris
Sunday, September 22, 2013
Friday, September 06, 2013
Back to software development
Back in 2002 I voluntarily left a position as a software developer at a major corporation. At the time it seemed like a great idea. Now over a decade later, I'm not so sure.
But back then I was serenely confident in myself and very naive about important things in the real world.
So I thought I had a duty to concentrate on what I knew then (and know now) was a major mathematical find. And that find is what mathematicians call a prime counting function, but which I've now found may be more commonly called a prime counter.
As my backup I also had an idea for a little app which was a tool for Java developers to check out basic class information. It was evolving from some test programs I'd written to help me study for the Java certification exam.
Besides, I felt confident that if necessary I could easily step back into the computer field considering how well I had been doing. I had been a lead developer. I had lots of experience with plenty of people recognizing my abilities.
So yeah, I was supremely confident and soon in for a shock.
Despite my ability to prove without a doubt the importance of my mathematical find, I got nowhere with mathematicians. And learned that they don't particularly feel motivated necessarily to help out someone like me. I'm not a mathematician. I'm just some guy who found this thing. Academics are not like what I thought.
But I'd been through adversity, I thought. I grew up as a black kid in the American South. While I think I got a lot of support from my rural South Georgia community, across races, I have to admit standing out as someone who went on to college on a full tuition scholarship and got my degree in physics in four years.
I'm used to finding my way.
But now I'm willing to admit--more than 10 years since my find--that academics have me stumped. I've since made more mathematical discoveries and come to the conclusion that I'm finally facing the greatest challenge of my life in getting any of it academically accepted.
Eventually after that pivotal decision of leaving my comfortable software developer position I found myself in San Francisco, and pondered trying to get back into the field then. That was in 2005 when I moved to California, and ended up, instead, working as a data entry person at a large insurance company.
But it paid the bills, gave me time to enjoy myself in the city, and left me time to focus on my continuing struggles with mathematical recognition, and with my various blogs or other online efforts.
I kept thinking: soon, soon, something will work.
And my open source project which I'd belatedly put on SourceForge in 2004, was still out there as a puzzle, and also as my continuing link to the development world. But I struggled with what to do with it, and wondered if it was even worth the effort.
Today I've given up on courting mathematicians for formal recognition and gone more to the long-term, which is just put the information out there and win in the court of better ideas. Meanwhile I've begun to accept that it's probably a good idea to focus a bit more on a job that actually pays well, as nothing else has come close to how well I was paid, now seemingly long ago, working as that software developer at that major corporation.
Now my open source project Class Viewer is critical in that effort, so I'm looking at it more critically.
Oh yeah, actually got laid off from that data entry job in San Francisco, which was a major blow to my ego. The nerve of those people!!! And then focused more on web efforts, pushing math ideas, and other ideas until I exhausted my naivete and delusions about how the real world works.
Ideas do not necessarily move the world.
Products DO, and groups of people DO.
Individuals with ideas who push them often get called nasty names, and make no money.
That making no money gives you a fascinating thing called--perspective.
It also gives you lots of unpaid bills. My apologies to creditors! I still plan on paying you all back.
My problem is that I don't like to lose. Dogged determination can carry you far in life, or leave you high and dry against a problem you can't seem to solve.
The idealist in me though believes that my actual failure was believing in some people who did not live up to great expectations, but the realist in me realizes that can be just a fact of life.
Great expectations may make a great novel title, but are not necessarily the most pragmatic views.
James Harris
But back then I was serenely confident in myself and very naive about important things in the real world.
So I thought I had a duty to concentrate on what I knew then (and know now) was a major mathematical find. And that find is what mathematicians call a prime counting function, but which I've now found may be more commonly called a prime counter.
As my backup I also had an idea for a little app which was a tool for Java developers to check out basic class information. It was evolving from some test programs I'd written to help me study for the Java certification exam.
Besides, I felt confident that if necessary I could easily step back into the computer field considering how well I had been doing. I had been a lead developer. I had lots of experience with plenty of people recognizing my abilities.
So yeah, I was supremely confident and soon in for a shock.
Despite my ability to prove without a doubt the importance of my mathematical find, I got nowhere with mathematicians. And learned that they don't particularly feel motivated necessarily to help out someone like me. I'm not a mathematician. I'm just some guy who found this thing. Academics are not like what I thought.
But I'd been through adversity, I thought. I grew up as a black kid in the American South. While I think I got a lot of support from my rural South Georgia community, across races, I have to admit standing out as someone who went on to college on a full tuition scholarship and got my degree in physics in four years.
I'm used to finding my way.
But now I'm willing to admit--more than 10 years since my find--that academics have me stumped. I've since made more mathematical discoveries and come to the conclusion that I'm finally facing the greatest challenge of my life in getting any of it academically accepted.
Eventually after that pivotal decision of leaving my comfortable software developer position I found myself in San Francisco, and pondered trying to get back into the field then. That was in 2005 when I moved to California, and ended up, instead, working as a data entry person at a large insurance company.
But it paid the bills, gave me time to enjoy myself in the city, and left me time to focus on my continuing struggles with mathematical recognition, and with my various blogs or other online efforts.
I kept thinking: soon, soon, something will work.
And my open source project which I'd belatedly put on SourceForge in 2004, was still out there as a puzzle, and also as my continuing link to the development world. But I struggled with what to do with it, and wondered if it was even worth the effort.
Today I've given up on courting mathematicians for formal recognition and gone more to the long-term, which is just put the information out there and win in the court of better ideas. Meanwhile I've begun to accept that it's probably a good idea to focus a bit more on a job that actually pays well, as nothing else has come close to how well I was paid, now seemingly long ago, working as that software developer at that major corporation.
Now my open source project Class Viewer is critical in that effort, so I'm looking at it more critically.
Oh yeah, actually got laid off from that data entry job in San Francisco, which was a major blow to my ego. The nerve of those people!!! And then focused more on web efforts, pushing math ideas, and other ideas until I exhausted my naivete and delusions about how the real world works.
Ideas do not necessarily move the world.
Products DO, and groups of people DO.
Individuals with ideas who push them often get called nasty names, and make no money.
That making no money gives you a fascinating thing called--perspective.
It also gives you lots of unpaid bills. My apologies to creditors! I still plan on paying you all back.
My problem is that I don't like to lose. Dogged determination can carry you far in life, or leave you high and dry against a problem you can't seem to solve.
The idealist in me though believes that my actual failure was believing in some people who did not live up to great expectations, but the realist in me realizes that can be just a fact of life.
Great expectations may make a great novel title, but are not necessarily the most pragmatic views.
James Harris
Wednesday, September 04, 2013
Why do we still use passwords?
I like puzzling over really dumb things that lots of people have to do, because it amuses me. And one of the stupidest things we all still have to do is use passwords, but why?
Early on, back when there were debates over whether or not "personal computers" were even worth having, as the web began to emerge, it was simpler to use passwords for access to sites. And the username and password way of operating took over.
But it's a dumb way to do things long-term.
People forget the darn things. Or re-use them endlessly. Or get infuriated when they have to come up with new ones on a schedule. And, oh yeah, computers are fiendishly good at cracking them.
But what to do? What else to do?
Why not use keys?
People don't use a username and password to start their cars, right?
Would you use a username and password to get into your house?
I wouldn't. I like keys just fine.
So how do you use keys instead of passwords?
The simplest is a dongle type device that plugs into a USB port with a unique and cycling identifier that runs through a key service. The key service tells people that you are you.
So, for instance, say Mozilla or Google were to provide a key service--or some other organization if you don't trust either of them--then they'd be the ones to tell a website who you are.
They just need to be sure you--are you.
So they would just need a way for you to tell them, which is what that device that plugs into your USB port would do.
And you can keep it, where?
How about on your key-chain?
(That's where a lot of people like to keep their keys. I think it's a decent place. Very familiar.)
How do you cycle it?
How about using the time of device connection?
That's a simple idea I gave away years ago after I failed to get a US patent on the concept which infuriated me, and earned my contempt of the USPTO from then on.
I think the USPTO is stupid. (Maybe I'm using words like "stupid" too much these days but the password thing is way past stupid into endlessly annoying.)
So, like, there's an algorithm that shifts a code on your "key" whenever you connect it to the key service.
The way it works is your key keeps up with how long you're connected because it has a timer and the service keeps up with that connection time too.
So your key calculates its new code after you disconnect and the service does as well. They both know how long you were connected, so each has the critical information. That time of connection is a number which can be pushed through shared formulas to generate a code. So you can endlessly generate codes, replacing a static password, or one that changes every 30 days.
With this idea, you send--by using your key--a new code with each connection.
Here notice that both your device and the key service have a useful bit of information which as far as I know is mostly just thrown away all the time on the web.
They BOTH independently have the time of connection.
It's called SHARED INFORMATION and my idea leverages such information. Simple.
If someone copies your key, and tries to be you, they start generating new codes, and then when you try to be you, the service starts howling as your codes are wrong. You can't both be you at the same time. So, you know you've been hacked. They know you've been hacked.
That simple technique is unbreachable, as long as you eventually use your key again.
If they just take your key then it's just like other situations if people just take your key. If you never use your key again, and they copy it, then it's also like if they just took your key. So technically the technique ensures only one key user is allowed with it impossible for duplicates to co-exist without detection.
I can prove that through logic because I'm really smart.
Our current system is really STUPID.
Do you think I used the word "stupid" enough in this post? I don't. I'd like to use it a bit more but I'm trying to be polite.
Our world is so much worse off because there are people who think they are highly intelligent who insist on ignoring ideas that can make our lives easier while requiring we do STUPID things like use usernames and passwords.
Ok, I feel better now, got one more in there.
So why is my idea a key while username and password is not?
Because your physical keys are unique to you. Yes, others MAY copy them, but it's not like you will not find out. Or probably will find out if you're smart about it, and oh yeah, I digress...they need your physical key to copy it!
Physical keys are awesome things which people should appreciate more, so we can move those key principles to the web.
When you think it, then it is possible it can be done.
If you can't think it, then how can it be made real?
With my idea someone wishing to steal your key needs your physical key to copy it--as the codes it generates shift all the time--and even with it, they may find it hard to hack the freaking thing and copy it. But even if they do, if you get it back, and use it, their copy is now worthless.
So it's actually better than a normal key.
If they just copy a current code from your key as it flies across the web, then they got NOTHING.
Oh yeah, and why give ideas away for free?
Because I don't like the USPTO and I STILL don't like them despite recent legislation.
What we lose is innovation as big corporations have the power to push their ideas through, while others can just keep using usernames and passwords indefinitely because in my opinion big corporations rarely push the best innovation.
(But they do have big legal departments so tread carefully in saying nasty things about them!)
Our world is changed by blocked innovations where people lose more than they often realize because they have no clue how much better things could be.
And that is just sad.
James Harris
Early on, back when there were debates over whether or not "personal computers" were even worth having, as the web began to emerge, it was simpler to use passwords for access to sites. And the username and password way of operating took over.
But it's a dumb way to do things long-term.
People forget the darn things. Or re-use them endlessly. Or get infuriated when they have to come up with new ones on a schedule. And, oh yeah, computers are fiendishly good at cracking them.
But what to do? What else to do?
Why not use keys?
People don't use a username and password to start their cars, right?
Would you use a username and password to get into your house?
I wouldn't. I like keys just fine.
So how do you use keys instead of passwords?
The simplest is a dongle type device that plugs into a USB port with a unique and cycling identifier that runs through a key service. The key service tells people that you are you.
So, for instance, say Mozilla or Google were to provide a key service--or some other organization if you don't trust either of them--then they'd be the ones to tell a website who you are.
They just need to be sure you--are you.
So they would just need a way for you to tell them, which is what that device that plugs into your USB port would do.
And you can keep it, where?
How about on your key-chain?
(That's where a lot of people like to keep their keys. I think it's a decent place. Very familiar.)
How do you cycle it?
How about using the time of device connection?
That's a simple idea I gave away years ago after I failed to get a US patent on the concept which infuriated me, and earned my contempt of the USPTO from then on.
I think the USPTO is stupid. (Maybe I'm using words like "stupid" too much these days but the password thing is way past stupid into endlessly annoying.)
So, like, there's an algorithm that shifts a code on your "key" whenever you connect it to the key service.
The way it works is your key keeps up with how long you're connected because it has a timer and the service keeps up with that connection time too.
So your key calculates its new code after you disconnect and the service does as well. They both know how long you were connected, so each has the critical information. That time of connection is a number which can be pushed through shared formulas to generate a code. So you can endlessly generate codes, replacing a static password, or one that changes every 30 days.
With this idea, you send--by using your key--a new code with each connection.
Here notice that both your device and the key service have a useful bit of information which as far as I know is mostly just thrown away all the time on the web.
They BOTH independently have the time of connection.
It's called SHARED INFORMATION and my idea leverages such information. Simple.
If someone copies your key, and tries to be you, they start generating new codes, and then when you try to be you, the service starts howling as your codes are wrong. You can't both be you at the same time. So, you know you've been hacked. They know you've been hacked.
That simple technique is unbreachable, as long as you eventually use your key again.
If they just take your key then it's just like other situations if people just take your key. If you never use your key again, and they copy it, then it's also like if they just took your key. So technically the technique ensures only one key user is allowed with it impossible for duplicates to co-exist without detection.
I can prove that through logic because I'm really smart.
Our current system is really STUPID.
Do you think I used the word "stupid" enough in this post? I don't. I'd like to use it a bit more but I'm trying to be polite.
Our world is so much worse off because there are people who think they are highly intelligent who insist on ignoring ideas that can make our lives easier while requiring we do STUPID things like use usernames and passwords.
Ok, I feel better now, got one more in there.
So why is my idea a key while username and password is not?
Because your physical keys are unique to you. Yes, others MAY copy them, but it's not like you will not find out. Or probably will find out if you're smart about it, and oh yeah, I digress...they need your physical key to copy it!
Physical keys are awesome things which people should appreciate more, so we can move those key principles to the web.
When you think it, then it is possible it can be done.
If you can't think it, then how can it be made real?
With my idea someone wishing to steal your key needs your physical key to copy it--as the codes it generates shift all the time--and even with it, they may find it hard to hack the freaking thing and copy it. But even if they do, if you get it back, and use it, their copy is now worthless.
So it's actually better than a normal key.
If they just copy a current code from your key as it flies across the web, then they got NOTHING.
Oh yeah, and why give ideas away for free?
Because I don't like the USPTO and I STILL don't like them despite recent legislation.
What we lose is innovation as big corporations have the power to push their ideas through, while others can just keep using usernames and passwords indefinitely because in my opinion big corporations rarely push the best innovation.
(But they do have big legal departments so tread carefully in saying nasty things about them!)
Our world is changed by blocked innovations where people lose more than they often realize because they have no clue how much better things could be.
And that is just sad.
James Harris
Wednesday, August 28, 2013
Print on demand and the post office
People can wonder why problem solving is not enough to get things changed, so I like finding real world examples which are FAMOUS to help get perspective. So, for instance the US Postal service is having well publicized difficulties.
And it turns out I actually first put out a post trying to help them three years ago back in August 2010.
My original idea talked about scanning a letter at the post office but the concept boils down to print on demand for an electronically sent document.
And here we are three years later and it's worth talking about some more. And three years isn't a long time in the world of ideas. Typical time frame, remarkably enough, is 20 years in the old world. Don't believe me? Then read then the Wikipedia article about sliced bread.
I'm thinking things can get a bit faster today, though the problem isn't just getting the idea out there. People can get stuck in their ways. So the real problem is shifting them out of their comfort zone, into recognition that the suggested change is a better way to go.
Now then, with the new idea, if you print out a letter at a regional center closest to where the letter is supposed to go, you shorten the distance a physical thing is carried, allowing cyberspace to help out by transmitting the information.
So the idea would be to let you deliver a physical letter through cyberspace by having print on demand local to the delivery location removing the need to transport a physical letter all over the place when you just wish the information in a PHYSICAL letter to be delivered, so for instance it gets a postmark.
Notice that also is another way to possibly do next day delivery for people and businesses who don't care if someone else prints and stuffs their letter into an envelope for them!
Print on demand has been around for a while, and I'm guessing there is machine envelop stuffing available.
And the post office could charge a premium for the service which could let people pay bills overnight, using their debit cards of course, to have a postal money order stuffed into there too! Or you could send money to a relative quickly, and I don't know what the post office can or cannot do, or whom they can or cannot compete with, but that is for the US Congress to work out.
But regardless, imagine mailing a physical letter to someone you need to contact, by the next day, by emailing it to the post office which will print it out, stuff it into an envelope and deliver it?
Or postcards! What if the post office printed out post cards on demand instead of shipping them around the globe?
Do I believe this will be possible some day? Yes. For all I know there are post offices in other countries already doing it.
Would I like to have it now? YES! I'd love to be able to send a physical letter, with that wonderful thing called a postmark, by emailing the post office or using some online form, and paying for it all online.
I actually trust the US Post Office. It is one of the most trustworthy government institutions.
I think a lot of other people trust the US Post Office as well, and feel SAFER with it than with using other sources, and also, yup, again, get that often critical POSTMARK.
New ideas can seem weird to people at first. But so did sliced bread. Someday I think people will puzzle that there was ever a time in an advanced, technologically savvy country that the post office didn't allow people to electronically send in letters to be physically printed out and delivered!
They'll wonder how such a simple idea could have taken so much to be implemented.
James Harris
And it turns out I actually first put out a post trying to help them three years ago back in August 2010.
My original idea talked about scanning a letter at the post office but the concept boils down to print on demand for an electronically sent document.
And here we are three years later and it's worth talking about some more. And three years isn't a long time in the world of ideas. Typical time frame, remarkably enough, is 20 years in the old world. Don't believe me? Then read then the Wikipedia article about sliced bread.
I'm thinking things can get a bit faster today, though the problem isn't just getting the idea out there. People can get stuck in their ways. So the real problem is shifting them out of their comfort zone, into recognition that the suggested change is a better way to go.
Now then, with the new idea, if you print out a letter at a regional center closest to where the letter is supposed to go, you shorten the distance a physical thing is carried, allowing cyberspace to help out by transmitting the information.
So the idea would be to let you deliver a physical letter through cyberspace by having print on demand local to the delivery location removing the need to transport a physical letter all over the place when you just wish the information in a PHYSICAL letter to be delivered, so for instance it gets a postmark.
Notice that also is another way to possibly do next day delivery for people and businesses who don't care if someone else prints and stuffs their letter into an envelope for them!
Print on demand has been around for a while, and I'm guessing there is machine envelop stuffing available.
And the post office could charge a premium for the service which could let people pay bills overnight, using their debit cards of course, to have a postal money order stuffed into there too! Or you could send money to a relative quickly, and I don't know what the post office can or cannot do, or whom they can or cannot compete with, but that is for the US Congress to work out.
But regardless, imagine mailing a physical letter to someone you need to contact, by the next day, by emailing it to the post office which will print it out, stuff it into an envelope and deliver it?
Or postcards! What if the post office printed out post cards on demand instead of shipping them around the globe?
Do I believe this will be possible some day? Yes. For all I know there are post offices in other countries already doing it.
Would I like to have it now? YES! I'd love to be able to send a physical letter, with that wonderful thing called a postmark, by emailing the post office or using some online form, and paying for it all online.
I actually trust the US Post Office. It is one of the most trustworthy government institutions.
I think a lot of other people trust the US Post Office as well, and feel SAFER with it than with using other sources, and also, yup, again, get that often critical POSTMARK.
New ideas can seem weird to people at first. But so did sliced bread. Someday I think people will puzzle that there was ever a time in an advanced, technologically savvy country that the post office didn't allow people to electronically send in letters to be physically printed out and delivered!
They'll wonder how such a simple idea could have taken so much to be implemented.
James Harris
Friday, August 02, 2013
Why talk math here?
With several posts now focusing on math results, some might wonder why I'm doing it on this blog, and I wonder as well! And I figure things out at times by typing up a post, as I like to think out loud, so here is a post where I try to explain it.
Best way is to put up a math result which isn't mine, and is ancient so I can talk around it, and what it means to me. I've posted about it before, so the information is already been put up, and I'll repeat to explain more about my motivations.
The equation in focus is x2 - Dy2 = 1, in rationals, which means you have fractions, so to program a solution to it that I'm about to give you need to use doubles.
Turns out you can solve it parametrically, which just means you only need to change one variable:
x = (D + t2)/(D - t2)
and
y = -2t/(D - t2)
So if you have a value for D, then you just shift t, and that gives you x and y.
Cool. Makes solving the thing with fractions--not integers--nice and easy.
And if that all seems strange, like why would you want to solve it parametrically with fractions, well notice that with D = -1, the first equation is the circle: x2 + y2 = 1
And, yeah, people have reasons to solve for circles, right? So what does D do? Well it shifts things around between ellipses, which includes the circle, and hyperbolas. So with it negative, you have ellipses, while with it positive, you have hyperbolas, and D=0 is worthless, as that just gives x=1 or -1, so we don't care about it.
That result has been known to humanity for over 340 years, which I say because Pierre Fermat, who is a famous math dude, knew about it, and he has been dead since 1665. And I noted the above when I posted about it before, so why bother mentioning again now?
Because I never heard of that solution for x and y, until I had re-discovered it myself, got all excited, ready to run off and BRAG, and found out it had been known for centuries. But I had to dig!!!
So why isn't it a standard result, routinely taught? The circle paramaterization IS routinely taught, and is, again, when D=-1, and you have:
x = (1 - t2)/(1 + t2) and y = 2t/(1 + t2)
And you can go look that up to verify, but the earlier result? Wasn't so easy for me to look up and find it, and I think it's a cool result and wish I'd had it years ago when I played around with programming things like drawing circles, and other things.
People who write computer programs appreciate parametric solutions as you can focus just on what matters, and here, the focus is on D, and you don't have to play with square roots, or all kinds of others things, and yes there are parametric solutions for ellipses or hyperbolas, but here is ONE for both of them!
Efficiency. I like efficiency.
And why isn't this thing regularly taught?
Well I have theories, and my best guess is most modern mathematicians don't care about practical. And to them it's a useless little thing, which they don't think is worth discussing!
But I like practical. I don't care if mathematicians like talking about something or not. I like to DO things with math, as I'm a practical guy who codes for a purpose.
When I write a computer program I want it to DO something. I really don't care if some academic somewhere thinks that a tool I'm using is exciting to him or not.
So I talk about it because it's interesting to me, and I think it's a cool tool.
Which is why I include math results that I think are cool tools. They have a purpose. You can DO things with them, like count primes. And they're simple! I love simple.
James Harris
Best way is to put up a math result which isn't mine, and is ancient so I can talk around it, and what it means to me. I've posted about it before, so the information is already been put up, and I'll repeat to explain more about my motivations.
The equation in focus is x2 - Dy2 = 1, in rationals, which means you have fractions, so to program a solution to it that I'm about to give you need to use doubles.
Turns out you can solve it parametrically, which just means you only need to change one variable:
x = (D + t2)/(D - t2)
and
y = -2t/(D - t2)
So if you have a value for D, then you just shift t, and that gives you x and y.
Cool. Makes solving the thing with fractions--not integers--nice and easy.
And if that all seems strange, like why would you want to solve it parametrically with fractions, well notice that with D = -1, the first equation is the circle: x2 + y2 = 1
And, yeah, people have reasons to solve for circles, right? So what does D do? Well it shifts things around between ellipses, which includes the circle, and hyperbolas. So with it negative, you have ellipses, while with it positive, you have hyperbolas, and D=0 is worthless, as that just gives x=1 or -1, so we don't care about it.
That result has been known to humanity for over 340 years, which I say because Pierre Fermat, who is a famous math dude, knew about it, and he has been dead since 1665. And I noted the above when I posted about it before, so why bother mentioning again now?
Because I never heard of that solution for x and y, until I had re-discovered it myself, got all excited, ready to run off and BRAG, and found out it had been known for centuries. But I had to dig!!!
So why isn't it a standard result, routinely taught? The circle paramaterization IS routinely taught, and is, again, when D=-1, and you have:
x = (1 - t2)/(1 + t2) and y = 2t/(1 + t2)
And you can go look that up to verify, but the earlier result? Wasn't so easy for me to look up and find it, and I think it's a cool result and wish I'd had it years ago when I played around with programming things like drawing circles, and other things.
People who write computer programs appreciate parametric solutions as you can focus just on what matters, and here, the focus is on D, and you don't have to play with square roots, or all kinds of others things, and yes there are parametric solutions for ellipses or hyperbolas, but here is ONE for both of them!
Efficiency. I like efficiency.
And why isn't this thing regularly taught?
Well I have theories, and my best guess is most modern mathematicians don't care about practical. And to them it's a useless little thing, which they don't think is worth discussing!
But I like practical. I don't care if mathematicians like talking about something or not. I like to DO things with math, as I'm a practical guy who codes for a purpose.
When I write a computer program I want it to DO something. I really don't care if some academic somewhere thinks that a tool I'm using is exciting to him or not.
So I talk about it because it's interesting to me, and I think it's a cool tool.
Which is why I include math results that I think are cool tools. They have a purpose. You can DO things with them, like count primes. And they're simple! I love simple.
James Harris
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