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 an 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)


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