some physical form of pi or phi or some nonsense like that?
Posted by abbas to Vleeptron_Z at 11/29/2006 01:36:06 PM
so, what is the Thing?
Posted by Jim Olson to Vleeptron_Z at 11/30/2006 07:32:01 PM
I hadn't heard much from my pal John diP lately, he lives on planet Maine, when he gets hungry he walks to the beach and collects a bucket of clams and then walks a little east and picks a bushel of potatoes, and he has a clambake, maybe with a couple of Atlantic lobsters tossed in.
But then I get this e-mail:
How's the old Zeta Beam working? Has Catherine Zeta Jones ever used
it? Would it survive Tropical Storm Zeta, or a frat party at Zeta Phi?
and it just totally flies right over my head, so I reply about how the Zeta Beam is broke again and I am waiting for a delivery of new vacuum tubes/valves manufactured by beaten political prisoners in the Peoples Republic of China and I really wish it was working again because of the war in Iraq which is bumming me out.
Essentially he has smashed the PizzaQ Answer into my face with a large speeding bus, and I didn't even notice, I am so distracted this week.
John diP replies:
Bob, you dope. You wrote:
> Oh, there's an open PizzaQ near the top, Identify An Odd
> Visual Object.
In my original message, I wrote:
> > How's the old Zeta Beam working? Has Catherine Zeta Jones ever
> > it? Would it survive Tropical Storm Zeta, or a frat party at Zeta
Get it? Zeta, zeta, zeta? Zeta ... zeta function? Riemann's zeta
The Oldd Visual Object is a three-dimensional model of Riemann's
zeta function. The troughs correspond to places where primes are likely
The Riemann Hypothesis is the most important unsolved question in mathematics.
Just to keep your attention -- i.e., if Pizza slices aren't enough -- if you Prove or Disprove the Riemann Hypothesis, some guy named Clay will send you a check for
and if this Clay guy hasn't been jiving everybody, the check will not bounce. But that's between you and the Clay guy, Vleeptron was only giving away Pizza.
Okay, now before we Prove or Disprove the Riemann Hypothesis, let's talk a little bit about Rapid Prototyping.
That equation above -- or the many other ways to describe the Zeta Function -- is pretty easy to cram into a digital computer and make the numbers dance around. And draw pretty color pictures on the screen. You got a Big Computer, you can make really fancy pictures of the behavior of the Zeta Function over vast ranges in all sorts of directions. Your Big Computer will be happy to plot the Zeta Function over gazillions of values.
In the 1980s some really clever human beings developed this goop (resin) which is sensitive to a laser beam. You shoot the laser at the goop in the precise places the computer says to aim the laser, and the goop evaporates exactly at those places.
What you get when you're done is a Solid Tangible Object shaped like the numerical data in the computer says a solid object should be shaped.
What pays the rent is that Rapid Prototyping can quick like a bunny make solid models of small industrial parts that were designed with Computer Assisted Design (CAD). You use the model to make the hundreds of real parts you need in a hurry for your new airplane or car or bicycle or toaster oven.
But RP has done some really spiffy things beyond toaster ovens.
A couple of years ago, surgeons wanted to separate infant twins conjoined at their shared spine.
First they shoved the twins into a CAT scan machine and filled its computer with numerical data of the 3D shape of the spine. Then they fed the numerical data into the Rapid Prototyper, and the RP's laser churned out a half dozen real-scale-size solid models of the spine. So the surgeons could practice the incredibly tricky, complicated separation surgery on the RP models before they even touched the conjoined infants.
Oh, it worked, the kids are fine, and playing in seperate rooms now, or going to different elementary schools. They're still twins, but one is There and the other is Here. I'll try to find an image of the RP practice spine.
The first RP Zeta landscape was cranked out as the display centerpiece for a big Riemann Hypothesis party at the Courant Mathematics Institute of New York University about eight years ago, and The New York Times ran a photo of the Dingus.
Well, as you can imagine, the crowd went wild, everybody wanted one of these things, just like the Sony Playstation and the Nintendo Wii. So here's another, from the University of California @ San Diego Supercomputer Center, which seems to own its own Rapid Prototype machine.
The masked bearded fellow holding it a few posts ago (to show that it was smaller than a toaster oven) is Professor Larry Carter, Department of Computer Science and Engineering, University of California, San Diego, and Senior Fellow of the Supercomputer Center.
(He and his images are all 404'd this morning; either he's gone somewhere else to supercompute, or he's ripshit at goofballs like me filching his images. I was gonna credit him and his Thing as soon as somebody won the Pizza.)
This PizzaQ is intimately related to the Highly Intelligent Question you asked about the Big Prime Number Thing -- which, if I am accurately paraphrasing it, was "Who gives a flying fuck, don't big computers just find these things all by themselves now?"
Vleeptron will address that and related questions shortly, we have been busy and distracted lately.
Oh, but it turns out the Riemann Zeta Function and the Riemann Hypothesis posit very deep questions about the whacky screwy mysterious unpredictable seemingly random pattern of the Prime Numbers within the Natural Numbers (1, 2, 3, 4, 5 ...). Riemann was the first to suggest that maybe the pattern of the Primes is NOT whacky screwy mysterious unpredictable and seemingly random after all! And the Zeta Function is (maybe) the key to perceiving the Order and Non-Whackiness of the Prime Numbers!
There's a REALLY EXCELLENT BOOK about all this called "The Music of the Primes" by Marcus du Sautoy, who is a Really Superb Writer, and it's all about Real Human Beings, not so heavy on the headache aspirin math equations. His website also will tell you how to get the U$1,000,000 and has lots of spiffy and coolio images and things to click on.
Oh, that there Equation above is the Absolutely Simplest Way I can write the Zeta Function on the blackboard. But if the Zeta Function was a car, it would be a Lamborghini or a Masserati or a Jaguar XK-E, and that thing at the top is uhhh sort of a Wal-Mart Skateboard version of it.
Take a handful of extra-strength aspirin and check this out. To get anywhere near the $1,000,000 , you have to ride the Zeta Function through both Real and Imaginary Space, you know, the place where -1 has a square root. As the Maine farmer told the tourist who asked for directions: You can't get there from here.