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Pi: It Just Keeps On Going
dominic7 sent us a link on the National Post about a new record for "knowing" Pi. Using the ol' distributed approach, a math major in Canada has found the quadrillionth binary digit of pi. It's a zero.
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Seriously, there *are* fundamental basic studies that need to continue that are several steps down from public use but if funded right, may lead to something big. Understanding what the next smallest division of matter is may lead to improved energy sources, new materials, etc, as an example.
But there are studies that are also mostly curiosity issues - finding the nth digit of pi where n is anything larger than 100 is a good example. It is necessary to know pi to decent accurracy for "large" fp calculations (large in decimal places), and in most scientific calculations, pi is multipled or divided into a measument value, which will probably, by our current standards, no more accurate than 10 to 12 digits of accuracy , which means that any digit beyond the 12th of Pi is lost in measurement error.
The only thing, based on what I've read on pi, that interests mathemations is trying to determine if pi is completely irrational (can't be expressed as a fraction of two integers) -- if there's any point where the digits in pi repeat ad infinitum, pi becomes rational, and most of the current foundation of advanced number theory will have to be rewritten. Seems silly, sure, but what happens if SETI returns a definite signal? It's like the question that 'Contact' raises, if we don't look for it, we may be missing something.
So while multi-billion dollar budgets shouldn't be spent researching the nth digit of pi, there should be a small but dedicated effort to continue that search. And by going to distributed cycle systems like SETI@home (I do believe there was one for pi), it becomes trival to maintain such a project.
"Pinky, you've left the lens cap of your mind on again." - P&TB
"I can see my house from here!" - ST:
All for naught, really.
Sorry, couldn't resist.
Actually, they didn't settle on just one value of pi, they had many... including 3.2. Here's the requisite hyperlink.
Mike Warot, Hoosier
Well, according to this, the farthest object we can see is about 1 billion light years away. Now, there are 5,865,696,000,000 miles in a light year.
So we'll say that the farthest object we can see is five sextillion, eight hundred sixty-five quintillion, six hundred ninety-six quadrillion miles away.
Now, at 56 digits, we're going to say that it can calculate to a precision of 10^-56.
10^-56 * 5865696000000000000000 = 5.865696*10^-35
So, a decimel at 10^-56 will represent a unit on this scale of 5.865696*10^-35 miles.
Now, there are 63,660 inches in a mile, so...
(5.865696*10^-35)*63660=3.7341020736*10^-30
So, a decimel at 10^-56 will represent a unit on this scale of 3.7341020736*10^-30 inches.
Now, the estimated size of a proton is 0.22 trillionth of an inch. That is twenty two hundred quadrillionths.
Size of Proton = .00000000000000022 inches
Size of Known Universe * 10^-56 = .0000000000000000000000000000037341020736
So, 56 digits of pi, as you can see,... is TOO accurate.
This is like, a change moment in mankind's science.......a paradigm shift; it will change the world as we know it. Suddenly, computers will be faster, people will stop needlessly shooting each other, and McDonald's will serve Egg & Bacon McMuffin's *all* day....
Acting stupid isn't much fun when there's someone around who knows better
only about 1 in 10 people...
//rdj
No one can understand the truth until he drinks of coffee's frothy goodness.
--Sheikh Abd-Al-Kadir, 1587
I had $50 on "1"!
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DO NOT DISTURB THE SE
Pi has been proven to be irrational. You can't perform this exercise hoping to find a sequence because you never will.
Mmmm.. Donuts
In other news, the RIAA gets a restraining order against PI.
I'm trying to teach myself to set people on fire with my mind... Is it hot in here?
Counterexample:
I think you meant to say there is no number we can't describe in less than 100 words. =)
Woz
Yeah, but you would need a *really* steady hand...
"I don't need a compass to tell me which way the wind shines." - Mr. Furious, Mystery Men
Well, I'm not in the US, I'm in Canada, so you can trust me ;)
Seriously though, if you want to check up on me, I can send you all of the intermediate results (partial sums of the sequence), and you can 1. verify that they add up to the result I gave, and 2. take partial sums at random and verify that they are correct.
A complete triple-check of the results would only take 600,000 cpu hours, actaully, so you could even do that if you like.
Tarsnap: Online backups for the truly paranoid
All you need to draw a circle around the entire visable universe that devieates from perfect circularity by only the width of one proton. IS 56 DIGITS OF PI.
But Pi does give us a good benchmark for computing sometimes.
Vote for me, and I'll set e=2.0, pi=3.0, and extrapolate the rest of the number line from there.
I recognize that that won't fix everything, but at least it will bring two of the worst freaks of nature into line with what the citizens expect from their number system.
Sheesh, evil *and* a jerk. -- Jade
A binary digit of Pi is zero? What a surprise.
I'll predict that of the next quadrillion binary digits, approx. 50% will be zero, and approx. 50% will be one.
Right, where's my slashdot story?
Yes. Pi has been proven to be a trancendental number, that is a number which cannot be expressed as a root of a finite polynomial equation. Trancendental numbers have been proven as a class to be non-terminating and non-repeating.
"Bite me, it's fun!" - Crowe T. Robot
There's much more information about this project on its home page at SFU. The guy behind it also has a page there.
M
GROGGS: alive and well and living in
If you take the second and the sixth decimal places, you get 42. Surely a more profound and significant result.
From '49 to '83, the calculated length gained an order of magnitude roughly every 10 years.
From '83 to '97, one order of magnitude roughly every 5 years.
From '97 on, an order of magnitude every 2 years.
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I'm impressed. It's been a long time indeed since someone has managed to trick me with a goatse.cx link. Disguising it as a part of Slashdot's own layout was a particularly nice touch.
This said, I think it's time to introduce a (-1, "goatse.cx trick") category into moderation. This is really getting out of hand, and I think it's safe to say that the vast majority of people who've seen goatse.cx never want to see it again.
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PI is an interesting phenomenon (as well as a decent movie). It is a good example of the intution behind Kolmogorov/Chaitin complexity.
For example, we can look at PI from the standpoint transmission through a channel, as envisioned by Claude Shannon (Communication Theory, which in turn, relates to Coding Theory). If we try to encode PI for transmission through a channel, we realize it never ends. This is a problem. However, the way the Kolmogorov/Chaitin method looks at it, they see a way to encode PI as an algorithm. Note the subtle difference. Now, the cool thing about this is that the algorithm for PI is pretty short, so encoding is easy.
There is another example with the Berry paradox. Imagine the smallest number not describable in less than 100 words. But wait a sec - I just described it in less than 100 words!
Both are good demonstrations that algorithmic complexity is quite interesting. I always use PI as an example because it is so well known. Just goes to show PI can be used for more than just eating up CPU time =)
Woz
Cue the music, lads!
o/~ Bye bye to one more mystery of pi,
Some idjit found a digit in binary base. Why?
So some good ol' boys in the computer lab cry,
"Zero's the quadrillionth digit of pi!
Zero's the quadrillionth digit of pi...." o/~
-- WhiskeyJack