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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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It means that if you do: ./compute_pi > /dev/dsp, sooner or later you will ear Behetoven's fifth, last Madonna's song etc...
(well, maybe not at the right speed)
Or if you stream the PI digits to the framebuffer, you (or your grand-grand-grand-children) will see a digital representation of Da Vinci's gioconda.
I wonder if this wold be accepted as 'prior art' in a patent or copyright lawsuit
Ciao
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FB
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:
My God, this guy was a century ahead of one-click.
The scary thing is, the USPTO would probably let him get away with it today...
Here's the link to the Nasa site with the formula for computing an arbitrary hex digit of Pi.
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
If you need it in more places than that, then go here.
"Ancillary does not mean you get to rule the world." --U.S. Circuit Judge Harry Edwards, speaking to the FCC's lawyer
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.
You're very wrong. When Bell Labs invented the Laser in the early 60's, they didn't know it would be used to play music in the 80's. Or that it would ring up prices in a grocery store.
(Or in deep pie?)
Carl Sagan said that there is a secret code buried
deep in the digits of pi, placed there by the
Builders of the Universe.
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
actually, from what i've heard, the digits of pi pass all statistical tests for "randmoness" (whatever that means). The problem is, nothing is truly random, except possibly brownian motion (
I have my doubts about that). The digits of pi, while not truly random, are pretty damn close.
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---- I made the Kessel Run in under 11 parsecs.
:)
www.HearMySoulSpeak.com
Sure, we could. We could also just code it as:
c/d, where we now c is a circumfrence and d is it's diameter.
The point of the Berry paradox was not to say we should encode PI in words, it was just to demonstrate there are algorithmic ways to express very complex messages. Saying "The smallest number not describable in less than 100 words" is the result of some algorithm to express large numbers in small ways. Essentially, it is just an example.
Woz
I had $50 on "1"!
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DO NOT DISTURB THE SE
This means that they have the Improbability Drive!
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
And I'll legislate for PI to be 8E+16 ^ (1/34), which is a close approximation, although as another irrational, not very useful.
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
It's not very telling though. There are 3 components to the speed of calculation. The raw machine speed, improved algorythms, and alogrythms which converge in a non-linear fashion, eg if you give it twice as much CPU time, you get 4 times as many digits. Without seperating these components, you can't tell why it's getting faster.
Actually, couldn't we just encode PI as follows:
PI is the ratio of the circumference of a circle to its diameter.
I just encoded PI in 65 characters or 13 words.
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
I tried submitting this when it was news and it got rejected (2000-09-11 12:24:13 The quadrillionth bit of Pi is zero (articles,science) (rejected)).
I guess things have to get into a major newspaper before they are considered newsworthy.
BTW, the original announcement is here.
Colin Percival
Author, PiHex
Tarsnap: Online backups for the truly paranoid
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
Something strange happens between the 127th and 327th decimal. It's the name of G_d or something like that. All subsequent digits have got to be leftover resonating turbulence.
I don't think you get the point. If you can predict the order of ones and zeroes, based on the preceeding numbers, you have shown that Pi is not a random stream of numbers. It's predictable. That was what I was told at school the whole point of calculating pi to huge numbers of decimal places was - to see if there was a pattern.
There are loads of uses for these algorithms, but you are all evidently too stupid to comprehend them, so I won't bother.
I took part in the earlier phase of the project, that found the trillionth digit, and was impressed by the fact that the person behind it, Colin Percival, was only 16 or so at the time. That wasn't so long ago -- I doubt he's even 20 by now. This may not be earth-shattering knowledge, but I'm impressed by the fact that someone so young is doing something so impressive.
It reminds me of a large-scale version of the mathimatical riddles that Paul Erdos is said to have constantly posed -- check out The Man Who Only Loved Numbers some time, it's a really good book. This kid may be on track to be the same caliber of mathematician. Who knows, the next puzzle he solves might not be trivial -- maybe he'll prove or disprove the P vs NP conjecture & break or affirm modern cryptographic systems. Maybe he'll find the real proof to Fermat's last theorem. I look forward to finding out...
DO NOT LEAVE IT IS NOT REAL
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.
{HUMOR}
Since PI is actually defined as the ratio of the circumference of a circle to its diameter this value changes with the geometry. Now I will not deny that finding the quadrillionth digit of this ratio in Euclidian/Plane/2-D Geometry can be a bit tricky. However, finding the quadrillionth digit of this ratio in "Taxi-Cab" geometry is quite simple -- it's 0. In fact this ratio is exactly 4!!! For that matter if they were working in 1-D the value of this ratio is exactly 2!!! Maybe they were working in "Taxi-Cab" geometry?????{/HUMOR}
This message has been formatted for the humor impaired.
Tomura: Hey Kanada, whadda want to do tonight while backups are running?
Kanada: I dunno, why don't we see if we can run off pi to 536,870,898 places
Tomura: Works for me.
Looking at that chart I can't help but wonder if this was all these guys ever did. And now Tamura, replaced by Takahashi, is on a street corner holding up a sign "Will calculate Pi to 1,073,740,800 places for food."
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A feeling of having made the same mistake before: Deja Foobar
err, it's irrational, so it's not quite a ratio...
Ratios can be irrational. Ratios of integers can not.
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
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
Maybe the current political climate in the U.S.A. has increased my already sky-high levels of cynicism, but exactly how do we know that he actually calculated that the billionth-millionth-squillionth (whatever) binary digit of Pi is a zero? He might just have guessed! After all, he's got a pretty good chance of guessing right and what are you going to do, prove him wrong?
--
The gift of death metal does not smile on the good looking.
SETI@Home. Or that new one for decoding genes or whatever. What's more important, knowing yet another binary digit in pi or knowing whether or not intelligent life exists outside of earth, or what genes turn off cancer?
J
My bad. You are correct. None-the-less, it was fun to write.
Anyway, I still think I have a counter-argument.
The conjecture is that there is no number that cannot be described in 100 words. While that was not the conclusion of the Berry paradox (there is no conclusion of the paradox - it's just a paradox), I think I can construct a contradition.
Let's say there are Num words in a natural language L. Since the number of words in a language is finite, an absolute upper bound of sentences that are 100 words long is Num ^ 100. This number is finite. Thus, there is a number that cannot be decsribed in 100 words. Bear in mind most of the sentences formed will be non-sensical, but this is an upper-bound.
Now, this is not really a proof, but it's the intuition behind one. This falls apart when the language is infinite, however, if it's countably infinite, we can always start using real numbers and there is bound to be one we can't describe, since that set is uncountably infinite.
This would be an interesting problem to look into...
Woz (with thanks to R. Kitto)
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?
Yep. I was blatantly wrong. It was wishful thinking on my part after seeing the 10.10110111 part.
<p>
Damn, I wish it had been true.
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Win dain a lotica, en vai tu ri silota
Yeah, sure, group theory and physics, but that was in the past, and times have changed. Science is dead, haven't you heard? killed sixty years ago by the secrecy of the Manhattan Project. Literature is dead, too, kidnapped and murdered by the Disney Corporation and the Sonny Bono (that jackass!) Copyright Act, all so a disgusting cartoon rat might continue to generate profits.
slashdot is a site devoted to hacking but the Digital Millenium (thousand-year-Reich) Copyright Act has made non-corporate computer programming a jailable felony; look at a MS Word document that you yourself wrote with a hex editor, and it's off to Miniluv for you.
Non-human psuedo-intelligent entities with indefinite and potentially endless life spans control society these days, and you have no right these days to disobey them, or even to complain. These entities are known as "corporations." Shut up, keep your head down, and work. Stockholders demand your labor; for just so long as your labor continues to increase their wealth, you'll be allowed to continue to eat.
Yours WDK - WKiernan@concentric.net
Noone's calculated a quadrillion bits of pi[1].
He's (organised a distributed computation of) the quadrillionth bit of pi. Without calculating the previous bits. That's why the algorithm is so clever. You can look for any digit and don't need to work out the previous ones.
FatPhil
[1] I have, actually. They're all 1s. I'm not telling you which bit positions they are in, however.
Also FatPhil on SoylentNews, id 863
Its seems strange to want to know the value of Pi down to some tiny decimal place, but it does have its uses, primarily in the field of space navigation. The accuracy allows trajectories and orbits to be calculated with a very small degree of error - a minor slip of a few millionths of a degree at the beginning of a spaceflight can mean the difference between a spacecraft reaching its destination and completely missing it. The effect of this sort of error is exaggerated most clearly over the astronomical distances between our planet and everywhere else in the solar system etc.
ManicHawk - Just because you're manic doesn't mean the walls aren't bouncy
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
Waaaaaaaay back in the day, the techs at UCal would run a calculation of Pi for a couple of weeks on any new kit, just to give it a rudimentary burn-in test.
Once, we had an interconnected series of three PDP-15s [With shared single 1/2" tape spools - the first incarnation of what would becoming DEC's famed VAX Galaxy clustering technology] that was hooked up to a huge auto-fed Adler high-speed line printer.
We set up our standard "Calculate Pi" test routine and left the hardware guys to power on all the peripherals. Us software techs then left to attend a conferance for a week...
When we got back we discovered that the door to the computer would no longer open... Upon investiagtion, we found that the damn HW geeks had turn the lineprinter on too, and it'd been set to echo all terminal output! It'd got through three metric tons of paper, spewing nothing but Pi!
Pity I didn't have a camera...
http://www.klub.org/
it would be a shame if there weren't just a few people who devoted their lives to figuring out where all my socks go after I put them in the washer.
I saw/heard in a science show/book (i forget where, it was during a period where I was gobbling up these facts) that your socks end up going up over the side of the washer bin and then fall down inside. I forget hwat happens after.
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ADVENTURERS! - ANTIHERO FOR HIRE - CARDMASTER CONFLICT
Honestly, I would have liked to, but oddly enough, the prevelant material concerning distances in the stellar and micronic fields were in english measures,... and converting would have only obscured the outcome.
> Its seems strange to want to know the value of Pi down to some tiny decimal place, but it does have its uses, primarily in the field of space navigation
No at all. We are talking about the quadrillionth binary digit alone (ie: without the preceeding ones).
Pi digits are interesting (I'd say fascinating) in a few ways:
* For the exploration value.
* For the algorithmic challenge. Going further in Pi basically mean doing better algorithm. And I don't talk about micro-optimisation, I talk about radically different ways of doing things. Discovering that getting the nth binary of Pi was easier than getting every preceeding one, have been a major breakthrougt.
* At a theorical level, the idea is knowing things about number-universe (don't know how it is said in english), which are numbers that include everything (ie: numbers typed by infinite monkeys).
* Lastly, exploring numbers may give us insight about what reality is really is, and what may be hidden behind.
It is definitely not to get increased precision.
Cheers,
--fred
Btw, you should try to see 'Pi', the movie. Pretty good one.
1 reply beneath your current threshold.
e is not normal - there's not much encoded in e. Ever wondered about that strange quasi-pattern at the beginning of e in base 10? It's an artifact from the real pattern that shows up in bases that are a power of 2. e in binary is this:. ..
10.10110111011110111110111111011111110111111110
--
Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Win dain a lotica, en vai tu ri silota
As with most of these inane 42 facts: yes.
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Win dain a lotica, en vai tu ri silota
Uh, right. We live in 3 dimensions. We've got circles. I think I just proved you wrong.
--
Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Win dain a lotica, en vai tu ri silota
e isn't popular because it isn't a normal number. If you look at it in binary, the 1's and 0's form a pattern, as I've noted in other comments. I'm not sure, but I believe this pattern could show up in a more obfuscated way in base 10. The whole reason we look for digits of pi is that we don't know what they're going to be, while it took me about 30 seconds to determine that the quadrillionth binary digit of e is 1. (Nothing unexpected. The number of 1's in e approaches 100% as you take more decimal places.)
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Win dain a lotica, en vai tu ri silota
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.
In general, all the approaches for specific finding digits within transcendental (non-rational, radix patternless) numbers require discovery in order, from the greatest significant digit down. You can't find out the 50th digit without finding the 49th first and refining the result.
So yes, the guy has worked from finding it to be a little more than 3.0, to finding the next quadrillion fractional binary digits.
[
A while ago, I got interested in various ways of calculating Pi and saw some of the discoveries made by simon plouffe (this guy memorized the first 5000 places of pi), especially the one he found that allows him to calculate the n-th hexadecimal place of pi without having to get the n-1 places first : this is called digit extraction ,and was kind of unexpected before it was discovered ! :
There is also a nice little formula from Ramanujan that is an exact sum from 0 to +infinity of Pi
At rank 0, it's got 6 places correct, and it adds 8 correct places each time you increment it (cool eh !)
A couple of Pi links
Plouffe algorithm
Ramanujan's formula
"The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers." Bill Gates,
Or, as one Tolkein character might say...
Precioussssssss Pi!!!! Givessss meee digitssssssss of Pi!!!!!! Gollum!
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
See this quote for an old take on the uselessness of knowing pi to the 100th decimal place. Still, my mind occasionally reels at the implications of an irrational relationship between fundamental concepts such as the circumference of a circle and its diameter. But I'm easily reeled.
http://www.urbanlegends.com/le gal /pi_indiana.html
According to the Guinness Book of World Records, it was actually France that declared pi was de jure 4. Apparently egomania isn't even limited by the laws of the universe.
Gamingmuseum.com: Give your 3D accelerator a rest.
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fat lenny's gonna lick your brain today.
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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Sorry, don't take this as a flame, but I'm shure you have no idea of what you are talking about.
There is NO pre-computable relation between the millionth digit of pi and the accuracy of any precalculation of trajectories of a spacecraft (and a million digits for pi is doable at home).
Don't belive me?
Then read something about calculating of errors and the physical meaning of 1E-1000 [insert favorite measure here] in light of quantum physics....
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