Pi: It Just Keeps On Going 323
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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Pi: It Just Keeps On Going
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"The hands that help are better far than the lips that pray." -- Robert G. Ingersoll
Official link (Score:1)
http://www.cecm.sfu.ca/projects/pihex/ [cecm.sfu.ca]
Re:Fun things to do with Pi (Score:2)
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
Re:Enough of this irrational nonsense! (Score:1)
Oh, that's way too complicated for lawmen to comprehend. You'd do better legislating for Pi to be 355/133, which not only is easier to type, but it also has had its share of signature space here on Slashdot.
Re:so? (Score:1)
Maybe doesn't. So what? It's a cool hack, just what /. is all about.
This reminds me of way back when Steve Wozniak wrote a program for the Apple ][ (8 bit processor, 4.xx Mhz, 64K (!) of RAM, no fan) that calculated pi to some huge number of decimal places. The program would churn for a week and then print out pages of numbers. Cool hack!
Re:Pure vs. Applied Research (Score:3)
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.
Re:stupid question (Score:1)
pi is 3.1415926....
As you can see it deviates at the third decimal place.
But then again I did use Microsoft's calculator
What an idiot! (Score:1)
Re:Enough of this irrational nonsense! (Score:2)
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...
Re:Warning! (Score:1)
Most Expensive Coin Toss (Score:1)
This is probably the most computationally expensive random single digit number generated ever.
It's worse than that, since it was in binary representation. It was the most expensive coin toss in history.
Of course, it's a so-called "coin toss" that comes up the same every time, but still...
Re:so? (Score:1)
And yes, an infinite stream of random numbers is probably an excellent place to look for a message from God. No matter what message you are looking for.
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Re:Do we know pi is of infinite length? (Score:1)
Re:Enough of this irrational nonsense! (Score:1)
Actually, pi=2.0
Draw a line segment of length 2.0
Connect the ends with a semicircular arc
The length of the arc is 2pi/2=pi
Now instead make two semicircular arcs of half the radius, and align them so they span the line segment. Picture of all this here [maine.edu].
The length of the arcs sums to pi again
Repeat with four semicircles of 0.25 radius, and so on
The semicircles converge to the line segment, so the arc length=pi converges to the line segment length=2.0
Thus, pi=2.0
Seriously (Score:1)
I seriously hope this guy does other things to earn his keep besides calculate PI.
Granted, I'm not math freak, but can anyone else out there think of reasons to know PI this deep?
Captain_Frisk
Re:my record (Score:1)
3.14159,
2653589,
7923284,
626 and a whole lot more!
It's a rhyme.
It's the essence of nerdness (Score:1)
Computing an arbitrary digit of Pi (Score:2)
All that computing power wasted! (Score:3)
Sorry, couldn't resist.
Re:pi: a universale mathmatical unit (Score:1)
Take 77/25. It comes out to 3.08.
Re:How is this a good use of idle computer time? (Score:1)
Re:so? (Score:1)
Yeah, but what if you go down the digits far enough and it stops being "random" :)
Do y'all realize the implications... (Score:1)
This sounds rather like the Mind of God(tm). Do we now need to worship Pi? Will prayer be reduced to chanting "three point one four one five nine two six five three five eight nine..."?
b&
Re:Enough of this irrational nonsense! (Score:3)
Mike Warot, Hoosier
3.1415926535897932384626433832795028841971369399.. (Score:2)
Re:Now all we need... (Score:3)
Well, according to this [nasa.gov], 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.
Re:Do we know pi is of infinite length? (Score:1)
Re:Seriously (Score:1)
luckman
Re:Pure vs. Applied Research (Score:2)
I bet... (Score:1)
(or took points off)
Hhhm.. so much effort for a zero? (Score:1)
Re:so? (Score:1)
secret of the universe deep in pi (Score:2)
Carl Sagan said that there is a secret code buried
deep in the digits of pi, placed there by the
Builders of the Universe.
Oh my God! (Score:4)
Re:Hhhm.. so much effort for a zero? (Score:3)
//rdj
Re:Fun things to do with Pi (Score:2)
I have my doubts about that). The digits of pi, while not truly random, are pretty damn close.
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Woops, rounding error... (Score:2)
:)
Re:PI and complexity (Score:2)
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
DAMMIT! (Score:5)
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Re:Oh well done (Score:2)
This means that they have the Improbability Drive!
Re:Enough of this irrational nonsense! (Score:2)
No, that will never happen (Score:4)
Fun things to do with Pi (Score:5)
In other news, the RIAA gets a restraining order against PI.
Re:PI and complexity (Score:4)
Counterexample:
I think you meant to say there is no number we can't describe in less than 100 words. =)
Woz
Re:History of Pi calculations (Score:2)
Re:PI and complexity (Score:2)
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.
Re:Now all we need... (Score:5)
Sigh (Score:2)
I guess things have to get into a major newspaper before they are considered newsworthy.
BTW, the original announcement is here [cecm.sfu.ca].
Colin Percival
Author, PiHex
Re:Errr... (Score:5)
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.
But as everyone knows from the movie, pi (Score:2)
Re:Oh well done (Score:2)
There are loads of uses for these algorithms, but you are all evidently too stupid to comprehend them, so I won't bother.
Interesting result (Score:2)
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 [fatbrain.com] 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...
Now all we need... (Score:5)
But Pi does give us a good benchmark for computing sometimes.
What Geometry ??? : (Score:2)
{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.
A slice of the Pi calculations (Score:2)
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 [netcom.com] 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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Re:what's more.... (Score:2)
Ratios can be irrational. Ratios of integers can not.
Enough of this irrational nonsense! (Score:4)
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.
Re:Oh my God! (Score:2)
Errr... (Score:2)
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Re:Seriously (Score:2)
J
Re:PI and complexity (Score:2)
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)
Oh well done (Score:5)
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?
Re:Do y'all realize the implications... (Score:2)
<p>
Damn, I wish it had been true.
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
today, science is dead (Score:2)
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 [panix.com]. 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
READ THE DAMN ARTICLE! (Score:2)
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.
Re:No, that will never happen (Score:2)
I've asked for a (-1, Misinformative) moderation before, and now I wish it would be used on me. Thank you.
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Re:so? (Score:2)
Re:Sigh (Score:2)
Congratulations, anyway.
/. is not a perfect medium.
FatPhil
Re:Do we know pi is of infinite length? (Score:4)
Re:secret of the universe deep in pi (Score:2)
So, that would mean DeCSS is hidden in pi as well! Wait till the mpaa sues!
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Re:Oh well done (Score:2)
I haven't actually verified their frequency, but I'd be all set to believe them pretty equal.
Re:Fun things to do with Pi (Score:2)
Re::D (Score:2)
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...
Re:effort re-allocation project (Score:2)
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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Re:Metric system (Score:2)
Re:Oh well done (Score:2)
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Re:Enough of this irrational nonsense! (Score:2)
Re:No, that will never happen (Score:2)
e in binary.
10.10110111011110111110111111011111110111111110..
and e is quite definitely irrational. However, Pi is what's called a "normal" number, and that means that it acts fairly random. Not completely, though - I believe it's been proven that there can't be 43 of the same digit in a row in pi. That lack of a pattern could be considered a pattern.
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Re:so? (Score:2)
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.
Re:Do y'all realize the implications... (Score:2)
10.10110111011110111110111111011111110111111110
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Re:Of course ... (Score:2)
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.
Re:What Geometry ??? : (Score:2)
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Re:There is a point ... (Score:2)
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
URL for the project (Score:3)
There's much more information about this project on its home page [cecm.sfu.ca] at SFU. The guy behind it [cecm.sfu.ca] also has a page there.
M
Of course ... (Score:3)
Re:Just one digit? (Score:2)
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.
Some Pi research : Plouffe, Ramanujuan (Score:2)
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 [mathsoft.com]
Ramanujan's formula [caltech.edu]
Pi Sites of more Interest (Score:2)
Or, as one Tolkein character might say...
Precioussssssss Pi!!!! Givessss meee digitssssssss of Pi!!!!!! Gollum!
Re:Enough of this irrational nonsense! (Score:2)
You have stated earlier that you will rationalize both e and pi. but what will you do with i ?
//rdj
Re:Now all we need... (Score:3)
http://www.exploratorium.edu/learning_studio/pi
Found two. They disagree somewhat.
-nme!
Re:so? (Score:2)
Pi in Indiana (1897) (Score:2)
Legislating Pi (Score:2)
Re:Now all we need... (Score:2)
Do you have a link or reference that backs up that assertion?
Re:Mmmmm... pi... (Score:2)
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History of Pi calculations (Score:4)
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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Re:so? (Score:2)
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....
Warning! (Score:3)
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 and complexity (Score:3)
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
Re:Fun things to do with Pi (Score:2)
I bet, that for most things you might want to find inside of pi, the offset number is longer than the data itself.
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Time to break out the guitar.... (Score:3)
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