# Are The Digits of Pi Random?

#### Hemos posted more than 13 years ago | from the answering-the-age-old-question dept.

478
Steve Hamlin writes *"A researcher at Lawrence Berkeley National Laboratory, and his colleague at the Center for Advanced Computation at Reed College, have taken a major step toward answering the age-old question of whether the digits of pi and other math constants are "random."
In addition, a simple formula discovered makes it possible to calculate the Nth binary digit of Pi without computing any of the first N-1 digits, and do the computation with very little computing power.
"*

## Re:yeth (1)

## Anonymous Coward | more than 13 years ago | (#2188988)

"pi is 3.14... which is close to 3

Dr. Donner

(Yes, this is really true.)

BTW:

Shouldn't that be

anti

ps:

yes, I should lookup my password.

## Re:To Random or not To Random (1)

## Anonymous Coward | more than 13 years ago | (#2188989)

## yeth (2)

## Anonymous Coward | more than 13 years ago | (#2188995)

## Re:nth digit of pi (1)

## phil reed (626) | more than 13 years ago | (#2188999)

Last I heard, the algorithm only worked in base 16, but that may have changed now.Uh, since the article says it finds the Nth

binary digit, I think it would be safe to say that the algorithm actually works in binary. That technically means you're right, since hex is a binary shorthand....phil

## Re:To Random or not To Random (2)

## Tim Macinta (1052) | more than 13 years ago | (#2189001)

here's a simple test... try to compress the "random" string of numbers; if you can compress a string of random numbers, it isn'tI don't think that's correct. Consider an irrational number whose digits after the decimal point each have a 9/10 probability of being a 0 and a 1/10 probability of being a 1. Here are some examples that satisfy this:

This is definitely random (you have no way of knowing whether the next digit will be a 0 or a 1), but it is also definitely compressable (each such number should be compressable to about 1/10th of the original size).Now, I'm not saying that PI can be compressed in this manner, but if any digit did happen to appear more than another it could be compressed while still being random. A simple Huffman coding should suffice for such cases.

## formula for nth digit != random? (5)

## Hitch (1361) | more than 13 years ago | (#2189008)

-----------------------------------

All that glitters has a high refractive index.

## Just one question (2)

## Odinson (4523) | more than 13 years ago | (#2189015)

Or maybe just rendering 5 min of Jar-Jar galumping around...

Shiver## pi vs. /dev/urandom (2)

## boinger (4618) | more than 13 years ago | (#2189016)

I think someone's said it before, but, doesn't having a formula that allows calculation of arbitrary binary digit, in fact, make it NOT random? I'm just trying to grok how something can be "easily calculated" and still be truly random.

## Another (this one working) link. (3)

## qwaszx (8209) | more than 13 years ago | (#2189029)

## Re:Hate to be a nag, but... (1)

## Maxx (9947) | more than 13 years ago | (#2189030)

## Re:nth digit of pi (2)

## shaka (13165) | more than 13 years ago | (#2189034)

http://www.mathsoft.com/asolve/plouffe/plouffe.ht

or for goatse.cx aware:

http://www.mathsoft.com/asolve/plouffe/plouffe.ht

Last I heard, the algorithm only worked in base 16, but that may have changed now.

## Re:To Random or not To Random (1)

## ethereal (13958) | more than 13 years ago | (#2189035)

It's tough with an infinitely long number, though. There's no requirement that the compression be done on the fly - I could write a compression algorithm which wouldn't work unless I had access to the entire number.

You could say that the first N digits of pi are random or not based on the compression test, and make some sort of argument that since so far every sequence of pi we've tested was random, it's likely that the whole thing is, but that wouldn't be a very rigorous proof.

Remember: it's a "Microsoft virus", not an "email virus",

## Re:The Digits of Pi? (1)

## maroberts (15852) | more than 13 years ago | (#2189041)

Huh... I thought pi was a movieOnly when pi is written in the US. Now its got a sequel - American Pi^2!!

## Re:Hmmm (2)

## platypus (18156) | more than 13 years ago | (#2189048)

People think that randomness is this impersonal force that makes things happen for no reason at all.

What it really is, is an explanation when the factors involved in the outcome are too complicated to grasp.

Nope,

there's just a difference between deterministical chaos and randomness.

That doesn't mean the the latter doesn't exist.

## Re:Students Discover Pattern in Pi Digits: (1)

## Seanasy (21730) | more than 13 years ago | (#2189056)

## Neumann is most likely correct (2)

## arasinen (22038) | more than 13 years ago | (#2189057)

If you pick digits from pi's decimal expansion with some deterministic method, say, every third digit, the sequence will be the same each and every time you run it. What you do get from pi are non-repeating pseudorandom numbers: you can eg. pick every nth digit where n is your seed (cf. usual (pseudo)random number generators)

To get truly random numbers from pi, you need pick the digits randomly... for which you of course need a random number generator...

## Re:Hmmm (3)

## PigleT (28894) | more than 13 years ago | (#2189063)

I'm just wondering, if there's a "formula" for the n'th bit of the thing, it *can't* be random, can it?

For values of `random' that mean `uncompressible' of course, it can probably rate pretty highly.

~Tim

--

## Pi and Sanity (1)

## mcwop (31034) | more than 13 years ago | (#2189069)

## Re:To Random or not To Random (1)

## jmauro (32523) | more than 13 years ago | (#2189072)

## Re:Hmmm (1)

## Blindman (36862) | more than 13 years ago | (#2189076)

Regardless of the existence of a pi formula, pi is not random any more than the constant e. Afterall, pi always starts with 3.

## Re:Pi is great as a random source. (2)

## csbruce (39509) | more than 13 years ago | (#2189077)

However, I have a feeling to "trust" Pi more than e, given that you can write e in form of continued fractions with repeating patterns, and nobody has yet found a pattern in the continued fractions of Pi.I though that you could construct Taylor series for functions like arctan(x) and arctan(1) = 1/4*pi, so pi = 4*(ArcTanTaylorSeries(1)).

## I just love these discoveries (1)

## chrysalis (50680) | more than 13 years ago | (#2189081)

-- Pure FTP server [pureftpd.org] - Upgrade your FTP server to something simple and secure.

## Re:To Random or not To Random (1)

## MartinG (52587) | more than 13 years ago | (#2189086)

isdescrete. they are a string of integers.## Re:Why? There are only 3 digits. (1)

## 1010011010 (53039) | more than 13 years ago | (#2189087)

(introducing a returning champion)

"With just one more execution, he'll be eligible for the governorship of Texas!"

- - - - -

## Re:The signature of the artist ... (1)

## be-fan (61476) | more than 13 years ago | (#2189095)

## Partly old news (5)

## LinuxParanoid (64467) | more than 13 years ago | (#2189104)

There was a distributed computing project called PiHex [cecm.sfu.ca] that lasted several years for computing the five trillionth, 40 trillionth, and the quadrillioth bit of Pi, using a variant of the Plouffe discovery, Bellard's formula [www-stud.enst.fr] .

A proof that digits of Pi are random would indeed be news, albeit not exactly a surprise; I'd comment on it but the article's link seems bad or swamped at the moment.

--LP

P.S. Google has a nice list of Pi links. [google.com]

## True story. (4)

## BlueUnderwear (73957) | more than 13 years ago | (#2189111)

For an even more spooky coincidence, click twice on

Find Next, and carefully note the 3 last digits of the error message (start position...).## Re:Neumann said ... (1)

## dismayed (76286) | more than 13 years ago | (#2189112)

## Re:To Random or not To Random (1)

## shockwaverider (78582) | more than 13 years ago | (#2189113)

The size of the decompressor has to be included in the compression calcs.

In addition splitting on a predfined series of bytes is consdered to be a "trick" as it merely offloads the data to the filesystem involved.

## Re:memory much? (1)

## x24 (81159) | more than 13 years ago | (#2189116)

http://www.cs.rpi.edu/~moorthy/moorthyjug.html [rpi.edu]

## Of course they're not random! (2)

## jefferson (95937) | more than 13 years ago | (#2189127)

pseudorandom. Like the digits of PI, they are deterministic, and with the same starting point in the sequence, you always get the same set of numbers.Pseudorandom numbers are often used in place of true random numbers, because usually what is needed is a set of numbers with certain properties common to random numnbers, e.g. uniform distribution. Note that for cryptography, pseudorandomness is often not sufficient, and truly random numbers are needed. These are usually generated by sensing the physical world in some way, where,

we assumethat the combination of chaotic processes and quantum effects makes the incoming values truly unpredictable.## Old News (1)

## SamBeckett (96685) | more than 13 years ago | (#2189129)

There has existed an algorithm to find the

nth hexadecimal digit of PI for a couple of years now. It seems to me, going from hex to binary is trivial.More info can be found http://www.mathsoft.com/asolve/plouffe/scimath.txt [mathsoft.com] - there.

## DOE - Interesting? (1)

## kannen (98813) | more than 13 years ago | (#2189131)

This may be the first time they've EVER had significant traffic on their servers. How often do YOU look for cool, interesting articles on the DOE's website. Not very often, I suspect. =)

## Base 5 (1)

## shpoffo (114124) | more than 13 years ago | (#2189148)

Ewige Blumenkraft!

-shpoffo

## Re:Hmmm, YABL (Yet, Another, Broken, Link) (1)

## shpoffo (114124) | more than 13 years ago | (#2189149)

## pi randomness and algorithmic information theory (1)

## jejones (115979) | more than 13 years ago | (#2189151)

Algorithmic information theory defines the amount of information in a string as the length of the (shortest, I would presume--you can always pad code) program that generates it. A random sequence is one that's uncompressible--the best you can do for a program to emit it is to have a copy of the sequence itself in initialized data and spit it out.

Now...if there's an algorithm to generate an arbitrary digit of pi, obviously you can use it to write a function to generate all of them (eventually, in the sense that for any fixed N, you'll only have to wait a finite amount of time for the Nth digit to come out). That seems pretty darned compressible to me, so how the heck can the digits of pi be random? Is my understanding totally off here, or do counterintuitive things happen for infinite strings?

## Re:nth digit of pi (1)

## daoine (123140) | more than 13 years ago | (#2189157)

## Re:Students Discover Pattern in Pi Digits: (2)

## SuiteSisterMary (123932) | more than 13 years ago | (#2189158)

## Homer (1)

## Nastard (124180) | more than 13 years ago | (#2189159)

## lalala (2)

## Lord Omlette (124579) | more than 13 years ago | (#2189161)

Peace,

Amit

ICQ 77863057

## More info on the Algorithm (5)

## regen (124808) | more than 13 years ago | (#2189162)

I couldn't get the link in the story to work, and found this while searching for the story.

## Depends on how you choose to define "random" (1)

## SLi (132609) | more than 13 years ago | (#2189169)

Function: adjective

Date: 1565

1 a : lacking a definite plan, purpose, or pattern b : made, done, or chosen at random <read random passages from the book>

2 a : relating to, having, or being elements or events with definite probability of occurrence <random processes> b : being or relating to a set or to an element of a set each of whose elements has equal probability of occurrence <a random sample>; also : characterized by procedures designed to obtain such sets or elements <random sampling>

---

So, pi probably has no plan or pattern, but arguably does have a definite purpose. It wasn't probably made, done or chosen at random, though it's hard to know.

I don't know if we can talk about

probabilitiestogether with pi, more than "if we pick a 5 from the decimal representation, which is the probability of the next digit being 8".## Re:To Random or not To Random (1)

## SLi (132609) | more than 13 years ago | (#2189170)

Explain to me why I can get this out of a "perfect" random number generator:Because the probability of a random number being equal to some predetermined value when the set of possible random numbers is not discrete is

exactlyzero. Perhaps that's why.## Re:To Random or not To Random (1)

## SLi (132609) | more than 13 years ago | (#2189171)

here's a simple test... try to compress the "random" string of numbers; if you can compress a string of random numbers, it isn'tSure, this is a good way of being sure some number is

notrandom. But it doesn't work the other way round. You can't compress already compressed files or encrypted files (well, from good encryption and compression programs), yet they're not random.## Re:Also depend on compression scheme... (1)

## SLi (132609) | more than 13 years ago | (#2189172)

Depending of your algorithm (repetion, fractal regression,...) you will get VERY DIFFERENT RESULTS using the same original file._No_ compression algorithm ever will compress purely random numbers.

Or to be more precise, no compression algorithm ever will compress more than 50% of all possible inputs of the size n or less for any given n. Proof left as an exercise (it's really simple).

## Re:To Random or not To Random (1)

## SLi (132609) | more than 13 years ago | (#2189173)

Mathematically, given two infinite sets A and B such that A is continuous and B a discrete subset of A, the probability of a randomly picked number from set A belonging to set B is not only very small (i.e. low probability), but zero. Now A is the group of all "numbers" and B is the group of all compressible numbers. Ergo, the chance is not there.

## Pi (1)

## SLi (132609) | more than 13 years ago | (#2189174)

t=pi*t_e, where

t = the time required to finish a project, and

t_e = the estimated time required to finish a project (which also happens to be equal to d-dt, where d is the deadline and dt is the current time).

## Cool Application! (5)

## FreezerJam (138643) | more than 13 years ago | (#2189188)

If it is possible to calculate digits of Pi starting at any point, then you could easily use Pi as a pseudo-random pad.

Once you know the starting digit location, you can easily decrypt something that has been XOR'd with the sequence from that point onward. But - given that each n-bit sequence occurs 1/n of all n-bit sequences, there are essentially an infinite number of options facing the code-breaker - even after each successful step!

If you are feeling particularly vicious that day, encrypt with two XOR sequences, based on two difference starting points.

## Did they crack it or not? (1)

## jessh (144140) | more than 13 years ago | (#2189195)

## Encryption (1)

## KhaliF (160350) | more than 13 years ago | (#2189203)

Because we can now skip forward in pi orders of magnitude further than before, we could (if we wanted) use pi (with a random and gigantic start point or seed) as an xor source for cheap and nasty encryption

## more haiku (1)

## ReidMaynard (161608) | more than 13 years ago | (#2189205)

I beg forgiveness, for I

ate all the pi, *sigh*

## Re:Hmmm (1)

## sqlrob (173498) | more than 13 years ago | (#2189214)

There you go, infinite digits in a small, finite space. You don't get better compression than that.

## Re:Students Discover Pattern in Pi Digits: (2)

## taliver (174409) | more than 13 years ago | (#2189216)

Sorry for the inconvenience## Why? There are only 3 digits. (2)

## pizen (178182) | more than 13 years ago | (#2189224)

---

## Re:So what? (2)

## Alien54 (180860) | more than 13 years ago | (#2189231)

Can someone tell me some down to earth, real reasons that anyone should care what the 12,345th digit of Pi is? I mean really, who cares?Well for most general engineering purposes 5 to 10 places is enough. How many car parts are manufactured to a milli millimeter spec, for example? and to tell the truth, once you hit the quantum level further precision can get a little silly.## I saw that movie last summer ... (1)

## Wordsmith (183749) | more than 13 years ago | (#2189233)

## Re:So what? (2)

## Abcd1234 (188840) | more than 13 years ago | (#2189238)

## Someone has to say it... (1)

## Junior J. Junior III (192702) | more than 13 years ago | (#2189244)

## nth digit of pi (1)

## Ummite (195748) | more than 13 years ago | (#2189247)

## Re:Base 5 (1)

## LoudMusic (199347) | more than 13 years ago | (#2189249)

Sorry, couldn't resist (:

~LoudMusic

## Re:Site Slashdotted, Alternate link! (1)

## el_nino-2000 (200437) | more than 13 years ago | (#2189250)

## Site Slashdotted, Alternate link! (3)

## el_nino-2000 (200437) | more than 13 years ago | (#2189251)

## Re:To Random or not To Random (2)

## 11223 (201561) | more than 13 years ago | (#2189253)

In other words, all strings of random numbers have entropy of 1? Nope. Explain to me why I can get this out of a "perfect" random number generator:

000000000000000000000000....

Now, granted, the probability of that is *low*, but it's there just the same.

Now, your statement would work just fine if you were talking about the *complete* digits of PI. In fact, if you give me a stack of disks with a complete listing of all of the digits of PI, I'd be happy to compress it for you.

## Re:Why? There are only 3 digits. (3)

## L41N14L (205602) | more than 13 years ago | (#2189257)

## To Random or not To Random (1)

## Morphine007 (207082) | more than 13 years ago | (#2189266)

## Biblical precidence (4)

## vslashg (209560) | more than 13 years ago | (#2189273)

pi = 3And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.

## Well, duh! (2)

## tswinzig (210999) | more than 13 years ago | (#2189275)

In addition, a simple formula discovered makes it possible to calculate the Nth binary digit of Pi without computing any of the first N-1 digits, and do the computation with very little computing power.In light of this article, the obvious method is now:

srand(time); #random enough, thank you$nth_digit = random();

Duh!

## Students Discover Pattern in Pi Digits: (4)

## tenzig_112 (213387) | more than 13 years ago | (#2189279)

And today, thanks to the hard work of a pair of students at Carnegie Mellon University, we can read that language.

And without further ado, here is the hidden message starting at the 74088 digit:

## Re:Why? There are only 3 digits. (2)

## b1t r0t (216468) | more than 13 years ago | (#2189284)

## Re:Why does this matter? (1)

## The Troll Catcher (220464) | more than 13 years ago | (#2189288)

Use *base pi*. Why didn't someone think of this before? It would save a LOT of effort... those silly guys!

Now, all we have to do is find out what pi^1 is... oh, wait.

## Here is the article (4)

## rabtech (223758) | more than 13 years ago | (#2189290)

===

Are the Digits of Pi Random? A Berkeley Lab Researcher May Hold the Key

A researcher at the Department of Energy's National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory, and his colleague at the Center for Advanced Computation at Reed College, have taken a major step toward answering the age-old question of whether the digits of pi and other math constants are "random." Their results are reported in the Summer 2001 issue of Experimental Mathematics.

July 26--Pi, the ubiquitous number whose first few digits are 3.14159, is irrational, which means that its digits run on forever (by now they have been calculated to billions of places) and never repeat in a cyclical fashion. Numbers like pi are also thought to be "normal," which means that their digits are random in a certain statistical sense.

David Bailey

Describing the normality property, David H. Bailey, chief technologist at NERSC, explains that "in the familiar base 10 decimal number system, any single digit of a normal number occurs one tenth of the time, any two-digit combination occurs one one-hundredth of the time, and so on. It's like throwing a fair, ten-sided die forever and counting how often each side or combination of sides appears."

Pi certainly seems to behave this way. In the first six billion decimal places of pi, each of the digits from 0 through 9 shows up about six hundred million times. Yet such results, conceivably accidental, do not prove normality even in base 10, much less normality in other number bases.

In fact, not a single naturally occurring math constant has been proved normal in even one number base, to the chagrin of mathematicians. While many constants are believed to be normal--including pi, the square root of 2, and the natural logarithm of 2, often written "log(2)"--there are no proofs.

The determined attacks of Bailey and his colleague Richard Crandall, director of the Center for Advanced Computation at Reed College, Portland, Oregon, are beginning to illuminate this classic problem. Their results indicate that the normality of certain math constants is a consequence of a plausible conjecture in the field of chaotic dynamics, which states that sequences of a particular kind, as Bailey puts it, "uniformly dance in the limit between 0 and 1"--a conjecture that he and Crandall refer to as "Hypothesis A."

"If even one particular instance of Hypothesis A could be established," Bailey remarks, "the consequences would be remarkable"--for the normality (in base 2) of pi and log(2) and many other mathematical constants would follow.

A simple formula discovered with the integer-relation algorithm dubbed PSLQ makes it possible to calculate the Nth binary digit of Pi without computing any of the first N-1 digits, and do the computation with very little computing power.

This result derives directly from the discovery of an ingenious formula for pi that Bailey, together with Canadian mathematicians Peter Borwein and Simon Plouffe, found with a computer program in 1996. Named the BBP formula for its authors, it has the remarkable property that it permits one to calculate an arbitrary digit in the binary expansion of pi without needing to calculate any of the preceding digits. Prior to 1996, mathematicians did not believe this could be done.

The digit-calculation algorithm of the BBP formula yields just the kind of chaotic sequences described in Hypothesis A. Says Bailey, "These constant formulas give rise to sequences that we conjecture are uniformly distributed between 0 and 1--and if so, the constants are normal."

Bailey emphasizes that the new result he and Crandall have obtained does not constitute a proof that pi or log(2) is normal (since this is predicated on the unproven Hypothesis A). "What we have done is translate a heretofore unapproachable problem, namely the normality of pi and other constants, to a more tractable question in the field of chaotic processes."

He adds that "at the very least, we have shown why the digits of pi and log(2) appear to be random: because they are closely approximated by a type of generator associated with the field of chaotic dynamics."

For the two mathematicians, the path to their result has been a long one. Bailey memorized pi to more than 300 digits "as a diversion between classroom lectures" while still a graduate student at Stanford. In 1985 he tested NASA's new Cray-2 supercomputer by computing the first 29 million digits of pi. The program found bugs in the Cray-2 hardware, "much to the consternation of Seymour Cray."

Crandall, who researches scientific applications of computation, suggested the possible link between the digits of pi and the theory of chaotic dynamic sequences.

While other prominent mathematicians in the field fear that the crucial Hypothesis A may be too hard to prove, Bailey and Crandall remain sanguine. Crandall quotes the eminent mathematician Carl Ludwig Siegel: "One cannot guess the real difficulties of a problem before having solved it."

Among the numerous connections of Bailey's and Crandall's work with other areas of research is in the field of pseudorandom number generators, which has applications in cryptography.

"The connection to pseudorandom number generators is likely the best route to making further progress," Bailey adds. "Richard and I are pursuing this angle even as we speak."--by Paul Preuss

===

Enjoy.

-- russ

## Hmmm (1)

## James Foster (226728) | more than 13 years ago | (#2189293)

Everything has its logical base... but alot of things can be way beyond our comprehension and thus can be considered "random".

## What do the mean random. (3)

## bmongar (230600) | more than 13 years ago | (#2189294)

Too bad I can't get to the article to see how they are defining random. I have studied random numbers quite a bit, and have worked on the assumption that any thing that can be calculated is not truely random. So under that definition no, it isn't random, and neither are any of the random number generator algorithms.

The comon test for randomness is the chi squared test which actually tests for dispersion of numbers. That is are number occuring in 'equal' frequencies in an order that isn't too similar to the order in other sections of the sample. Failing the chi squared tests shows you aren't 'Pseudo Random' passing it only proves your numbers are dispersed not random

## Neumann said ... (5)

## (H)elix1 (231155) | more than 13 years ago | (#2189296)

(John Von Neumann, 1951 )

## Hmmm, YABL (Yet, Another, Broken, Link) (2)

## gwizah (236406) | more than 13 years ago | (#2189299)

## Re:So what? (1)

## HoldmyCauls (239328) | more than 13 years ago | (#2189304)

## Why does this matter? (3)

## Bonker (243350) | more than 13 years ago | (#2189316)

Also, since Pi is a ratio that we 'choose' to express in a base10 numerical system, would the fact that the digits are random in a decimal system mean that they would be random if we expressed Pi in a hexidecimal or octal system?

## Hate to be a nag, but... (2)

## RareHeintz (244414) | more than 13 years ago | (#2189319)

And does anyone know if that link is incorrect in some way? My DNS can't resolve it.

OK,

- B

--

## Pi is great as a random source. (5)

## acidblood (247709) | more than 13 years ago | (#2189333)

Here's the output of John Walker's ent [fourmilab.ch] program for 512 megabits of Pi:

For the entropy test, a completely random sample would have an entropy of 8.0 bits per byte, and the ideal Chi Square distribution would be 256.0 (considering there are 256 degrees of freedom in an 8-bit data structure, or 2**8 possibilities.) As you can see, that's about as random as you can get. And the larger the samples you feed it, the more it converges to the ideal values.I've also done some testing with other transcendental numbers, such as e (2.718281828...), and they all seem to show great randomness properties, in the information-theoretic sense at least. However, I have a feeling to "trust" Pi more than e, given that you can write e in form of continued fractions with repeating patterns, and nobody has yet found a pattern in the continued fractions of Pi.

As for my pseudo-random library project, my programming skills are quite bad, but if you have some knowledge of scientific computing (multiplication algorithms using FFTs, for example), you can contact me and I might revive the idea.

## Re:The signature of the artist ... (1)

## Pov (248300) | more than 13 years ago | (#2189337)

## Re:Hmmm (1)

## OpCode42 (253084) | more than 13 years ago | (#2189339)

Everything has its logical baseI thought that all your logic base belonged to us...

## Zounds!!!! (1)

## TigerBaer (264665) | more than 13 years ago | (#2189350)

ZOUNDS!!@$!$## Formula for a != message. (1)

## KupekKupoppo (266229) | more than 13 years ago | (#2189351)

description of thought.

contradiction or deviation from thought of article.

semi-insightful, semi-obvious, somewhat-karma-whoring conclusion.

(posted after seeing a X != Y on every story for the past day)## Re:Why? There are only 3 digits. (1)

## BillX (307153) | more than 13 years ago | (#2189365)

--

## Re:lalala (2)

## vidarh (309115) | more than 13 years ago | (#2189366)

--

Remove Trash+ to reach my actual inbox

## Memorizing Pi... (1)

## SirJimbo (320247) | more than 13 years ago | (#2189387)

That would make it even easier to trip them up in the middle

Who is more foolish, the fool,

or the fool that follows him? (Obi-Wan Kenobi)

## So what? (1)

## Uttles (324447) | more than 13 years ago | (#2189390)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## Re:So what? (1)

## Uttles (324447) | more than 13 years ago | (#2189391)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## Re:So what? (1)

## Uttles (324447) | more than 13 years ago | (#2189392)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## I suspect... (1)

## gamgee5273 (410326) | more than 13 years ago | (#2189397)

## Kolmogorov complexity (2)

## s20451 (410424) | more than 13 years ago | (#2189398)

try to compress the "random" string of numbers; if you can compress a string of random numbers, it isn'tNot really. Since pi is some constant, and not generated by a random process, the most meaningful description of its compressibility is its

Kolmogorov complexity, which refers to the shortest program capable of re-generating the original string. Unfortunately, Kolmogorov complexity is not computable in general.## Also depend on compression scheme... (1)

## da5idnetlimit.com (410908) | more than 13 years ago | (#2189399)

+ PI having no end in itself, can you please send me the method you think you will use before actually compressing pi, and which involve calculating pi to it's end ? 8)

Please call me 5' before World's End, so I can come and check youir results 8)

## Low probability ? as in Free - As - Beer ? (1)

## da5idnetlimit.com (410908) | more than 13 years ago | (#2189400)

I also have a LOW probability to win the Lotery 8|

(1/14 600 000, under French Lotery system)

## PI IS STATIC AND PREDICTABLE ! (2)

## da5idnetlimit.com (410908) | more than 13 years ago | (#2189401)

the famous "Golden Number" is more impressive, I think

## Algorithm sources and other stuff (3)

## Zarhan (415465) | more than 13 years ago | (#2189402)

http://www.nersc.gov/~dhbailey/ [nersc.gov]

Check out the piqp.c in the middle of the page.

## Re:formula for nth digit != random? (1)

## the_2nd_coming (444906) | more than 13 years ago | (#2189408)

## Re:Hmmm (1)

## stoolpigeon (454276) | more than 13 years ago | (#2189427)

Randomness is the 'god' of the scientific age. We have simply moved from "God did not create the universe- Random did."

People think that randomness is this impersonal force that makes things happen for no reason at all.

What it really is, is an explanation when the factors involved in the outcome are too complicated to grasp.

## Re:Students Discover Pattern in Pi Digits: (1)

## Captain_Vegetable (470429) | more than 13 years ago | (#2189458)

## memory much? (3)

## emoeric (470708) | more than 13 years ago | (#2189460)

Where do they find these guys? He memorizes pi, i play snake on my cellphone. eh

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## Are The Digits of Pi Random? (1)

## JimEL (471364) | more than 13 years ago | (#2189461)