Pi Computed To 10 Trillion Digits

An anonymous reader writes "A Japanese programmer that goes by the handle JA0HXV announced that he has computed Pi to 10 trillion digits. This breaks the previous world record of 5 trillion digits. Computation began in October of 2010 and finished yesterday after multiple hard disk problems, he said. Details in English are not fully available yet, but the Japanese page gives further details. JA0HXV has held computation records for Pi in the past."

Comments

What Does This Mean?

[Frosty Piss]

Is there any practical application to this sort of thing, either having the number itself, or whatever method this guy used to arrive at it? Or is this a thumb gazing exercise?

Re:What Does This Mean?

[Anonymous Coward]

a message from god shows up in binary once you get to 20 trillion digits.

Re:What Does This Mean?

[Kenoli]

A couple dozen digits of pi exceeds all practical necessity. Calculating it to 10 trillion digits is obviously pointless.

Re:What Does This Mean?

[Rizimar]

I believe that the correct term is "mathsturbation"

Re:What Does This Mean?

[Anonymous Coward]

No, you only need about 50 decimal places to have an accurate enough approximation to calculate the circumference of the entire universe with less than 1 planck length of error.

This is just a "because we can" exercise. (Also, supposedly, to determine if PI is actually infinite or whether it contains a repeating pattern after you get to a certain point)

Re:What Does This Mean?

[boristhespider]

I can guarantee that this isn't the case. Some of us are excessive and use it to sixteen significant figures or so. Seriously, if we're doing calculations we're using C or Fortran. What type of float do you know that stores so many digits? I just do what I think most people do and fill up the number of bits in the float I'm using - and even that's more than needed.

Re:What Does This Mean?

[hcs_$reboot]

You'll never need more than 10 significant figures

Do you work at the CERN?

Re:What Does This Mean?

[FrootLoops]

The only practical application I've ever heard of for projects like this is as an integrity check on new supercomputers. They compute the first X digits of pi and then compare it to a known result which someone computed and verified earlier.

On a completely separate note, it's "pi", not "Pi". The Greek letter used is lowercase, and the standard English version is similarly lowercase.

Re:What Does This Mean?

[hedwards]

Which if you think about it is really strange for pi to not be a proper noun.

Re:What Does This Mean?

[FrootLoops]

(Also, supposedly, to determine if PI is actually infinite or whether it contains a repeating pattern after you get to a certain point)

What? There's a mathematical proof that pi is irrational (in fact, transcendental). Specifically, if it were not, -1 would be irrational (in fact, transcendental) thanks to the Lindemann-Weierstrass theorem and the fact that e^(pi*i) = -1. The digits cannot simply start repeating after a while (in particular, they cannot eventually just become 0, as happens with, for instance, 1/2 = 0.5000... .

Re:What Does This Mean?

[neyla]

Even then, this has no practical consequence whatsoever. If you want to compute the circumference of the galaxy, to accuracy such that your answer is off by less than a nanometer, you still need only ~100 digits of pi.

So yes, in principle you could need more than 10 digits, allthough in practice it's pretty unlikely (it wouldn't matter unless you knew the -radius- with that high precision).

But raising the bar from 5 trillion digits, to 10 trillion ?

Irrelevant in the real world. (possibly there's math-applications, I suppose)

Re:What Does This Mean?

[oloferne]

I imaging that it has applications in astronomy. When you want to precisely compute something over the distance of light years, you may want more than just 10 digits for Pi.

As a professional astronomer I can guarantee that distance scale measurements are a little bit less precise than one part over 10^13. Even for most precise measurements, e.g. gravitational waves experiment, 16 digit suffices!

Re:What Does This Mean?

[nicvsor]

Tis more than gazing. At last, one can now go out singing "Yo, I know pi to 10 trillion places".

Re:What Does This Mean?

[MichaelSmith]

There are floating format mathematical libraries which support arbitrary precision, but that said I can't see a use for trillions of digits of pi in engineering or science. You can't even write it down given the cost of toner these days. It might be useful as a cryptographic key of course.

Re:What Does This Mean?

[FrootLoops]

Perhaps it is a proper noun which just breaks the typical capitalization rule since it's the transliteration of a lower case letter. That is, capitalizing it would change the meaning of the translation.

Re:What Does This Mean?

[fph il quozientatore]

You can switch to German to solve this problem.

Re:What Does This Mean?

[maxwell demon]

But maybe the question is: "What is the 20 trillionth digit of pi in base 97?"

Re:What Does This Mean?

[LordLucless]

No more stranger than one, two three, four, five, fi or e.

Re:What Does This Mean?

[idji]

Yes, if they keep looking they will eventually find the DNA of our beloved overlords.

Re:What Does This Mean?

[hcs_$reboot]

The primary reason for this is to confirm the never-ending nature of pi,

Or find a cycle in the digits, a pattern that repeats itself (like 27/11 = 2.454545...).

Re:What Does This Mean?

[maxwell demon]

The radius of the part of the universe visible to us is about 46 billion light years or about 4*10^26 meters. The planck length, assumed to be the shortest length there is, is about 1.6*10^-35 meters. That is, the radius of the known universe is 2.7*10^61 planck lengths. Thus with just 62 digits of pi you are as accurate as the laws of physics allow. In practice you'll never need even that. Indeed, you'll not even measure cosmic distances to the meter (27 digits), or even to the kilometer (24 digits). Even measuring to the light year (12 digits) is probably impossible for objects that far out.

Re:What Does This Mean?

[Kilrah_il]

I can calculate any digit of pi in binary off the top of my head with 50% accuracy.

Re:What Does This Mean?

[boristhespider]

You're talking to astronomers - if you saw any codes we've written you'd know full well that most of us can't program for toffee :) What's pretty much standard is to use the float size built into your compiler. Some people redefine them in the headers of their codes and then just ignore it. I dread to think how much numerical noise has been touted as a result over the history of astronomy, only to vanish when looked at a bit more closely at the cost of only a few hundred man-hours and CPU time. Thankfully not much of it will have been published.

Re:What Does This Mean?

[vikingpower]

Ever heard of cryptography ? There are lots of practical applications, e.g. random number generators, microprocessor tests, software tests....

Re:What Does This Mean?

[nacturation]

If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle and when you get to the end of the circle (based on the digits of pi you memorized) you'll be off by less than the width of a human hair.

Re:What Does This Mean?

[FreakyGreenLeaky]

What Does This Mean?
42

Re:What Does This Mean?

[TheWanderingHermit]

Any 1st year calculus student should know both that it's been proven that Pi is irrational and does NOT repeat, but should be able to do that proof on their own.

Re:What Does This Mean?

[Anonymous Coward]

As for the value itself, unequivocally no (as others have pointed out). Even a thousand digits is overkill.

If I remember correctly, a previous 2.7 trillion digit was intended to showcase a sexy multiplication algorithm for really really big inputs. That's from memory though, and I still can't track down much in the way of details. In particular, I couldn't see if they claim to be asymptotically faster than the other state-of-the-art approach, which uses FFT and is pretty close the the theoretical lower bound on multiplication complexity.

Also, I suppose it's an exercise in supercomputer engineering. Damn impressive, to be sure.

Re:What Does This Mean?

[FrootLoops]

Do you mean "phi" instead of "fi", that is, the golden ratio (which is also for some reason not a proper noun)?

Re:What Does This Mean?

[maxwell demon]

The primary reason for this is to confirm the never-ending nature of pi, if I'm not mistaken.

The never-ending nature of pi is well-confirmed by mathematical proof. It is proved to be irrational (which already implies the never-ending nature) and even transcendental. What might be a motivation is checking the normality, i.e. the assumption that there's no pattern in the digits of pi. Normality has AFAIK not yet been proved.

That is, if we were to discover, for example, at the 12 trillionth digit, that pi finally does end, that has wide-spread implications on everything from the microscopic creation of semiconductors to the macroscopic terraforming of a (presumably round) planet.

No one doing semiconductor physics or terraforming cares even about the tenth digit, let alone the 12 trillionth.

Re:What Does This Mean?

[Anonymous Coward]

If you're off by nearly the width of a human hair, it's not a perfect circle now, is it? Sheesh.

Re:What Does This Mean?

[Joce640k]

Even then, this has no practical consequence whatsoever. If you want to compute the circumference of the galaxy, to accuracy such that your answer is off by less than a nanometer, you still need only ~100 digits of pi.

That assumes we know the radius of the galaxy to within a nanometer, which, ummm...we don't. Best estimates are more like "rounded to the nearest million light years".

Re:What Does This Mean?

[nacturation]

If you're off by nearly the width of a human hair, it's not a perfect circle now, is it? Sheesh.

You can navigate in a perfect circle, but when you reach the end of the perfect circle there will be a little left over because the number you were using for pi to calculate the circumference was off.

However, don't let me interrupt what must be a satisfying eye roll for you. I'm glad to see cowards on Slashdot have remained as polite as ever.

Re:What Does This Mean?

[Pseudonym]

It depends how it's done. Many record holders develop new algorithmic or implementation techniques in the process, and that's actually very useful.

Re:What Does This Mean?

[maxwell demon]

(Also, supposedly, to determine if PI is actually infinite or whether it contains a repeating pattern after you get to a certain point)

What? There's a mathematical proof that pi is irrational (in fact, transcendental). Specifically, if it were not, -1 would be irrational (in fact, transcendental) thanks to the Lindemann-Weierstrass theorem and the fact that e^(pi*i) = -1. The digits cannot simply start repeating after a while (in particular, they cannot eventually just become 0, as happens with, for instance, 1/2 = 0.5000... .

Well, if pi were not irrational, e^(i*pi) would not be -1.

Re:What Does This Mean?

[dkf]

Indeed. The symbol indicating the ratio between a circle's diameter and its circumference (pi) means something totally different in math when upper-cased. There it's used to express the product of the terms of a series. Given that, upper-casing it (except when it's the start of a sentence) really would change the meaning hugely.

Re:What Does This Mean?

[JasterBobaMereel]

pi is irrational (not the ratio of two numbers)
pi is transcendental (not the solution to an algebraic formula)

pi might not be normal - the distribution of digits might not be balanced and even ...it looks like it is but it has not been proven to to be...

Re:What Does This Mean?

[Pieroxy]

People think in binary here. It's either perfect or not. In your case, it is not.

Re:What Does This Mean?

[nacturation]

Roughly how many digits is that?

No need to google it... here you go: 3.14159265358979323846264338327950

Re:What Does This Mean?

[laejoh]

Maybe he wants to measure the _exact_ lenght of his tool, perhaps the length of it equals PI?

Re:What Does This Mean?

[a_n_d_e_r_s]

Well if they search long enough. They will find the collected work of shakespear hiding in pi.

Re:What Does This Mean?

[nacturation]

How irrational of me.

Re:What Does This Mean?

[nacturation]

You mean if they search along the circumference of the universe for Shakespeare? What a strange notion. Or perhaps you replied to the wrong post.

Re:What Does This Mean?

[ogl_codemonkey]

Even then, this has no practical consequence whatsoever. If you want to compute the circumference of the galaxy, to accuracy such that your answer is off by less than a nanometer, you still need only ~100 digits of pi.

... and a measurement of its radius to within a nanometer ;-)

Re:What Does This Mean?

[muon-catalyzed]

This is all about the Armstrong/Aldrin Moon moment, reach somewhere where nobody else ever wandered.

Same with the those prime number hunters, or those who are finding exoplanets etc., you can get it named after yourself (not in this case obviously), but you can get yourself a Wikipedia entry, get your effort immortalized, so still very worthy!

Re:What Does This Mean?

[FrootLoops]

I've never seen "Pi" written out to indicate a product in standard writing, so I'm not sure if there's any issue here (in reality that is; theoretically the issue clearly might occur). That I've never seen it is probably just because "Pi" (now I want to write \Pi) is only really used in higher level contexts than "pi".

Re:What Does This Mean?

[FrootLoops]

Perhaps I'm missing your point. If pi were rational, e^(pi*i) would itself be irrational, so it couldn't be the rational number -1, as you suggest, though it is, a contradiction: hence pi is irrational. That was implicit. Did you just mean to fill a gap? If so, I left larger ones unfilled--for instance, even if you were to take the theorem on faith (which, incidentally, I do; transcendental number theory is interesting for me to read summaries about, but no more), specializing the theorem's positive transcendence degree to give irrationality takes a little bit of churning through terminology.

Re:What Does This Mean?

[m50d]

IIRC pi has not been proven to be normal yet, so there's some value in gathering statistical evidence on that.

Re:What Does This Mean?

[Compaqt]

True, no one will need to know pi to more than 640x1024 digits.

Re:What Does This Mean?

[FrootLoops]

Correct, it hasn't been shown to be normal.

Re:What Does This Mean?

[FrootLoops]

I've always thought this sort of thing is a "second rate" way to get your name remembered, like writing a definitive biography on someone who actually did enough stuff to be remembered, or organizing/editing such a person's collected works. Ah well; we can't all be {Newton/Einstein/Bach/...}.

Re:What Does This Mean?

[V!NCENT]

There was once a reason for doing this: people tried to look for a pattern in the number, but figured they needed more digits, because they couldn't find a pattern.

Now we know that at least in a decimal system; there is no pattern.

But for some nerdy reason this "MOAR DIGITZ!" thing continues.

Re:What Does This Mean?

[Tinctorius]

In computing pi, the method is much more important than the value. Without further details, I don't know if the programmer's method is novel, but perhaps the implementation is.

The value itself is of little use, except that there is still no answer to the question whether pi follows a pattern, beyond being irrational and transcedental. Keep in mind that the Champernowne constant is irrational and transcedental too, but follows a relatively simple pattern.

Re:What Does This Mean?

[Tinctorius]

Update: it seems that the software itself is not new. The programmer mentioned the use of y-cruncher.

Re:What Does This Mean?

[michelcolman]

That would actually be a good idea. Transform it to base 26 (or a few extra for spaces and punctiaton) and look for words. There will be lots of them, obviously. Maybe here and there you'll find a small sentence. Some phrases like "here he is" would be likely to turn up. 10 trillion is about the ninth power of 26, and there are lots of possible small phrases of that size. For whole chapters, you'll need slighty more digits to have any chance of finding them, though. "Slightly" actually meaning humongously exponentially more. To increase the expected phrase length by one character, you would need 26 times as many digits. But they are bound to be in there somewhere! (No guarantee, we don't know how truly random pi is, even transcendental numbers can have some sort of system in their digits, for example a copy of pi with all the shakespearean parts removed would still be transcendental)

Re:What Does This Mean?

[michelcolman]

I imagine that's applied mathematics then. From a theoretical point of view, it may be very interesting. For example, the question of how randomly the digits are distributed, and if there might be a pattern to be found in them. (Not a simple repeating pattern, obviously).

But probably the most important benefit to science is the progress in numerical algorithms used to calculate pi that can also be used to calculate other, more useful things. Beating a world record is a great way to motivate programmers to come up with new, innovative ways to squeeze more power out of computers.

Re:What Does This Mean?

[slartibartfastatp]

I don't think that's something to do with maths, but with computing. very practical computing. Like, how to run a job for one year (or ten months, as the pages said).
However, I couldn't find anything resembling a computer setup in the japanese page. maybe because I can't really read japanese.

Re:What Does This Mean?

[julesh]

How irrational of me.

Get real.

Re:What Does This Mean?

[msobkow]

So really his achievement is uptime, not science or R&D.

Re:What Does This Mean?

[rhade]

I thought the plan was to find out if it ever repeats...

Re:What Does This Mean?

[Dogtanian]

I believe that the correct term is "mathsturbation"

Given that Pi never ends, could we also call it "onanonanonanonanism"?

Re:What Does This Mean?

[nashv]

Yes. Algorithmic methods developed to do such a thing are often useful in many other areas involving computation. The Chudnovsky algorithm , which is the current favorite has dramatically sped up modelling and simulation processes and is used in nearly every code package that does that sort of thing. Since that algorithm is only workable upto 17 billion significant digits, clearly this is a different method or modification thereof. (I didn't RTFA).

Really, this is the case with every achievement of number theory. Solutions to problems we don't know are problems yet. Think lasers.

Re:What Does This Mean?

[2fuf]

you don't need to go trough the whole list of decimals in order to find the answer to that one: http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula

Re:What Does This Mean?

[martin-boundary]

I can do you one better. I can calculate any binary digit of pi that happens to be 1 with 100% accuracy: It's zero... uhm, I mean one.

Re:What Does This Mean?

[catmistake]

sure, in base-10... I wonder if there are in other bases. And I wonder what the world would be like in base-Pi, where calculating Pi was literally as easy as counting to 1.

Re:What Does This Mean?

[vlm]

AFAIK, we still have no conclusive answer to the question whether Pi has finite or infinite digits.

No.

http://en.wikipedia.org/wiki/Proof_that_pi_is_irrational

There's five different approaches. There are more, mostly closely related cousins.

http://en.wikipedia.org/wiki/Irrational_number

rational = terminates (your "finite") or repeats (your "infinte"). Which doesn't matter because pi is irrational as per numerous different proofs and all irrational numbers are infinite in length.

If this is some sort of "holy book" "intelligent design" thing where the bible says pi is actually 3, then I can't help you there...

Re:What Does This Mean?

[vlm]

Maybe he wants to measure the _exact_ lenght of his tool, perhaps the length of it equals PI?

Pi is not used for that. Pi shows up all over the place in math, but the geometry is the ratio of circumference to diameter for all circles. "If its round and so much across then its so much around".

Your tool post finally makes goatse a legitimate /. posting reference. Take the distance around the "grand canyon" of goatse and divide it by the distance across. Assuming its a perfect circle, that ratio will be pi. In fact it will be pi for any non-tearing perfectly round goatse like picture.

Re:What Does This Mean?

[ConceptJunkie]

Practical application? Perhaps not. But you can study the string of digits to make sure it is truly random, as theory predicts. If the digits of pi do turn out to have a pattern to them, then a lot of interesting and important things we think we know about math are wrong.

Re:What Does This Mean?

[Coward Anonymous]

The beauty of these things is that you just never know. Sometimes, just the knowledge gained from attempting these exercises has unexpected benefits.
Just because it may not have an immediate benefit does not mean it will never have a benefit. It's his time and effort and he wants to do it. Good for him.

Re:What Does This Mean?

[ConceptJunkie]

... probably more like "rounded to the nearest 10,000 light years".

There is no practical use for this many digits, but math boffins can have lots of fun studying the string of digits. If it turns out they truly aren't random, a lot of interesting and important things we thought we knew are wrong.

But from what I've read, it seems they are truly random, as far as we can tell.

Re:What Does This Mean?

[ConceptJunkie]

Well, to be fair, they are always striving to make their own lives easier.

I am of German ancestry and I find the German mindset (minus the nationalism and the bad things that came from that) to be very appealing.

Re:What Does This Mean?

[ConceptJunkie]

Thanks for pointing that out... I just thought it was a weird typo. It didn't even occur to me, even though phi has been a favorite number of mine ever since I discovered some its amazing properties at random while playing with a calculator during math class.

Kids these days... if something looks weird, I have to remember to try reading it phonetically to figure out what they are trying to say.

Re:What Does This Mean?

[the entropy]

yes?

Re:What Does This Mean?

[MurukeshM]

Towels, my man, towels!

Re:What Does This Mean?

[fatphil]

Read more. The Plouffe formula (apparently the input from the other 2 was minimal, according to Simon himself) is only computationally efficient in base 2 (and therefore powers thereof). You have to do more work in other bases in order to avoid calculating earlier digits, it's simply not worth it.

Re:What Does This Mean?

[History's Coming To]

Yup. You need a whole 19 digits to calculate the circumference of the observable universe to the resolution of one Planck Length. Of course, the Universe could be much bigger than just the observable bit, then we'd need more figures. If we need to use all of pi to define the circumference, then we're in an infinite universe.

Re:What Does This Mean?

[fatphil]

It's not useless for those interested in computational efficiency with huge datasets. (Things like weather modelling, climate modelling, nuke aging analysis, fusion research, etc.)

If you look at a naive theoretical model for a computer, then you would predict that certain classes of algorithms would be most efficient for calculating digits of pi. (These algorithms use huge FFTs in order to do bignum arithmetic.) Several world records were broken using this technique. However, as the problem size grew, the FFTs started to become impractical, as the communication overhead started to dominate, and eventually algorithms that didn't have such a communication overhead became favoured. Better models of computational efficiency were arrived at, and new records were broken. We now understand time/space trade-offs better.

However, your loaf of bread won't be cheaper because of this, nor will the number of homeless on the street decrease.

Re:What Does This Mean?

[ciderbrew]

Yes, we can't have a proper shave without those. I like your thinking. Around this 8 place Oak Dining Table & Chairs we'll have the grandest meal on any pole.

Re:What Does This Mean?

[JoeMerchant]

Or, put another way: How can you tell? Who can verify that the method is correct? Do we even have a good independent check on the first 1 trillion digits?

Re:What Does This Mean?

[sourcerror]

Hi, Bill Gates.

Re:What Does This Mean?

[mla_anderson]

If this is some sort of "holy book" "intelligent design" thing where the bible says pi is actually 3, then I can't help you there...

2 Chronicles 4:2

Re:What Does This Mean?

[MightyYar]

Given that Pi never ends

The summary says he's Japanese, but maybe he's from Missouri?

Re:What Does This Mean?

[Nadaka]

What is more impressive is that I can predict that the least significant digit of pi is going to be 1 in binary.

Re:What Does This Mean?

[heironymous]

Hilarious! I can't believe the moderators haven't gotten the reference yet.

Re:What Does This Mean?

[gfolkert]

How irrational of me.

Get real.

Imaginary my surprise!

Re:What Does This Mean?

[Muad'Dave]

You mean like this?

There is no DEADBEEF in the first 4 billion digits of pi. but there is a DEADBABE.

Re:What Does This Mean?

[hcs_$reboot]

CERN / OPERA project / neutrino / FTL ...

Re:What Does This Mean?

[mikeru22]

Does this take into account the expansion of the universe, or does this assume that you are traveling at the speed of light?

Re:What Does This Mean?

[mikeru22]

How irrational of me.

Get real.

Imaginary my surprise!

multiply yourself by your complex conjugate

Re:What Does This Mean?

[jellomizer]

Simple though experiment.
Take a 1 unit Diameter circle. And put it in a 1 Unit by 1 Unit square. Then lets equally divide up that perfect squares fill the larger square.
Now choose one of those square where the circle partially fills up the square. And repeat the process.
You notice the square which has no rounded edges will need to try to fill in a shape with a rounded edge. So you will be going on forever smaller and smaller trying to fill in most of the shape however never really filling it in because squares against a curve will have gaps.

There isn't any Magic to PI. It is just a number coming from the fact that we measure area in squares, or volume in Cubes and the fact that those shapes don't fit into the circle.

Now my though experiment isn't a good proof of Pi being an irrational number (as it doesn't prove the number can repeat) Except for the fact that as you zoom in your curve becomes closer and closer to a straight line without actually becoming straight. But it shows that the number can go on for infinite digits.
   

Re:What Does This Mean?

[Teancum]

Because the computational resources must be tested anyway for some kind of test, often extreme calculations like this are used as a part of the "break-in" process for computing equipment. If used in that manner, you can confirm the quality of the equipment when you start comparing previous attempts at calculating pi and then perhaps contribute something for the greater good simply by running the tests.

If I recall correctly, one of the early tests that Steve Wozniak performed on the original Apple ][ computer was an assembly language calculation which ended up using all 64k RAM in that computer with just enough room left to display the results. He did it in part to test the equipment, and to say he could do it. Other computer developers/engineers have performed similar tests for many of the same reasons.

As a break-in/burn-in test, calculating pi sounds like a really neat exercise and certainly isn't wasting either time nor resources which would have to be used anyway.

Re:What Does This Mean?

[petermgreen]

sure, in base-10... I wonder if there are in other bases.

In any integer base any ratio of integers can be converted to a terminating or recurring pattern of digits (with a point seperating the integer and fractional part if relavent) and conversely any terminating or reccuring pattern of digits (with a point seperating the integer and fractional part if relavent) can be converted to a ratio of integers. The procedures taught at school for converting ratios to recurring decimals (long division along with the principle that their are a finite number of possible remainders for a given divider and so the pattern produced must eventually repeat) and converting recurring decimals to fractions (multiplying both sides of the equation and subtracting) work just as well in any integer base.

I'm not convinced that non-integer bases make any sense as a concept. The whole point of a positional numbering system is to represent a number as a series of small integers but IANAM.

Re:What Does This Mean?

[MattBecker82]

2 Chronicles 4:2

In the KJV, the biblical "value" of 3 for pi is clearly indicated to be an approximation:

Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.

(Emphasis added)

Re:What Does This Mean?

[kelemvor4]

People think in binary here. It's either perfect or not. In your case, it is not.

Unless you work for a government agency, isn't that how it works everywhere?

Re:What Does This Mean?

[Teancum]

I guess somebody else in this universe actually read the book by Carl Sagan besides me? That aspect of the book was never put into the movie, if some here don't get the reference. Dr. Arroway supposedly finds a message in the number pi itself as a sign of intelligence that created this universe. The message was a series of digits which formed a circle when printed out as ASCII art.

Re:What Does This Mean?

[jamiesan]

Negative comments have absolutely no value.

Re:What Does This Mean?

[Archangel Michael]

I hate derivative jokes

Re:What Does This Mean?

[gfolkert]

Given that Pi never ends

MMMMMM... I like Pi.

Re:What Does This Mean?

[sconeu]

Those are integral to the /. sense of humor

Re:What Does This Mean?

[_0xd0ad]

If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle and when you get to the end of the circle (based on the digits of pi you memorized) you'll be off by less than the width of a human hair.

I'd ask if that's inclusive or non-inclusive... but that would probably be splitting hairs.

Re:What Does This Mean?

[idontgno]

Naah. He's commenting that with an appropriate mapping between digits and characters, you can find a stretch of digits of pi which maps perfectly to the works of Shakespeare. Since the digits of pi are infinite and non-repeating, it's just an alternate expression of the "infinite monkeys" premise.

Re:What Does This Mean?

[Rizimar]

That just means that the line circled around the molten sea, not that the length of the line was approximated. Several of the other translations on that Bible.cc page also show this:

King James 2000 Bible (©2003)
Also he made a molten sea of ten cubits from brim to brim, round in shape, and five cubits its height; and a line of thirty cubits did measure its circumference.

Webster's Bible Translation
Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the hight of it; and a line of thirty cubits encompassed it.

New International Version (©1984)
He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.

Re:What Does This Mean?

[Anonymous Coward]

I think his point was that e^(__*i) is -1 IFF the missing value is pi, so if pi was something else, e^(__*i) wouldn't be -1.

Re:What Does This Mean?

[smitty97]

In a base-pi world, we'd be reading about how some idiot calculated 1(base-10) to a a trillion digits

Re:What Does This Mean?

[nickersonm]

Obviously you need to memorize at least enough that you're off by less than a Planck length.

Re:What Does This Mean?

[_0xd0ad]

The fact that a number is infinite and non-repeating does not imply it contains every possible series of digits. It could, for example, contain no 1s at all and still be infinite and non-repeating.

Re:What Does This Mean?

[_0xd0ad]

1 is 1 no matter what the base is. b^0 = 1

Re:What Does This Mean?

[c 0xFF]

I'm afraid you were the victim of a practical joke. Did a thin guy wearing a black hat tell you this?

Re:What Does This Mean?

[ObsessiveMathsFreak]

If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle and when you get to the end of the circle (based on the digits of pi you memorized) you'll be off by less than the width of a human hair.

To put numbers on that.

pi ~= 3.14159265358979323846264338327950

The first zero in pi appears 33 digits in. Memorising digits up to this first zero gives an error of less than 10^(-32). The radius of the known universe is 4.6 * 10^10, light years, and since a light year is close to 10^16m, the radius r is about 4.6 x 10^26m

Now, the circumerence is 2 pi r, so the error will be of the order of 2 r 10^-32. With r=4.6x10^26, this gives an error of 9.2 x 10^-6 m or essentially around 10^-5m or 10 micrometers. The width of a human hair is about 100 micrometers, so no, there is no real practical purpose to calculating digits beyond this point.

Re:What Does This Mean?

[nacturation]

I get that. My tongue-in-cheek response was because it had absolutely nothing to do with what I wrote.

Re:What Does This Mean?

[The Grim Reefer2]

If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle and when you get to the end of the circle (based on the digits of pi you memorized) you'll be off by less than the width of a human hair.

To put numbers on that.

pi ~= 3.14159265358979323846264338327950

The first zero in pi appears 33 digits in. Memorising digits up to this first zero gives an error of less than 10^(-32). The radius of the known universe is 4.6 * 10^10, light years, and since a light year is close to 10^16m, the radius r is about 4.6 x 10^26m

Now, the circumerence is 2 pi r, so the error will be of the order of 2 r 10^-32. With r=4.6x10^26, this gives an error of 9.2 x 10^-6 m or essentially around 10^-5m or 10 micrometers. The width of a human hair is about 100 micrometers, so no, there is no real practical purpose to calculating digits beyond this point.

Not true. Back in school I used to win free beer by betting people that I could recite Pi to 50 digits.

Re:What Does This Mean?

[evilWurst]

Well, with a few more digits of pi, you could get the error down to some arbitrarily small fraction of one Planck length. Then you're well below the absolute hard limit of measurability, and therefore the circle really would be perfect.

Hmm. A bit of googling, and someone else has already done the calculations. Apparently that only requires 61 digits of pi.

That's only the visible universe, though. You might want a few more digits, just to be sure. You're still not going to need ten trillion digits, though. Probably not even a hundred digits.

Re:What Does This Mean?

[Shoe Puppet]

If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle and when you get to the end of the circle (based on the digits of pi you memorized) you'll be off by less than the width of a human hair.

To put numbers on that.

pi ~= 3.14159265358979323846264338327950

The first zero in pi appears 33 digits in. Memorising digits up to this first zero gives an error of less than 10^(-32). The radius of the known universe is 4.6 * 10^10, light years, and since a light year is close to 10^16m, the radius r is about 4.6 x 10^26m

Now, the circumerence is 2 pi r, so the error will be of the order of 2 r 10^-32. With r=4.6x10^26, this gives an error of 9.2 x 10^-6 m or essentially around 10^-5m or 10 micrometers. The width of a human hair is about 100 micrometers, so no, there is no real practical purpose to calculating digits beyond this point.

Not true. Back in school I used to win free beer by betting people that I could recite Pi to 50 digits.

Stallman will not approve of this.

Re:What Does This Mean?

[brantondaveperson]

It is known beyond any shadow of a doubt that pi does not repeat or end.

The reason for calculating it to absurd precision is simply because we can. And also to explore the statistical properties of the digits, about which much less is known.

Re:What Does This Mean?

[aynoknman]

The sequence of digits you are looking for is "100", which occurs about 1200 digits into the sequence. The mapping is:f(X)=http://www.gutenberg.org/ebooks/X

Re:What Does This Mean?

[agrif]

In a more Contact way of thinking, if you were programming a complex formal system capable of producing sentient machines and wanted to leave a signature, the dimensionless physical constants would be a great place to hide them.

And yes, it's hopelessly unlikely we would ever find them even if you think it likely that they're there. It still makes me feel all warm and fuzzy inside.

Re:What Does This Mean?

[mr_stinky_britches]

Binary numerical representation always has some limit on precision (albeit sometimes very high). Clearly you do not understanding how floating-point and decimal representation works in digital systems.

Re:What Does This Mean?

[schroedingers_hat]

Except that spacetime is not going to be anywhere near Euclidean over the whole length of that trip.
Especially if you happen to pass near a galactic core.
So really you'd be way off, no matter how many digits you memorized.

Re:What Does This Mean?

[nacturation]

You mean to tell me that after such careful thought into the practicality of the voyage, you have no concerns about the fact that you'd turn to dust long before you made any significant progress on the journey?

Re:What Does This Mean?

[black soap]

In this case, the voltage rounds up.

Re:What Does This Mean?

[Hognoxious]

I don't see the point of calculating the circumference of a planet to an accuracy of less than the width of an atom, given that 1) planets are rarely (if ever) perfect spheres 2) atoms move 3) your input measurements aren't going to be anywhere near that level of accuracy.

Re:What Does This Mean?

[mwvdlee]

What did the actual bible say?

Re:What Does This Mean?

[MattBecker82]

Whoosh

Re:What Does This Mean?

[Pieroxy]

Clearly you do not understanding how floating-point and decimal representation works in digital systems.

And you clearly need some fine tuning to your humor detector.

Re:What Does This Mean?

[Metabolife]

This will factor into your paycheck.

Re:What Does This Mean?

[idontgno]

You're right; any given irrational number may or may not be normal, which means the number's expansion in any given numerical base is predictably uniformly distributed (every digit in the decimal base occurs 1/10 of the time, for instance).

I'm presuming the nomality of pi in this little joke, but that's the keystone of the metaphor: you really do need an infinite number of truly random (i.e., evenly distributed) inputs to make the Shakespeare monkey thing to work.

As it stands, the normality of pi is unproven. Some mathematicians believe it's unprovable. Others are working on alternate approaches that may get there.

You can't say it's proof, but pi appears to be quite normal in decimal expansions of thousands, millions, or billions of digits. It would have to go terribly sideways after, say, the trillionth digit for it not to be apparently normal. It's just not provably normal that way.

Madness

[aglider]

All that CO2 for nothing!

Re:Madness

[wanzeo]

What a pi in the sky project.

Re:Madness

[Compaqt]

>All that CO2 for nothing!

All those digits were calculated with Occupy San Fran bicycle-powered laptops, you insensitive clod!

Re:Madness

[michelcolman]

And how much CO2 did those people breathe out while pedaling? And how much extra did they have to eat afterwards? Where did that food come from? Etc...

Re:Madness

[JoeMerchant]

>All that CO2 for nothing!

All those digits were calculated with Occupy San Fran bicycle-powered laptops, you insensitive clod!

How many cans of beans were consumed by those bicycle powering homo-sapiens? I doubt their internal microbial colonies are carbon sequestering.

Why not

[JustOK]

would just using =Right(Pi, 1) be quicker?

Re:Why not

[hcs_$reboot]

would just using =Right(Pi, 1) be quicker?

There is an overflow risk. Try Right(Pi,1,10000000000000) instead.

Re:Why not

[FrootLoops]

That only works in Haskell, which nobody uses.

Ham Radio Callsign

[storkus]

Kind of obvious to me, being one. Here is his info:

http://hamcall.net/call/JA0HXV

And although I'm not first, let me congratulate Shigeru on a job well done! Oh, and to the idiot complaining of all the wasted CO2, please turn in your geek/nerd card now: computing Pi (and e and...) is NEVER a waste! :P

Re:Ham Radio Callsign

[thephydes]

Damm, you beat me to it. Yes Shigeru, as a fellow ham operator I salute you and your work. Tim VK4YEH

Re:Ham Radio Callsign

[robthebloke]

computing Pi (and e and...) is NEVER a waste!

Of course it's a waste. The result (by definition) is always inaccurate - so why bother? You know, there are some very good reasons why mathematicians use the symbol for Pi. Allowing an idiot Ham operator to burn the worlds resources for a useless result, is not one of them. Ask a mathematician if he'd like to calculate with an accurate symbol, or an inaccurate number requiring several hundred petabytes of data storage; which do you think he/she will go for?

And for calling me an 'idiot' for complaining about CO2? Screw you. I will not turn in my geek card for this. This guy has done *NOTHING* of merit. I will applaud new advances in human knowledge, but I will not applaud someone for running a for loop longer than the last guy did.

Re:Ham Radio Callsign

[BasilBrush]

There are still ham radio operators? In this day and age when we can use a cellphone to call a specific person on the other side of the world? When we can chat to anyone and everyone of whatever interest set via the internet?

Did you start before or after these wonders of modern technology arrived?

Re:Ham Radio Callsign

[AB3A]

Yes, there are. Modern radio systems are meant to be good enough to be reliable. Ham radio systems are the art of the possible. Most hams these days are experimenters who enjoy trying odd things. I've seen voice powered radios, I've seen radio systems designed to communicate via lunar reflections, I've seen radio systems designed to pick up spacecraft in deep space.

Some hams like to study radio wave propagation. Again, this is the art of the possible, not the engineering of the certain. Bouncing signals off of thunderstorms, sporadic E layer reflectors or meteor trails are all in this category. Occasionally, they stumble across something that works surprisingly well.

Some still tinker with modulation methods. Hams were playing with spread spectrum radios in the mid 1980s --long before the engineers sat down to work on the so-called wireless standards. Today, work continues with all sorts of forward error correction codes and modulation techniques.

So, yes, there still is a ham radio. Yes, there still are a more than a few slobs who like to do nothing better than listen to themselves talk on short-wave. But there is still a vibrant core that continues to study all sorts of forgotten alleys in the technology.

Quantum Computing?

[luke923]

Supposedly, this ran for nearly a year -- imagine how fast someone can come to the same result if he/she was dealing in qubits.

Re:Quantum Computing?

[MacTO]

Quantum computing is about algorithmic efficiency, not speed. So calculating pi will be a whole lot slower until you find and implement an quantum algorithm that is more efficient than classical solutions.

Re:Quantum Computing?

[orange47]

yeah but he/she wouldn't be sure of result..

Contact

[GrahamCox]

The big question is, does it turn out to contain the plans for a teleporting device?

Re:Contact

[Black Parrot]

The big question is, does it turn out to contain the plans for a teleporting device?

Undoubtedly it does, embedded somewhere in the sequence.

Also the text of every novel that will ever be written.

Just got to figure out what the encoding is. And figure out where the relevant substring starts.

Re:Contact

[rossdee]

No, the Teleporting device plans came by radio singnal (along with a few prime numbers and the TV broadcast of Hitler at the 36 olympics.

The first message that was found in pi was a circle drawn in 1's and zeros in base eleven.

This was in the book anyway, I think they left the whole pi thing out of the movie.

Re:Contact

[Eddie the Jedi]

The big question is, does it turn out to contain the plans for a teleporting device?

Undoubtedly it does, embedded somewhere in the sequence.

Also the text of every novel that will ever be written.

If you're referring to the notion that the decimal expansion of Pi contains every possible sequence of digits, this has not been proven. Certainly it's not true of every transcendental number — Liouville's constant is an obvious exception. For that matter it's not even known whether Pi is normal, that is whether each digit occurs as often as every other.

And to grandparent: the idea that Pi contains a message from the Creator is interesting, but Contact is fiction and just because it comes from Sagan is no reason to take it more seriously than any of the ideas put forth in the works of J.K. Rowling. It is tempting to think of Pi, being the ratio of a circle's circumference to its diameter, as just like all the constants physicists know and love (G, e, c, lambda, et al.) only more fundamental and therefore more AWESOME! But Pi is not like those, as should be apparent from the fact that we know 5 trillion digits of Pi and only about a dozen of each the others. Pi is not really a physical constant at all; it's a mathematical constant, the limit of the infinite series 4*(1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...), and hence a whole different beast entirely. It seems to me that the creator of the universe couldn't tailor the value of Pi any more easily than She could the value of 3.

Re:Contact

[GrahamCox]

Also the text of every novel that will ever be written.

Surely that could be true of an infinitely long purely random number, but not Pi, which is after all, the actual ratio of a circle's diameter to its circumference; i.e. it's not random.

Re:Contact

[Black Parrot]

Also the text of every novel that will ever be written.
Surely that could be true of an infinitely long purely random number, but not Pi, which is after all, the actual ratio of a circle's diameter to its circumference; i.e. it's not random.

IANAMathematician, but IIRC the going conjecture is that long substrings of pi's digits have the properties of random sequences.

If so, you could use it for an RNG. Let the seed be the offset to where you want to start, and then take the digits (or bits) sequentially from there.

Someone pick a number between 0 and 9!

[sgraar]

I just computed pi to 10 trillion and 1 digits!

Finally!

[Wattos]

Finally!

I was working on drawing a perfect circle and 5 trillion digits were just not good enough.

Thank you for wasting the earths resources (electricity, etc..) to make the world a better place!

Re:Finally!

[FrootLoops]

Thank you for wasting the earths resources (electricity, etc..) to make the world a better place!

Aren't you wasting those resources by reading such a story in the first place?

Only 10 trillion? In a whole year?

[Billly Gates]

I was under the impression a modenr Icore 7 could do 70,000 mips. That is 70 billion instructions per second. With that and cheap ram you could get to 10 trillion digits in minutes. You can just page the previous digits to disk as you move along.

Am I missing something?

Re:Only 10 trillion? In a whole year?

[chrism238]

"Am I missing something?" Ummm, they require calculation, not just generation.

Re:Only 10 trillion? In a whole year?

[FrootLoops]

He was using a processor with an outdated instruction set. It was missing the "compute next digit of pi" instruction, so he had to cobble together his own.

Re:Only 10 trillion? In a whole year?

[wvmarle]

70 billion instructions per second.

10 trillion (10,000 billion) instructions in 143 seconds (just over two minutes).

Somehow I have the feeling that the calculation of one more digit of pi involves a bit more than one processor instruction. The instructions to store the result to hard disk will require more than that already. If the calculation and storage of a single number, including all overhead, amounts to just 1,000 processor instructions, then it would be one month on your icore7 already. And I wouldn't be surprised if the number of instructions required is several orders of magnitude higher. I'm sure there are people in this forum that will have a reasonable idea on that.

Re:How to actually verify?

[hcs_$reboot]

how do they verify that it isn't random numbers

They actually verify the formula, method and hardware used, and if it is actually feasible within a reasonable time.

Even better

[timeOday]

The last three trillion digits were all 0, since pi turned out to be rational after all, which turned out to be the key in efficiently factoring large numbers and proving that P=NP. So, we can all go home now, math is done.

Re:Even better

[FreakyGreenLeaky]

This reminds me of a scifi (short) story I read too many years ago - I forget the title or author - I think pi was also being calculated to the Nth and some some magic number was reached and the universe started to unravel. The stars started blinking off, etc.

Wonderful stuff. I read so many short stories in my youth, I can't remember many, what I do remember though is the slightly-musty smell of the books in a library and immediately having to go to the toilette for a nice bowel movement... olfactory triggers are a sometimes weird and inconvenient thing (to this day).

Anyway, this anecdote has as much use to you as the 10 trillionth digit of pi.

Re:Even better

[newcastlejon]

This reminds me of a scifi (short) story I read too many years ago - I forget the title or author - I think pi was also being calculated to the Nth and some some magic number was reached and the universe started to unravel. The stars started blinking off, etc.

Do you mean Clarke's "The Nine Billion Names of God?"

Re:Even better

[fnj]

Sounds to me like you're thinking of Aurthur C. Clarke's The Nine Billion Names Of God .

Re:Even better

[FreakyGreenLeaky]

I think you're right, that looks like it. Thanks for the reminder.

Re:Even better

[tibit]

I loved Clarke's way of saying big things with small, unassuming words. "Overhead, without any fuss, the stars were going out.". The effect of throwing a sledgehammer at something, achieved with an overcooked pea. Yummy.

Re:Even better

[DerekLyons]

This reminds me of a scifi (short) story I read too many years ago - I forget the title or author - I think pi was also being calculated to the Nth and some some magic number was reached and the universe started to unravel. The stars started blinking off, etc.

This sounds like a jumbled recollection of Clarke's Nine Billion Names of God , in particular because the last line of your description is pretty much the last line of your story. (And a line that's stuck with me too over the forty odd years since I first read it.)
 
Sir Arthur was a master at writing memorable one liners and then constructing an entire story around them.

What's the message?

[wisebabo]

Isn't that one of the plot ideas in the book (which the movie was based on) "Contact"?

Scientist travels across interstellar space to meet super-advanced aliens and asks:

"Do you believe in God?"

To which they reply "Yes".

(A little surprised) "Why?"

"We have proof"

(Very surprised) "Proof?! What is it!"

"If you calculate Pi to the n-th digit you will find a message..."

Since I didn't read the book, I'm not sure this is how the exchange went, nor do I know what the "message" was. But it makes a good story! (I think in the Douglas Adams rewrite it was "42").

Anyway how would you determine, when looking at an infinitely long string of "random" numbers, what is a "message"? Couldn't you find, when looking long enough, ANYTHING; like the complete works of Shakespeare (written in the original Klingon?). I think (but again am not entirely sure) that that was the idea behind one of Stanislaw Lem's stories, that the U.S. government detects a signal from deep space and then finds more and more "messages" (meanings?) by subjecting it to more and more sophisticated(?) cryptographic analysis. (Will arbitrarily "strong" cryptanalysis of random noise produce anything you want?)

I guess this sort of thing is the ultimate case of "finding what you're looking for".

P.S. To the mathematicians: are there different kinds of Random numbers? Like aren't some systems are "chaotic" but not truly random? So while, for example, a Mandelbrot pattern may never repeat, does that mean it will show every possible pattern? So maybe Pi is a non-repeating numbers that is not Random. Or is it another kind of Random?

Re:What's the message?

[SpryGuy]

Wen calculating pie in a given number base (I forget which base), there was an abnormally long string of zeros and ones. The length of this string was the product of two prime numbers.

Arrange the zeros and ones into a two-dimensional matrix with one prime's units on the X axis, and the other prime's units on the Y axis.

The result was a "picture" of a circle.

Re:What's the message?

[Frosty Piss]

Anyway how would you determine, when looking at an infinitely long string of "random" numbers, what is a "message"?

And I suppose people are thinking it's going to be something in a current language... But I'm thinking some DNA-like thing instead.

Re:What's the message?

[d474]

Yeah, if I remember right, at some point deep inside pi, there is a message primer. It establishes that there is a message to get your attention. Then you begin to decode it, like you said. The trippy part of that is that the message is embedded into the very fabric of the universe through math.

Re:What's the message?

[BlackPignouf]

Good question.
I suppose you'll find this article interesting :
http://en.wikipedia.org/wiki/Normal_number

We're not sure pi is normal.
So it is believed that the complete works of Shakespeare in Klingon are hidden in pi, but you'll probably need a whole library to describe its location.

Re:What's the message?

[neyla]

By using statistics. If a message is significantly longer than you'd expect, compared to how far you've calculated pi, then it's statistically odd.

Calulating pi to 1000 digits and somewhere finding 12 would be expected. finding 1234 would be odd, finding 12345 would be highly unlikely. Finding 12345678901234567890 in the first 1000 digits of pi, would be *extremely* odd.

At some point, believing that something that a message is a message, rather than random noise, becomes more rational than the alternative. Though I suppose you could always debate at *which* point that happens.

Re:What's the message?

[Plunky]

Yeah, if I remember right, at some point deep inside pi, there is a message primer. It establishes that there is a message to get your attention. Then you begin to decode it, like you said. The trippy part of that is that the message is embedded into the very fabric of the universe through math.

Can we have xkcd now?

Re:What's the message?

[FrootLoops]

To decipher the math-speak on that page for the less mathematically inclined, here's my explanation of what a normal number is, geared towards a programmer.

Say you generated a number by randomly picking digits 0-9. After generating 100 digits, you'd expect close to 10 of them to be "7" (1/10). After generating 1000 digits, you'd expect about 100 to be "7" (1/10 again), but you'd expect only about 10 copies of the string "57" (10/1000 = 1/100), since there are 100 possible two-digit strings ("00", "01", ..." 99") and there are about 1000 length-2 substrings in a string of 1000 digits (999, to be precise). In general, for such a string of length N, we'd expect about 1/10th of the digits to be "7" and 1/100th = 1/10^2 of the substrings to be "57". If we made N very large we would also expect these estimates to get closer and closer to the truth.

You might get some strange abberations by random number generation. For instance, with astronomical bad luck you might generate 0 each time, and then your estimated fraction of "5"'s would be completely wrong. Still, the above properties are pretty good measures of how "well mixed" the digits of a number are, and they're taken (with mild generalizations) as the defining conditions of a normal number.

Specifically, for a given number x, imagine writing out its (infinitely many) digits in base b. Pick a substring of length m that you're interested in--say an encoding of Shakespeare's complete works in the original Klingon. In the first N digits, we would like to require the fraction of substrings matching our given string to be 1/b^m in analogy with the above (1/10^2 came about from b=10, m=2). That's too much to ask, so instead specify a small tolerance above and below 1/b^m. The key condition for normality is that if we look at the first N digits where N is larger than some number (which depends on the tolerances, the substring we picked, and x itself), the actual fraction of matching substrings will be within our tolerances of 1/b^m. A normal number is one where you can perform this operation in any base, with any substring, and with any tolerances.

If pi were normal, there would have to be at least one (indeed, infinitely many) occurrence of a given encoding of Shakespeare's works, since otherwise for N large enough the number of matching substrings would be near 0, and we could specify our tolerances to be between, say, 1/2 * 1/b^m and 3/2 * 1/b^m, which is strictly greater than the fraction of matches for N large enough since that fraction tends to 0, so it can't be within these bounds.

It's not too surprising that proving the normality of a number is much harder than believing it. Essentially, any number whose decimal digits appear "quite random" feels normal.

Re:What's the message?

[wisebabo]

Yikes! Well there's a reason why I'm not a mathematician :(. Anyway, thanks, I think I got something from this and I'll chew on it some more.

Re:What's the message?

[julesh]

Anyway how would you determine, when looking at an infinitely long string of "random" numbers, what is a "message"?

For any given "message" you can calculate the probability of something containing at least that much order occuring within any given number of digits. If that probability is too low for what you have found in the region in which you found it, then it can be reasonably inferred that it is actually not a random occurrence.

Re:What's the message?

[julesh]

I think we can be pretty sure that somebody with a PhD in astrophysics has at least a vague understanding of the fact that pi is transcendental. However, I see no reason to believe that simply because a number is transcendental it cannot contain some message. In fact, as far as I can see it, the set of transcendental numbers being infinite, it seems that there must therefore be at least one transcendental number that encodes any given message within any given number of digits of its beginning in any given base.

Re:What's the message?

[FoolishOwl]

It was in the book, at the very end -- I think the last paragraph described the protagonist looking at the circle.

What puzzles me is that I thought Carl Sagan was an atheist, so I'm not sure why there's a "message from God" subplot. Perhaps an indication of what he thought would constitute a persuasive message from God?

Re:What's the message?

[JoeMerchant]

Couldn't you find, when looking long enough, ANYTHING; like the complete works of Shakespeare (written in the original Klingon?).

First trick is to determine the encoding scheme. Even going for a relatively efficient 5 bit character, finding "i think, therefore i am." in a transcendental stream of bits will (statistically) take 2^120 bits. Every 2^10 is roughly equivalent to 10^3, so 2^120 is more or less 10^36. (If you want to include capital letters in your encoding scheme, that will increase your character size and scale up the search time accordingly.)

If you're content to find "ROSEBUD" that's only 2^35, or less than 35 billion digits to search. Choose your encoding and get cracking, it's in there somewhere.

Re:What's the message?

[Salsaman]

Indeed you are correct - you could have an approximately equal distribution of all digits, but it doesn't tell you anything about the substrings. As a trivial example, a number which contained "13" but never "31" could never contain the string "431". So, to know for sure that you eventually find any given substring within the digits of pi, you need to prove that there is a roughly equal distibution of all digits, plus that all those digits are arranged in every possible ordering.

Re:What's the message?

[Sperbels]

Why does that puzzle you? It's just a work of fiction. Not a manifesto.

Re:What's the message?

[camperdave]

Wen calculating pie in a given number base (I forget which base), there was an abnormally long string of zeros and ones.

Base 2?

Re:What's the message?

[_0xd0ad]

More likely he was simply amused by the notion of mathematicians thinking they'd found a message from God in the randomness of pi, much like I'm amused by people who think they see Jesus in potato chips or coffee stains.

Re:What's the message?

[julesh]

It's been years since I read it, but IIRC the main theme of the book is that everyone should question their beliefs. So, the atheist scientist ends up accepting that there are things that exist but which cannot be proven to exist, while the evangelical Christian preacher comes to question whether the god he has worshipped his entire life really exists. I think Sagan's primary point was that we should avoid being blinkered into thinking anything we believe is the absolute truth.

Re:pi, not Pi

[hedwards]

No we couldn't, that would be double u as w is vv. And due to the Romans not having a u, they would use v instead hence double u looking more like double v.

Now that is a key!

[FlyingGuy]

Talk about the best one time pad set ever.

Re:Now that is a key!

[Anonymous Coward]

A one time pad that can generated perfectly by anyone using simple maths and published techniques? Try worst pad set ever, by telling your adversary the pad is found in the first 10 trillion digits of pi, you just reduced the search space to at worst log2(10*10^12) 45 bits.

Re:Now that is a key!

[julesh]

2^43, ie. far worse than any standard encryption algorithm in use today.

The best published cryptanalysis on AES256 requires 2^99.5 steps. While this will undoubtedly come down in future, it is unlikely to halve. Also, each of those steps is somewhat more complex than calculating a bit of PI and running one modular addition per bit of message.

Re:Now that is a key!

[FlyingGuy]

Well since everyone else was AC I will ignore them.

You have 10 trillion numbers to pick from and they are pretty much random sequences. Pick ANY starting point and then pick any say 512 numbers randomly based upon any other set of factors.

Lets say we start at oh the 565,324,234,345 digit.

Good luck figuring that out.

Pretty much the same principle as the RAND book only one hell of a lot bigger.

Re:Now that is a key!

[LighterShadeOfBlack]

Except that now pi isn't really the key at all, the method of selecting which digits is. If the method is using preset random digits then just use them instead of pi (but of course then the usual one-time pad problems arise); if it's an algorithm then that is now the thing to break and the strength of the encryption relies solely on that, making the encryption method not a one-time pad at all, contrary to OP's concept.

Re:Electricity usage

[Arlet]

Probably not nearly as much as other useless endeavors, such as playing computer games, updating facebook status, or watching super bowl. And reading slashdot, of course.

Re:pi, not Pi

[Patch86]

You would be assuming that Slashcode can handle displaying a Greek letter. I'm not going to try, but that's probably a ropey assumption to make...

Re:Electricity usage

[Black Parrot]

I am curious to know how much electricity was wasted on this apparently useless endeavour.

I think you're just suffering pi nos envy. He's obviously got way more pi nos than you do.

Sagemath.org can do many digits

[beachdog]

The sagemath.org open source computation engine has a 2 line benchmark that computes Pi to 5 million digits.

It took my Atom desktop computer about 15 minutes. I watched it with Top. It sucked up 99 to 100% of the CPU and strangely only 200 Mb out of 2 Gig of RAM.
Also, it didn't use the Linux swap at all. It kind of got me puzzling that my Ubuntu Linux might be missing some performance optimizations.

What to do with it? Resume studying mathematics. Make a pretty good symmetric encryption gadget with a CD of huge encryption keys.

easy:
sage: numerical_approx(pi,digits=50)
3.141592653589793238462643383279502884197169399

takes a long time:
sage: time a = N(pi, digits=5000000)

Computers get faster and faster

[Lord Lode]

So the record will be broken over and over and over again...

Re:too much time

[Hognoxious]

... and when it gets sore from doing that, then you fill in the time by calculating the digits of pi ...

Re:too much time

[localman]

Yes, like reading about it on slashdot and complaining that he's wasting time :)

Re:Proof?

[Zerth]

You can calculate any particular digit of pi(in base 16) without calculating all the preceding digits to verify they are correct.

Pi = SUM(k=0 to infinity) 16^(-k) [ 4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6) ].

Hopefully that won't get mangled.

Last digit

[lazykoala]

What's the 10 trillionth digit of pi? I've got my money on 7.

Re:Last digit

[hcs_$reboot]

RTFA, it's actually a 5.

Re:Last digit

[Sulphur]

What's the 10 trillionth digit of pi? I've got my money on 7.

http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula

--

Has your cloud been running slowly?

Re:Electricity usage

[wvmarle]

Hey! Without reading Slashdot we wouldn't know about those useless endeavours, let alone be able to discuss them. That in itself proves already that reading Slashdot is not a useless endeavour.

Re:Pi?

[maxwell demon]

I raise a 22/7. That's slightly closer.

And 355/113 is also easy to remember (if you write the numerator first, you'll get 113 355, i.e. the first three odd digits twice each), and already about as close to pi as an IEEE single precision float approximation.

Re:How to actually verify?

[EvanED]

I think there are formulas for calculating the nth digit without knowing the previous ones. Assuming this is so, you can get a probabilistic proof very easily: just pick 100 random digits, compute their values, and check against the claim. (It may require some computational power to do this, but it should still be plenty tractable.) If they all match, you've got solid evidence it is correct.

Re:pi, not Pi

[EvanED]

In the case of 'pi', the fact that most keyboards don't have a 'pi' key on them might have something to do with it.

Re:pi, not Pi

[maxwell demon]

Actually all that Slashcode would have to do is not removing it. Displaying it is the job of the browser.

Thanks for the answers (so far)

[wisebabo]

Thanks for the answers to some of my questions. I didn't read the book, but might if it recommended (and if it's an e-book).

Likewise, never heard of "normal" numbers before (like I said, I'm not a mathematician). So thinks for the info.

Uh, is there any way to check this person's answer (short of duplicating the entire calculation)? Like I heard there's a way of confirming If a number is prime that's easier than figuring out what's the next prime number.

Re:Thanks for the answers (so far)

[Salsaman]

I believe there is an algorithm for generating just the nth digit of pi. So to check the results they could take a few digits at random and check them. The checking would likely take a long time, but not as long as generating the whole set.

Re:How to actually verify?

[EvanED]

So I'm sort of right and sort of wrong. There are digit-extraction methods for pi, but according to wikipedia, they work in O(n^2) time (for the n'th digit). But it also looks like there's an algorithm to compute up to the nth digit in time O(n log(n) log(log(n))).

Which means that asymptotically, if the storage requirements of the second alogrithm don't preclude its use in those cases, there's some N for which it's actually faster to compute all of the first N digits than just do the N'th digit directly.

pi hex

[thcip]

Pi Hex was a project to compute three specific binary digits of pi using a distributed network of several hundred computers. In 2000, after two years, the project finished computing the five trillionth (1012), the forty trillionth, and the quadrillionth (1015) bits. All three of them turned out to be 0.

Mistake

[fnj]

It looks to me like there is a mistake in the 34,518,296,721th digit. Could you repeat and compare please?

Re:Mistake

[Wootery]

You joke, but this wouldn't actually be hard.

It's natural to assume that one can't calculate the n'th digit of pi without first calculating all previous digits, but this isn't actually the case.

The same applies for 'e'.

"Spigot algorithms" are where it's at.

Re:Mistake

[tibit]

The base is where the problem is at. You can get arbitrary digits of pi calculated in base 16. But to do base conversion to base 10, you need to know all of the previous digits. So you can only use the spigot to give you hex digits of pi. But the pi, as we have it, is probably in base 10 or some other base that's easy t convert to base 10 (say base 10^7). Doing base conversions from base 10 to base 16 on the existing 10 trillion digit result is not trivial either: it might take more time than calculating the value of pi in the first place.

Re:Electricity usage

[Plunky]

I think you're just suffering pi nos envy. He's obviously got way more pi nos than you do.

Yeah but my circumference is larger because I rounded up

Actually calculated 10 billion digits

[alexhs]

The guy is using short scale.
This being Slashdot, you could have written 10^13, that being unambiguous.
Call me back when someone actually computes 10 trillion (10^19) decimals of Pi :)

Re:Actually calculated 10 billion digits

[FrootLoops]

What English speaking country/region uses the long scale today? I didn't see any on the page linked. It seems that short/long scale is a historical issue for English speakers and a modern issue for translators into various other languages.

Re:Actually calculated 10 billion digits

[julesh]

What English speaking country/region uses the long scale today?

While the wikipedia article may reflect current media & government use, unofficially the long scale has been more popular up until very recently in the UK. It was the method taught in schools up until (at least) the early 90s, and as such most British people are more comfortable with it than short scale.

Note, specifically, that the Oxford English Dictionary still suggests the long scale is more common:

(from the definition of 'billion')

In the 19th century, the U.S. adopted the French convention, but Britain retained the original and etymological use (to which France reverted in 1948).
Since 1951 the U.S. value, a thousand millions, has been increasingly used in Britain, especially in technical writing and, more recently, in journalism; but the older sense ‘a million millions’ is still common

That's from the 4.0 CDROM edition, i.e. one that contains revisions up to 2008.

Re:Actually calculated 10 billion digits

[Tomato42]

English? Don't know, though the names for million and above are basically the same for French, German, Italian, Polish, Spanish, Portuguese, Swedish, etc. and they all use the long scale... The English speakers are the odd-balls, not the other way round. One would think that the UK wouldn't take ideas from States, but they started using the American scale in the '70s so it's not like people that remember its use died yet...

Re:Electricity usage

[neonsignal]

let me keep alive a bit of usenet history:

On Tue, 22 Jul 1986 06:33:45 +1000, Calum T. Dalek, chairentity wrote
> In article eugene@ames.UUCP (Eugene Miya) writes:
> > We have just received a letter from Japan that a newer record for
> > computation of digits of Pi was accomplished. Previously David Bailey
> > here at Ames did a 30 million digit computation on the Cray-2.
> > The new computation was done on an older Hitachi 810 supercomputer
> > using extended storage. The new record is 33 million digits.
> > Dave replied, "This means war!"
>
> I think NASA should pay more attention to launching rockets and less attention
> to calculating the next million digits of pi.
> --
> Greg
> gjk%a@lanl.arpa and greg@harvard.harvard.edu

I think Los Alamos should pay more attention to developing high tech methods
of mass destruction and less attention to flaming NASA in net.math.

Hugs and kisses,
Calum

Is there a prize

[rossdee]

Is there a prize for memorizing, and then reciting all 10 trillion digits?

Re:Is there a prize

[sam_nead]

The prize is that you die of old age first.

Re:Is there a prize

[catmistake]

Is there a prize for memorizing, and then reciting all 10 trillion digits?

I was always amazed by those contests and contestants... but it made me wonder... wouldn't it just be easier to actually calculate pi in your head than memorize a million numbers?

Re:Is there a prize

[Salsaman]

Well, if you were to recite 1 digit per second, it would take around a million years to read the entire number out. I think the audience and speaker would be long gone before that happened.

The calculation was commissioned

[msobkow]

The calculation was commissioned by an anonymous group known as Occu-Pi.

That's the....

[ArcadeNut]

Same number I have on my luggage!

Takes awhile to open though....

Actually, 10 trillion

[jbov]

What makes you think it was 10 billion digits? The TFA reads 10 trillion digits. Maybe you were being funny, and I misunderstood. In which case, mod funny.

Is this a 'use'?

[jago25_98]

Since Pi is considered to be the pattern of nature (or rather, 'everything'?). Then perhaps Pi tells us more about ourselves. That is, how far our current thinking is from truth.

Thus, any attempts to calculate could be used to hone our view of the world. Can the process be reversed? To see everything from Pi and look at how we view the world from that?

Is the best science goalless?

Re:Is this a 'use'?

[nashv]

Pi is as much a 'a pattern of nature' as is root 2. Pi just happens to be related to circles, and root 2 is to squares or right-angled triangles. There is no reason to attach any mysticism to it. Too much pop-sci there, huh?

The real constants of nature , i.e, the Planck constant or the related Fine-structure constant have certain real physical interpretations. Those are the ones that seem to have certain values, when they could in principle have other values (and we see no reason that their be fixed). These are the subject of intense theoretical physics studies, and probably would be more justified as objects of metaphysical fantasy

Re:Is this a 'use'?

[Asic Eng]

[...] perhaps Pi tells us more about ourselves.

No it doesn't. It does tell us the ratio of a circle's circumference to its diameter, though.

Useful for Halloween: You can divide the circumference of a pumpkin by it's diameter and get pumpkin pi.

Re:Is this a 'use'?

[jago25_98]

Yeah I didn't mean to attach any mysticism. But that tends to happen when Pi is mentioned. Fun but too easy.

  Regards Planck Constant, well that's calculated in part by Pi right anyway?

"These are the subject of intense theoretical physics studies, and probably would be more justified as objects of metaphysical fantasy"
Here's something I'm going to say a bit riskè. Perhaps these theoretical studies are actually a mathematical expression of the authors repressed beliefs? No bad thing though, maybe dodgy perhaps more productive in the same way science was born from religion, expedited by a friction in the head between belief in truth and belief in belief aka faith.

"Pi just happens to be related to circles"
Then it's got to be circles all the way down right? All the way down like turtles on turtles!

Re:pi, not Pi

[maxwell demon]

No, in most other editors which support HTML, if you simply type &pi or &#960, you should get the formula of pi.

You would also get the character pi on Slashcode if Slashcode wouldn't filter it away. Slashdot wouldn't have to interpret it. It would just have to pass it on to the browser, which then knows that π, π or π has to be rendered as the character U+03C0 GREEK SMALL LETTER PI. Slashcode doesn't need to interpret it at all (well, for the numeric form it probably wants to minimally interpret it in order to make sure that it's not some control character or some invalid character; that's of course a simple lookup in the Unicode table).

One's not asking them to support Unicode, where they risk plenty of posts in Mandarin or Arabic, but rather, just support the entire HTML character set.

There's no reason not to support Unicode. Blocking posts written in Mandarin or Arabic would be the job of the lameness filter, should it turn out a problem (just demand a minimal percentage of characters in the basic ASCII range). But then, already today you could without problems write entire posts in German, French or even in transcribed Mandarin. It doesn't seem to be a problem.

The funny thing is: Slashdot once did support Unicode. But then, apparently someone misused a control character (RTL marker) to write over Slashdot UI elements, and Slashdot overreacted by not only disabling control characters, but almost all Unicode characters. Indeed, initially you couldn't even write Schrödinger's name correctly because ö was not in the whitelist.

On the above story, assuming that the trillion digits were done on computer, where did he get the RAM to store it?

I didn't RTFA, but he almost certainly didn't store all the digits at once in RAM, but on disk. A trillion digits is about a terabyte, so storing ten million digits isn quite possible today.

However, if he e.g. has used a cluster of 640 machines with 16GB each, it would actually have been possible to hold all the digits in RAM at once (well, probably he would have needed some more machines, because the operating system and the program code also need some memory).

Prove it

[gsslay]

Just as importantly; how does anyone prove they actually calculated all this? How does anyone know that the additional 5 trillion digits aren't just random crap?

Re:Prove it

[Goose In Orbit]

The usual method is calculate it twice, using different algorithms, then compare the results and claim up to the point that the two methods start to differ

Re:Electricity usage

[vlm]

I am curious to know how much electricity was wasted on this apparently useless endeavour.

Not enough to really matter.

In english he writes that it took 191 days to calculate it, which is only 4500 or so hours.

I can't read enough Japanese to figure out what he was doing, but he certainly comments a lot about hard disk failures and stuff. That would seem to imply something more like a repurposed desktop and less like a professionally managed cloud NAS. Or maybe not.

Anyway I think you can safely assume "your average civilian" can't afford more than 500 watts of CPU, so figure 9000 KWh.

Today, the price of a KWh where I live is 11 cents. It used to be less but the idiots sold all their nukes and installed lots of natgas turbines, so the price has exploded. This is a common strategy for mostly unregulated monopolies to make more money; F it all up. Anyway historically according to my Japanese teacher years ago, electricity costs about twice as much in Japan as in the US. So lets round up to a quarter.

We'll also round up the KWH to 10e3. Multiplying, thats a mere 2500 cents, or a whopping earth shattering $25.

The problem is finding high end computation hardware that depreciates less than $25 in a year, so the energy consumption is more than just noise in the environmental budget. Another way to phrase it, is take the price of an incandescent lightbulb and multiply it by 10, thats how much energy they use. On the other hand, heavy computational equipment usually approaches the cost of electricity. Light computational equipment like i-devices are physically incapable of the end user using as much energy as it took to make them.

The other problem with waste is the guy ran it during the summer, apparently. If he ran it in winter, for many people it would cost nothing at all, and for almost all people it would cost a fraction less. For example, my aunt's electrically heated house could run a 1 KW floor radiator thingy for an hour, or a 1 KW pi calculator for an hour. No energy difference, but one calculates pi and the other does not.

Stupid question

[argStyopa]

....but how is this done, basically?

Do they do something as simple as draw a circle, measure the radius and back-calculate to pi (in which case I can't see getting past about 1000 digits before measurement error would exceed the calculated precision anyway), and it's irrational so (as far as I know) it's not as simple as taking 22/7 and letting it run to the trillionth decimal place....so what calculation do they do to get to the trillionth+ decimal place?

Thanks for the reply.

Re:Stupid question

[MattBecker82]

There are various (infinite) formulas for computing pi to any given precision. You just have to be patient enough to compute to as many digits as you need.

So advances in computing pi boil down to one or more of the following:
1. Finding a better formula or algorithm
2. Finding a better implementation of a particular algorithm
3. Throwing more resources (computing power x time) at the problem

As far as I can tell, it's just a case of the latter in this particular instance, which isn't that exciting.

Re:Stupid question

[tibit]

Let's see if that would work out. There are algorithms out there where you draw a circle doing nothing but additions/subtractions. It's "reasonably" easy to accumulate the length of such a circular octant while updating the x/y coordinates - we don't have to accumulate the bitmap at all, just count the pixels. To get the length accurate enough, we'd need on the order of N pixels on the circumference, so that means about that many updates through the loop. Since the loop does additions, the cost of an iteration is also N. That means O(N^2) performance. That won't work. Alas, it is possible to get the result in the right base without doing further divisions (ratio of circumference to radius): we simply set the radius to a suitable number, such that division is just shifting the fractional point around, in whatever base we chose.

Re:Stupid question

[tibit]

It should be perhaps pointed out that this algorithm's lower bound shifts quite dramatically depending on the number of digits sought. As long as it fits machine precision, it's Omega(N) since addition doesn't care how many digits of the addends are "used up". Once N gets large, the cost approaches N^2, and that's what counts in asymptotic complexity...

Pi is *exactly* 1

[KlaymenDK]

Pi is exactly 1, if your numbering system uses base pi.

Re:Pi is *exactly* 1

[MightyYar]

Oh pish. If Pi = 1, and 1*1=1, then Pi*Pi = 1*1 = 1!

Re:Pi is *exactly* 1

[catmistake]

I bet a more useful base would be base-pi/10 or even base-3pi/4 or base-10^pi

Re:Pi is *exactly* 1

[_0xd0ad]

Pi is exactly 10, if your numbering system uses base pi.

FTFY.

Re:Pi is *exactly* 1

[_0xd0ad]

Why not base-pi/180 or even base-pi/200?

Re:Pi is *exactly* 1

[KlaymenDK]

What a brain fart. Thank you.

Hello Gentlemen

[MattBecker82]

FTFA:

I calculated on October 10 2010 started, and a calculation stopped by the trouble of the hard disk many times, I made completion (including verify calculation) on October 16. It was about 191 days at real calculation time.

Somebody set up us the bomb!

omega

[epine]

Every true geek must read Metamath! or at least vaguely grok the concept.

It's the finishing touch on a brilliant little geek high-ball made from Heisenberg, Turing, Godel, Kolmogorov, Chaitin with a Mandelbrot cherry. Toss it back then bite the lemon! Warning: There's a lot of peel in A New Kind of Science. Chaitin is short and dense and accessible to a thinking 15 year old, for some value of "ignores assigned homework". Wolfram is pointing out that the mathematical Chaitinverse is a five minute walk from the financial district; a few steps past the edge of city limits you spot your first cactus.

In fact, as far as I can see it, the set of transcendental numbers being infinite, it seems that there must therefore be at least one transcendental number that encodes any given message within any given number of digits of its beginning in any given base.

There exists a message which this little strip of paper is too small to contain. Bursts into flames.

The significance of trillions of digits of Pi is akin to the Apollo program. An alien civilization who spies a little shard of metal emitted from the earth's atmosphere, winging very directly to the moon where it loiters for a few orbits, then winging back to earth (in a vacuum!) would probably be thinking "Petunias! Whale meat!" Life, in other words.

Catching a glimpse of a million digits of Pi from the billionth page on the Hollywood hills of a distant galaxy, they would think exactly the same thing--after Zaphod Spader conducts the kindergarten refresher class on algorithmic complexity theory.

Tau, not Pi!

[Phrogz]

That's all well and good, but what about digits of tau?

Re:Tau, not Pi!

[RubberChainsaw]

Just multiply by 2.

Re:Tau, not Pi!

[_0xd0ad]

SAL pi, 1

Re:Tau, not Pi!

[AP31R0N]

It's +5 Funny that people are modding your post Informative.

Did they find the circle yet?

[Prototerm]

(Obligatory reference to Carl Sagan)

Obvious

[PopeRatzo]

Is there any practical application to this sort of thing

It's not rational.

Did they find a string of 0s?

[140Mandak262Jamuna]

Some scientist, Carl Sagan I think, predicted that after about a billion digits we will see some unusual sequences like long strings of 0s followed by long strings of 1 and then there will be a coded message from God. Did they find it?

Seriously?

[hesaigo999ca]

Come on, how much investing into finding out how many numbers in another number can you do, could we not instead focus on more important research especially if this takes up some resources from a supercomputer that could be used for another project, say....how to cure cancer!

NA

[Kashgarinn]

Anyone know the function or formula used to calculate pi in this manner?

Obligatory

[kerrbear]

Is there any practical application to this sort of thing, either having the number itself, or whatever method this guy used to arrive at it? Or is this a thumb gazing exercise?

http://www.youtube.com/watch?v=H20cKjz-bjw

Re:exponential growth

[MattBecker82]

Is there a "Moore's Law" for the calculation of PI digits?

Yes.

Doing a quick calculation using this data, I'd say that, very roughly, the precision (number of decimal digits calculated) has doubled about once every two years since the start of the computer age.

What are you complaining about?

[Cro Magnon]

Everyone knows, you can't ever get too much pi.

What difference does it make?

[wfstanle]

After 1 million digits what does it matter? Even if you are planning to launch an interstellar rocket you would never need that much accuracy. The only benefit of this is in math theory.

Mistakes in computing pi.

[wfstanle]

Actually, there was just such an error. In the 1800's two mathematicians attempted to calculate pi to as many digits as was humanly possible. They worked independently but at the end of each day they compared their work. The assumption was that any errors would be caught that way because it was unlikely that both of them would not make the same error. If any error was found, I assume that they would revert to the previous day's calculation and proceed from there. This method worked well for quit a while (I think it was a several years!) until both mathematicians made the exact same error. All their calculations after that point were worthless but they of course didn't know it. It took computers to discover the error.

Pi vs. E

[jacobsm]

Pi goes on and on
and E is just as cursed
I wonder which is larger
When their digits are reversed

Pi is believed to be a normal number

[bigsexyjoe]

A normal number goes on forever and contains all sequences of numbers. So it is believed that every message you can think of is in the number Pi if you calculate it far enough.

That is only true for measuring circles

[bigsexyjoe]

There is a lot more to Pi than calculating circle sizes. There are open mathematical questions about Pi.

For example, is Pi a normal number? (A normal number is one in which all digits appear with the same frequency in every base). And if this product turns out to be true for the at least the first 10 trillion digits, it can be a great random number generator.

Morgan talks about this kind of thing

[SMACX guy]

In "The Ethics of Greed" CEO Morgan criticized scientists for doing things similar to this. If I may paraphrase him: You ivory tower intellectuals must not lose touch with economic needs. It is all very well and good to pursue mathematical challenges, but supercomputer time is expensive. You must justify your existence by providing not only knowledge, but concrete and profitable applications as well.

Obligatory Contact reference

[LihTox]

Did they find a rasterized circle?

Enough with all this pi nonsense...

[ArcCoyote]

I know all about not reinventing the wheel, but what kind of idiot invented the wheel using a silly number you can never get to the end of? I say we just make it so pi=3. Going around the pi is three times across the pi. Not "3 and a bit," just 3.

an' I've got this here wheel to show you can do it...

Re:pi, not Pi

[Rastignac]

With the Amstrad PCW, one was able to enter Greek characters, AFAIR.

Circle

[Silpher]

Did he find the circle yet..

I think you might have missed something....

[TiggertheMad]

If you memorize up to the first zero in pi, you can navigate the circumference of the universe in a perfect circle

I get your basic point about the accuracy conveyed in ten or twelve digits of accuracy, but I think you might be missing out on something rather crucial. PI is a ratio that is for a circle inscribed on a flat plane. Evidence show that the universe is probably fairly curved, so if you are trying to navigate a circumference inscribed on a 3d space with a map based off of a 2d ratio, you are likely going to be way off.

Re:I think you might have missed something....

[nacturation]

Then I guess you'll have to do it as a mental exercise rather than packing 10^80 lunches for the voyage.

JA0HXV - Amateur Radio callsign

[brindafella]

JA0HXV is an Amateur Radio callsign, and owner of that callsign is Shigeru Kondou. Well done, Shigeru-san.

Tods fashion style look through the centuries

[backpack2]

Tods office site has indicated that demand for luxury boots, shoes and leather bags remained strong despite the global uncertainty. The company's first half performance the continued global momentum of the tods brand, Worldwide retail revenues rose by 39 percent, The tods company, which is famous for its pure handmade workmanship and makes well-tailored. These leather handmade bags and shoes are not only fashionable, but also funcitonal. Tods fashion style look through the centuries, you can easy to buy tods online.This is the reason why Tods continued remained strong in the crisit Tods new all-leather tods handbags for Autumn Winter 2011. They’re made from 100% up-cycled oil-tanned cowhide leathers and feature hand stamped brass hardware. The vintage-style cases that are reminiscent of old steamer trunks-except with a modern twist. Get fashion forward with tods handbags. This medium sized satchel has a simple yet sophisticated design that will become a classic addition to your handbag collection. The top leather exterior with contrast stitching trims and glossy silver hardware. An envelope-style front pocket has space to keep your phone or keys, and has a snap-hook closure. An additional exterior back pocket is the perfect hidden storage. Dual structured handles can be worn on the crook of your arm or carried on your shoulder. Attach the fully adjustable leatherette shoulder strap to convert the Andie into a messenger bag. Open the full-zip top closure to find cotton canvas lining in a whimsical bubble print. Numerous compartments make organizing a cinch, with two open-top compartments with snap closures, and a zip-shut center compartment. Two small open-top pockets and a zip-shut pocket complete the interior of this store-all bag. Tods shoes are produced for not merely casual satisfy on but in add-on it is satisfy for sports activities .Tods may be deemed getting a warm selected brand name using the youthful generation. These tods sneakers are created from amazingly versatile alternatives also for the primary is generally created of rubber. around the beginning, the pattern of all those footwear experienced been vital but as time went by, the pattern transformed according toward pattern utilizing the sports. They may possibly be employed for running. Tods footwear is accepted for best outstanding shoes, accepted for their abundance and achieved outstanding leather with the best craftsmanship. Due to the fact the adherence of look through the centuries. Therefore, you went to some airing Tod's, you do not demand any additional footwear for ongoing days. such as tod s loafers are adapted inside bounce of 2011 good argent band. whenever you purchase Tod's footwear you are abiding to purchase a capable area of Italian style.

How is pi calculated, rather than measured?

[AP31R0N]

This is a non-rhetorical, non-troll question.

How is it that we a calculating (something w/o a pattern)? Seems to me that it's something we'd have to measure: measure disc radius with laser, measure disc diameter, do math.

Re:How is pi calculated, rather than measured?

[_0xd0ad]

Nobody calculates pi by dividing a circle's circumference by its diameter. There's no way to measure them accurately enough, and besides which, at least one of the numbers must be irrational (in other words, you can't measure it accurately - it's just as infinite as pi is).

Because pi is intrinsically related to circles, it is also intrinsically related to all of the trigonometric functions. For instance, off the top of my head I recall that 4*arctan(1) = pi. That's not an approximation or an estimate; it must be exactly pi because of how the trig function is related to circles.

According to Wikipedia, the arctan function can be calculated as an infinite summation:
arctan z = z - z^3/3 + z^5/5 - z^7/7 + ...
i.e., the summation from n = 0 to infinity of (-1)^n * z^(2n+1) / (2n + 1)

Computing 4*arctan(1) in that manner for the first 5000 terms yields about 3.1413926535917... (it keeps going - as it's a rational approximation of pi, it has to start repeating somewhere, although I don't see where that is - my program only used 200 decimal places in computing it). Obviously, it's a very inefficient way of computing pi, but I obviously wasn't going for efficiency. There are better methods of calculating pi which give you significant digits much more quickly, so if you're interested in more efficient ways of computing pi, my non-troll reply is that I'm sure Google could help you...

Re:How is pi calculated, rather than measured?

[AP31R0N]

Thank you.

Someone toss this guy some Informative points.

i prefer to ask people than Google.

My PIN Number...

[IBitOBear]

This guy is trying to break into my bank account. I use the last four digits of Pi as my PIN. Once he finds them, my hundreds of dollars are sure to be his.

Re:My PIN Number...

[FredFredrickson]

hahaa, oh man, thanks for that.