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A Much Bigger Piece Of Pi
Punk_Rock_Johnny points to an AP story on Pi-obsessed Professor Yasumasa Kanada. A snippet from the story: "Kanada and a team of researchers set a new world record by calculating the value of pi to 1.24 trillion places, project team member Makoto Kudo said yesterday. The previous record, set by Kanada in 1999, was 206.158 billion places." Trillion!
"
Why?
How about we see this bad boy!? I'd sure like to paste it into my "info.txt" file for future referance. It could come in handy sometime.
No sig for you. YOU GET NO SIG!
I think I read somewhere that to draw a circle to circumscrible the known universe with a an error of +/- the width of a proton, you only need to know Pi to about 20 places. What practical purpose is there to know pi to 1.whatever trillion places. Unless, of course, you're Count Duckula, in which case it's a party trick.
If Mr. Edison had thought smarter he wouldn't sweat as much. --Nikola Tesla
We would have either found the end by now or discovered a pattern.
heh.
"Everything you know is wrong. (And stupid.)"
Moderation Totals: Wrong=2, Stupid=3, Total=5.
Sig (appended to the end of comments you post, 120 chars)
The number Six!
Does the problem that pi can't be expressed in decimal notation extend to other base systems? For example, if you tried to write pi out in binary or hex would you encounter the same problem? Is there a special base system (other than base pi) which can describe pi in a finite number of digits?
Someone you trust is one of us.
A Much Bigger Piece Of Pi
Doesn't matter, I still want seconds. With ice cream!
How could this ever be useful? I mean that as an honest question, what could anyone, ever, use this for?
Mod point free since 2001
Here's how it works. You'll need several boxes of toothpicks. Get a large piece of chart paper, and draw parallel lines on it, from one side to the other. The lines should be separated by a distance just slightly larger than the length of a toothpick.
From a height of about one metre, drop a measured number of toothpicks onto the chart paper, so that they all fall randomly somewhere on the paper. Count how many toothpicks are touching a line (or would be, if they weren't resting on another toothpick).
Repeat this process as many times as you can. Lots of people can do it at once. All that's important is that, each time you drop some toothpicks, you write down how many you dropped, and how many of those ended up touching a line. When you're done, find a total for each quantity.
You now have all the numbers you need to calculate Pi:
Now here's the formula you need to calculate Pi:
Fill them in the formula, and work out your own value of Pi!In the book version of Contact by Carl Sagan, but skipped in the Jodie Foster movie, was the notion that the aliens had discovered proof that the universe was created by a higher intelligence. A God or society of Gods far higher and more advanced than the aliens. The whole point of dragging Human-kind to that remote beach to talk with daddy was to tell Human-kind that it was time for them to look for God's signature on this universe.
As any artist, the creator signed the creation. Where? Deep into the insignificant but irrefutably valid digits of several of the fundamental mathematical constants such as pi and e.
The main character finds one of the signatures at the end of the book: if calculating digits of pi in base 11, after a few million or billion places, a 500x500 digit span is almost entirely zeros. If the span was rendered as a square of pixels, the non-zero digits drew a perfect circle inscribed in the square. A circle in a square. The key concept defining pi, in the digits of pi itself. The whole way the universe works is affected by that constant, so any such 'design' in it has, if you pardon the pun, a transcendental import.
Why base 11? It's left to the reader to decide, but I expect Sagan wrote it because it is considered one of the possible designs of the universe, one of the string theories is based on an 11-dimensional all-inclusive physics model. As the alien explains to the main character, it wouldn't be base 10, because what's the likelihood that the creator also happened to have ten fingers?
[
Um, you have 1.24 trillion digits of pi. I think you can begin a statisticall analisys now.
If Mr. Edison had thought smarter he wouldn't sweat as much. --Nikola Tesla
You can calculate Pi by doing:
..) x 4
(1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 +
Obviously the more iterations you do, the closer you will be to the 'true' value of Pi.
Some people here seem to bee a little uninformed. pi has been proved irrational and trancedental (duh).
42 really is the answer to life, the universe, and everything!!!
This story reminds me of conversation we had in High School at the computer club about guys memorizing pi up to the 10 thousandth decimal. At which point, one of the less cool geeks, who happened to pronounce DOS, dose, chimmed in enthousiastically, "I once hear of a guy who memorized 30,000 numbers!"
You can bet your ass the room filled up with Louis Skolnick type laughter, along with ribbing along the lines of, "Once I hit 30,000 I stop counting..."
That was BEFORE we had beowulf cluster jokes!
"Communism is like having one [local] phone company " - Lenny Bruce
Dr. Math's Pi FAQ. Very informative.
Pi is represented usually by a fraction or relatively simple equation, it's just the division that makes the number go on for ever. I don't understand why we must break pi down into a decimal when it can already be represented by a simple fraction.
This is a bit misleading - since Pi is irrational, representing it as a fraction (eg, 22/7) is only an approximation. Representing these divisions usually produce an infinite expansion in decimal (if that's what you mean by "it's just the division that makes the number go on for ever"), but that number is recurring, and thus easy to work out any arbitrary digit since it repeats. This article is about working out the true value of Pi, whose decimal expansion is infinite and non-recurring, and this has nothing to do with divisions.
Taking the equation two divided by three I have found the 100000 trillionth digit ... it's "3"
Yes.. working out digits of rational numbers is slightly easy than irrational ones. Irrational numbers, by definition, can't be represented as the ratio of two integers.
22 / 7 = PI
Ignore the "p2p is theft" trolls, they're just uninformed
(c) Austin Powers and MPAA and protected by the DMCA
Ignore the "p2p is theft" trolls, they're just uninformed
Pi is represented usually by a fraction or relatively simple equation, it's just the division that makes the number go on for ever.
... but these are just approximations; 22/7 is a good enough approximation a lot of the time, but that's just an approximation too)
Nope. If pi was rational (a fraction), it wouldn't go on for ever without repeating. (reference)
In fact pi is irrational, i.e. there are no integers p, q such that pi = p / q. (proof)
You can approximate pi as a fraction, which is what projects like this do. (pi is approximately equal to 31/10, or 314/100, or 31416/1000, or
As for math, I don't think there is anything at all learnable from actual digits of pi. We know they neither end nor repeat. Actual values are just trivia. It could as well have been 3.76421403038164659... and nobody would care.
Gentlemen, you can't fight in here, this is the War Room!
Taking the equation two divided by three I have found the 100000 trillionth digit ... it's "3"
... but what do I know ;)
Actually, if you divide two by three the 100000 trillionth digit would be "6"
I found it hilarious that the story "Professor breaks own record -- for thrill of pi" ended with a link named "Subscribe to the P-I".
And well it should! For it is from the Seattle Post-Intelligencer, whose logo is a globe with the initials "P-I". Someone should get those guys to put it on their top page.
Perhaps they held back since it also was posted exactly 61 years after the invasion of Perl Harbor. Oh well.
FWIW, I've been hoping desperately that they'd find some neat geometrical patterns in Pi. My guess is that the reason the mathematicians cannot prove that all those digits are random is that they aren't.. they are just using an extremely good hash algorithm to encrypt the darn thing.
http://www.math.clemson.edu/~rsimms/neat/math/pipr oof.html
That's the great thing about maths, you can prove things like pi being infinitely long without actually calculating any digits.
I'm curious. These guys spent 5 years writing the software and then used some 400 hours of computer time on this supercomputer to calculate it. Is there really any advantage besides getting into Guiness to justify this expense? I'm not bashing it, I just don't know. Seems kind of wasteful to me, personally.
Cartman may be round, but even he had to say...
No... more... pie...
-Zaphod
Anyone have any recommendations for books on the current theories and the history of pi? I found comments like:
"Among the most puzzling mysteries: Mathematicians are pretty sure, but still cannot prove conclusively, that the numbers following 3.141592 occur randomly."
interesting and want to be able to read more indepth.
mathematicians are pretty sure, but still cannot prove conclusively
In the best case, statistical analysis could come up with something like "there is a 99% probability that the numbers occur randomly". That's not a proof, that's just quantifying "pretty sure".
So who sets the limits? Why didn't Kanada just let his computer algorithm run for another year or even just another few minutes to get an even more accurate number? Who decided 1.2 trillion digits was enough and why?
It's just intersting to note that the measurement objective reality is always hampered by subjective, practical matters. And it might also prove that it is impossible for man to ever know the universe---it's just too damn expensive! I'm sure someone out there has thought about this before.
<a href="http://www.joblessjimmy.com">Work is dumb and so is Jobless Jimmy.</a>
Why would he have some prime number of fingers? 12 or 16 would make a lot more sense!
Is it just me, or does this seem like irrational research into an irrational number?
-1 * LOGe(-1) / i........that's simple, but not the ratio of two integers, of course.
Here's a bunch of simple fractions: (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) etc.etc. Repeat to desired precision (this is the slowest possible way to compute pi, you're taking the average of series of ratios of circumference of polygons to their altitude as number of sides increases, get a life!)
Kanada and a team of researchers
MPAA forces have today invaded Canada, when asked their reasons they replied:
"While we were looking through through the binary version of Pi, and one of our special forces noticed that hidden in from digit 12,166,133,883 onwards was a c source to DeCSS. Obviously these terrorists must be stopped!"
When pointing out that it was Kanada, the researcher, and not Canada the country, the Canadian government sued for trademark violation.
The case is not expected to hold up, as it is doubtful canada will be able to proove it has the computing power to calculate Pi beyond 4 decimal places - and no confusion can occur.
I'm not trying to be flamebait here, but I'm confused on why Math doesn't deal with reality very well.
Example:
Using Standard measurements, a 10ft length can be split into three equal lengths of 3ft 4in.
Why can't that same 10' length be broken with decimal math? Why is it 3.33333333333...ad infinitum?
Also:
If I were to take a 10' length and bend it on itself so it made a circle I have a 10' circumfrence right? Then in theory I could get out my ruler and measure the radius and get a measurement that made sense. I can get real numbers by measuring, but the math doesn't agree...Why?
-- Wiccan Army, 13th Airborne Division "We will not fly silently into the night"
The problem with this argument is that pi has the same value in all possible universes. So its value implies nothing at all about the existence of anything in our universe or in any other.
True, you get different digits if you use different bases. But this is also unaffected by the existence of any god or gods. In base N, you get the same sequence of digits no matter what universe you are in, regardless of whether there's a god.
There is also a conjecture, undecided as far as I know, that pi is what mathematicians call a "normal" number. (Look it up.) If this is true, then the expansion of pi in any base will turn up the pattern that Sagan described. The pattern (and all others) will turn up an infinite number of times, in a frequency distribution determines solely by the number of digits in the pattern.
Those who do study history are doomed to stand helplessly by while everyone else repeats it.
The Indiana legislature at the time came within 1 vote of voting pi as "de jure 3.2"? Dumb-ass politicians couldn't even round the correct way, and we allow them to make budgets?
Do you have a reference for a proof of the normality of pi? The last I read, this was still at the "conjecture" stage, though there have been enticing arguments in its favor.
Of course, proof of the normality of e would also suffice, since pi and e are related by a well-known equation that has no other transcendental terms.
Those who do study history are doomed to stand helplessly by while everyone else repeats it.
Buy the complete six DVD set!
You'll need to insert all six one after the other next time you #include <math.h>
Once more unto the breach, dear friends, once more, Or close the wall up with our American dead!
Cheers for that. That will save me the trouble of actually reading the book.
that stated that somebody proved each number subset within pi appears as often as every other subset: '123' appears as often as '321' and '213' and '312' and such... it went on to state that this proves that every possible set appears somewhere, and as often as every other set...
this means that any electronic file could be represented as a start and stop position within pi if you knew the proper place to be... in other news MPAA/RIAA declare PI to be illegal...
pi=4*arctan(1).
Using radian units, of course!
make world, not war
3.14159265358979323846264338327950288...... ah, this is gonna take a while :-/
A google only has 100 zeros, thus 100 places.
:-P)
:-)
10^trillion is 1 followed by 1 trillions 0's... Assuming we are following the american system that would be equivalent to.
10^(10^12)
Okay... now.. let's get some interesting facts with this.
The absolutely smallest length measurable by quantum theory is the planck length which is approx 10^-34 m. Needless to say, if we have a diameter of an incredibly small perfect circle, we'll know it's circumference beyond what is possible by quantum theory (but since there are no perfect circles, and quantum theory adds probability, this doesn't mean anything really useful.
Now, since we know the smallest measurable... lets look at what the estimates for the size of the universe are. Recent estimates put it as 10 billion light years in radius source
Which works out to about... (assuming american notation on billion)
10^9 * 300,000,000 m/s* 365*24*3600 ~= 10^25 m
Okay... now if we were to measure the circumference to as accurate as allowed by quantum theory we'd have.
pi*2.10^25 ~= 6.28*10^26 10^27 with an accuracy of about 34 decimals...
So... to get perfect accuracy as allowed by quantum theory we would have at most 35 decimal places afterwards... therefore, we'd need pi with an accuracy of
~10^63...
We have pi with an accuracy of 10^(10^12) which is
63 : 10^12 ~= 1: 1.59x10^11
Way more accuracy then we really need.
That's absolutely insane, but it is fun math.
Just some food for thought.
~ kjrose
Actually, right outside my office in the physics department is a poster with a picture of Rutherford and that quote. The way it's written there,though, is (roughly, becuase i'm not there right now) "The only real science is physics. All the rest is stamp collecting."
make world, not war
is EXACTLY 3.
Sorry about that. I just wanted to get your attention. Glayvin!
I betcha if I draw a circle with pi equalling 22/7 and you use the 124 trillionth spot ... they'll look pretty similar, know why? Because calculating pi beyond 22/7 is silly.
Ignore the "p2p is theft" trolls, they're just uninformed
Were you laughing at his grammar?
Below is an interpretation of the overall joke my post tried to present.
He was a bigger geek than we were. He pronounced DOS, dose, despite constant correction! His statement sounds so stupid! It was stupid! ha ha ha ha ha! It was stupid!
He should have said, "I heared of a guy who memoried pi up to the 30,000th decimal."
Not, "I heared of a guy who memoried 30,000 numbers!"
That's so stupid!!! Don't you get it??? It's so stupid!!!
He was inferior, thus we rediculed him like we were ridiculed by the football team.
This concludes the interpretation. Further layers of humor will not be interpreted...
"Communism is like having one [local] phone company " - Lenny Bruce
I can't believe you report this and don't even include the value of Pi he calculated in the article!
I guess I'll have to wait for one of the page widening trolls to post it.
while it's true (I think) that any fininte sequence of digits will eventually appear in a non-repeating, infinite sequence, I think the point in the book was that the odds of our being able to find it, given the tiny tiny tiny tiny tiny tiny portion of the number space we're able to search with our extremely finite computing power, would be evidence that it was placed there if we ever did manage to find it.
Put another way, it would have to be hanging in easy reach for us to be able to find such an insanely improbable thing as (say) a 500x500 block of pre-arranged digits. In base 11, that would be 11^(25,000), a number too hideous to contemplate, and think of the size of the space you'd need to search before such a number would be found just based on probability. So if we found such a thing, we either beat bazillion^bazillion-to-one odds, or we found something that was left there for us. Interesting.
-- http://frobnosticate.com
my question is how exactly does it take multiple people 5 years to create a program to calculate pi. Granted, I have no experience in doing things like this - in fact I have no idea how to go about calculating pi to 30 digits nonetheless 1.3 trillion, but maybe 5 years seems excessively long.
This was from the cnn article.
Now I finally have the measurements needed to make my cookies PERFECTLY round.
Your assertion that pi is the same in all possible universes seems quite silly to me. Assuming that those universes have two spatial dimensions and that the symmetry of that universe causes 360 degrees to subtend a full, symmetric rotation in those dimensions. In short, just because it represents the only kind of universe you and I can commonly conceive of doesn't mean shit, because everythin on the basis of which we conceive of that is part and parcel of the universe itself, including the laws of physics.
What if we used a beowulf cluster of toothpicks?
"I have never let my schooling interfere with my education." - Mark Twain
You could at least give credit where due ;)
Here's one of the nicer sites I've seen that has a java applet to simulate this.
"Not knowing when the dawn will come, I open every door." - Emily Dickinson
The number is the subject of numerous books -- from "The Joy of Pi" to "Sir Cumference and the Dragon of Pi: A Math Adventure" -- and has fascinated and confounded mathematicians for centuries.
:-P
Sir Cum-ference? Ewww... I wonder why the weird mathematicans got "fascinated"
Beware: In C++, your friends can see your privates!
Comment removed based on user account deletion
"Google" - search engine.
"Googol" - 10^100.
I mean, I hear this repeated a lot. but just because something is infinite and nonrepeating does not mean that every possible combination exists.
Imagine this program screaming along calculating a few more trillion places when all of a sudden it stops. Pi is NOT infinite after all.
Imagine the hiliarity that would ensue (oops, wrong web site...)
according to a quick calculation, downloading pi to this many decimal places would cost $7,810.15 (cdn) in over-your-bandwidth charges if you are connected through bell sympatico DSL.
long live pi. down with bell.
Your assertion that pi is the same in all possible universes seems quite silly to me. ... because everythin on the basis of which we conceive of that is part and parcel of the universe itself, including the laws of physics.
Sorry, you're dead wrong here. First, pi and circles have nothing to do with physics. There are no circles (as mathematicians define them) in our universe. Pi is an abstract concept, not a physical object. We can conceive of them nonetheless. The human mind is hardly limited by the physics of our universe. Suggesting that it is is, well, silly, and flatly contradicted by watching an hour or so of Saturday-morning cartoons. I can conceive of things that don't exist in our universe, and so can you.
It's possible that another intelligent species might not conceive of pi. But any that do will come up with the same value (though they may represent it in a different base). Or they may use circumference / radius, giving a value of 2*pi, but that doesn't affect the discussion.
Pi's value is what it is. It has nothing to do with anything in any physical reality. It's a pure mathematical concept, and as such, will have the same value for anyone who conceives of it.
This is really no different that observing that 1 and 2 have the same value in all possible universes. You may name and write them differently, but that doesn't affect their values. Pi is merely another (somewhat more compicated) number. Not even a god can change its value. They can define another value, but it won't be pi.
--
Those who do study history are doomed to stand helplessly by while everyone else repeats it.
355/113 is much better, plus it has a nice structure.
Mea navis aericumbens anguillis abundat
but the sequence isnt random, pi's sequence is.
Just how is Pi calculated?
As a matter of fact, I happen to know that this system used a cunning mechanism containing a Canadian-built robotic arm, a No. 10 coffee can, a piece of string and a ruler. The machine measured the circumference and diameter of the can over and over again, and then sort of calculated the margin of error (correlated against 22/7) over and over again. And voila! It was discovered that pi is in fact 3.142857143...
Mind you, the article said they calculated pi to over a trillion places. They didn't say it was *accurate*.
Cheers,
Ethelred
Everyone wants to be Ethelred. Even I want to be Ethelred.
Divide 555,000,000,000,000 by 555 and
you get 1,000,000,000,000
I didn't want to type out a number 500 digits long, but you get the point
..........FULL STOP.
Area of a circle is
:)
(pi)*( radius^2 ), not (pi*radius)^2.
And, the volume of a sphere is
(4/3)*(pi)*( radius^3 ), again not involving pi^3.
Also, 'cause the Earth isn't a perfect sphere you'd have to do a LOT of measurement.
No, it isn't. Pi's digits are the same every time I look.
What exactly do you think "random" means? If "random" means "normal," noticing that random numbers are normal isn't much of a shocker.
I Can't Believe It's A Law Firm, LLP does not necessarily endorse the contents of this message.
Okay, maybe this is a stretch, but hear me out. I believe pi is considered to be normal. See here and here for background on what "normal" means. Essentially, it says the digits are equally distributed over the long run. I believe then, that you can also prove that by exploring sufficiently deep within pi, you will find every conceivable string of digits (ie, in any order you desire and of any length). I think my math is reasonably correct here, but feel free to put me back on track.
Anyways, if this is the case, all digital works are already rendered in pi. All past and future audio master recordings are already in pi. All source and binary distributions of all software are already dumped in pi. Etc.
So the implication is: Am I breaking simple copyright law or the DMCA by computing pi? Am I a criminal for posessing a sufficiently large dump of pi's digits? If I find the rip of a new audio CD in pi, can I keep it?
Only in Indiana
This differs from the true value 3.14159265358979 by less than 0.00001% while 22/7 has an error of 0.04%.
It is also easy to remember:
start with 113355 (first three odd digits repeated)
break it up with a / : 113/355 and
invert 355/113
If you're in a time wasting mood, you can try these:
Search for a string of numbers in the first 100 million decimal digits of pi. Try your birthday, or whatever.
Search for a char or hex string in the binary representation of pi. Find your name in pi, woohoo!
More pi time wasting stuff.
The plots are given high levels of water, heat, carbon dioxide and nitrogen in different combinations to simulate predicted global climate change in the next hundred years.
Unless there is something more solid that they aren't reporting, this looks more like politics than science. At least, the way they report the findings sounds very skewed:
"The three-factor combination of increased temperature, precipitation and nitrogen deposition produced the largest stimulation [an 84 percent increase], but adding carbon dioxide reduced this to 40 percent," Shaw and her colleagues wrote.
In other words, they are saying that high Co2 levels increased plant growth 40%, but because of their agenda they are reporting this effect as a reduction because it is less than they would have seen if they'd done something else.
A more likely/solid conclusion might be: if the climate changes plants in a given area might not be as well adapted to the new conditions as they were to the old.
And this is news...how?
-- MarkusQ
I don't know why over a trillion digits of pi would be useful, but I have seen something similar. There was a book I once saw that contained nothing but pages and pages of random decimal digits. I imagine that pi would be quite suitable for whatever purpose this first book was for.
:)
Looks like there is some competition in the random number book business
Prof. Frink: Pi is exactly 3!*other scientists gasp and snap to attention*
"Sic Semper Tyrannosaurus Rex."
Didn't the Alabama department of education already calculate the value of pi out to a trillion places? 3.000000... and I think their trillionth digit is zero too...
What a timesaver for the kids!
You, Sir, despite your low member number, would get an F- for information theory at the university I was tought and now teach.
There is nothing that compresses to one bit. There is such thing as a most efficient way of encoding any message. Counted in bits. and no, not just one bit. One bit would just contain enough information to say "Pi" or "Not Pi". "Not Pi" would according to my intuition not be an acceptable answer, you also have to say "What kind of 'Not Pi'". And that takes bits. You forgot that your algorithm is supposed to possibly generate all possible messages, or else it's "not fair".
Pi would not compress at all, given it's an infinitely long number. (To be precise, it's length would be reduced from inf to inf/(alphabet entropy) which is still inf, although a "smaller" inf). If you are content with a finite number of digits, its length would be reduced by about a little more than three bits per decimal (because log2(10)=3.???) with any decent entropy encoder. You could try to reduce this further by taking two decimal digits at once, but unfortunately it would not work, as not only are Pi's digits uniformly distributed from 0 to 9, pairs of digits are also distributed uniformly from 0-99, so you would remain with 6.???? bits (log2(100)) per decimal digits pair.
Another approach you might take, if you want infinite precision (silly on a finite machine), or more generally random precision, is to write a code in a predetermined programming language, in this case a series developement, or whatever the number thorists use nowadays to calculate pi, and decide that the "decompression algorithm" is a compiler (that is perfectly legal, as any finite message can be passed that way, eg "#include <iostream> int main(){cout << "The message";}").
My idea is that the c compression algorithm would be beat by a perl compression. Maybe try in BrainFuck, it might beat perl, but BF sucks at multiplications.
Anyway, the most optimal compression for pi is probably saying "Pi" by itself. Any decent geek knows at least one way to calculate that/ find it on project gutenberg/whatever. But don't ever think that you could compress it to two bytes or less : you gotta be sure that I will not understand "the string of decimal digits a.k.a. Pi, do write it in numbers when decompressing", not just "mu turned over", "Pi the string" or "Private investigator". This certainty takes bytes.
Another example is : "you cannot encode '3 4 8 15 3.141592653 78 54' as '3 4 8 15 pi 78 54', because that would increase the number of symbols in the alphabet, and all the other symbols would have to contain more bits as a result, so the compressed message length would suffer- hope there are a lot of 'pi' in the compresed message".
I must leave now, gotta go bowling with friends. Start your flames, I can see blatant holes in my reasonments. Hope you get the point. Mailing a link to the message to my signal theory professor (formally one of my bosses), so I will suffer if I told bullshit.
Care to enlighten us with a possible use then?
Gentlemen, you can't fight in here, this is the War Room!
Are we starting this story again? The fact is that there are a lot of files that CAN NOT be compressed. Period.
See the rationale about it, thanks to the guys at news:comp.compression. There you will find the story behind some scams involving 'infinite' compression or 'universal' compressors.
Fh
They're gonna get my PIN number for the ATM machine...
It's the last four digits of Pi.
Do we know this? Has anyone actually translated this to ASCII or something? Had been great fun to run it against a dictionary to check for words.
However, I'm fairly sure the number 42 has a meaning inside Pi..
BTW, I use "larger" in human intuitive sense in that case: The computable numbers is larger then the rationals because the computable numbers contains all rationals, plus more numbers.
;-)
Of course mathematically, both sets are the same size, the cardinality of the set of integers; we can talk of Turing Machines running forever but not of "infinitely long" Turing Machines, which is counter to the definition.
(Which highlights the interesting point of that idea, that all the numbers we ever use are still just the integers in a very real sense, even when we talk about "pi" or "e". Not necessarily groundbreaking stuff, but interesting to some of us math wonks.)
I post this in an effort to forstall the inevitable "correction"...
aparently you've never eaten Thanksgiving dinner at my place. Give it an hour or two, and you're bound to see it make a reappearance...
At first when I read Sagan's book at the impressionable age of 15, I was dumbfounded by this idea.
Now I am older and more cynical, I became somewhat disappointed that good old Carl himself have fallen into his own trap of "hiding signatures" in randomness. Basically, if you look hard and long enough into a series of random numbers, you might find an apparently "unrandom" event, perhaps the 1432323th decimal place of PI spelling out "God is Here". He had himself written about this in his book The Demon Haunted World.
In science, you only cares about experiments that are repeatable, or at least statistically sound if not repeatable (e.g. The Big Bang happens only once but...). Finding a circle in PI is exactly the kind of unrepeatable, unpredictable idea that is beyond the realms of science.
So that's too bad.
BTW, Sagan could not have used the motivation from String Theory since at that time he wrote the book 11-D ST has not been invented yet. He probably used base 11 because you can paint an ASCII picture with 0 and 1. (Base 2 is the other common example, wonder why he didn't use it.)
Mode (3) smart-aleck mode. Press * to return to main menu.
Dude, they measure it to 1.24 Trillion, not 10^(Trillion).Someone had pointed that out, but...
If you think about it, you could not have fitted the entire observable universe with enough paper to record (even if you write in very very very very small fonts) the number of decimals if you know PI to 10^(Trillion).
In fact the entire observable universe had about 10^120 atoms. So you are out of luck very soon. (You can imagine packing more atoms, but then the universe will become too dense and collapse on herself so fast you won't have time to expand to her current volume).
Mode (3) smart-aleck mode. Press * to return to main menu.
Has e been found to more decimal places? Pi and e are so related [Euler's equation, e^(i * pi) + 1 = 0], I wonder if precision in one will lead to precision in the other.
I just pulled up Mathematica and ran some amusing stats:
Assuming that 2000 characters can fit on a 8.25 x 11 inch page, you can print 10 pages/second, a page is 1 micrometer thick, you can print 2000 pages/toner cartridge, and you can speak 2 numbers per second...
Printed pages: 6.2 x 10^8 pages (620 million)
Printing time: 117.96 years (excluding leap years)
Stack of printed paper: 62 km high
Toner cartridges: 310,000 cartridges
Time to speak the entire number: 19,660 years
Length of a continuous-page printout (ala dot matrix): 170,500 km, which could go around the earth 4.25 time, or get us halfway to the moon.
Feel free to check my work, or to add stats to this:?)
The best way to predict the future is to invent it.
I completely agree that this is not a useful method for calculating pi.
However; I think it is very very important in the shear fact that it exists. Mathematics is represented all around us in nature in ways we simply don't see. This is one of them, and I think people should realize that there is a logical underpinning of how nature works, even if we will never comprehend it
"Not knowing when the dawn will come, I open every door." - Emily Dickinson
This post was supposed to go here.
-- MarkusQ
This is from the Old Testament. (found in my History of Pi book).
"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."
Egyptians and Babylonians had a much better approximation of Pi, long before the Bible was written. The Babylonians calculated Pi to be 3 1/8. The Egyptions had it at 4 * (8/9) ^ 2.
I'm not saying that the Bible was making an absolute claim that Pi was 3, as they're attempting a general description of an object in the quote. But my main point was that this senator took it literally, and I'm sure he had a large backing of complete idiots.
Square root of 9 to 500000 places? wouldn't that just be 3. with a string of 500000 zeros after it?
If that's the case, it can definitely be compressed!
The best way to predict the future is to invent it.
Right. If we actually found such a "signature" in Pi, even if we could prove Pi was normal, and that we should find any length sequence of digits in it, I would be astounded enough to have my faith in Atheism shaken (back to agnostic probably).
Knowing that the sequence does exist in Pi, doesn't change the fact that actually FINDING such a long sequence would be remarkable. We have to deal with the physical limitations of exanding Pi, after all.
So, at least as a literary device, I don't think it is invalid (but while perhaps suggestive, it isn't "proof of a creator" by any means)
I think the movie "Pi" had similar issues, BTW.
"It's overkill, of course. But you can never have too much overkill." - Anonymous Slashdot Coward
How do you actually calculate PI?
I thot it was an irrational number, that could not be represented fully in any form. Thus you wouldn't be able to 'calculate' it?
Or, don't tell me they drew a really good circle and got to measuring it's circumference etc.....
I'm sure someone here must know how it's done.?
Nifty, if you walk the line inbetween the Gypts and Babs its only off from the real Pi by ~.001154! More accurate than 292/93 (~.0018077 differential).
Neither of them are easier or more accurate than remembering 3.141 though...
Oh! 355/113 is only off by ~.00000027, competing with 3.1415926.
Do I get a cookie?
Someone set us up the bomb, so shine we are!
1. Promote interest in mathematics
2. Provide unassailable code publication anywhere in the galaxy (works on Earth too).
Okay, take your decss or whatever and gzip it. What are the odds that this archive exists in the teradigit string (probability indexed by archive length please)?
Obviously you just need to provide the offset in the teradigit string which ought to be available online somewhere.
But even if it isn't publically available, since (thanks to Zapman (2662) 's link) you can get any digit of pi without calculating the whole thing, you can resurrect the archive easily.
If SETI incorporated this kind of analysis we might even have a free distributed client..
Actually, if pi is normal, then the string we're looking for will appear an infinite number of times.
Staggering, isn't it?
~Idarubicin
You know, that was the most sense of an answer I've ever gotten. I never figured it to be a matter of Base-n before.
Thanks
-- Wiccan Army, 13th Airborne Division "We will not fly silently into the night"
Among the most puzzling mysteries: Mathematicians are pretty sure, but still cannot prove conclusively, that the numbers following 3.141592 occur randomly.
The word random has a very specific mathematical and information-theoretical meaning. In brief: a number, as represented by a sequence of symbols (digits), is random if it is incompressible; that is, if there is no algorithm, expressed using symbols which define a Turing-complete language, which can generate said number using fewer symbols than the number they generate. In other words, it takes fewer characters to write down the number itself than it does to "generate" the number using an algorithm. This is most certainly not the case with pi, as there are many finitely-expressible algorithms out there which generate it.
This post expresses my opinion, not that of my employer. And yes, IAAL.