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5 Trillion Digits of Pi — a New World Record
KPexEA writes "Alexander J. Yee & Shigeru Kondo claim to have calculated the number pi to 5 trillion places, on a single desktop and in record time. The main computation took 90 days on Shigeru Kondo's desktop. Verification was done using two separate computers. The program that was used for the main computation is y-cruncher v0.5.4.9138 Alpha." Looks like the chart of computer-era approximations of Pi here might need an update.
If there's ever a robot uprising, I bet it's going to be started by us making them do stuff like this.
Does this rag smell like chloroform to you?
I've heard that in the book (not movie) "Contact" that when Jodie Foster's character meets the uber-aliens she asks them:
"Do you believe in God?"
-"Yes"
Taken aback "Really, why?"
-"We have proof, when PI is expended out to (some number), there is a message"...
I really wish I read the book to know what the message is (maybe "Nietsche is dead"?)
I no longer login because I feel that while attacking a company's products is fair game (specifically Apple), having stories singling out their users as "selfish" and unkind is not "news for nerds stuff that matters". Am I an Apple fanboi? Let's just say I've used NIX for decades (yes I'm old) and I'm not talking OS X.
Actually there is an algorithm to compute the n-th digit of Pi without computing the rest.
The BBP formulas handle this. A quick Google for Bailey-Borwein-Plouffe should give you all the citations you ever need.
A working example of the BBP formula can be found in Javascript on this webpage. http://www.csc.liv.ac.uk/~acollins/pi
Warning: it WILL hang some web browsers as the author does not use web worker API.
How can we be sure all those digits are correct?
Use it to draw a circle. If the circle ends up looking more square than round then you know they've made a mistake. Seriously, do I have to do everything around here?
Summation 2
If you want to prove that all the digits are correct, you only have to check a few things:
1. There is a sound mathematical proof that the algorithm used in fact does generate the digits of pi, and
2. The algorithm was coded correctly. This should be even easier to check, though likely more tedious.
Now, what it's good for is a little harder. There is no physical application for such a highly accurate value of pi (39 digits should be sufficient to calculate the circumference of the known universe given its radius to within the diameter of a hydrogen atom). However, large numbers of digits of pi are useful as arguments in number theory, statistics, and information theory. For instance, there is no real proof that pi is a normal number, but as more digits of pi are found and the statistical properties of the digits are analyzed and shown to be consistent with the definition of normal numbers, that makes the conjecture that pi is actually normal a little closer to being true (see experimental mathematics).
Qu'on me donne six lignes écrites de la main du plus honnête homme, j'y trouverai de quoi le faire pendre.
Knowing that the algorithm is correct and the implementation was codec correctly doesn't help you when you have faulty RAM that flips a bit.
Okay, so what's the last digit of Pi?
Forget magic. Any technology distinguishable from divine power is insufficiently advanced.
They just took the number 3.14159 and added a load of random digits to the end - let's face it, nobody's going to check!
Reminds me of the MAX light rail station in the zoo tunnel in Portland, Oregon. Apparently there is the first 100 (1000?) digits of pi chiseled into one of the walls. A writer noticed that the first digits were correct, but quickly went astray. But later in the sequence, there was a recognizable early string of digits. The writer sleuthed that the sculptor had used the Book of Pi, which has the numbers in blocks of ten digits in five (or so) columns. In the book, you read the first row and then the next row.* The sculptor had read the first column, then the next column...
* or the other way around
Their they're doing there hair.
Yes, we do. Mathematical algorithms, i.e., equations on paper.
Absolutely not. The algorithms have to run on practical, exists-on-the-Earth-today computers. Try to multiply two, million-digit numbers together on your laptop and you'll see what I mean. These achievements are all about computational optimizations. RTFA -- especially the sections entitled "Arithmetic Algorithms" and "Maximizing Scalability." Even the algorithm used for multiplication changes (dynamically!) during the program's execution, based on the size of the operands.
Not even close. The computations are so long, and so intense, that errors caused by hardware imperfections can be expected, so error detection and correction algorithms have to be added. If "I left my pi calculating program running longer than the last guy" it would not produce the correct result -- even if the data structures and algorithms it used were up to the task.
In a word, yes. Could you do it? It's a very, very difficult technical feat, one that required hardware powers and software abilities far beyond those of mortal men. Besides, you're worried about newsworthiness when the two previous /. articles are on wall-climbing robots and the popularity of video game arcades in New York?
This isn't about needing pi to 5 trillion digits. This is about learning how to do large computations faster. Like, improving the state of the art.
The moment we know, the stars will start to fade out.
Actually the last digit of PI is 1 in binary.
As 0.1b is the same as 0.10b