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Pi Calculated To Record 2.5 Trillion Digits
Joshua writes "Researchers from Japan have calculated Pi to over 2.5 trillion decimals using the T2K Open Supercomputer (which is currently ranked 47th in the world according to a June, 2009 report from Top500.org). This new number more than doubles the previous record of about 1.2 trillion decimals set in 2002 by another Japanese research team. Unfortunately, there still seems to be no pattern."
Otherwise how would you calculate it? The "pattern" is it matches the stream of digits produced by a simple algorithm!
I fail to see how not understanding the word "seems" is insightful.
To travel from one point to another, an object must pass through all the points in between. There are an infinite number of points "in between," thus to move at all, an object must travel through an infinite number of points in a finite time. Clearly this definition of reality is flawed: stop using it.
When you're afraid to download music illegally in your own home, then the terrorists have won!
Knowing (thinking) that something doesn't repeat and PROVING that it doesn't repeat are two ENTIRELY different things. I am guessing your maths/science education either stopped very early or you didn't do too well in either.
I think it's funny that you are insulting someone's math education immediately after you imply that no proof exists showing pi not to repeat.
So you are criticising my preparation for the afterlife? Other people memorise wodges of religious texts, I choose to memorise digits of pi ...
-- open source? sounds like the real book --
Not necessarily. We can't really know about anything smaller than the Planck length, so in practical terms your paradox probably fails. The universe may be discrete on those scales.
They make a machine to take every job. Before I know it they'll have a machine loafing at the corner bar, smoking cigarettes and downing Jim Beam and Coke like it was water.
I see you've met Bender.
The article isn't really that informative. It takes things too literally, using the known size of the universe to determine the largest possible physical circle and the smallest possible length (planck length) to determine the maximum precision and he comes up with 50 digits. But it wouldn't be too hard to come up with an application that uses more than 50 digits of pi. A new encryption algorithm could use sequences in pi, but this has nothing to do with physical circles. Math is abstraction, and there are fields in math that are so abstract that you can't even correlate them with a physical measure. It's very silly to say that knowing pi to more that 50 digits is useless.
LS
There is a fine line between being a cultivated citizen and being someone else's crop. - A. J. Patrick Liszkie
It's a great way to test the performance of these supercomputers, to ensure that their calculations are correct. The calculation of pi to additional decimal places beyond what was previously known is never done with just a single method--otherwise, it is impossible to verify the additional digits. It is always done with two different algorithms to ensure that the result is valid. There are many rapidly converging algorithms (e.g., variations on AM-GM methods can be quadratically convergent or better; BBP-type digit extraction methods; and of course, classic Ramanujan series-type methods). However, computing pi to so many decimal places has much less to do with the chosen algorithm than it has to do with the memory- and computing time-efficient implementations of such algorithms in massively parallel architectures. Thus these calculations serve as very good tests for the robustness of supercomputers. The result is also verifiable to previously known digits, and even beyond the previous record, it is possible to perform statistical analyses to determine whether there are any significant deviations in the distribution of digit frequencies.
So, in summary, it is hardly a useless computation. Not that you're going to get an explanation like this from your usual news sources, which generally do not write for technical audiences.
Also note that distributed computing resources such as Folding@home, or even the Great Internet Mersenne Prime Search don't bother with calculating pi, as the purpose of these projects is to make new discovers in their respective fields of interest.