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Gigapixel Tapestries & Gigadecimal Pi
RobotWisdom writes "The new New Yorker magazine has posted two long non-technical articles about the Chudnovsky brothers and their homebrew supercomputers. One is a 1992 article about how they calculated pi to over two billion decimal places using a $70,000 cluster with 16 nodes. The other is a brandnew piece about how they spent months creating a seamless multi-gigabyte image of a fifteenth century tapestry for New York's Metropolitan Museum of Art.
Tapestries are essentially pixel-art on a non-rigid (cloth) matrix, so the manual labor of photographing it inch by inch had introduced many tiny deformations in the images, which they had to mathematically iron out. Old lo-res pix of the tapestries are on the Met's site, pix of the brothers are in the world brain."
If you're in New York, you should definitely check out the Cloisters, where the Unicorn Tapestries are held. It's right at the Northern Tip of Manhattan. A number of my friends have gone to the Met and not seen it, thinking that it'd be there. The Cloisters is probably the most stunning collection of medieval art in America in a very beautiful setting, so you should definitely check it out!
It's a fascinating structure, with excellent pieces for close inspection. I encourage anyone within a couple hours drive of Manhattan to take the trip to see these in person. It's at the north end of Manhattan at Fort Tryon Park (there's also one high-resolution picture in my gallery from the park).
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How about reconstruction and preservation? These tapestries are in terrible condition, compared to when they were completed in the 1400s. Any work that is done on them is done with magnifying glass, tweezers and a well-trained hand. Any reference works should be as clear and detailed as possible. They don't want it to erode any more than it already has, and they had no such detailed records of it in previous ages and conditions.
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Read it again. That is a link to pictures of the brothers.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
RTFA.
Since the tapestry was "released" from its frame for the first time in 500 years, it started to slowly contract (sort of like a rubber band that has been released). Additionally, the photographers was in contact with the fabric when taking the pictures, which meant that they moved it ever so slightly.
What took these brothers several months to do was to undo these transformations of the individual fabrics through modelling them with a vector field. The actual stitching together took 24 hours.
I agree with you, I don't think that practical uses for the billionth digit of pi will be found in the near term. However exploring Pi is a good exercise for numbers theorists because it allows them to peer inside the irrational numbers and their properties. There is still a lot if uncharted territory in that area. One of the most sought after peculiaritis of an irrational number (Pi in particular) is to check if any kind of patterns can be discerned in the long list of decimal digits.
Carl Sagan, dreamed long ago (through one of his characters) to find a "circle" pattern inside Pi (i.e another series of Pi inside).
Who knows, perhaps something interesting will be found.
I've used a Flash-based system called Zoomify to display higher resolution mosaics (up to 50 megapixels, myself). It works well, but since it's all based on jpegs, the tile deconstruction process can introduce more compression artifacts and a little bit of softening. It's worth the space and super-simple to install and use, in my experience.
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Some people believe it holds insight into patterns. Thus if you could crack PI, you could crack the stockmarket, the bible, etc.
See the movie:
PI
There are also several interesting books on the topic including The History of PI, by Peter Beckmann.
The Life of Pi by Yann Martel, however, has nothing to do with the number.
See: http://slashdot.org/comments.pl?sid=144891&cid=121 34000
Hooptie
"Heavens, it appears that my weewee has been stricken with rigor mortis!" -- Stewie Griffin
Uh, pi is the limit of a convergent sequence. One can easily derive identities with which to calculate pi to any accuracy desired. A simple one is:
pi^2 / 6 = Sum_{n=1}^{oo} 1/(n^2)
It is straightforward to prove this identity. (Just take Fourier coefficients on the function f(x) = x on the interval -pi to pi).
If you're looking for an experiment with 2 billion significant digits of accuracy, you're never going to find one. That's physically impossible, for several hundred reasons.
After all, I am strangely colored.
No, pi's value never changes. But the ratio of the circumference of a circle to its diameter, which is approximately pi (and only exactly in a flat space-time) varies. Consider a circle drawn on the surface of a balloon. For a small circle, the local balloon surface is nearly flat, and the ratio of the circumference to the diameter is nearly pi. But for a big circle, the circumference is much less than pi * diameter, as the diameter has to be measured around the curvature of the balloon.
Thats not a circle, thats a disc that has been bent in some odd shape (somewhat like a bowl). That is a 3d object. a circle is 2d. Flat. No depth.
"Something's wrong with you...and I hope we never do meet again." - Deftones When Girls Telephone Boys
Putting the actual tapestry through a large drum-scanner would be the ideal solution, but I bet the museum was looking for a slightly gentler process. Seems like the photo-mosaic approach was a decent compromise.
It is a circle in the 2-D coordinate system over the surface of the balloon. Just as a circle in 3-D space would be a bowl if you looked at in 4 dimensions in the vicinity of any significant space time curvature. consider a black hole. the circumference of the event horizon is easy to compute. the radius approaches infinity.
There's no such thing as flat in the real world. Space-time is curved.