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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."
Link?
:)
"This is Zombo Com, and welcome to you who have come to Zombo Com" - www.zombo.com
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!
Is this another April Fools article?
David told me that they were working with I.B.M. to design what may be the world's most powerful supercomputer. The machine, code-named C64, is being built for a United States government agency.
I mean, I loved my C64 too, but it's no supercomputer.
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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...was breaking the tapestry's copy protection. Starting in the 14th century, nobility decreed all tapestries contain a pattern of knotting designed to prevent any scanning or printing of tapestries. By the end of the 14th century, all scanner and printer manufacturers had added this anti-tapestry copying technology into their products.
One is a 1992 article about how they calculated pi to over two billion decimal places
;)
Hrmm.. They should've just rounded down?
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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David informed her that the brothers would need to obtain the complete set of raw data from the Leica camera. The next day, he went to the museum and collected, from Bridgers, two large blue Metropolitan Museum shopping bags stuffed with more than two hundred CDs, containing every number that the Leica had collected from the Unicorn tapestries. There were at least a hundred billion numbers in the shopping bags.
Bags...and...bags...of numbers!
And now for something completely different...a man with three buttocks.
"Here is a circle, with its diameter:"
.. paranoid crackpot leftover from the days of Amiga.
rather than stich a bunch of digital photos, they should have simply photographed it with a very large format camera, and had the resulting negative drum scanned at 8000dpi. These folks do it that way, and if you take a look, the resolution is amazing.
Douglas P. Price
I disagree with your analogy. Aerial mosaics have nothing to do with the work that the brothers had to accomplish.
For instance, in aerial photagraphy the landscape being photagraphed changes very little if it changes at all (most of the changes are not even perceptible at the resolution of the cameras). Therefore reconstructing the full image is pretty much trivial (finding the overlapping sections is straightforward).
In this case, and from TA, the images changed from frame to frame! because of several factors, temperature, humidity, light conditions etc. Also the paper cover that the photographers used also disturbed the fine threading in the images. So determining the overlapping sections between tiles could not be easyly automated, in fact from the article it seems that they were not even discernible with the naked eye.
I thing that the time spent in that project was actually productive, and that in the process a bunch of original algorithms were created (I hope they are published in some place).
The colours in tapestries are usually vegetable dyes and they fade very badly with exposure to light. If you go around a museum, the tapestries almost always look dingy and you need to use a lot of imagination to try to picture how they might have originally looked.
However the back of the tapestry has been kept in the dark and the colours there are still dazzling. So ... if you have a good picture of the front and the back and you can resample the back image to get it to line up with the front to within a knot size, you can use the back colour to "re-tint" the front image and get an excellent visualisation of how the tapestry might have appeared soon after it was woven (you need to take a bit of care with colour management too).
A friend of mine did this as part of his PhD thesis. I can't find any of his images online (I guess there would be copyright problems), I'll see if I can dig some low-res ones up.
Ah! Found it.
Pi's definition is mathematical, not physical. No one really knows the exact ratio between the circumference of a circle and its diameter, but it definitely varies depending on how curved space-time is in the vicinity of the circle, and on the size of the circle.
...). (Or the limit of that series as its length tends to infinity, for the mathematical formalists among you.) Your accuracy in computing pi depends on how many terms of the series you can calculate (actually, there are alternative formulations that converge much more rapidly, but are less easy to write down in ASCII.)
Pi is 4 x (1 - 1/3 + 1/5 - 1/7 + 1/9 + 1/11
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.
How do we *know* that pi is exactly the result of the formulas that these people use to calculate pi?
I only ask because I assume that pi (as defined by the number of times the diameter of a circle can be wrapped around its circumference) might differ at some arbitary point into the calculation?
How do we know that these calulations actually produce a number that matches reality?
Pete
Who cares whether they calculated Pi to n-billion digits? Who cares if they photographed the tapestries to the precision of an atom??
The important question that needs to be answered is: how did they end up with wives who (a) work; (b) don't force these two nerds to work; and (c) let them buy all the toys they need? Where can I get a wife like this??
Pfft. There's another mile (and change) of Manhattan north of the cloisters.
Either that, or my apartment is actually in Yonkers and I should be paying a lot less rent.
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