Gigapixel Tapestries & Gigadecimal Pi 215
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."
I met the curator (Score:1, Interesting)
Still, I love the way the author describes him as 'thoughtful'.
Pi Accuracy (Score:2, Interesting)
Re:Gigabyte, gigapixel artwork? (Score:5, Interesting)
several months?? (Score:2, Interesting)
This is basically a classic close range photogrammetry problem. In fact even easier than that, a tapestry is essentially a "flat" scene (think throwing a bunch of kitchen utensils in a pile on the floor and constructing a scene out of it which is more typical of this type of problem. Or photographing the inside of a chemical plant and reconstructing accurate blueprints).
At work we can process 50GB worth of aerial mosaics per person per day using a specialization of a custom close range photogrammetry solution.
These guys have a bundle adjustment which could be used to adequately solve the necessary equations for and instructions for recontructing the tapestry: http://www.ics.forth.gr/~lourakis/sba [forth.gr]
Pi (Score:2, Interesting)
The only interesting part of all this is the way that the algorithms (invented by Al Gore, hence the name) to calculate have become lossless in binary.
Part of the issue I had when I was in grade school and crate my own pi generator using the 4 * (1 - 1/3 + 1/5 - 1/7....) algorithm, was the rounding error that creeped in. My TRS-80 model one would get the 3.141 part correctly, but depending on the implementation method, would round the rest in strange ways.
Now, you can get an absolutely correct n binary digits of pi, and pick up where you left off. I've read over these algorithm proofs, and only get a headache
Film (Score:5, Interesting)
The middle ages weren't that simple (Score:2, Interesting)
This tapestry embodies a culture that we no longer understand. In fact, the makers of the tapestry may not have completely understood the references they were making. (Just as we don't. Think of all the figures of speech that you use and can't completely explain.) Understanding the meaning of the tapestry will take a much bigger supercomputer. (Eventually the answer will be 42.)
Re:Why? (Score:5, Interesting)
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.
Re:Why? (Score:5, Interesting)
Billion Places Of Pi (Score:3, Interesting)
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
Re:Pi (Score:3, Interesting)
Not sure if this is meant to be a joke or not but...
Algorithm, as it is used in mathematics means a systematic procedure to solve a problem. The word is derived from the name of the Persian mathematician, al-Khowarazmi (See algebra). The first use of the word I am aware of was by G W Liebniz in the late 1600.
Source: http://www.pballew.net/arithme1.html [pballew.net]
Other Source: http://www.disc-conference.org/disc2000/mirror/kh
With pi calculated with so many decimals... (Score:3, Interesting)
I mean, with an enormous amount of decimals calculated, you'd think there was some pretty cool sequences in there?
Re:Why? (Score:1, Interesting)
I think this is one the most interesting, and troubling, of the issues raised in this article. Once you have this much information about a painting an exact duplicate could be created. Think of a CNC milling machine but with paint.
ummm I'll decorate my apartment with the DaVinci and ohhh that dark Rembrandt would go great in my den.
Re:Billion Places Of Pi (Score:1, Interesting)
Pi is the ratio of the circumference of a circle to its diameter. A circle is not a physical object. It exists only in the mind. Therefore, it is impossible to physically "measure" pi; just like it is impossible to find the weight of linux. Linux is software, it doesn't have a weight. Likewise, Pi is not a physical quantity, but a mathematical one. So it doesn't have a physical measurement.
However, you might be interested in this method for finding the digits of Pi that uses a physical experiment along with probability theory:
http://mathworld.wolfram.com/BuffonsNeedleProblem
Of course the experiment suffers from the same fundamental problem that trying to directly measure a drawn circle suffers from. That is that the physical situation is not the same as the mathematical one. Physical lines will never be perfectly parallel and the needle will not be a perfect needle. You need a way to correct for the fact that your lines aren't parallel.
I would say that the best physical method for measuring Pi is with a computer. That way you can ensure that the differences between the physical situation and the mathematical one are corrected. That is the beauty of digitizing things. You can guarantee error free results.
Upon further reading... (Score:3, Interesting)
I have watched the movie PI - and I know that in part it was based on these two. I think about the computer as depicted in that movie. I think about other people I have known and about myself. I have known people who have had "vast collections" of parts and computers, books and papers - scattered and ordered, on shelves, on the floor. I myself to an extent am that way (but I try to confine it to my workshop and my office - bits creep out now and then and I have to shoo them back). Some of those I have known, though - come closer to the Chudnovsky brothers than I do. Though they have, supposedly (given the lack of pictures), realized tools and such - I know of people who theorize tools, come up with gradiose plans, all the way up to almost the point of execution (bits of paper, writing, etc) - then do nothing with it, claiming the problem solved and moving on to the next. Such minds stagger me, because it indicates a certain level of laziness - but more so, because all the theory in the world will never prove whether the theory is realizable as fact. Many such theories that sounded like they would work fine actually broke down as they were realized in the real world - but later became workable as the real-world constructs were fiddled with, or as the real world advanced to allow for them. But how would one ever know without trying? It is frustrating to see this - to see the unrealized potential - to see the possibility of unrealized possible profit to be had from these ideas...
True, that some of this is the need for thinkers and doers - after all, even Tesla's ideas needed Westinghouse to profit from them (and this is frustrating further still - why couldn't Tesla or the multitude of others then and now cash in on their hard work themselves - why must they all die virtually broke and alone?). It doesn't have to be this way - but something about how these individuals (and group minds?) work seem to preclude this as the "way it must be"...or something.
Another note - the Cloisters wanted an ultra-high resolution image of the tapestry. I agree that for preservation reasons, it has to be exact. So I don't fault the Brothers for finding the small faults which would cause them much pain to reassemble the mosaic, and have to figure out a way around this - but this is an example of something else I have noticed in this class of brilliance - making mountains out of molehills. It seems that for any given task (no matter how simple it could be), these people insist on finding the most complex solutions possible to solve them. In the case of this tapestry - maybe that is the best thing (for future generations?). But even in everyday situations, it seems that simple solutions won't work for them - the solutions must be extremely complex, or it won't work. They also get terribly upset when you prove or show to them that a simple solution works equally as well and gets the job done faster (an example: a tight nut on a bolt needs to be loosened - these individuals will tend to go about needing complex tools or methods, theorizing forever on whiteboards on this or that angles and torque and whatnot, hours later with nothing accomplished - damnit all, just squirt a bit of wd-40 on it, stick a damn socket and wrench on the thing, add a pipe extension, and give it a bit of leverage and bust the bastard free).
I will give the brothers this: they at least will build their own tools and realize things - though I will always find it madenning that the only "output" we ever seem to hear about these people, despite their genious, seems to only come from the pages of the New Yorker magazine. It seems like they are almost fiction...