Slashdot Mirror
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).
[
...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.
I can see why one would like to calcutate Pi as far as possoble, .. but tapestries ?
Spending months on a multi-gigabyte picture of a tapestrie? Geez, and it's probably not even "correct" as they had to mathematicly correct some deformation or whatever errors.
Seriously, what's the point?
Are they doing this "just because we can", or is there some "higher goal"?
That's a lot of pie! Thanks, I'll be here all week.
One is a 1992 article about how they calculated pi to over two billion decimal places
;)
Hrmm.. They should've just rounded down?
How do you ascertain that your 2 billion decimal places of pi are correct? After about 50 significant decimal places doesn't the accuracy get too small to test against reality? There are formulas for calculating pi but it would then seem that your "accuracy" in calculating pi just depends on which formula you chose and how big your power bill was that month. Is the act of calculating pi still a modern yardstick of computer accuracy or is this just what you need to do to get a feature in the New Yorker?
Why do we need anything more than the low-res picture that they already have? Going super-high-res simply magnifies the imperfections. Art isn't meant to be enjoyed with your face pressed up against it.
/., EVER. Or a clever troll. Art wasn't meant to enjoy from 40 feet away either (well actually some art is, but not in this case). Just like with movies/photos/music, it's always better to have the highest quality original and you can always downgrade for mass copies. Imagine if something were to happen to the tapestry itself, without a very high quality scan, you'd be screwed.
This has got to be one of the most short sighted posting on
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.
These guys are pretty inefficient or they wrote a bunch of software from scratch.
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
The unefulness of calculating pi to this number of digits is nill. After about thirty digits, you have the orbit of the earth calculated, with an accuracy equal to the size of an atom. Computing the circumference of a circle with diameter equal to size of known universe takes about fifty digits.
:)
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
See my journal for slashdot ID's by year. Mine created in 2005. http://slashdot.org/journal/289875/slashdot-ids-by-year
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
Everybody seems to think the middle ages were some kind of throw-back. Because Roman civilization was gone, people think that Europe had sunk back nearly to the stone age. In particular, they think that because the art is not photo-realistic that it must be primitive.
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.)
Don't forget the Strugatsky brothers!
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
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??
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.
Frink: [drawing on a blackboard] Here is an ordinary square.... ... but suppose we extend the square beyond the two dimensions of our universe, along the hypothetical z-axis, there.
Wiggum: Whoa, whoa - slow down, egghead!
Frink:
Everyone: [gasps]
Frink: This forms a three-dimensional object known as a "cube," or a "Frinkahedron" in honor of its discoverer, n'hey, n'hey.
Laws do not persuade just because they threaten. --Seneca
Has any numerical analysis been done to its decimals to find any particularly mathematically or esthetically "interesting" sequences? Anyone know any links to websites for that? The "monkeys banging on a typewriter" thing. :-)
I mean, with an enormous amount of decimals calculated, you'd think there was some pretty cool sequences in there?
Beware: In C++, your friends can see your privates!
The first problem: They hired amateurs to photograph priceless artifacts. Though the description is short it does include some tip-offs, "skateboard wheels." Sounds like they hired some real flakes that couldn't control the environment they were photographing and they were using inexpensive equipment... I applaud the brothers for their work but it seems like a wasted effort because it could have been avoided if they had hired professionals to photograph the damn thing.
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.
News for Nerds. Stuff that Matters? Like hell.
That seems excessively irrational.
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...
Reason is the Path to God - Anon
With this kind of processing power, a project of mine which I've always wanted to bring to birth, Infinity Generators, might be a reality.
... are brought into birth!
Take, if you will, a simple 640x480 image, with 256 colours. (It could be any image size and any number of colours, but this is just a standard image format). With it's 640x480 dimensions, there are a total of 307,200 pixels. If each pixel can have one of 256 colours, thats a total of 307,200^256 = 6e+1404 possible permutations of that image.
Such a system as this could in theory calculate all these permutations in a reasonable timeframe.
WHY?! you might cry.
Here's why... if we calculated every possible permutation of that 640x480 image, we could have every picture of everything that ever existed. Most, granted, would be junk, but there would be a ton of interesting, and spooky images.
Taken a little further, we could apply these generations to textual applications.
For example, remember the classic Infinite Number of Monekys on an Infininte Number of Typewriters will eventually generate Shakespeare's plays.
We could bring this into reality. Since textual documents are usually much smaller than images, we could do it faster with an Infinity Generator.
Just imagine, not only the complete works of Shakespeare, but poems, plays, songs, books that have ever and never been written
Again, we could apply the generators to create MP3 files, Films, and anything...
From Infinity, comes Creativity...
Vote devolution! http://www.devolution.co.uk