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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!
Link to the multigigabyte image was not linked from the article on the front page of slashdot.org
Prepare for a cataclysmic event.
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?
I met the chap in charge of tapestries at the Met. He was very nice, but I just couldn't quite understand his passion for the medium. Some of them were rather nice, but I'd much rather have been in the Met's excellent old-master or C20 galleries.
Still, I love the way the author describes him as 'thoughtful'.
They should have just used photoshop! (haha)
The zooming seems to work wrong. For example, I tried to get a close look at some faces, and at the maximum magnification half the faces get cut on the bottom. Even when clicking on the bottom of the image it still scrolls it up, which is annoying.
Wasn't it actally Al "Teh Intarweb" Gore who invented the Daylight Saving?
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.
But I think unicorns are really kickass!
"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
Wachowski brothers - The Matrix and other films
Chudnovsky brothers - Supercomputers
I have no brother. Now I know why I'm an utter failure. Oh well, back to Slashdot.
Somebody enlighten me. Is there any use in knowing Pi to 2 billion decimal places (or even just a few hundred!) Do we hope to find a hidden message, or make the world's most accurate circle, or is it just because we can calculate it? And how do you check for errors?
----------------------------------- My Other Sig Is Hilarious -----------------------------------
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 understand the reason for fixing it to have a record of what dot went where for restoration into the future, but I wonder if they isolated out each thread's color so that people can experiment by replacing the "red" threads with a given new "red" and stuff like that without having to mess with the original. You more or less have to use the real thing if their image doesn't allow this, which would be a total waste in terms of usefulness to art historians.
stuff |
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.)
I don't get it. What do the Mets have to do with tapestries? Shouldn't they be more interested in keeping Pedro Martinez and Mike Piazza healthy?
Don't take that tone with me, my good man. Now buttle off and tell Baron Brunwald that Lord Clarence MacDonald and his lovely assistant are here to view the tapestries.
You should take a course on English sometime.
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??
You call Google the world brain? I hear they are renaming it skynet.
The Internet is full. Go Away!!!
(Pause...)
More or less.
Seriously, the actual value is not the issue. Pi is irrational and the challenge is to encode a very large string of digits without using all previous digits to compute the next few digits.
If they'd used 4.7GB plain ol' single-layer DVDs, it would have been 200/6.714... = just under 30 full DVDs. Which would have fit on a single spool. My "Babylon 5" collection takes up more space. And they chose to, what, put two hundred CDs in jewel cases to take them across the street? What a buncha maroons.
--grendel drago
Laws do not persuade just because they threaten. --Seneca
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
Considering that this work was done in '92 I suspect that they were inspired by the character in Twin Peaks that spent all his time looking for patterns in Pi. There are people that really do this, even today.
I am becoming gerund, destroyer of verbs.
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.
I once read that it is possible to calculate any decimal (without intervening decimals) using some formula. However, this required the calculation to be performed using hexadecimal numbers. Anyone with further info on this?
It seems we arrived at the Base10 system pretty arbitrarily. Isn't it just because we have ten fingers? If calculated Pi is ever going to reveal a pattern I would imagine it would be more likely to happen in a "natural" system like Base2, or Base12. All your base are belong to us, after all.
...or dont do it at all!!!
/. baby... remember that ;)
Your r on
I know the last digit of pi. It's 'd'.
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
I mean... is there any particular use to knowing two billion decimals of that particular number? Does this make an even rounder circle, or is it just the computerized version of the ancient "my cod piece is bigger than yours" "yeah, but I have more IN mine" argument?
Of course, they got a bargain if you count it per digit, but otherwise I'd say they are pretty messed up. Isnt there some complicated atomic yadda yadda caculations they could spend that power on instead of impressing people with the length of their... Pi...
is this thing yellow?
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.
Why is it that despite the Chudnovsky Brothers claims, which no one doubts, there doesn't seem to be any pictures of their apartment supercomputer? Does it still exist? Is it still running? Is it still computing PI? One would think that a machine that allowed them to compute so many digits of PI would be "immortalized" with at least one image, right? Can anyone point me to pictures?
Reason is the Path to God - Anon
That seems excessively irrational.
In the article, they say that they solved the equations by hand, and programmed it from scratch. They were given photographs of a "flat" scene at such a close range that it caused perspective issues with the height of the threads in the tapestry...
a tapestry that was suspended in purified water, free floating in 3 dimensions...
with a camera that was held at varying heights above the tapestry, since they were suspended by scaffolding over the work of art...
art that was bumped by the photographers as they were moving the photograph backing under the tapestry in the water, which created eddys that moved the fabric, causing it to stretch in some photos and bunch up in other photos...
not to mention that in some frames, an outside doorway was left open, which changed the lighting contrasts...
oh, and they had over 200 CDs worth, which I conservatively calculate at 170GBs of images that needed stitching at full scale.
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
Because poly grads can not get jobs after graduating with a degree in CS/EE/CompE/etc. due to offshoring and H1-B and L-1, Poly is facing a massive drop in enrollment, resulting in Polytech facing budgetary problems. Polytech has tried to merge with NYU but that fell through. I mean you should see that so many recent grads are being forced to take jobs fields such as construction, police officer and priest since they can not find jobs in their respective majors. Who the hell is going to go into debt for $80,000+ when they graduate they will barely be making $30,000 in fields they DID NOT need a engineering degree to begin with!!!
Of course, the Poly trustees have decided to answer to their corporate masters and vastly increase F-1 visa enrollment because companies want cheap h1-b workers. Too bad the 2nd oldest engineering school in the country is going to be shutting its doors.
-- A disgusted Polytechnic Alumni
PS> About half of the students in the NSA scholarship program at Poly are VERY recently naturalized citizens because Professor Memon obviously only wants his fellow countrymen in the program. The NSA should not be allowing people who they can not do thorough background security checks into sensitive positions. That does not make any sense. In applying for a TS/SCI position, they really go back and check who you are, your friends, your teachers, your parents, etc. Did the US govt. go to India and check these people out!?!?!
The real problem with using 4*(1 - 1/3 + 1/5 - 1/7...) to approximate Pi, as any Calc II student knows, is not exactly rounding error but rather that it takes a freakin' long time to converge! The error when using n terms in this series is approximately 1/(2*n+1), which means to get 14 digits correct you need 5*10^13 terms. Rounding error comes into play only because you start to accumulate significant error when doing that many additions; almost every floating-point computation has rounding error though.
All is Number -Pythagoras.
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
Um...1 gigapixel = 31,623 x 31,623 pixels, low print quality of 300dpi, that's only about 8.8 x 8.8. That might give you a wall size display. Photo-realistic ranges from 1200-4800 dpi. At those resolutions a photo quality print would range from 2.2 x 2.2 feet to as small as as 6.5 x 6.5 inches.
Does anyone remember what the comparable dpi for, say, 35mm photos? Say
I want to blow it up to the size of the original tapestry?
From the gigapixel FAQ:
"The facial expressions of an half a stadium of fans can be captured at passport resolution in a single instant..."
http://www.gigapxl.org/faqs.htm
Does this ring of privacy concerns for anyone else? What with passport facial recognition and all... Seems to me it could be an easy way to identify who was at the big game/peaceful protest/mall on sunday...
Yep, you got the shaft here =). 2003 the jobs started coming back. And we aren't closing.
There sure was too much breathless fawning in that article. These men are extremely sharp. Let there be no doubt. While I cannot rule it impossible, I have never heard of someone who needs such air filters. I have heard of hypochondriacs. It's praise praise praise. It might be perfect for a New Yorker reader who does not know much, but wants to feel edified.
Poly is having massive financial problems. Notice the layoffs of the older professors for the cheap new hires/grad students. Poly might have a year left. Obviously you do not know about the dorm overruns and how the corrupt administrators at Poly blew away the Othmer endowment by sweet heart deals with contractor associates. There is no more money left.
BTW, schools like Columbia Mund School of Engineering, the CS dept of MIT, CMU, et. al. are reporting massive declines in enrollment as well so there soon will not be any more CS studies in this country as school after school close their departments for lack of enrollment. Read Norman Matloff, PhD. before you open your mouth.
have got more or less the same idea....
ok, you have this giantcomputer to generate this infinity(ies) of pictures (or text, book, music):
1..2..3...done.
but now for this stack of data to become "something"/"art", you have to see it!
talk about an infinity of time
However, with that said, I know individuals who do go to those same extremes with common, everyday simple problems, exactly as I described. A simple problem, and a complex solution is what, in their minds, is needed. They will then proceed to argue with you, pontificate on end the why's and how's, produce immense diagrams, force vector calculations, etc - needlessly spending hours upon hours on end on a problem. In many cases, these same individuals will come up with a technically correct solution, then say "Eh, its done!" - and never attempt to try it out to see if it would work. In their mind, it works, that's it! But without trying, how do they know? In the real world, such a solution may fail.
Furthermore, for most problems, it is a solution much greater and grander than what is actually needed. For the hypothetical nut/bolt problem - the solution is simple, tried and true, in use for many, many years, with little change. I agree, that for some problems (like say, removing a very rusty stud on an engine block that is 30 years old), you might want to give some consideration to the possibility that if you torque too hard, the stud will break off. But the sane person says "Well, that is a possibility, and if that happens, then I just need to drill it out and re-tap it - thems the breaks!", and just go for it. Otherwise, you will sit there all day and accomplish nothing.
Which is what many of these individuals (the Brothers are an exception it seems) seem to do...
Reason is the Path to God - Anon
Totally - I can see the secrecy needed for their projects, new and old - but I am not asking for a source code (or even schematic) dump here - just some pictures of their old machine in its historical (apartment) setting. Likely, their new machine(s) incorporates ideas/algorithms/learning from their old - and someone is likely to make some money off of it, so the need to protect this sensitive information. But a picture of the machine isn't going to tell anyone anything that can't be gleaned from the text of the New Yorker article, but they would help to put things in historical perspective for future generations. Besides all which, if there were really great secrets to protect, why would they show everything to the reporter/interviewer in the first place? They seem to be very open and generous individuals, and I agree that they would likely be the kind of people to invite you in, and discuss their work and yours - likely for hours upon hours on end, with tangents and everything (I would be just the sort of person to be "sucked in" to something like that - to the chagrin of my wife, unfortunately - but she understands, all the same). But they seem to have no interest in preserving their role in history in any concrete way. They are (seemingly) haphazard with their research and documentation - too the very point of dangerous fire hazard at best (they seem to have a "pack-rat" mentality to an extreme, at least when it comes to their research and notes - but they lack the proper skills to organise the same information). I can only hope that when it comes time, and they pass on, that their work is somehow preserved, and isn't seen by their heirs as a jumble of disorganized mess, best left to the garbage man to dispose of...
Reason is the Path to God - Anon