Slashdot Mirror
Mandelbrot Set Originally Found In 13th Century (Early April's Fool)
lines writes "I was amazed to find out that the Mandelbrot Set was discovered by a 13th century monk -- way, way before the advent of non-human computers. Apparently, a mathematician spied a mini-mandelbrot masquerading as the Star of Bethlehem in an illuminated manuscript's depiction of the Nativity scene. It turns out that this particular monk, Udo of Aachen, was attempting to mathematically describe a soul's path to Heaven. (For those unfamiliar with it, here's a quick introduction to the Mandelbrot Set.)"
Update 30 mins later by J : Yes, this is an
old April Fool's joke
- and a cleverly done one, too.
about as well done as most of the "All your base are belong to us" Photoshop jobs, and just about as easy to spot. Hemos really
You mean those aren't real? Somebody didn't really tattoo 'all your base are belong to us' onto his ass and get chased by cops through a corn field?
- A.P.
--
* CmdrTaco is an idiot.
"Remember when the U.S. had a drug problem, and then we declared a War On Drugs, and now you can't buy drugs anymore?"
The Europeans at this time (13th century) were still counting with Roman numbers and thus were merely capable to multiply.
There is a very famous letter from a merchant to a mathematician in Germany were he asks where he should send his son for studying so that he can learn proper mathematics. The reply from the mathematician was that if he were just to learn how to add and substract, it would be sufficient to stay in Germany. But if he wanted to learn how to multiply it would be necessary to go to Florence (in Italy, has a very old university).
The problem for mathematics in Europe were the Roman numbers. They didn't allow a purely syntactical calculation like the arabian numbers we use now (try to add II and CIIX by writing them in a table like we learn now in school!).
Arabian numbers were first introduced in Europe with Adam Ries in the 16th century (I think).
Sebastian
2. The bit about "disputing the bible's claim that pi = 3" really ruins the plausibility. No one except atheists trying to disprove the bible has ever claimed that the bible says pi = 3.
Actually, there's a bit in the OT about Solomon's Temple where pillars are supposed to be one cubit across, three cubits around, and circular. Jewish scholars debated this in the Middle Ages; generally they agreed that the measures recorded were merely approximate, but one school argued that the presence of God actually changed the geometry of parts of the Temple to a non-Euclidian form where pi really did equal three.
Steven E. Ehrbar
(and I skimmed over the article) but does this seem fake to anyone else? :) The only reason I'd think it wasn't fake is simply because it's really not THAT funny of a hoax.. just kind of silly really.
If it's not a fake, then, well, wow. IIRC, the mandelbrot set is a plot on the real/imaginary axes of the "rate" at which the function approaches infinity for each coordinate.. it seems odd that a monk would use the same technique for describing the fractal. Especially since this technique is just begging for a high amount of computation. Unless I'm missing something, aren't there many possible ways to describe the mandelbrot set other than using this technique? I'd imagine a monk with limited computational resources would decide on a description of the fractal that would be more concise and elegant and less computationally intense than plotting it!
--
Probably not the algorists, as they tend to punch the wrong dots.
--
--
"Outlook not so good." That magic 8-ball knows everything! I'll ask about Exchange Server next.
Would that be the algorists or the abacists?
---
I've just checked their news page and the team seem to be alive and well and signing copies of the program at SourceForge.
--- Hot Shot City is particularly good.
Uh, out of all the silliness in the article, that's the one you have to catch the author on? Youch...
I've been studying art history and composition (as a way of figuring out how to make my web pages suck less). I think you can date the original pretty accurately this way: after the discovery of perspective, but before the devleopment of advanced methods of composition. Probably mid 15th c to early 16th c.
Medeival artists followed the classical Roman practice of strict symmetry. Ancient mosaics look like stiffly posed group photos -- the most important figure is placed in the center and larger, flanked by other figures carefully balanced on each size by number, size and importance. This scheme was so engrained that even the greatest artists always followed it slavishly. Leonardo's Last Supper (ca 1495) used the science of perspective, but followed the careful convention of balancing every element on one side with a nearly identical element on another. At the end of the Rennaisance artists began to try alleviate the monotony of exact symmetry by replacing it with symmetrical balance -- several persons on one side might be balanced by a horse on the other.
By one hundred years later, symmetry was entirely out of the window as artists used perspective, value, and advanced composition techniques subtly draw the eye to the main subject obliquely. Compare a rennaisance painting by Michelangelo or Titian to a baroque painting by Carvaggio.
This illustration is too symmetrical to be late 16th c (although it might have been done in an antique style), but must be at least 15th c due to the use of perspective (although subtle) and the attempt to avoid exact duplication while keeping strict symmetry.
Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
Myself, I was noticing the background was very da Vinci-esque, and was thinking late 15th, but willing to grant maybe mid-15th, because the style of illustrating the rocks in the foreground was not sufficiently naturalistic. I was being conservative: 1449 minus 150 equals 1299, or the last moments of the 13th century.
The means of arranging the subjects was typical of the fifteenth c. and earlier; the landscape and certain foreground elements were probably only technically possible with at least 15th c drawing technique. I expect the schematic way the rock was rendered was due to it coming from an illuminated majiscule and aside from the unwelcome distraction of a carefullly rendered rocky surface in the middle of a letter, it had to be rendered in colored ink instead of paint (it might even be an engraving -- I don't remember). The style would have been highly implausible in the full swing of the baroque era, but allowing that the context demanded a somewhat old fashioned design I'd be willing to grant early baroque. It might also be much, much later and much, much more self consciously old timey(e.g. like Wm Morris). I don't know much about medieval art though.
Please! They had a different, but not wholly unfathomable aesthetic. They found symmetry beautiful, and it is not merely in their paintings this appears. We find it, for instance, in their dance choreographies: what is done to the left is then done to the right. It was an expression of order and "mesura" (measure, balance, harmony).
That's a good point, but the painters of the time definitely were really laboring to find ways to break out of symmetry. They experimented with numbers, sizes and values so that compositions maintained an overall visual symmetry while breaking topical symmetry.
I don't dispute that they found symmetry appealing (nor that they had gorgeous results), but the new techniques of perspective certainly demanded a more naturalistic way of integrating the subject with the background. Works of this era often have the characters almost floating in a plane in front of a carefully rendered perspective landscape. Tremendous compositional energy swirled in the topical plane while the background served as decoration. The baroque masters really found a way to both liberate that energy into three dimensions and integrate perspective into composition -- it was unambiguously and advance in technique if not necessarily aesthetics. I think their closeness to the problem of liberating that energy accounts for the strong diagonal arcs that move through their paintings.
So to criticise the composition of an early Ren painting by the standards of a Baroque composition, is like criticising a work of prose fiction for not rhyming and having iambic pentameter. That's not what it's supposed to do, not how it's supposed to work, never what it was intended for. It misses the point.
Well, I'm criticizing in the sense of analyzing, not disparaging. I find the works I cited very pleasing and indeed ingenious. They were less technically sophisticated, but nonetheless innovative.
Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
In high school (over 10 years ago - eeek!) me and a friend would set up an Apple IIe hooked to a color monitor in our programming class (we took it for the points, and as a break - nothing more) with a Mandelbrot program written in BASIC (!), utilizing the funky 16 color mode (oooh!) that you could hack if you had an 80 column card. At any rate, we would let it run until our class, in the 5th period or so, where it would complete by the end of class, and save to floppy. We would then work out where we wanted to "magnify", and start the run the next day. Got some pretty neat pictures... for an Apple IIe...
Worldcom - Generation Duh!
Reason is the Path to God - Anon
Nah, the other poster was closer - it was like 89 or 90 when we did this (you see, our programming class was stuck with Apple IIe's, while the Computer class, where one learned how to wordprocess, had 286's, and the Mac lab was, well a Mac lab - best machine was a Mac II color - don't know any other specs on it). Anyhow, you figure 1989 - my home computer was a Tandy CoCo 3 with 512K, 286's were the mid-range machine, and the 386 was top-of-the-line. But a CoCo was cheaper than either, and Apple IIe's were still expensive (but not the ones we had, which broke down more often than not, needing new drives, etc - they were ancient - but a lot of kids learned coding on them)...
Worldcom - Generation Duh!
Reason is the Path to God - Anon
Fractint is a classic. Runs on DOS (yuck), Linux (supposedly, segfaults on my 2.4 kernel), Win 9x and, I think NT.
Best Slashdot Co
Myself, I was noticing the background was very da Vinci-esque, and was thinking late 15th, but willing to grant maybe mid-15th, because the style of illustrating the rocks in the foreground was not sufficiently naturalistic. I was being conservative: 1449 minus 150 equals 1299, or the last moments of the 13th century.
YKYBITSCATLW! I spend a-lot-but-not-enough time looking at early 13th century pictoral evidence of/for women's clothing. If all -- if any 13th century illuminations were as naturalistic and clear as this one, my life would be much, much easier. I confess my first thought was "13th century? Bah! You can tell what she's wearing! I wish!"
Now, as a med/ren-geek myself, I must take issue with your tone in:
Please! They had a different, but not wholly unfathomable aesthetic. They found symmetry beautiful, and it is not merely in their paintings this appears. We find it, for instance, in their dance choreographies: what is done to the left is then done to the right. It was an expression of order and "mesura" (measure, balance, harmony).
Furthermore, the positioning of people (and, interestingly, buildings) in Italian (at least) Ren painting had all sorts of complex symbolism which was evident to contemporary viewers, but not to the naive modern viewer. When we moderns look at a painting, we expect to look into a window; we expect to look at the figures of a painting. But the contemporaries of da Vinci read paintings. They expected them not merely to be beautiful, but to have meaning, to, perhaps, tell a story, or express and opinion. When you think about it, they were much more semiotically aware.
So to criticise the composition of an early Ren painting by the standards of a Baroque composition, is like criticising a work of prose fiction for not rhyming and having iambic pentameter. That's not what it's supposed to do, not how it's supposed to work, never what it was intended for. It misses the point.
-*- Any technology indistinguishable from magic is insufficiently advanced -*-
... how an allegedly medieval monk knew how to paint a picture with renaissance perspective.
Mandlebrot, schmandlebrot. According to the accompanying picture, he figured out the vanishing point 150 years before anyone else!
-*- Any technology indistinguishable from magic is insufficiently advanced -*-
Besides, the mandelbrot set relies on a pretty recent advancement in mathematics: the use of complex numbers as (x,y)-coordinates on a plane.
Complex numbers have been studied for centries, but it was not until 1797 that the Norwegian Casper Wessel, in a paper read before the Royal Academy of Denmark, brought out the fact that since i^2 = -1, and since -1 could be looked upon as a unit vector which has been rotated through 180 degrees, then i could be looked upon as a unit vector which has been rotated halfway, or 90 degrees, or from the x-axis to the y-axis.
Reference: "Laplace Transforms for Electronic Engineers" by James Holbrook.
So our 13th century monk would have had to invent the concept of geometry on the complex plane, as well. Smart monk!
--
My word processor was written by Stanford Professor Donald Knuth. Who wrote yours?
April fools. From last year.
Cheers,
Rick Kirkland
I think that sums it up.
In high school (over 10 years ago - eeek!) me and a friend would set up an Apple IIe ... with a Mandelbrot program written in BASIC..., we would let it run until our class..., where it would complete by the end of class, and save to floppy.
Wow, and at the same time (1990), I was using an Ardent Titan supercomputer, and made a realtime flythrough program. It could generate a 512x512 plot in 1/30th sec, and wherever your mouse was centered, it would zoom in just a little closer for the next frame. Psychedelic.
Talk about opposite ends of the spectrum. :)
[
How many 17th century computing machines are you familiar with?
Well, I don't actually know how to operate or build one, but Blaise Pascal built a mechanical computer in the 17th century.
1. It's entirely plausible -- you can get a good approximation with only a few hundred multiplications per pixel. That a 13th century monk would think of it, not too plausible.
2. The bit about "disputing the bible's claim that pi = 3" really ruins the plausibility. No one except atheists trying to disprove the bible has ever claimed that the bible says pi = 3. It says there was a lake 30 cubits around and 10 across. Maybe St. John the Mushroom Head thought that "I saw a molten lake of fire 30 cubits around and nine and five hundred forty-nine thousanths cubits across" didn't fit the meter very well. Overall, the bit about pi should just be rewritten to make it more plausible.
3. profanus et animi is great: Material vs. Spiritual. Or maybe better translated as Real and Imaginary.
4. Fractals don't have "infinite detail" anymore than x*x + y*y 4 has infinite detail. Yes, you can keep bumping up the resolution, but the information content is totally captured in the equation generating it. (i.e. fractal image compression isn't magic.)
5. The update that this is a hoax should be removed from the summary so that people have an opportunaty to fall for it before they read the comments.
It's about as well done as most of the "All your base are belong to us" Photoshop jobs, and just about as easy to spot. Hemos really had his head up his butt on this one. It's a two year old joke for crying out loud!
And the brethren went away edified.
"I was stunned," Schipke says. "It was like finding a picture of Bill Gates in the Dead Sea Scrolls. The colophon [the title page] named the copyist as Udo of Aachen, and I just had to find out more about this guy."
I don't think the All Mighty is going to be to pleased with this comparison.
I mean, I personally frequently find it hard to believe that it was 20 years ago that I got my first computer. I mean, *20 years*? It doesn't seem like that long ago that people who were 20 years old were "old".
Rich
This could be explained by an error of translation, but the florin (the gold coin of Florence) was not coined until 1252. I doubt that they would have been in sufficient circulation within ten or fifteen years for them to be a standard currency of gambling at Irrendorf, even assuming that the gambling took place toward the very end of Udo's life. Given the florin's size and value, it also seems to me unlikely that an abbot would win 32 of them at a time.
Plus, there is no Harvard Journal of Historical Mathematics, or if there is, Harvard's libraries don't know about it.
My medieval history studies finally serve me well...
http://freshmeat.net/projects/charities.cron/
They're not imaginary numbers, they're complex numbers. If you want to call them imaginary, you might as well call negative numbers imaginary.
My other
gee, if you're going to try to strictly parse semantic labels of mathematical terms, they're not really complex, either, they're pretty straightforward. They're all numbers.
I am, and no they're not. They're complex because they have two parts.
Besides, imaginary numbers are just the nonreal part of complex numbers; "complex" implies you're going to see both real and imaginary values
You are, zero is the real number. And before you point out that any real number can just as easily be considered complex because i has a coefficient of zero, you're right, but that doesn't change the fact that imaginary number is a poor label.
My other
Besides, the mandelbrot set relies on a pretty recent advancement in mathematics: the use of complex numbers as (x,y)-coordinates on a plane.
We didn't even have the X,Y plain back then, either.
Rate me on Picture-rate.com
"and dear god does this website suck now." -- CmdrTaco
Yes non-human computers. Go educate yourself on what the work computer meant before WW 2 and the comment will make sense. It is *very* accurate.
Cypherpunks: Civil Liberty Through Complex Mathematics. Those who live by the sword die by the arrow.
--
When all you have is a hammer, everything looks like a skull.
Mandelbrot considers himself the 'father' of fractals.
This may be just the ego 'punch' that he needs.
Keeping
wow, im amazed anyone could spend the time to calculate that by hand, belive me, ive tried and after a few points it gets really really boring, i commend him for his effort, but must say im glad i have a computer to do it and dont have to waste a few years doing caculations by hand
The guy lucked out in my opinion. He had an interest in something already known and other people developed the technology for him to take the credit. The sad thing is that this is worse than patent law since Mandelbrot will always get way more credit than he deserves.
Gaston Julia did not discover the Mandelbrot set. He discovered the Julia sets. These are related to the Mandelbrot set, but are not the same. For every point in the Mandelbrot set, there is a corresponding Julia set.
Both sets use the formula z := z^2 + c, but they differ in what z0 and c are. In the Julia Sets, z0 is the point on the plane and c is a constant that defines which Julia set it is. For the Mandelbrot set however, z0 is always 0, and c is the point on the plane. In this way, the Mandelbrot set is a table of contents for the Julia sets. Each point on the plane that is in the Mandelbrot set corresponds to a Julia with that point's coordinates as its c that is connected. All the points not in the Mandelbrot set correspond to Julia sets that are not connected. This was the work that Mandelbrot did, and that is why the fractal is rightfully named after him, just as the Julia fractals are named after Gaston Julia.
Lorentz was not working on either the Mandelbrot or Julia fractals. He was working on simplified differential equations for modeling weather. This led to his discovery of the Lorentz attractor. Basically, his work showed that fractals and chaos were abundant in nature. The fact that we will never be albe to accurately predict the weather more than a month in advance also stems from his work. This is commonly known as the Butterfly effect, i.e. a butterfly flaps its wings in Central Park and a 3 months later, a hurricane doesn't hit Japan.
To the best of my knowledge he never acknowledged the work done by the meterologists. When I saw him he also claimed the results of the conjectures as his own and went out of his way to disparage the people who did the real work.
I've never heard Mandelbrot try to disparage anyone in anyway. In fact, its mostly the other way around. People disparaged him because he would write papers in many different journals in widely varying fields, although really they were all in the field of non-deterministic systems, or whatever they are calling it now. People viewed him as an outsider, and therefore dismissed his work without considering it.
.."I was amazed to find out that the Mandelbrot Set was discovered by a 13th century monk -- way, way before the advent of non-human computers".
as compared to those pesky human computers. Smartasses is what we call them suckers.
Well, this story is clearly a joke. But what I want to remark is that in truth lifetimes of impassioned research were sometimes driven by things akin to the search for the mathematics of "a soul's path to Heaven". You only have to remember Johannes Kepler, who devised the Laws of Planetary Motion (Astronomia Nova 1600-1609), which later became the basis for much of Newton's astrophysics. The funny thing is, Kepler was only pursuing a fancy that the planets in the Solar system are arranged in proportion to the classical Pythagorian hierarchy of the 5 fundamental polygons. Of course, this was only a pipe-dream, and the purported relationships merely accidental. Nevertheless, in 30 years of work, Kepler, using primitive pre-calculus mathematics, made one of the great advances in planetary physics ever. Nothing would sound strange to me after this ...
"I am just a customs officer; but I, too, wish to understand what is going on" -- Bertold Brecht