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Mandelbrot Set Originally Found In 13th Century (Early April's Fool)

Hemos posted more than 13 years ago | from the my-history-degree-does-matter! dept.

122

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.

cancel ×

Re:Oh, come on! (3)

Anonymous Coward | more than 13 years ago | (#345976)

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?

Well, hey.... (2)

Wakko Warner (324) | more than 13 years ago | (#345977)

Yale gave George W. Bush a degree, so they can't be worth much...

- A.P.

--
* CmdrTaco is an idiot.

It would not have been possible, Roman numbers (2)

Wastl (809) | more than 13 years ago | (#345978)

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

Gullible isn't in the dictionary. Look it up. (1)

yelvington (8169) | more than 13 years ago | (#345982)

O Fortune,
like the moon
you are changeable,
ever waxing
and waning;
hateful life
first oppresses
and then soothes
as fancy takes it;
first posting
and taking away
just an April fool's joke.

Re:I could be wrong.. (1)

nebby (11637) | more than 13 years ago | (#345983)

Yeah, but the colors are determined by the "rate" .. right?

I could be wrong.. (2)

nebby (11637) | more than 13 years ago | (#345984)

(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!

Re:hand calculations (1)

kevlar (13509) | more than 13 years ago | (#345985)

Probably just pinching gullible people.

Re:Which ones? (2)

sharkey (16670) | more than 13 years ago | (#345986)

Probably not the algorists, as they tend to punch the wrong dots.

--

Re:A math teacher once told me... (1)

Kimble (17437) | more than 13 years ago | (#345987)

I'm not really sure how hard it is to go from a picture to a fractal, but it's doable. When you do that, you get a good level of compression. Also, once the picture is encoded as a fractal, you can create much better enlargements than possible with just bicubic interpolation.

Altamira has a Photoshop plugin, Genuine Fractals [206.63.152.155] , that does this. I haven't tested it out yet, but I remember favorable reviews for it. It only requires a "G1" Mac with 32 megs, so the process of generating the fractals can't be too hard (of course, Photoshop users are accustomed to waiting for ages for something to happen).

For a (seemingly exhaustive) survey of the state-of-the-art (as of 1999) in fractal image encoding, check out this page [ucsd.edu] , which Google seems to like a lot.
--
How many classes do you have to take

Re:Oh, come on! (1)

rueba (19806) | more than 13 years ago | (#345988)

I think its fairly good as far as these kind of things go.
It's semi-plausible and appears to have a lot of details.
Also, just because its two years old doesn't mean everyone has heard about it.
What I am trying to say is that hindsight is 20/20.
Anyone can be a genius after the facts come out.
Give Hemos a break, at least he spelled everything right!

Re:Didja know "gullible" isn't in the dictionary? (1)

Darth Hubris (26923) | more than 13 years ago | (#345989)

Thelonius was quite real, I assure you. He managed to rescue some older Greek texts that became the Apocrypha [chapters that didn't make it into the Bible] of Biblical fame. Nice fellow too.

Free My Soul! (1)

SEWilco (27983) | more than 13 years ago | (#345990)

My soul is trapped in a maze of twisty little passages, all different.

Which ones? (2)

TheDullBlade (28998) | more than 13 years ago | (#345992)

Would that be the algorists or the abacists?
---

Re:A fractal generator (1)

Hew (31074) | more than 13 years ago | (#345994)

To get a taste of what Fractint can do, you could try Fractal Map [samurajdata.se] (basically a web frontend to Fractint).

Re:Wrong date on Florins (2)

Hadean (32319) | more than 13 years ago | (#345996)

Uh, out of all the silliness in the article, that's the one you have to catch the author on? Youch...

Re:other resources... (2)

cr0sh (43134) | more than 13 years ago | (#346000)

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 [worldcom.com] - Generation Duh!

A fractal generator (2)

wiredog (43288) | more than 13 years ago | (#346003)

Fractint [fratint.org] is a classic. Runs on DOS (yuck), Linux (supposedly, segfaults on my 2.4 kernel), Win 9x and, I think NT.

No, I was too busy marvelling... (3)

goliard (46585) | more than 13 years ago | (#346005)

... 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!

A little early for April Fools, isn't it? (1)

jlowery (47102) | more than 13 years ago | (#346006)

This looks like a hoax. A crafty one, though.

complex numbers as coordinates (2)

klund (53347) | more than 13 years ago | (#346007)

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!

--

I believe he was refering to the date... (2)

Rix (54095) | more than 13 years ago | (#346008)

April fools. From last year.
Cheers,

Rick Kirkland

Anyone notice this at the bottom (5)

ptevis (56920) | more than 13 years ago | (#346009)

© Ray Girvan (raygirvan@freezone.co.uk), April 1st 1999.

I think that sums it up.

Re:hand calculations (1)

Cuthalion (65550) | more than 13 years ago | (#346010)

And shouldn't a book title be underlined?

Historically underlines were standardized upon as a way of adding emphasis or setting somethign apart only after the typewriter made it impractical to italicize the things you ought. Now that this is no longer the case, I think that that convention is slowly evaporating, and both underlines and italics are considered appropriate.

Re:Actually it's a Julia Set (1)

Cuthalion (65550) | more than 13 years ago | (#346011)

For some reason I thing that Lorentz was one of these people I don't know of Lorenz (I assume that's who you meant) doing any work with fractals directly. However he did a lot for chaos theory, by discovering a normal problem that displayed sensitive dependance on intitial conditions (he had a weather simulator. After seeing some interesting behaviour, he wanted to watch it again, so he typed in the same seeds, but they weren't printed out with the full precision that was used interally, so before long he got qualitatively different results. Trying to isolate this behaviour which struck him as odd (how can 0.000001 difference change everything?) he simplified his system and came up with the Lorenz Attractor [swin.edu.au] - rather than settling on a point or into an oscillating pattern, his system approached a curve of infinite complexity - a strange attractor.

Sorry, once I start typing, I just can't stop!

Re:A math teacher once told me... (1)

Kalani (66189) | more than 13 years ago | (#346012)

Any function that approaches infinity can represent all of the stars in the universe (at least as far as counting them.)

to wit:

f(x)=1/x

x->1/n f(x)=n

Where "n" is the number of stars in the universe.

As for going from a fractal graph to a formula ... that's a little backwards. You go from a formula to a graph, just like every other graph.
____________________

Re:other resources... (2)

Speare (84249) | more than 13 years ago | (#346013)

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. :)

Re:Non-Human Computers? (2)

kevin805 (84623) | more than 13 years ago | (#346014)

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.

kevin805 (84623) | more than 13 years ago | (#346015)

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.

Re:Oh, come on! (1)

CaptainCarrot (84625) | more than 13 years ago | (#346016)

You fell for it, but I'm the dumbass?

Pphhphptthththtpptththt!

Re:Oh, come on! (1)

CaptainCarrot (84625) | more than 13 years ago | (#346017)

The only reason I didn't post earlier is that it would have been -1, Redundant. Several others had spotted it before I bothered to read any comments. The idea that a 13th century monk would have invented both the Cartesian coordinate system and complex numbers, both of which are required to draw the Mandelbrot set in the form to which we are accustomed, is ludicrous on the face of it and not at all "semi-plausible." And the copyright date specifying 4/1 when it ordinarily contains only the year should have been a dead giveaway to anyone.

Oh, come on! (3)

CaptainCarrot (84625) | more than 13 years ago | (#346018)

Update 20 mins later by J: Yes, this is an April Fool's joke - very well done, too.

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!

Watch out for lightening bolts. (3)

nublord (88026) | more than 13 years ago | (#346019)

From the article:
"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.

How to generate simple fractals (1)

BobGregg (89162) | more than 13 years ago | (#346020)

Ignoring the hoaxiness (oh, the hoaxiness!), it's easy to generate many fractals. My science project my junior year in high school was a program on an Apple ][ to generate simple fractals algorithmically from a couple of basic rules. Here's the easiest one to picture:

* On the X,Y plane, pick three points which are the corners of an equilateral triangle.
* Now pick any fourth point, and plot it.
* Now randomly choose one corner of the triangle, and move the plot point halfway towards it. Plot that point, then pick another corner, move halfway, and plot again. Repeat.

If you let this run for a while, the points converge into a shape called a Sierpinski Gasket, which is a readily-recognizable series of nested triangles. By varying the location and number of the control points, the transformation rules used to alter your plot point (use different movement rules, for instance, or weigh the probabilities of choosing those rules in some way) you can produce a wide variety of interesting and beautiful fractals.

Re:Anyone notice this at the bottom (1)

SuperguyA1 (90398) | more than 13 years ago | (#346021)

Think before you post, foo.

Could BSDevel be.... Mr T?

Oh, come on (1)

gazz (101967) | more than 13 years ago | (#346022)

oh, please..you're telling me this is new?
I saw this about 4 years ago..
And how could it not be a fake.?
I have to say, there're a lot of things on /. that I'd been looking up around the time I was still playing Dizzy on an Amiga 1200..

Re:Oh, come on! (1)

gazz (101967) | more than 13 years ago | (#346023)

well, if you're looking at it from a Pratchettesque viewpoint, Capt. Carrot's not exactly the smartest resident of AnkhMorpork.....

Re:Anyone notice this at the bottom (1)

RoninM (105723) | more than 13 years ago | (#346025)

Now you've gotten yourself in a fix, 007. Here are my suggestions for extricating yourself: the cyanide capsule located in your tooth -- chew it. If that's unappealing, you can apply Usenet tactics and claim that you really were trolling (no, really!). That might not fly, but since we're only a short spell away, you could try to call it an early April Fool's joke...

Speaking of April Fool's, you do realize he was pointing out the date and not the copyright?

Trick Of Course.... (1)

blazin (119416) | more than 13 years ago | (#346027)

It should be noted that the mathematician's name mentioned in the article can be rearranged to "SHE BE TRICK PRO" Of course that is using Robert instead of Bob, but the point is obvious :)

Wrong date on Florins (2)

sachsmachine (124186) | more than 13 years ago | (#346028)

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...

Re:Non-Human Computers? (1)

Some12 (129970) | more than 13 years ago | (#346031)

*laugh* That's all i have to say!

not really that funny (1)

yzquxnet (133355) | more than 13 years ago | (#346032)

It might have been funny... IF IT HAD ACTUALLY BEEN APRIL 1ST.

Re:Non-Human Computers? (1)

wfaulk (135736) | more than 13 years ago | (#346033)

From Merriam-Webster's online dictionary [m-w.com] :

computer
Pronunciation: k&m-'pyü-t&r
Function: noun
Usage: often attributive
Date: 1646
: one that computes; specifically : a programmable electronic device that can store, retrieve, and process data
bold emphasis mine

How many 17th century computing machines are you familiar with?

hell... (2)

elegant7x (142766) | more than 13 years ago | (#346034)

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 [picture-rate.com]

This is a hoax. (1)

alleria (144919) | more than 13 years ago | (#346035)

Read MLP in Kuro5hin [kuro5hin.org] for details.

I guess none of the editors read Kuro5hin (1)

MikeApp (151816) | more than 13 years ago | (#346036)

Although I don't see the hoax on the front page at Kuro5hin.org any more, it was in their slashbox earlier today.
-Mike

Suppression of valid work (1)

Perdo (151843) | more than 13 years ago | (#346037)

History is full of instances of powerful organizations suppressing valid work. However, what has been done cannot be undone. What we must do now is insure that no organization ever seeks, or is able to suppress good ideas simply because the individuals in the organization do not understand them. In times past it has been the catholic church. Who is it now? The U.S. Government? Microsoft? The US Patent Office? The American Cancer Society? The Nobel Foundation?

And in other news... (1)

Saint Aardvark (159009) | more than 13 years ago | (#346038)

Amazon.com still claims that this has no bearing on their patent for a single-click fractal.

Re:Non-Human Computers? (2)

SquadBoy (167263) | more than 13 years ago | (#346039)

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.

Dr. Kinbote (171352) | more than 13 years ago | (#346040)

It's a very, very, very obvious hoax.

Re:Actually it's a Julia Set (1)

Gibbys Box of Trix (176568) | more than 13 years ago | (#346041)

I went to a talk by Mandelbrot, and he is basically a monster ego with feet and a big mouth.

I went to a lecture by Mandelbrot, some 10 years ago. He was very self-effacing, and claimed he was embarrassed by the use of his name to describe the set.

When did you see him? Perhaps someone took him down a peg or two in between the two dates?
--

Didja know "gullible" isn't in the dictionary? (3)

isomeme (177414) | more than 13 years ago | (#346042)

A monk named Thelonius [achilles.net] ? C'mon, guys...my suspension of disbelief was sagging well before I got that far, but that snapped it entirely. It is a pretty funny hoax, though.

--

Re:It's not a moandelbrot set (1)

jerkface (177812) | more than 13 years ago | (#346043)

You don't need imaginary numbers to define the mandelbrot set. Start with point (x[1],y[1]). When you do the iterations, x[next] = x[previous]^2 - y^2 + x[1] and y[next] = -y[previous]^2 + y[1]. And the image shown is most definitely a rendering of the mandelbrot set. Other than that, you're right that complex numbers and cartesian coordinate systems weren't used when this drawing was supposedly made. The article even claims the monk performed 70 iterations on each point to test whether or not it was in the set! It took my Commodore 128 almost 24 hours exactly to do a 320x200 picture that only tested points for 12 iterations. The implication is that the monk performed 1,008,000 calculations just to create the 120x120 grid. April fool.

Oh, and wouldn't it be nice if slashdot supported the tag?

--

Re:It's not a moandelbrot set (1)

jerkface (177812) | more than 13 years ago | (#346044)

I meant to say <sup> tag

--

Re:hand calculations (1)

jerkface (177812) | more than 13 years ago | (#346045)

and James Gleick eludes to it in "Chaos".

Don't you mean "alludes"? And shouldn't a book title be underlined?

All in good fun. And my punctuation is intentional.

--

A math teacher once told me... (1)

Sir_Real (179104) | more than 13 years ago | (#346047)

I was once told by a math teacher that a complex enough (mandlebrot?) fractal can represent all of the stars in the universe. Had I paid more attention in that class I would be able to expand on this claim, but I leave that up to wiser heads. I know that they can be used to simulate (or represent) coastlines. How hard is it to go from a fractal graph to a formula?

Yes that is a blank stare.

other resources... (1)

meatplow (184288) | more than 13 years ago | (#346048)

I'd love to get a hold of some progs to do this at home.
I was always, fascinated by it in school.
Does anybody have any links ??

meatplow.

fuckbunny.org [fuckbunny.org]

Re:hand calculations (1)

shokk (187512) | more than 13 years ago | (#346049)

You have no appreciation for the amount of spare time people in the middle ages must have had. If they had the brains to, they probably would have counted to 10,000 just for fun each day.

Let's see. What shall we do today? Kill some innocents out of complete ignorance...did that twice this week. Kick some pebbles? Done that. Work slavishly for the fiefdom...every day this week. Guess I'll stare at this wall for a while and then let my imagination run wild to think up some daemons so we can go kill some more neighbors.

It's not a moandelbrot set (1)

javaDragon (187973) | more than 13 years ago | (#346050)

Just think that the mandelbrot set is the result set of an imaginary numbers equation. When were the imaginary number invented ?

Furthermore, this image bears only a very remote oliking to a mandelbrot set image in a x-y plane (which in turn is a recent invention too).

It can be anything artistic, but definitely not a mandelbrot set image.

Since nobody else will admit it... :) (1)

Abcd1234 (188840) | more than 13 years ago | (#346051)

I was *totally* taken in by this one. :) 'course, I don't read Kuro5hin, and I usually don't pay attention to the copyright dates on the pages I read. Frankly, it isn't a particularly *funny* April Fools joke, just kinda strange... well put together, though.

Re:hand calculations (2)

grammar nazi (197303) | more than 13 years ago | (#346054)

This is good in another way too. Mandelbrot is known throughout the dynamical systems community as being a pompous and arrogant jerk. I don't know him personally, but I've heard this from others and James Gleick eludes to it in "Chaos".

Mandelbrot considers himself the 'father' of fractals.

This may be just the ego 'punch' that he needs.

hand calculations (2)

edwarddes (199284) | more than 13 years ago | (#346056)

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

I recommend... (1)

Vuarnet (207505) | more than 13 years ago | (#346057)

Fractint. I used it back in college during my Computer Graphics classes, and eventually my teacher just gave everyone else a copy so they would all see what a fractal was, and which fractals were the most popular.

You can get it at the Fractint WWW pages [triumf.ca] .

Tongue-tied and twisted, just an earth-bound misfit, I

Are things like this really a surprise?? (1)

puck01 (207782) | more than 13 years ago | (#346058)

I mean, come on, these guys were rather well educated, and besides doing their daily duties, what else did they have to do all day, but persue what ever interested them. I bet monks thought made a lot of interesting discoveries that may have never been passed on. Mendel (also a monk), despite fudging some data, was for example the first to propose the allele concept in genetics, and no one even noticed his work until long after the fact. puck

Re:Anyone notice this at the bottom (1)

while (213516) | more than 13 years ago | (#346059)

Actually, I think this does: YHBT.
This one's on Hemos :)

(end comment) */ }

Re:Didja know "gullible" isn't in the dictionary? (1)

vinnythenose (214595) | more than 13 years ago | (#346060)

Thelonious Monk... oh that's a good spoof... *wipes tear from eye* ahhh, good piano playing though.

I told 'em (1)

ackthpt (218170) | more than 13 years ago | (#346061)

Millenium hand and shrimp!

Bugrit!

--

Re:hand calculations (1)

ackthpt (218170) | more than 13 years ago | (#346062)

I can still remember coming up with an idea for an electromagnetically accelerated projectile, when I was 14 (1974). I was somewhat dejected to find it had already been 'invented' sometime in the 50's. Now people call these things Rail Guns. Some ideas are obvious, eh?

--

Is it just me... (1)

MWoody (222806) | more than 13 years ago | (#346063)

Is it just me, or does the little "Einstein" picture next to this article look angry?
---

Re:A math teacher once told me... (1)

jrockway (229604) | more than 13 years ago | (#346064)

have you a non-recursuve definition for the Mandelbrot set? I think not... but if you do, post it!!

Re:Oh, come on! (1)

RandomPeon (230002) | more than 13 years ago | (#346065)

I'll admit it - I fell for it. Reasons why:

0. Didn't look at the copyright.
1. It's well written.
2. Ramajun - if a poor Indian college dropout can come up with hundreds of new mathematical insgights (and rediscover others) in his spare time, it seems plausible that a monk (who could have been copying the bible by hand) could have some astounding mathematical insights.
3. The stuff about imaginary numbers being associated with the devil reminded me of "true" Greek tales about the gods being angry with the discovery of irrational numbers - the legend may be the source for that part of the hoax.
4. After enough math courses, the ideas expressed here (except for the Mandelbrot set) strike me as elementary. Imaginary numbers, probability axoims, ordinal infinity, and Cartesian coordinates seem intuitive. They're not, of course, and I would never come up with all of them on my own, but halfway through a math minor they seem like givens.

OK, I got taken. Just trying to feel less stupid.

Score one for /. (1)

Usquebaugh (230216) | more than 13 years ago | (#346066)

Nice to see the team are on their toes and checking the stories out.

The only thing left to prove the integrity of /. is when Timmy or Mikey posts this in a day or so and adds some air head comment.

'News for nerds. Stuff that matters.' That was a long, long time ago. Now it should read, 'News for herds, Stuff that generates ad revenue'

Re:I Love Calculus (1)

Usquebaugh (230216) | more than 13 years ago | (#346067)

Calculus de agony dx/dt :-)

Re:Score one for /. (1)

Usquebaugh (230216) | more than 13 years ago | (#346068)

I'm sorry to say it comes naturally. It seems we must have a common ancestor :-)

I've read the FAQ, and notable by it's omission is any forum for a discussion on /. its self! Also the FAQ contains inaccuracies, deletion of comments being one such area.

But back to the point at hand, /. seems to be slipping from when I first started reading. Prehaps, it's me that's changed or the site has grown. I'm not sure, but I am aware that other users feel the same way.

The /. crew stead fastly refuse to answer or discuss this. At the same time they are starting to ask for comments on how /. should be funded.

Re:I could be wrong.. (1)

GMontag451 (230904) | more than 13 years ago | (#346069)

the mandelbrot set is a plot on the real/imaginary axes of the "rate" at which the function approaches infinity for each coordinate.

Actually, the mandelbrot set itself doesn't take into account the rate. The mandelbrot set is just the set of all points that don't escape to infinity ever. You cannot actually have a picture of this, without computing for an infinite amount of time (at least with current methods). All the computer pictures of the Mandelbrot set are just approximations. Anyway, in a normal Mandelbrot fractal picture, the actual Mandelbrot set is everything in black.

Re:other resources... (1)

GMontag451 (230904) | more than 13 years ago | (#346070)

One of the best fractal generator programs around, even if the interface is somewhat clunky: Fractint [triumf.ca]

Another good one that even lets you compile your own fractal algorithms into it. For Mac only though. Fractal Designer [unige.ch]

Re:I could be wrong.. (1)

GMontag451 (230904) | more than 13 years ago | (#346071)

Kind of, they are determined by the number of iterations that it takes to get past the radius 2 circle. You can consider that a rate of a kind. But, as I said, that isn't part of the Mandelbrot set.

Re:other resources... (1)

GMontag451 (230904) | more than 13 years ago | (#346072)

Formulas are different than algorithims. With Fractal Designer you could concievably make a faster algorithm for a formula it already had. Besides, its got a better interface.

Re:Actually it's a Julia Set (2)

GMontag451 (230904) | more than 13 years ago | (#346073)

I think you should read up a little more on the history of fractals before you post things like

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.

April 1 is not quite here yet (1)

Dr. Awktagon (233360) | more than 13 years ago | (#346074)

You guys posted this a little too early methinks..

This may be a hoax But... (1)

lmake (240649) | more than 13 years ago | (#346075)

... Fractals were theorised before computers were invented. Of course they were only able to draw basic abstract diagrams, nothing like the one drawn in the monk's picture.

I came across this while researching some maths assignment. Can't remember where though.

Re:I believe he was refering to the date... (1)

thomash (250125) | more than 13 years ago | (#346078)

April fools. From last year.
Oh well, you're still living in the last millenium...

Fake? (1)

anon757 (265661) | more than 13 years ago | (#346080)

I have my doubts as to wether this article is real or not. I once wrote a program to plot fractals, and know that there can be anywhere from 100-thousands of calculations PER PIXEL, as you have to calculate wether the formula for each set of X/Y coordinates either approches infinity or not. Even at a fairly low resolution, this can add up to taking longer than someone's lifetime.

Re:Fake? (1)

anon757 (265661) | more than 13 years ago | (#346081)

And... The pictures sure look doctored. The image on Codex Udolphus looks like it's in a higher resolution than 120x120 pixels, and you dont get that well defined of a fractal only going to 70 iterations. (at 120x120 with 70 iterations, that's the possibility of having to do 1.008 million calculations)

Re:Anyone notice this at the bottom (1)

BSDevil (301159) | more than 13 years ago | (#346082)

That means that this Ray Girvan holds the copyright on his writing up of the work - NOT the work itself (done by the Monk). If you don't beleive it, check the referenced sources. I haven't (and am too lazy to do so), but I would assume that they would clearly tell wether the thing is genuine or not.

Think before you post, foo.

Re:Score one for /. (1)

Chyron (304285) | more than 13 years ago | (#346083)

Do you practice being this stupid, or does it come naturally?
Hint: Read the FAQ. Hell, you know what, I'm feeling kind to dumb animals today, I'll help you out.

How do you verify the accuracy of Slashdot stories?
We don't. You do. :) If something seems outrageous, we might look for some corroboration, but as a rule, we regard this as the responsibility of the submitter and the audience. This is why it's important to read comments. You might find something that refutes, or supports, the story in the main.
--

Re:Score one for /. (1)

Chyron (304285) | more than 13 years ago | (#346084)

Fairy nuff... flame retracted. At least partly. Sorry 'bout that, just my day for snapping, I guess.

I still maintain that Slashdot shouldn't _have_ to check up on the validity of every single story. But I think I see your point of view.

In the interest of fairness, I will now insult myself: I'm an offensive, inconsiderate moron. We're even now, methinks.
--

Actually it's a Julia Set (1)

capt.Hij (318203) | more than 13 years ago | (#346085)

According to the article the monk used a 2D plane and worked through the points in the plane. The algorithm he used is very close to the algorithm which looks much nicer using complex numbers. (By the way Leonhard Euler first proposed the use of \sqrt(-1) in 1777.) It certainly looks like the Julia set.

The algorithm to find the set was thought to have been proposed by Gaston Julia. In the early sixties (me thinks) several meterologists actually toyed with the algorithm not knowing what Julia had done. (For some reason I thing that Lorentz was one of these people.) They even printed out pictures of it using fortran programs that went through a grid literally marking the converging points with an '*'. (Just think we can now do this using excel in half the time! :-)

Later, Mandelbrot looked at the same thing and was able to use the technology developed at IBM to make decent pictures of it. He went on to make many conjectures which were all proved by other people. I went to a talk by Mandelbrot, and he is basically a monster ego with feet and a bifg mouth.

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.

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.

Re:Non-Human Computers? (1)

PorcelainLabrador (321065) | more than 13 years ago | (#346086)

I don't discount this, but words are *funny*. And so are your sentences.

I totally agree, though, about people sitting down and hammering out codes through WW2. Amazing, really. In this sense human computers does describe it best.

Non-Human Computers? (2)

PorcelainLabrador (321065) | more than 13 years ago | (#346087)

.."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.

Infinite Detail (1)

fractalus (322043) | more than 13 years ago | (#346089)

Fractal images don't have infinite detail because computers can't render an infinite number of pixels or perform an infinite number of iterations. However, if either of those two feats could be accomplished, the graph of the equation would have an infinite frequency spectrum, infinite detail.

Re:other resources... (1)

cwry (323706) | more than 13 years ago | (#346091)

Fractint allows you to add your own fractal formulas too. Even if it didn't, it's open source, so it wouldn't be difficult to adapt it.

Re:Fake? (1)

cwry (323706) | more than 13 years ago | (#346092)

You don't actually have to calculate each pixel to the maximum iteration level, the vast majority of points that do approach infinity - you can either quickly tell they will, or they start repeating in a short cycle. Once they repeat you can give up and go to the next pixel.

Almost as fun as Taiwanese Aircraft Carrier hoax (1)

flacco (324089) | more than 13 years ago | (#346093)

Remember that one last April Fool's?

not as absurd as the real thing, sometimes ... (2)

Montecristo6 (398332) | more than 13 years ago | (#346094)

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 ...

Wow (1)

CybrGuyRSB (410357) | more than 13 years ago | (#346095)

He probably wasn't able to carry it as far as we can with computers, but its still pretty cool. I commend him for his patience.

I Love Calculus (1)

Derivatater (410642) | more than 13 years ago | (#346096)

Everybody Derivatate! dy/dx

well, hmph... *i* was taken in... (1)

lines (410893) | more than 13 years ago | (#346097)

i guess i should've read the references section and the april 1 date below it. but really, who cares to read (and verify) references anymore? ;) damn.
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