
The Mandlebrot Monk - barrkel
http://classes.yale.edu/Fractals/MandelSet/MandelMonk/MandelMonk.html
======
RevRal
<http://en.wikipedia.org/wiki/Udo_of_Aachen>

Have a very happy un-April Fool's day.

~~~
GFischer
I fell for it... :)

By the way, over here in Spanish-speaking countries the equivalent to "April
Fool's" is in December ("Día de los Inocentes" - see the "Other Prank days in
the World" section <http://en.wikipedia.org/wiki/April_Fools%27_Day> ).

That has caused me problems in the past :P (I totally believed and acted upon
a prank, since I didn't expect April 1st to have any significance back then)

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forinti
Oops, that got posted a few days too early...

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camccann
Perhaps it is bad form to pick nits in an amusing bit of April Foolery, but as
an interesting aside, with a better technique it would take nowhere near nine
years to produce manually a 70 iteration 120x120 rendering of the M-set--by
avoiding explicit calculation entirely! A geometric interpretation of the path
taken by each point gives a simple, easily mechanized transformation, that
could be implemented with a system of gears, levers, and other basic
mechanisms, plausibly reducing the time necessary to a few seconds per
iteration.

~~~
pvg
A much bigger nit that gave it away for me in the very first paragraph is that
13th century is far too early for complex numbers and Cartesian
representation.

~~~
barrkel
You don't need to have invented complex numbers with concepts like imaginary
numbers to have invented a scheme isomorphic to complex numbers.

For example, you don't need all the concepts behind analytic trigonometry to
solve problems with what amount to Sine, Cosine, etc. All you need is the
concept of similar triangles, and you can build a scale model of your problem
and solve it empirically. If you make your hypotenuse of length 1 in whatever
base, then you'll actually be working with Sine and Cosine but not even know
it.

As to Cartesian planes, if all that need be represented is a truth value, when
expressed compactly in the form of a simple table, a picture should emerge,
even if one has to stand back.

Speaking personally, I think the Cartesian plane is the bigger stumbling block
to believability, as it requires a leap of insight to bridge the analytic and
the geometric; but on the other hand, it's so well known that it might easily
be taken for granted by the reader.

~~~
pvg
Yes, if if, isomorphic, if, etc. The fact is you need to invent a whole pile
of stuff that was nowhere on the horizon between 1200 and 1270 to draw a
Mandelbrot set. And that's plainly obvious to anyone with the most superficial
knowledge of the history of maths.

~~~
fh
Not to disagree, but I'd like to mention that you don't actually need full
complex number arithmetic to draw a Mandelbrot set. If you translate the
Mandelbrot update rule into pairs of numbers, you get the following recursive
equations:

    
    
        x_{n+1} = x_n^2 - y_n^2 + x_0
        y_{n+1} = 2 x_n y_n + y_0
    

(Not 100% sure I got this right, but it's late.) The Mandelbrot set is then
the set of points x_0, y_0 for which these values don't escape to infinity, or
even more simply, escape the circle of radius 2 around (0, 0).

~~~
pvg
I think we're getting a little hung up on 'complex numbers' and things they
might be isomorphic to. My point was that in order to come up with the
Mandelbrot set in the 13th century you need bits of mathematical apparatus
that were not invented till centuries later. I liked the piece, it's just that
the eye-poking anachronism right off the bat sort of gave it away too early,
for me.

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cjauvin
I would say reading this article was a good exercise in testing my critical
thinking, because I could feel all the warning red lights flashing one by one
while reading it: even though it would have been a marvelous discovery, I was
really not ready to accept it without questioning it a bit further. An
interesting hoax idea nevertheless!

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arethuza
Anyone else think of Anathem when they read this? Although avout would
probably calculate fractals by singing...

~~~
Vivtek
My hand's up, yes.

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lukev
You know those things that you just _want_ to be true, because they would make
the world so much more interesting?

This is one of those things.

~~~
lincolnq
This is what tipped me off (due to its attractiveness -- making me think "wow,
this fits TOO well"):

 _Initially, Udo's aim was to devise a method for determining who would reach
heaven. He assumed each person's soul was composed of independent parts he
called "profanus" (profane) and "animi" (spiritual), and represented these
parts by a pair of numbers. Then he devised rules for drawing and manipulating
these number pairs. In effect, he devised the rules for complex arithmetic,
the spiritual and profane parts corresponding to the real and imaginary
numbers of modern mathematics._

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viraptor
For an April fools joke, it really seems interesting. It was a good read, even
if not true. Reminds me of "the real rocket car" story - so full of really
convincing details you start wondering if it is true or not.

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maxdemarzi
Wow...Now that is crazy. Add another to the list of where we could have be if
religion and science could have co-existed peacefully.

~~~
mjgoins
I think it's an april fool's joke. See the bottom.

~~~
gwern
Right:
[http://web.archive.org/web/20040804030030/http://abcnews.go....](http://web.archive.org/web/20040804030030/http://abcnews.go.com/sections/scitech/WhosCounting/whoscounting010401.html)

