From: hal@finney.org
Date: Sun Dec 03 2000 - 15:28:18 MST
Scerir writes:
> Udo of Aachen (XIII sec.), copyist, monk,
> mathematician, the poet of Carmina Burana.
> Discovered the Mandelbrot (fractal) set
> well before Mandelbrot (1976), but without
> any help from computers.
>
> http://www.freezone.co.uk/rgirvan/udo.htm
> (interesting pictures)
This is too astonishing to be believed.
It shows a nativity scene with the Star of Bethelehem represented as the
Mandelbrot set. The claim is that Udo actually calculated it using the
same rules used today, taking 9 years to do it.
"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."
"In Salus, Udo describes how he used these numbers: 'Each person's soul
undergoes trials through each of the threescore years and ten of allotted
life, [encompassing?] its own nature and diminished or elevated in stature
by others [it] encounters, wavering between good and evil until [it is]
either cast into outer darkness or drawn forever to God.'"
For this to work, the rules for updating (r, i) have to be:
(r, i) = (r^2 - i^2, 2*r*i)
Udo would have had to come up with exactly these same rules for updating
his "profanus" and "animi" and applied them in the same way, using
decimal numbers. I think considerable accuracy (many decimal points)
would be needed to get even approximately the right shape of the boundary
as we see it in the drawings.
I'd be curious to know if anyone else can confirm this unbelieveable
story.
Hal
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