From: Michael M. Butler (butler@comp-lib.org)
Date: Sun Dec 03 2000 - 15:54:32 MST
It's either really cool or really funny. Can someone check the cites and
see if they are real?
hal@finney.org wrote:
>
> 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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