## Re: Udo of Aachen

1

Springtime indeed. Aren't you two and 2/3ds months late?

Posted by: LizardBreath | Link to this comment | 06-22-17 7:32 AM
2

Isn't it fun?

Posted by: heebie-geebie | Link to this comment | 06-22-17 7:33 AM
3

This seems like the sort of thing that should figure in a Tim Powers novel somehow. Maybe you should send him the link.

Posted by: AcademicLurker | Link to this comment | 06-22-17 7:37 AM
4

It IS fun. Imaginative, but plausible enough to make for great fiction.

Heebie, I have a math novice's question. When Gavin says,

"In mathematical terms, Udo's system was to start with a complex number z, then iterate it up to 70 times by the rule z -> z*z + c, until z either diverged or was caught in an orbit,"

does "caught in an orbit" actually mean anything to a mathematician, or is it bullshit that a discerning expert might question?

(First comment after much lurking.)

Posted by: echoes | Link to this comment | 06-22-17 11:06 AM
5

4:

It means that as you continue to apply the transformation rule the numbers you produce cycle through a fixed, finite set of values.

Posted by: bza | Link to this comment | 06-22-17 11:16 AM
6

So that's real. I would have been totally duped by this story.

Oops, and I guess it's Girvan, not Gavin.

Posted by: echoes | Link to this comment | 06-22-17 11:42 AM
7

Girvan published on April Fools day.

https://en.wikipedia.org/wiki/Udo_of_Aachen

Posted by: lw | Link to this comment | 06-22-17 12:15 PM
8

Even without remembering any previous internet history about this being a joke article, it seemed off just from the excerpt quoted in the OP. My first reaction was that 1200-1270 was way early for anyone to be playing around with complex numbers in even a primitive way, much less doing the kind of detailed iterative calculations that would only really make sense once we had decent visualization software to see the results. Sure enough, Wikipedia reports the first known use of complex numbers in the 16th century, in connection with finding solutions to cubic equations. The idea of the complex plane, which is most assuredly needed for the Mandelbrot Set to even make sense, much less be plotted, didn't arise for a couple more centuries:

The idea of a complex number as a point in the complex plane (above) was first described by Caspar Wessel in 1799, although it had been anticipated as early as 1685 in Wallis's De Algebra tractatus.

Posted by: Dave W. | Link to this comment | 06-22-17 12:50 PM
9

It means that as you continue to apply the transformation rule the numbers you produce cycle through a fixed, finite set of values.

No, it could be an infinite orbit, or a continuous orbit, and it could mean that the iterations get arbitrarily close to the orbit.

And Echoes,"arbitrarily close" does have a precise definition: that no matter how small a distance you pick, there is an extremely large iteration such that all iterations thereafter will be within that distance to the orbit.

Posted by: heebie-geebie | Link to this comment | 06-22-17 1:41 PM
10

How can "arbitrarily close" have a precise definition?

Math is so weird!

Posted by: peep | Link to this comment | 06-22-17 1:53 PM
11

Unlike law, which says "reasonable doubt" without specifying a p value.

Posted by: Moby Hick | Link to this comment | 06-22-17 2:00 PM
12

Well, this is fun.

I think I get what orbits are just by watching what happens when c is changed in the complex plane. (It's better if you have the lines displayed. Totally caught up trying to trace the edges of the set.)

Posted by: echoes | Link to this comment | 06-22-17 3:10 PM
13

No p-values for "reasonable fear" either, I suppose.

Posted by: echoes | Link to this comment | 06-22-17 3:42 PM
14

Tom Stoddard's play Arcadia is like this. It has a 19th century girl with her own private tutor. She plays around with iterated processes.

Posted by: Robert | Link to this comment | 06-22-17 3:55 PM
15

The really great bit, for me, was where he 'realises' that O Fortuna is referring to Buffon's needle:

We are cast down / like straws upon a ploughed field / Our fates measuring / the eternal circle

It's really convincing!

Posted by: One of Many | Link to this comment | 06-22-17 6:00 PM
16

Really!

Posted by: One of Many | Link to this comment | 06-22-17 6:00 PM