Mathematician Henrik Lenstra

August 6, 2002 2:38 PM

Mathematician Henrik Lenstra was intrigued by a blank space in he middle of a drawing by MC Escher. Over two years he managed to describe the mathematical structure of the drawing, project what should go in the missing space and produce an extraordanary animation of the result.
posted by alms (32 comments total)

great link.

thanks!

obligatory [this is good]
posted by fishfucker at 2:48 PM on August 6, 2002

That's really cool! The addition blends perfectly, and creates an interesting fractal effect on the arches.
posted by me3dia at 2:51 PM on August 6, 2002

ooh! An extension of Escher.

::gets all tingly::

Thank you!
posted by vacapinta at 2:54 PM on August 6, 2002

i love m.c. escher! that man can sure busta rhyme!
no, really, i DO love escher!
posted by quonsar at 2:55 PM on August 6, 2002

Isn't this a repost? Exceptionally cool regardless, though.
posted by The Michael The at 2:55 PM on August 6, 2002

Wow. That was great. Worth downloading the movie.

Thanks.
posted by perplexed at 2:58 PM on August 6, 2002

wicked cool.
posted by o2b at 3:02 PM on August 6, 2002

*yawn* boring...

just kidding, it's cool. nice link alms!
posted by madprops at 3:08 PM on August 6, 2002

No need to discuss anything here folks. It's just everybody saying how cool the links are.

Damn are those links cool.
posted by zpousman at 3:13 PM on August 6, 2002

That is really cool. I'm sure it would be even more cool if I could understand how he did, but its still cool nonetheless.
posted by rift2001 at 3:24 PM on August 6, 2002

*head implodes*
posted by mr_crash_davis at 3:25 PM on August 6, 2002

Method to madness:
1) Download both versions of 10MB .mpg animations (0,1 and 1,1).
2) Share them out to twelve lab computers, alternating between them...0,1/1,1/0,1/1,1...
3) Start media player on each, set to full screen and repeat.
4) Turn off lights.
5) Curl up in fetal position in office chair and weep.
6) Disappear.
posted by eyeballkid at 3:31 PM on August 6, 2002

Nice one.

About Henrik Lenstra: He has been known, when walking to a friend's house, to factor the street address into prime numbers in order to better fix it in his mind.

Ah, but don't we all?
posted by MUD at 3:31 PM on August 6, 2002

Ah, but don't we all?

Actually, as I've mentioned before, I see and remember numbers by placing them within a logarithmic spiral - much like the one Lenstra uses to reconstruct Escher's picture.
posted by vacapinta at 3:42 PM on August 6, 2002

A bigger version of Escher's print.

Lenstra's homepage at Leiden with (p)reprints (though, sadly, none about Escher). He's a stud.
posted by gleuschk at 4:11 PM on August 6, 2002

An important part of the math behind this is the fact that Lenstra realized that the way Escher distorted the plane was an approximation of a conformal mapping. Conformal mappings (nice pictures in that second link) are really powerful tools that were developed by, among others, Rieman who was one of the all time great ninja hacker mage lords of math.

posted by slipperywhenwet at 4:16 PM on August 6, 2002 [1 favorite]

Just for the record, I have to say that an untold fraction of the wonder of Escher's creations would be lost to the world had he never used LSD.

Good thing he didn't live in America under the War On (Some) Drugs, eh?

Absolutely wondrous link, thanks for sharing it.
posted by beth at 4:20 PM on August 6, 2002

one of the all time great ninja hacker mage lords of math.

*spit-takes*

Um, whoa. I just changed what I want to be when I grow up.
posted by gleuschk at 4:25 PM on August 6, 2002

re: all time great ninja hacker mage lords of math, who else would you add to the list?

I think Gauss goes on there, surely.

vacapinta: your number spiral sounds fascinating and extremely cool. Also, thanks for pointing to that thread about synesthesia. Sorry I missed that one, it was good.

ObSynesthesia: two is yellow, three is most certainly red, and four is blue. Five is green, six is purple, I dunno about seven, it's sorta shadowy, but eight is orange.
posted by beth at 4:39 PM on August 6, 2002

note: My previous comment seems self-absorbed but is, in actuality, a genuine plea for anyone else who thinks like this or knows of a name for this condition to contact me (email in my profile) Thanks.
posted by vacapinta at 4:42 PM on August 6, 2002

All right who slipped the acid into my coffee?
posted by mogwai at 4:51 PM on August 6, 2002

vacapinta, i would be that if you went to a hypotherapist and took a mathematician along with, you could get the spiral plotted out. i'd be interested in seeing the results. i wonder what sorts of math secrets could be unlocked with your spiral.

manero
posted by manero at 5:02 PM on August 6, 2002

Makes my brain itch. Nice link!
posted by Tacodog at 5:33 PM on August 6, 2002

re: all time great ninja hacker mage lords of math, who else would you add to the list?
I think Gauss goes on there, surely.

Gauss would totally be on there. Riemann (of course, I had to misspelled his name in the first post) was one of Gauss' students, and a professor I know claims, the only one Gauss respected.

I think the most badass of the bunch has to be Euler (pronounced "Oiler") who is actually the most prolific scientist ever, with, I think, something like 700 volumes to his name - some of which were written after he went blind, via dictation to his son. There isn't a single area of modern math he didn't have a finger in. There's also the Bernoullis who had a sort of family mathematical Mafia going. There's Lord Kelvin, who Neil Stephenson's written about in his article on the laying of the FLAG cable - Kelvin was an early telecom pioneer. And of course, Archimedes came this close to inventing calculus two thousand years before Newton.

Finally, I have to admit, the only woman mathematician I can think of is Agnesi which is purely patriarchal bullshit - there should be tons of major women mathematicians, I think they just haven't been recognised.
posted by slipperywhenwet at 6:49 PM on August 6, 2002

Man, this thread just reminds me I really need to pull out my copy of Godel, Escher, Bach and read it again...
posted by scribblative at 6:55 PM on August 6, 2002

Wow, repeating what everyone else has said: mad link.

In re: women math ninjas -- the two that always spring to my mind are Sonya Kovalevsky (I seem to recall that she had an affair with fellow math ninja Weierstrass) and of course Emmy Noether, at whose shrine all algebraists pray nightly.
posted by evinrude at 8:42 PM on August 6, 2002

Man, this thread just reminds me I really need to pull out my copy of Godel, Escher, Bach and read it again...

No kidding - and read it voluntarily this time. (Education is wasted on the young)
posted by GriffX at 8:44 PM on August 6, 2002

GriffX -- you were forced to read Godel...? At what institution of learning was this? I'll send my children there, if I ever have any. Or attend myself...
posted by evinrude at 8:51 PM on August 6, 2002

at whose shrine all algebraists pray nightly.

Yep, just finished.
posted by gleuschk at 9:32 PM on August 6, 2002

Thanks for sharing the Escher/LSD connection. I never knew he'd partaken of the sacrament (though it's not at all surprising).

Does anyone know of any links describing Escher's use of LSD? A google search just reveals a lot of people describing how they saw things that looked like Escher drawings while they were on acid!
posted by alms at 5:59 AM on August 7, 2002

All right who slipped the acid into my coffee?

There's also DMT if that's more to your liking.
posted by homunculus at 10:32 AM on August 7, 2002

a little off-topic, but yesterday's NYT science section had a cool article on Frances E. Allen, a female computer pioneer I'd never heard of... and that reminded me of Ada Byron-Lovelace, a chick cool enough to have a programming language named after her...
posted by gwint at 11:33 AM on August 7, 2002