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Escher and Elliptic Curves
melquiades writes "Mathematician Hendrik Lenstra was struck by the blank spot in M. C. Escher's Print Gallery . Why is the spot blank there, he wondered, and what should go in it? Although Escher, who had only a high-school mathematics background, drew the picture by brilliant and methodical intuition, the mathematical machinery underlying the image turned out to be elliptic curves (which come up in factorization, cryptography, and the proof of Fermat's Last Theorem). Lenstra and his colleagues were able to generate several breathtaking possible completions for the missing space. Read the story at the ever-registration-required NYT."
It's supposed to make individuals think. Without the space it's just an optical illusion. Whats next, threories explaining Mona Lisa using computers? Morphing?
What?! They've already done that. Well, fuck it, I'll go back to coding...
Easy. Because it was too frigging difficult to draw what would go inside it. Look at the computer generated blank spot replacements. Escher would have had a very hard time to calculate and draw that.
This is perhaps one of my favorite drawings by esher and has been so for many years. Oddly enough, when I first saw the picture I was sorely pissed off because the picture didn't seem complete. What the hell was in that spot? I wanted to know badly and I couldn't possibly like the drawing until I did.
It was only when I came back to the picture years later. I tried to figure out what I would put in the spot that I realized how excellent the drawing is. It is a stunning metamorphosis between images and I believe the spot only serves to compound that perfectly. If the spot was there you would spend more time staring at the spot them following the transforming images around the outside. The subtly of the picture would be lost on people who were fascinated by the damn spot in the middle (as it was with me).
I'm not denouncing their work. It is very impressive and interesting to read. However I have no intentions of ever hanging a print up without that damn spot. (insert appropriate Shakespeare joke here)
This brings up another debate which is more interesting than why did escher leave a hole in the picture. What constitutes genius or brilliance? Is the artist who draws instinctively a genuis? Or is the mathematician who applies complex theories to pictures and natural patterns a genuis? Are both the artist and scientist manifestations of two sides of a coin? Or are we just playing into stupid labels? In the end, does it really matter that escher left a hole in the picture, or that people wonder why the hole is there?
You guys are missing the big point... Freedom of speech, this is hardly a troll post (like what we get from the CLIT)... This is a well thought out and good post, just because you don't agree with it doesn't make it flamebait. /. at one time was about unpopular opinions, now it's about Troll-Bashing... If you don't love X, and you think MS can make a product that runs your company's LAN then you don't have a say on slash. It's boring, it's old, and it's killing slashdot. If your goal is to prove to the world that linux is the operating system to use, and that open source software is the greatest thing since sliced bread then you are going to need an audience to preech too, but if you call them all fucktards then I don't know who is going to listen, and it will be nothing but a blow to the /. community.
Your mammas flamebait.
I have trouble believing anyone will take tech people seriously these days without a degree
...
AFAIK M.C. Escher was not a tech person
but I think it's great to see that there's still an opportunity for a true genius to break that belief.
1) Escher lived ~100 years ago. Things (for scientists as well as for artists) are MUCH harder now.
2) Perhaps you really are that true genius. But even if you are, you'll probably need to study a LOT before you'll be able to make a deep impression.
Studying is much easier when making a degree in a serious institution, than when studying alone. A degree is not a must, but it makes you study (professional) things you don't know about, and sometimes don't like very much, but will be beneficial for your future career.
in short: studying is a must. formal education is not the only education form in existance, but it has many advantages.
Besides, if you're the Autodeductive type, you can try studying at the open university.
Working for necessity's mother.
I think Escher meant to leave that area blank since it seems like the rest of the drawing is being drawn towards it. It's the focal point of the picture since that's where the picture in the gallery actually connects to the gallery. If you look closely, you'll notice that the frame of the picture is on it's way to meet with the picture itself, which is infact the gallery (woah, I've fallen into the loop). I think this dot was left up to the imagination. There is no correct solution, but this method is a terrific idea.
- A real programmer uses $ cat > a.out
Degrees are handy if you want to work for others, as it makes it easier for them to believe you when you say "Im worth hiring". But makes not one ounce of difference when you want to do things for yourself.
Just get out there and do what you want, measure your own success by your own values - not by the size of your car - and you'll be happy.
Forget all societal measures of your worth - they mean nothing. Except karma of course - anything less than excellent and your a twat!
Perhaps. Some people's brains are better than other at extrapolating phenomenon after a cursory glance; mathematics simply attempts to formally describe the extrapolation, so people who are unable to extrapolate by themselves can do so by applying the formal principles. Maurits Cornellis Escher was amongst the former people, and university gratuates are amongst the latter.
I don't think they've improved on Escher, any more than I think they've "ruined" him. They've just used his artwork as a springboard for their own. For a community that likes to rhapsodize about the value of the public domain and the intellectual commons, an awful lot of slashdotters seem to object to this.
The Mongrel Dogs Who Teach