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When mathematicians describe equations as beautiful, they are not lying. Brain scans show that their minds respond to beautiful equations in the same way other people respond to great paintings or masterful music. The finding could bring neuroscientists closer to understanding the neural basis of beauty, a concept that is surprisingly hard to define."
In the study, researchers led by Semir Zeki of University College London asked 16 mathematicians to rate 60 equations on a scale ranging from "ugly" to "beautiful." Two weeks later, the mathematicians viewed the same equations and rated them again while lying inside a functional magnetic resonance imaging (fMRI) scanner. The scientists found that the more beautiful an equation was to the mathematician, the more activity his or her brain showed in an area called the A1 field of the medial orbitofrontal cortex.
Skipping down to the last three paragraphs...
The study found, for example, that the beauty of equations is not entirely subjective. Most of the mathematicians agreed on which equations were beautiful and which were ugly, with Euler's identity, 1+eiπ=0, consistently rated the most attractive equation in the lot. "Here are these three fundamental numbers, e, pi and i," Adams says, "all defined independently and all critically important in their own way, and suddenly you have this relationship between them encompassed in this equation that has a grand total of seven symbols in it? It is dumbfounding."
On the bottom of the heap, mathematicians consistently rated Srinivasa Ramanujan's infinite series for 1/π most ugly.
"It doesn't sing," Adams says. "I look at it, and I don't learn anything new about pi. And those numbers, 26,390? 9801? As far as I am concerned, you could switch in other numbers, and I couldn't tell the difference."
Scientific American
11 comments:
E=MC2 is THE BOMB!
But would Ramanujan find that equation of his beautiful? LOL, that might be an interesting comparison, to find out who finds what beautiful. It also reminds of a story about boring numbers, but I'll spare you barbarians.
And yes, if you don't find Euler's Identity and Euler's Formula beautiful, you shouldn't be in Mathematics.
(Euler's Identity is a particular case of Euler's Formula where x = pi.)
Such equations express fundamental equalities.
But don't forget the fundamental beauty of mathematical inequalities.
They invite mystery.
My son was working on some basic order of operations problems in beginning algebra not long ago. He complained that they were boring, so I said, "But it has to be at least a little satisfying. You're taking these ugly, needlessly complicated things and simplifying them down to much more pleasing little equations." He agreed and complained no more.
A guy was telling me Sunday how he figure that when people say they need patience what they are really saying is they have anger issues. It boils down to anger.
A little light bulb went on in my head.
I like the idea of simplifying things, so then I can complicate them.
I noticed a very similar phenomenon when I first encountered great Indian C++ programmers.
My code was serviceable and did the job.
The Indians rendered C++ as an art form. They didn't even seem to need to go through the analysis and testing process that I did.
They would just sit down and write. Their construction of classes seemed to flow like poetry, and their code just looked pretty, compared to mine, which had no recognizable artistic shape.
An IC engineer from France once complained about the job our company's router did when wiring up the logic "Ees not beautiful. If it ees not beautiful, it will not work beautiful".
There was something to be said for that.
We used to have to use an equation to calculate impedance in parallel signal lines - I always liked that one, but my notes are long gone now, and I can't find a copy of it. It was just a good looking equation.
Neat, Freeman.
Music of the spheres. Math and music are deeply intertwined.
Euclid alone has looked on Beauty bare said Edna St. Vincent Millay.
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