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Thread: Beautiful Mind - Jason Padgett and Fractals
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05-01-12, 10:46 AM #12
Re: Beautiful Mind - Jason Padgett and Fractals
that's a bit harsh bunni, the man needs a purpose. what's irritating isn't that someone may or may not need him, it's that as a genius, like so many geniuses, he's not able to create something useful with his talent himself (yet anyway). i leave you with this thought:
"Nothing in the world can take the place of Persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not; the world is full of educated derelicts. Persistence and determination alone are omnipotent. The slogan 'Press On' has solved and always will solve the problems of the human race." - Calvin Coolidge
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05-01-12, 11:13 AM #13
Ah that makes sense in regards to your comment. Thank you. I took that as less of a slight and more of a comment or statement about the novelty or oddity (at least with respect to "common" perceptions of intellect) of a highly intelligent individual doing a more mundane set of tasks. I realize the false assumption there, but also see it for a literary device and not an insult or aspersion in this instance.
Sent via highly charged bolt of electricity.
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05-01-12, 11:27 AM #14
Re: Beautiful Mind - Jason Padgett and Fractals
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05-01-12, 02:01 PM #17
Re: Beautiful Mind - Jason Padgett and Fractals
BTW Derek (if you're still paying attention to this thread that you commented on) - you should read pages 3-5 of the paper, IRB approved and funded too, where it talks about his drawing of Pi and his mathematical proof proving it:
https://docs.google.com/file/d/0B0GE.../preview?pli=1
JP then made a drawing
of Pi with a ruler and compass (Fig 1, 2). The result was amazing. He didn’t know what it meant.
But he instinctively knew it was important. He later realized his drawing represents an equation
and proved it (Fig 3). Pi is the ratio of the perimeter, Pn, of a regular polygon with n sides
circumscribed around a circle with diameter d to d, as n increases to infinity. With n = 6 (a
hexagon), we get 3. With n = 360, we get 3.141552779, and with a higher n, we get an even
better approximation. Regardless of how high we set n, we will never quite get Pi, because Pi is
a limit. As JP points out, the problem of getting the exact value of Pi is similar to the problem
that Mandelbrot had with measuring the perimeter of a coastal line. The smaller the yardstick
you use the longer the perimeter, and if you were to keep making the yardstick smaller, you’d
have an infinite perimeter. This is also known as the “Yardstick Problem”.
Sometime after JP begun drawing, he had started working in a furniture store, and he was
eager to show his drawings to people. He realized that while people thought his drawings were
fascinating, most people didn’t understand what he said about them. A mathematician told him
that he had to learn to speak the language of mathematics if he wanted to make himself
understood. He then went and took a trigonometry class and a couple of calculus classes at a
local community college. This made him realize that his drawings depicted approximations of
mathematical fractals. In 2010 JP won Best International Newcomer in the Art Basel Miami
Beach competition.
Synesthesia and Savant Syndrome
JP never received an official diagnosis of his condition. An assessment of his symptoms,
however, suggests that he has synesthesia, savant syndrome, OCD and atypical function of
areas in the occipitotemporal intersection.
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05-02-12, 05:03 PM #18Re: Beautiful Mind - Jason Padgett and Fractals
That is a fractal. The pictures in the article (including the circle) are not fractals. They are envelopes, which are completely unrelated.
As JP points out, the problem of getting the exact value of Pi is similar to the problem
that Mandelbrot had with measuring the perimeter of a coastal line. The smaller the yardstick
you use the longer the perimeter, and if you were to keep making the yardstick smaller, you’d
have an infinite perimeter. This is also known as the “Yardstick Problem”.
Taking a look at the picture of the proof in the article, it is circular and therefore meaningless. The final lines, as far as I can read, say f(x) = x*sin(pi/x), f(x)->pi as x->infinity. This is true, but useless for defining pi, because the formula already includes pi. Furthermore, based on reading the article, it appears that the proof is based on calculating the perimeter of regular n-gons as n goes to infinity. If this is correct, I did the same thing in 10th grade and my math teacher correctly pointed out to me that it is circular, for the reason above.
I hate to be the party pooper here, but this man is no mathematical genius.Last edited by Derek; 05-02-12 at 05:12 PM.
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05-02-12, 05:22 PM #19Re: Beautiful Mind - Jason Padgett and Fractals
enf-Jesus its been like 12 minutes and you're already worried about stats?! :-P
Bigdog-Sweet home Alabama you are an idiot.
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05-02-12, 09:49 PM #20
I agree that it will be interesting to see what he accomplishes, if anything. I'll be honest and say that this story fascinates me.
I'm a bit curious as to why you're doubtful of the savant description though. He seems to match many of the descriptions that I've read about over the last few days. This fascinates me because I went to school with a boy who was a mathematics savant and a functional autistic. So that's basically my interest. I have no reason to discount the IRB paper or the author's hypothesis. It seems reasonable to me at this juncture. Granted more research is needed. Hopefully there will be more research. But I can says he's not the first person to "become" a savant after trauma of some type.
As for the fractals, I'm not a mathematician. In math I am a layperson. I freely admit that. But what I am is a highly analytical person and am paid quite well for my analytical skills. With that said I take in concepts pretty well and pretty quickly. With that said, many of his drawings have, what appear to me, fractal like qualities, namely self-symmetry across various levels of magnification. His point about Pi perhaps is not well explained (or perhaps his thought process through the explanation) but I find it an interesting thought nonetheless and see it as perhaps a novel new way of thinking about an old concept.
At any rate, the jury on this is still decidedly out. If it turns out to be insignificant that's ok. It is cool art regardless. But if it turns out to be something more than substantive, that would be cooler still.
Sent via highly charged bolt of electricity.
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