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gravenewworld
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http://abcnews.go.com/blogs/health/...al-genius-draws-complex-math-formulas-photos/Don't know if he really is a genius at math now, but at least he can draw some cool pictures. So who wants to hit me on the head?
The author of that article is no judge of mathematical genius.Pi, that infinite number that begins with 3.14.
Jimmy Snyder said:The authors of that article are no judges of mathematical genius.
gravenewworld said:http://abcnews.go.com/blogs/health/...al-genius-draws-complex-math-formulas-photos/Don't know if he really is a genius at math now, but at least he can draw some cool pictures. So who wants to hit me on the head?
... some call a mathematical genius of unprecedented proportions.
You're right.Dembadon said:Articles like that grieve me. I think he has a promising career in graphic design, but I saw nothing in that article which justifies the use of the word "genius" to describe his mathematical ability. I'm really not trying to be pretentious here, I just don't like it when the media bastardizes math and science to make a story.
EDIT:
Are you effing kidding me?! Riiiiiight: Euler, Gauss, Euclid, Riemann, Newton, etc. don't have anything on this guy! :uhh:
I have officially moved from grief to complete disgust.
There is no connection between brain damage and autism. The criteria for a diagnosis of autism can be found here:zoobyshoe said:You're right.
The story here, what is authentically of interest, is that his brain trauma completely changed his personality, narrowing his focus from the standard general range of interests to a dedicated obsession with geometric looking patterns. He virtually went from a normal person to something indistinguishable from a high functioning autistic savant. This is the first time I've ever heard of this happening, and the particular brain damage he suffered should be thoroughly studied for what it may have to say about autism.
The criteria for the diagnosis is a separate consideration from the cause. The DSM declines to ascribe a cause. That's true of just about every diagnosis in the DSM except those involving drug abuse. There is, however, a vast amount of research, past and present, trying to uncover the cause. The fact this man's brain damage has rendered him so much like an autistic savant is definitely of interest in what it may say about autism.Jimmy Snyder said:There is no connection between brain damage and autism. The criteria for a diagnosis of autism can be found here:
DSM-IV
Besides monomania, what other criteria does he exhibit?zoobyshoe said:The criteria for the diagnosis is a separate consideration from the cause. The DSM declines to ascribe a cause. That's true of just about every diagnosis in the DSM except those involving drug abuse. There is, however, a vast amount of research, past and present, trying to uncover the cause. The fact this man's brain damage has rendered him so much like an autistic savant is definitely of interest in what it may say about autism.
Monomania?Jimmy Snyder said:Besides monomania, what other criteria does he exhibit?
zoobyshoe said:The fact this man's brain damage has rendered him so much like an autistic savant is definitely of interest in what it may say about autism.
Remembering back to algebra we learned that you can graph any equation. So if you take a basic function say f(x)= 2x + 1 and graph it you translate the points onto a graph and make a line. If x=0 then y=1, if x=1 then y=3 etc. We are doing the same thing with fractals only we are translating the ENTIRE SHAPE instead of just a point.
http://www.fantastic-fractals.com/Make-a-Fractal.html
At the hospital they told him he had a concussion, and to get some rest. But when Padgett went back home, he immediately went on the longest drugless acid trip of all freaking time. On sunny days, the little bit of light that bounced off a car's window would suddenly explode into an array of triangles. Every time an object moved, it left strange patterns behind. The edges of clouds and liquids became spiraling lines. The dude thought he was either going crazy or being haunted by the ghost of geometry. Either way, he stayed mostly inside his house for three freaking years.
...Padgett decided he'd go ahead and start drawing the shapes he saw.
...someone who saw his art noticed that the drawings looked kind of mathy, so they suggested that Padgett take math classes at the community college so he could learn how to describe them.
http://www.cracked.com/article_19504_6-people-who-gained-amazing-skills-from-brain-injuries.html
Padgett...is widely acknowledged as the only person able to hand-draw fractals (for a tidy profit, of course!). He also has advanced the fields of math and physics with his intuitive understanding of those weird repeating shapes. He even discovered that Einstein's E=mc² is a fractal.
I like the way you put this. It's clear the vague allusions to pythagorean theorem and pi and fractals are a poor attempt at rationalizing what he's doing. It's obvious on the first reading of the OP's link he did not acquire mathematical genius, or even above average math skills. All he's seems to have acquired is an obsession with drawing geometric patterns, which is quite a different proposition than doing and understanding geometry.apeiron said:Then later he learned to retrofit some mathematical justification to the simple patterns he was obsessively drawing.
Yeah. A few years ago I taught myself how to tie a Turk's Head knot:Dickfore said:I used to do these kinds of drawings in my 6th grade geometry class, as well as my Computer Science in QBasic :)
[/PLAIN]
Spirograph, anyone?
zoobyshoe said:I like the way you put this. It's clear the vague allusions to pythagorean theorem and pi and fractals are a poor attempt at rationalizing what he's doing. It's obvious on the first reading of the OP's link he did not acquire mathematical genius, or even above average math skills. All he's seems to have acquired is an obsession with drawing geometric patterns, which is quite a different proposition than doing and understanding geometry.
In a series of functional MRI studies in Finland, Brogaard's team found uni-lateral left-side activity in parietal and frontal areas when Padgett was exposed to the mathematical formulas that give rise to synesthetic fractals in him and bi-lateral activation when he was exposed to non-sense formulas or formulas that don't give rise to synesthetic fractals.
http://en.wikipedia.org/wiki/Berit_Brogaard
Yes.apeiron said:Digging into it a bit more, I see he is also tied in with this lot...
http://www.consciousness.arizona.edu/WorkshopSynesthesia2012.htm
So a lot of bad science behind the bad journalism.
Here is Padgett describing his symptoms first hand in a short clip...
His description of trailing and jitter effects are not synesthesia at all in my book. More the kind of visual disturbances that you get from brain damage that results in integrative failures in the visual hierarchy. Or Hallucinogen Persisting Perception Disorder (HPPD).
There is a wiki page claiming that brain scans show he only reacts to actual fractal equations, but I've not been able to track down the papers as yet, so that looks like unpublished stuff. And given the other information, I would still be dubious.
However, giving the case for the other side (because whatever the explanation, it is interesting the spin that is getting put on all of this)...
And here is a clip which suggests the test stimuli were actual objects rather than equations. Possibly this was just a different experiment, but it does give yet more first-hand accounts of what Padgett experiences, and ties it to motion processing issues.
It is believed that the reason why these form constants appear has to do with the way the visual system is organized, and in particular in the mapping between patterns on the retina and the columnar organization of primary visual cortex. Concentric circles in the retina are mapped into parallel lines in visual cortex. Spirals, tunnels, lattices and cobwebs map into lines in different directions. This means that if activation spreads in straight lines within the visual cortex, the experience is equivalent to looking at actual form constants.
zoobyshoe said:A guy I know here, who's been diagnosed as somewhere on the autistic spectrum, described this same difficulty with following the motion of cars or busses to me.
zoobyshoe said:Sacks mentioned a woman whose visual field would freeze and stick due to the sight of certain motions. Pouring tea was one trigger.
zoobyshoe said:If the sight of the formula for a fractal causes him to see the pattern of a fractal, I still wouldn't call that synesthesia, just hallucination. I wouldn't call him a savant either, unless they've conclusively determined that the image he sees is the one that would, in fact, be generated by the formula they showed him.
zoobyshoe said:I have an inkling he may only be seeing "form constants". Hallucinogenic drugs, and many other things that affect the brain cause people to see geometric patterns that a guy named Kluver dubbed "form constants". (Migraine aurae are another well known cause of this.)
One region that stands out as a possible target area for JP’s lesion is the lateral occipital complex (LOC). Lateral occipital complex is the lateral-posterior area of the occipital lobe (visual cortex), just abutting the posterior area of the motion-sensitive area MT/V5. LOC shows preferential activation to images of objects, compared to a wide range of texture patterns (Malach 1995, Grill-Spector et al. 1998, Wong et al. 2009, Pourtois et al. 2009). As LOC generates the same response for objects regardless of their shape, it may be considered an intermediate link in the chain of processing stages leading to object recognition in visual cortex.
LOC is also known as ‘visual memory’. It is responsible for object persistence for a few seconds after the stimuli was been removed (Wong et al. 2009) and is involved in rotation-invariant shape processing (Silvanto et al. 2010). As JP does not see object boundaries as smooth and invariant over time, it is possible that the assault in 2002 caused injury to LOC.
https://docs.google.com/file/d/0B0GEjtSycjTKNmUzYjgyMjctOWFjNC00N2Q1LThlMzUtNTk0MzM3YzAyODU3/edit
It may well be common, but I haven't heard it specifically described by anyone except the one guy I met. Donna Williams doesn't specifically describe anything like this in the above link, and I don't recall Temple Grandin mentioning anything like it in Sack's writings about her.apeiron said:I thought this was quite a common symptom - and one that fits with autism being a low-level integration issue.
Donna Williams described her perceptual issues well in her autobiography, which you would enjoy - http://www.donnawilliams.net/about.0.html
When I say he might just be seeing form constants, I'm not talking about the jerky motion disturbance, which is a separate problem. I'm talking about the geometric patterns that he sees and tries to draw.Yes, it sounds very much like the kind of things reported with migraine auras.
Though rather than form constants, Brogaard at least cites the kind of boundary and motion perception distortions that can result from targetted brain damage.
And you've probably seen this useful classification of visual disturbances...
http://www.migraine-aura.org/content/e27891/e27265/e26585/e48971/e48980/index_en.html
zoobyshoe said:It may well be common, but I haven't heard it specifically described by anyone except the one guy I met. Donna Williams doesn't specifically describe anything like this in the above link, and I don't recall Temple Grandin mentioning anything like it in Sack's writings about her.
...bestselling autistic author, Donna Williams, in her book Like Colour To The Blind wrote about her experience of tinted lenses (Irlen filters) after being diagnosed with scotopic sensitivity. In this book she described the lenses as enabling her to have cohesive, unfragmented vision, able to see faces, bodies and objects as a whole for the first time and reducing the extremity of experiences such as meaning-blindness, face blindness, inability to learn to read facial expression and body language and the social consequences of these impairments. This led to a worldwide raised awareness of scotopic sensitivity as a sensory perceptual problem common in many (but not all) people with autism and expanded awareness of the potential effects of Scotopic Sensitivity far beyond that of reading disability, also leading to awareness of the effects of fluorescent lighting on those with this perceptual disorder.
http://en.wikipedia.org/wiki/Scotopic_sensitivity_syndrome
...individuals with autism. The accounts of remarkable people like Temple Grandin, Donna Williams, Jim Sinclair, Darren White, Sean Barron, Thomas McKean, Georgina Stehli...Some of the most fascinating insights are the descriptions of sensory perception. Almost every first-hand account has described some distortion of one or more of the sensory channels to the brain - seeing, hearing, smelling, tasting, or feeling. These individuals describe in detail distortions in both extremes of hyper- and hypo-sensitivity which often fluctuated, alternated and changed over time. Temple Grandin's book Emergence: Labelled Autistic, (1986) recounted her sensitivity to touch:...
http://dragonflytoys.com/specialneeds/universalaccess/resources/articles/browsedetail/usa/Article/All/1/174/0
The first classification of sensory dysfunction in autism was introduced by Carl Delacato (1974) who suggested that each sensory channel could be hyper-, hypo-, or “white noise” (interference within the system). Concerning vision, hyper- means that too much sensation comes to the brain through eyes; hypo- means, not enough sensation gets into the brain, while “white noise” occurs when the eyes are “directed inside” (Delacato, 1974).
http://www.google.co.nz/url?sa=t&rc...yNnhBA&usg=AFQjCNFVDE4blJdVKJNmaYfhCUNxPNsSMQ
zoobyshoe said:When I say he might just be seeing form constants, I'm not talking about the jerky motion disturbance, which is a separate problem. I'm talking about the geometric patterns that he sees and tries to draw.
At the Migraine link, one sufferer submitted an image he created of his visual aura..Have a look. It strikes me as a superimposition of two form constants.
ThomasT said:Not to disrupt the flow of the discussion, which is interesting, but as an aside, are the images that Padgett is drawing actually fractals?
Ok, that's what I'm seeing. As far as I can tell Padgett's drawings are not graphing fractal sets.apeiron said:Not by any strict definition I would say. They are not scale invariant - zoom in and you don't continue to see exactly the same thing.
What he seems to mean by fractal is he draws some basic unit - like a pentagon inside a circle divided up by right triangles. Then repeats. There is no scale change in the exercise. Though you do then get a messy intersection pattern because of the overlap.
Interesting, and essential, considering the claims.apeiron said:That is why it would be interesting to see the "fractal equations" Brogaard claims to have used in her brain scan experiment.
So far ... I agree.apeiron said:So far, the whole maths slant looks bogus.
Maybe I'm just too ignorant. But, this doesn't make any sense to me.fantastic-fractals.com said:This is a hand drawn fractal of the structure of space time at the quantum level (Planck length/Planck Particle size frame). It shows a time lapse film of a mathematical savant, Jason Padgett, hand draw the fractal. Color was added by computer and wave equations make his drawing vibrate. The equation describes the geometric connection between the quantum energy (very small, hw) and the the energy described by Einstein's famous E=mc^2.
Is that what fractals arise from? I don't know. Just asking.fantastic-fractals.com said:Jason Padgett discovered how fractals arise from relativity and limits.
ThomasT said:Maybe I'm just too ignorant. But, this doesn't make any sense to me.
Is that what fractals arise from? I don't know. Just asking.
Thanks for the replies. Now back to your more interesting discussion regarding what changes might have happened to Padgett's brain via his injury, and how that might have affected his behavior.apeiron said:No need to take this seriously at all. You can see the whole story as a very neat bit of cultural myth making. Brain-damaged nobody becomes scientific/artistic genius. Padgett is at least probably enjoying the fame and the cash.
The art world does this all the time. I once even got paid handsomely to write up a blurb on the science of memory for some guy's exhibition catalogue. He was a proper artist doing good stuff. But it was just marketing - adding a bit of scientific gloss to make the work seem deeper.
You can see other examples of Padgett's drawings that look more self-consciously fractal...
http://fineartamerica.com/featured/-quantum-tree-jason-padgett.html
http://fineartamerica.com/featured/quantum-nautilus-spotlight-jason-padgett.html
This is what I'm also saying about the guy I know whose visual disturbance (cars moving forward with a "jerky motion") sounds like Padgett's: I haven't run across anyone else on the autistic spectrum who reports this particular distortion. Therefore, I was surprised to hear you say you thought it was common. Apparently you didn't realize I was only referring to the jerky motion distortion.apeiron said:The sensory disturbances in autism do not sound like Padgett's though...
I would suspect form constants first, because they are so widely reported and many different things can cause them.It could be that. Form constants are visual disturbances focused in the lower visual hierarchy - V1 and V2.
While there is no scientific evidence to support a direct link between getting mugged and becoming a mathematical savant, some studies have shown that traumatic events can trigger changes in the brain that lead to enhanced cognitive abilities, including in the realm of mathematics. It is possible that the stress and adrenaline rush associated with being mugged could have a similar effect.
No, not everyone who experiences a traumatic event will develop savant-like abilities. It is believed that a combination of genetics, brain structure, and environmental factors all play a role in determining whether someone will exhibit savant-like abilities after a traumatic event.
The specific abilities gained may vary depending on the individual, but common traits of mathematical savants include exceptional memory and pattern recognition skills, as well as an ability to perform complex calculations quickly and accurately. Some may also develop a heightened intuition for solving complex mathematical problems.
Yes, while some individuals may retain their enhanced mathematical abilities for a long period of time, it is not permanent and can fade over time. Additionally, there are cases where individuals have regained their previous level of mathematical abilities after losing them for a period of time.
While there have been documented cases of individuals gaining enhanced mathematical abilities after a traumatic event, there is no evidence to suggest that being mugged specifically triggers savant-like abilities in other areas. However, it is possible that other types of abilities, such as artistic or musical abilities, could also be triggered by a traumatic event.