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# When I was a little kid, my mother told me not to stare into the sun, so when I was six I did.

so what was I doing when I was drawing Sierpinski triangles and Koch snowflakes in the margins of my notes in boring classes?

posted by madcaptenor at 8:53 AM on July 25, 2011 [4 favorites]

You're thinking of Achilles. Hercules could get close enough to the hare for all practical purposes and then grab it and wring its neck.

posted by madcaptenor at 9:02 AM on July 25, 2011 [6 favorites]

SPACE IS A 4-DIMENSIONAL TIME-FRACTAL.

posted by atrazine at 9:03 AM on July 25, 2011 [7 favorites]

Aesthetic choice, bonobothegreat. I consider myself fairly well versed on the double-slit experiment, since it's a foundation of my career field, and the "halo" is only there to make the phenomenon of interference make sense as a visual aid.

Put another way, it's a piecewise approximation to a diffraction wave front, drawn from four different times in the propagation: initial source, first halo time choice, time of passing through the slits (= end of 1st halo), second halo time choice, and final (end of 2nd halo) time choice.

posted by IAmBroom at 9:31 AM on July 25, 2011

Best art dealer line ever!

posted by R. Mutt at 9:33 AM on July 25, 2011 [2 favorites]

THAT'S that guy's name! I have the disinfo's 'Book of Lies' that has a great interview with him. I love his works, they all looks like very well-produced diagrams taken from a detailed handbook titled 'HOW TO BE FUCKING NUTS'.

posted by FatherDagon at 9:50 AM on July 25, 2011 [3 favorites]

I see what you did there.

posted by orme at 10:19 AM on July 25, 2011 [1 favorite]

Mine is pegged to "potential Gene Ray contender". I don't think he actually knows what either "quantum" or "fractal" actually mean, but neither are represented by what amounts to string art. None of his art is even actually recursive. And he's not the first to do any of this. I was making curves out of lines by using grids and rulers when I was in grade school, and like many other people I've found myself doodling natural Sierpinski triangles and foams before I ever knew what they were.

I still make recursive geometric art, too, but it's

I have to correct people fairly frequently who say "Oh, those are nice fractals. What program did you use to make those?", which is frustrating. I do illustrate them in a vector graphics program, but there's no "automatic" image generator or anything. I could easily be making the same art with ink and paper and a graphic arts camera. I just can't get 5 decimal places of precision on paper with a pencil, compass and french curve, and the step and repeat work on camera would take months or years and thousands of dollars in film to recreate the same thing I can do in Illustrator or CorelDraw in hours. A computer generated bezier curve also has a functional and conceptual width of "zero". That arbitrary precision is important to me not just as a designer but as an aesthetic tool. There's no way to draw a line with "zero" width on paper. Cutting photo-masking film with an x-acto blade still wouldn't be precise enough for my tastes.

Fractals are a very specific kind of math formula. You can't actually accurately render a fractal on a computer screen or a piece of paper. There's a reason why fractal generators work with grids of pixels - you can't physically represent a fractal without telling the algorithm to "bail out" at a certain level of calculation and stop calculating more detail. You can't tell it to draw, say, a precise bezier curve of the actual fractal without defining a "bail out" level. You would literally run out of atoms. As in, there aren't enough atoms in the universe to accurately map it whether it's in pure math in the form of electrons stored on a computer or graphically as a visual display or printout.

It would probably be easier to actually define how long England's coastline is. Which as we know... is also impossible. Or nigh impossible, at least.

Here, check this out. It's about fractals and arbitrary precision in an old homebrew fractal exploring program called Fractint (fractal+integer) and it neatly illustrates how insanely complex fractals really are:

posted by loquacious at 11:15 AM on July 25, 2011 [6 favorites]

I've read the paper.

I've hidden prime numbers and Fibonacci sequences and other recursive or generative math in my art as well. It's seems to be rather inherent when playing around with geometric or math-based art. Prime numbers are aesthetically pleasing when conveyed visually. The numbers I choose for step-and-repeat patterns and the scaling/skewing values between iterations are intentionally chosen.

People have been embedding things like Pi, the Golden Ratio and prime numbers in art for centuries, if not since the dawn of art. The Golden Ratio in particular has been used in composition for a long time to calculate an interesting visual center. Look at the fantastic tiled mosaics of a mosque. Or the arrangement of idols in a Buddhist temple. Many so-called "primitive" pre-historic art attempts to convey "entoptic visions" from shamanistic psychedelic experiences - which are also arguably often directly related to math and even fractals.

Which brings us back to synesthesia. I know exactly what he's talking about because I've taken psychedelics and I've experienced the same things. It's qualitatively the same thing - you can see math everywhere. In the foam of bubbles in the kitchen sink, in the branching of trees, in the splitting of atoms and how subatomic particles move and interact, in the topological complexities of membranes. It's not an uncommon thing at all, in fact it seems to be fundamentally involved with how we're able to visualize symbology and formal systems in our minds, and how we think about and explore things like math.

The only unique thing here is that he's suffered a traumatic brain injury that gives him easier access to these mental states, which is illuminating to scientists who study the mind because it challenges their erroneous assumptions about how the brain works.

Which in my estimation the brain doesn't work in the linear, concrete ways that classical philosophers and psychologists want it to work. It works with fuzzy math and fractal-like constructs because nature is fuzzy and fractal-like, but follows predictable rules. We've evolved to find useful information in that noisy, fuzzy natural world, things that stand out and contrast from the fractals and noise that surround us every day.

Sure, I think that what he's seeing and trying to describe is valid, but I still think he's mis-using the terms "quantum" and "fractal", and that Brit Brogaard doesn't actually know what a fractal is, either. The drawings he's creating are very much

I'm not doubting he's gained savant-like abilities from his head trauma. I'm doubting the accepted scientific definition of "savant". We all naturally have and use some of these savant-like abilities every day just by being conscious.

You can even experiment with some of these sensations and fascinating processes yourself by way of an sensory deprivation tank or the Ganzfield experiement. (Ignore the parapsychology part, just replicate the sensory isolation.) Or you could eat mushrooms or acid, or meditate until you're tripping. Same difference, really.

posted by loquacious at 1:11 PM on July 25, 2011 [5 favorites]

It phenomenally seems to you that you see all this stuff. But do psychedelics actually make you better at calculation? Do they make the user able to solve math problems with Kim Peek/Rain Man speed? I'm skeptical. JP's not special for making drawings that use mathematical patterns. The claim that his drawings are exceptionally accurate geometric representations of exceptionally complex equations. He's not just tossing a couple of recursive elements into a piece of art; he's building images that using algorithms that are so heavy-duty that normal people like the rest of us could not do without a ton of computer aid. If that's true, that's really cool, and I don't see any reason to think it's not true.

(I don't really see your objection to calling his drawings "approximate fractals," which seems to be a well-defined term.)

That's still an open question, hence the Dehaene/Brogaard debate.

posted by painquale at 1:41 PM on July 25, 2011

Point taken. I'm not out to approximate pi in an unusual way or anything.

I do think this post is interesting and good, but there's a lot of hubris around the artist's own claims and as worded in the post. I nearly choked on my coffee when I read "including hand-drawn approximations of fractals, the first time anyone had ever done so."

This hubris is reflected in the prices of his art, but that's not uncommon in the art world, either. If he actually sold a geometric line drawing (and not a small amount of woo) for 100k I'll admit I'm jealous.

People have been doodling "fractals" - in particular, various kinds of Sierpinski foams - since long before telephones were invented.

Be skeptical, by all means. I have seen people do really intense things with math and/or programming and/or logic in the fugue-state of a psychedelic experience, but they were mathematically minded to begin with.

What I'm describing is more akin to the mental math someone does when catching a ball. When you catch a ball you're naturally calculating a lot of complex, dynamic and time sensitive math. Sure, you're not going to be able to call out the formulas and real numbers that describe the arc of the ball as you're catching it, or the complex geometry of your arm and body moving to catch the ball, much less measure the velocities (paging Heisenberg) - but you still caught the ball. And we do and understand and use this kind of math in our heads all the time.

So, we all have this innate, natural grasp for math, and this really shows up for a lot of people when they take psychedelics. It's like you get to observe and sense the math underlying your own sensory perceptions, like you can suddenly see the texture and artifacts of the codec algorithm driving your own senses. And then you can observe how that naturally interacts with the math and geometry all around you.

Transcribing those internalized symbologies into real words or formal system symbols that aren't merely thoughts is where the savant part really comes in, though.

Last: He is arguing from a position that states that there's no such thing as a circle, or by definition, a true curve, and that's how he's approaching his "proofs" as they were. As others have pointed out there have been others throughout history that have done this and approximated pi with what is more or less trigonometry.

I argue there's no such thing as a straight line in nature or anywhere in the universe, outside of a symbol or a mathematical abstraction. Take a laser pointer and beam it into the sky, then wave it. You're not waving around a straight line, that stream of photons "bends" and behaves just like water from a garden hose. Even the individual photons will have bent and curved paths in the presence of gravity. The shortest path between two points in reality is almost always curved.

Space is curved, man. Space is curved.

posted by loquacious at 2:14 PM on July 25, 2011 [4 favorites]

It sounds like a relatively simple experiment to conduct, given that all that is needed are a willing mathematician, a suitable psychedelic, and some prompting stimuli.

posted by aeschenkarnos at 2:54 PM on July 25, 2011

Man, I'd love to see that experiment, but it would probably be more effective with someone who has had prior experience with psychedelics. But you could run the experiment both ways.

Anecdotal: I once babysat for a pretty good programmer on his first trip. 30 minutes into it at first onset of effects he was scribbling C code out in longhand on pads of lined paper, and didn't stop for hours. I can't tell you if the code was any good but he kept shouting things like "SO MUCH FASTER THIS WAY" and "MY GOD, WHY DIDN'T I THINK OF THIS BEFORE?"

I can't speak for pure mathematics but psychedelics have a long history and deep roots with programming.

I would wager that everyone here has benefited from it and used concepts, application or code that was either written or conceived under the influence.

posted by loquacious at 3:11 PM on July 25, 2011 [2 favorites]

That's a funny example to pick, because it's a case where we don't actually perform that much computation. Studies have shown that people trying to catch a ball, amateurs and professional ballplayers alike, use a relatively simple heuristic: keep the ball in the center of your visual field. We don't actually compute the arc.

But the particular example's not essential to what you're saying, and the computations involved in keeping the ball in the center of the visual field are non-trivial, so point taken.

posted by painquale at 12:21 AM on July 27, 2011

Post

# When I was a little kid, my mother told me not to stare into the sun, so when I was six I did.

July 25, 2011 8:32 AM Subscribe

Jason Padgett is the first person to acquire synasthesia and savantism by head trauma. Three years after his mugging, he began drawing complex geometries, including hand-drawn approximations of fractals, the first time anyone had ever done so. Eventually a mathematician suggested Padgett take a math course; with trigonometric notation Padgett offered a proof of his approximation of Pi.

Description of JP's case by Brit Brogaard, professor of philosophy and psychology at University of Missouri. Includes rather captivating comparison of some of Padgett's art and a real picture of electron interference patterns. Via her site.

Most of Padgett's art doesn't make a lot of sense to me, but I completely love his depiction of the double-slit photon experiment.

Some mathematicians and physicists don't seem impressed. Link not offered due to train-wreckiness (google it for yourself if you like), but Padgett's posts on some specialist forums result in derision.

Previously:

Daniel Tammet the savant

Kim Peeks, the real life Rain Man, dies

Temple Grandin

Savant for a day

Synesthesia

Description of JP's case by Brit Brogaard, professor of philosophy and psychology at University of Missouri. Includes rather captivating comparison of some of Padgett's art and a real picture of electron interference patterns. Via her site.

Most of Padgett's art doesn't make a lot of sense to me, but I completely love his depiction of the double-slit photon experiment.

Some mathematicians and physicists don't seem impressed. Link not offered due to train-wreckiness (google it for yourself if you like), but Padgett's posts on some specialist forums result in derision.

Previously:

Daniel Tammet the savant

Kim Peeks, the real life Rain Man, dies

Temple Grandin

Savant for a day

Synesthesia

Judging from his handwriting I'm guessing he uses rulers and protractors.

posted by nathancaswell at 8:41 AM on July 25, 2011 [1 favorite]

posted by nathancaswell at 8:41 AM on July 25, 2011 [1 favorite]

Whoops, just noticed this in a sidebar...

posted by nathancaswell at 8:42 AM on July 25, 2011

*All are HAND DRAWN using only a pencil, ruler and compass.*posted by nathancaswell at 8:42 AM on July 25, 2011

Not that these aren't neat drawings, but on first pass I don't see anything out of the reach of the average dedicated person with a ruler and a mechanical pencil.

posted by odinsdream at 8:43 AM on July 25, 2011 [3 favorites]

posted by odinsdream at 8:43 AM on July 25, 2011 [3 favorites]

I wonder if my spirograph is still up in Mom and Dad's attic....

posted by Brodiggitty at 8:47 AM on July 25, 2011 [3 favorites]

posted by Brodiggitty at 8:47 AM on July 25, 2011 [3 favorites]

This is really oversold. If the story was 'This guy got hit in the head and suddenly developed an interest in making these precise, repetitive geometric drawings', it would be interesting. Trying to claim he's tapped into the mathematical secrets of the universe is much too much, and ruins it for me.

Hell, I learned how to do those exact drawings in sixth grade. Tick off evenly spaced points on two lines, then use a ruler to connect pairs in sequence. Takes a lot of patience, but I liked it a lot when I was 11.

And they're really not fractals, which have the defining property of being self-similar at different levels of magnification. I don't see any drawings here that do that.

That said, I'm sorry he got injured and glad he's found a bright side to a traumatic event. I hope he keeps enjoying geometric drawing; it can be almost like meditation when you really get into it. But I also hope he drops the woo.

posted by echo target at 8:49 AM on July 25, 2011 [6 favorites]

Hell, I learned how to do those exact drawings in sixth grade. Tick off evenly spaced points on two lines, then use a ruler to connect pairs in sequence. Takes a lot of patience, but I liked it a lot when I was 11.

And they're really not fractals, which have the defining property of being self-similar at different levels of magnification. I don't see any drawings here that do that.

That said, I'm sorry he got injured and glad he's found a bright side to a traumatic event. I hope he keeps enjoying geometric drawing; it can be almost like meditation when you really get into it. But I also hope he drops the woo.

posted by echo target at 8:49 AM on July 25, 2011 [6 favorites]

Yeah, the "approximation of pi" drawing is what anyone would get drawing a bunch of evenly spaced line segments tangent to a particular circle (no right angles necessary). The description that accompanies it in the sidebar is a mixture of trivially true statements and "not even wrong" quantum woo-woo bullshit.

posted by AkzidenzGrotesk at 8:50 AM on July 25, 2011 [2 favorites]

posted by AkzidenzGrotesk at 8:50 AM on July 25, 2011 [2 favorites]

I have some string art on black velvet somewhere that looks a lot like the double slit test. Can someone can explain what property defines the width of the "halos"?

posted by bonobothegreat at 8:51 AM on July 25, 2011 [1 favorite]

posted by bonobothegreat at 8:51 AM on July 25, 2011 [1 favorite]

*including hand-drawn approximations of fractals, the first time anyone had ever done so.*

so what was I doing when I was drawing Sierpinski triangles and Koch snowflakes in the margins of my notes in boring classes?

posted by madcaptenor at 8:53 AM on July 25, 2011 [4 favorites]

Oh man, I didn't even read the bit jcreigh quoted until just now. Either someone is a well-intentioned crank with absolutely no clue about real physics, or we are being trolled.

posted by AkzidenzGrotesk at 8:54 AM on July 25, 2011

posted by AkzidenzGrotesk at 8:54 AM on July 25, 2011

Most of the hype is built by Jason himself, and I think he mistakes the interest of psychologists in his case to be an interest in his physics itself. According to the Brit Brogaard piece, mathematicians have been consulted to confirm that he's drawing geometries that do approximate what he's reporting he sees, but the real interest of the neuroscientists is in the synesthesia and OCD.

posted by Made of Star Stuff at 8:55 AM on July 25, 2011 [1 favorite]

posted by Made of Star Stuff at 8:55 AM on July 25, 2011 [1 favorite]

Wow, yeah, just read the description on the "approximation of pi" drawing. The woo is strong with this one. Of course there's no such thing as a perfect circle in the physical world, just as you can't duplicate a solid in the real world, but mathematics is not the "real world". And then he gets into relativity and how it relates to circle approximations which is just... what?

Next, find out why Hercules will never be able to overtake the hare!

posted by kmz at 8:56 AM on July 25, 2011 [1 favorite]

Next, find out why Hercules will never be able to overtake the hare!

posted by kmz at 8:56 AM on July 25, 2011 [1 favorite]

Some MeFites don't seem impressed, either.

posted by Curious Artificer at 8:58 AM on July 25, 2011

posted by Curious Artificer at 8:58 AM on July 25, 2011

The only similarity I see between one of his drawings and the electron interference pattern is that they have a fairly simple six-fold symmetry - and the latter comes not from the electrons but the grating they're passing through. Which I think breaks any link suggested in the article text. There's nothing insightful in noting a similar symmetry.

posted by edd at 9:02 AM on July 25, 2011

posted by edd at 9:02 AM on July 25, 2011

*Next, find out why Hercules will never be able to overtake the hare!*

You're thinking of Achilles. Hercules could get close enough to the hare for all practical purposes and then grab it and wring its neck.

posted by madcaptenor at 9:02 AM on July 25, 2011 [6 favorites]

Drawing circles by drawing a shitload of tangents to the circle you want to draw, until the tangents accumulate enough to approximate the perimeter, is

I don't think I was actually demonstrating anything fundamental about physics or mathematics (except "a visual representation of a circle's perimeter can be approximated given a sufficient number of tangents to that circle"), and I don't recall any significant impacts to the head.

posted by penduluum at 9:02 AM on July 25, 2011

*super fun*. I used to do it all the time as a kid. It used to be one of my go-to doodles.I don't think I was actually demonstrating anything fundamental about physics or mathematics (except "a visual representation of a circle's perimeter can be approximated given a sufficient number of tangents to that circle"), and I don't recall any significant impacts to the head.

posted by penduluum at 9:02 AM on July 25, 2011

*His latest discovery is how all fractals arise from limits and how E=MC2 is itself a fractal. Showing that energy is a fractal shows the reason that all shapes are fractals.*

SPACE IS A 4-DIMENSIONAL TIME-FRACTAL.

posted by atrazine at 9:03 AM on July 25, 2011 [7 favorites]

Cosmic string art?

posted by stinkycheese at 9:11 AM on July 25, 2011

posted by stinkycheese at 9:11 AM on July 25, 2011

Oh man, I just noticed you can buy the original "Shape of Pi" drawing for A MILLION DOLLARS. Nobody's bitten yet, but apparently someone shelled out a hundred grand for the double slit drawing that looks like it was all but copied from a Google image search. I've got to move this guy over to the "scammers and bullshit artists" column.

posted by echo target at 9:11 AM on July 25, 2011

posted by echo target at 9:11 AM on July 25, 2011

My son at age 4 was doing incredible patterns with only note cards and colored pencils. No rulers or protractors or compass. He is very smart indeed, but not a savant.

posted by Katjusa Roquette at 9:11 AM on July 25, 2011

posted by Katjusa Roquette at 9:11 AM on July 25, 2011

This is not an owl. It is actually the first known precise realization of the equivalence between the categories of commutative Frobenius algebras and two dimensional topological quantum field theories.

posted by Wolfdog at 9:17 AM on July 25, 2011 [6 favorites]

posted by Wolfdog at 9:17 AM on July 25, 2011 [6 favorites]

Give this guy another few years and I bet he'll be producing Paul Laffoley level batshit art. That said, I wouldn't mind his double slit print (or a Laffoley print) hanging on my wall.

Really? Let me know when a head injury renders someone capable of building a functioning TARDIS. Only a matter of time right?

posted by cirrostratus at 9:17 AM on July 25, 2011 [4 favorites]

*"the first person to acquire synasthesia and savantism by head trauma"*Really? Let me know when a head injury renders someone capable of building a functioning TARDIS. Only a matter of time right?

posted by cirrostratus at 9:17 AM on July 25, 2011 [4 favorites]

Echo target: it might have a superficial resemblance but I can't see much of the physics inthis guy's work.

posted by edd at 9:22 AM on July 25, 2011

posted by edd at 9:22 AM on July 25, 2011

*I have some string art on black velvet somewhere that looks a lot like the double slit test. Can someone can explain what property defines the width of the "halos"?*

Aesthetic choice, bonobothegreat. I consider myself fairly well versed on the double-slit experiment, since it's a foundation of my career field, and the "halo" is only there to make the phenomenon of interference make sense as a visual aid.

Put another way, it's a piecewise approximation to a diffraction wave front, drawn from four different times in the propagation: initial source, first halo time choice, time of passing through the slits (= end of 1st halo), second halo time choice, and final (end of 2nd halo) time choice.

posted by IAmBroom at 9:31 AM on July 25, 2011

*Right now is the time to own one since currently he is the only person who can do it.*

Best art dealer line ever!

posted by R. Mutt at 9:33 AM on July 25, 2011 [2 favorites]

*Paul Laffoley level batshit art.*

THAT'S that guy's name! I have the disinfo's 'Book of Lies' that has a great interview with him. I love his works, they all looks like very well-produced diagrams taken from a detailed handbook titled 'HOW TO BE FUCKING NUTS'.

posted by FatherDagon at 9:50 AM on July 25, 2011 [3 favorites]

Someone I knew in college got hit on the head and developed synesthesia. It was useful for publishing design, as I recall: he could

That's what he said, anyway. He later had it cured with acupuncture, so who knows what was really going on.

posted by The corpse in the library at 9:57 AM on July 25, 2011 [2 favorites]

*see*(not just imagine) how a page would look if they used green for the background, which was a big deal back in the day of coal-powered computers. But it also made it difficult for him to concentrate on his schoolwork, as every noise was also a visual distraction.That's what he said, anyway. He later had it cured with acupuncture, so who knows what was really going on.

posted by The corpse in the library at 9:57 AM on July 25, 2011 [2 favorites]

Heh. I work with a guy named Jason Padgett - a

posted by mosk at 10:03 AM on July 25, 2011 [1 favorite]

*different*Jason Padgett. I think he'll get a kick out of reading this. I can even offer to hit him in the head if he wants, just in case this latent talent is name-specific.posted by mosk at 10:03 AM on July 25, 2011 [1 favorite]

As far as I can tell, there's only been one Mefi post about Paul Laffoley, and all the links on it are dead. Time for a new one, methinks.

posted by stinkycheese at 10:12 AM on July 25, 2011

posted by stinkycheese at 10:12 AM on July 25, 2011

*a functioning TARDIS. Only a matter of time right?*

I see what you did there.

posted by orme at 10:19 AM on July 25, 2011 [1 favorite]

Berit Brogaard is such an awesome philosopher.

posted by painquale at 10:46 AM on July 25, 2011 [1 favorite]

posted by painquale at 10:46 AM on July 25, 2011 [1 favorite]

Once I got my head knocked pretty hard and immediately and without thinking said "pug dogs and Fig Newtons are the same color."

Which is kind of true, I guess, but has so far netted me neither acclaim nor money.

posted by little cow make small moo at 11:05 AM on July 25, 2011 [11 favorites]

Which is kind of true, I guess, but has so far netted me neither acclaim nor money.

posted by little cow make small moo at 11:05 AM on July 25, 2011 [11 favorites]

*...absolutely pegs my bullshit detector.*

Mine is pegged to "potential Gene Ray contender". I don't think he actually knows what either "quantum" or "fractal" actually mean, but neither are represented by what amounts to string art. None of his art is even actually recursive. And he's not the first to do any of this. I was making curves out of lines by using grids and rulers when I was in grade school, and like many other people I've found myself doodling natural Sierpinski triangles and foams before I ever knew what they were.

I still make recursive geometric art, too, but it's

*a fractal.*

**not**I have to correct people fairly frequently who say "Oh, those are nice fractals. What program did you use to make those?", which is frustrating. I do illustrate them in a vector graphics program, but there's no "automatic" image generator or anything. I could easily be making the same art with ink and paper and a graphic arts camera. I just can't get 5 decimal places of precision on paper with a pencil, compass and french curve, and the step and repeat work on camera would take months or years and thousands of dollars in film to recreate the same thing I can do in Illustrator or CorelDraw in hours. A computer generated bezier curve also has a functional and conceptual width of "zero". That arbitrary precision is important to me not just as a designer but as an aesthetic tool. There's no way to draw a line with "zero" width on paper. Cutting photo-masking film with an x-acto blade still wouldn't be precise enough for my tastes.

Fractals are a very specific kind of math formula. You can't actually accurately render a fractal on a computer screen or a piece of paper. There's a reason why fractal generators work with grids of pixels - you can't physically represent a fractal without telling the algorithm to "bail out" at a certain level of calculation and stop calculating more detail. You can't tell it to draw, say, a precise bezier curve of the actual fractal without defining a "bail out" level. You would literally run out of atoms. As in, there aren't enough atoms in the universe to accurately map it whether it's in pure math in the form of electrons stored on a computer or graphically as a visual display or printout.

It would probably be easier to actually define how long England's coastline is. Which as we know... is also impossible. Or nigh impossible, at least.

Here, check this out. It's about fractals and arbitrary precision in an old homebrew fractal exploring program called Fractint (fractal+integer) and it neatly illustrates how insanely complex fractals really are:

So how far can you zoom? How does 10^1600 sound--roughly 1600 decimal digits of precision. To put this magnification in perspective, the "tiny" ratio of 10^61 is the ratio of the entire visible universe to the smallest quantum effects. With 1600 digits to work with, you can expand an electron-sized image up to the size of the visible universe, not once but more than twenty times. So you can examine screen-sized portions of a Mandelbrot set so large all but a tiny part of it would be vastly farther away than the billion or so light year limit of our best telescopes.Anyway, his art is just art. It's cool. It's an interesting story and makes for a good link. But it doesn't really appear to be that uncommon, art wise, and I think his savant-ness is highly questionable since he's not actually explaining anything new about what he claims to be talking about. I've seen people have the same reactions to getting stoned or dropping acid.

posted by loquacious at 11:15 AM on July 25, 2011 [6 favorites]

Yeah, that dual slit experiment "interference pattern" is pure bullshit. This guy is no savant. This is like bad Op Art by someone with OCD instead of talent. Compare those works to an artist who spent a lifetime developing his talent, like Richard Anuszkiewicz.

I've seen this sort of story before. I recall a NYTimes article about a woman who had a stroke or some sort of brain injury, and developed a mania for painting. Her work was crap too. This sort of story is a typical anti-intellectual hoax, intended to undermine the work of artists as a symptom of mental illness, some sort of affliction of madmen. It's bullshit.

posted by charlie don't surf at 11:31 AM on July 25, 2011 [2 favorites]

I've seen this sort of story before. I recall a NYTimes article about a woman who had a stroke or some sort of brain injury, and developed a mania for painting. Her work was crap too. This sort of story is a typical anti-intellectual hoax, intended to undermine the work of artists as a symptom of mental illness, some sort of affliction of madmen. It's bullshit.

posted by charlie don't surf at 11:31 AM on July 25, 2011 [2 favorites]

Yeah, some of his drawings are pretty, but the web page is 100% pure, grade-a woo-woo.

posted by empath at 11:55 AM on July 25, 2011 [1 favorite]

posted by empath at 11:55 AM on July 25, 2011 [1 favorite]

The descriptions of the art by the media and by Jason himself are obviously full of crazy, as you'd expect, but I don't see why you guys are doubting that he gained savant abilities and that his drawings are the result of deploying them. There's no way you could tell just from looking at the jpegs whether they're mathematically complex or not: the precise placement of the lines matters. Did you guys read the Brogaard paper? He can apparently predict vectors for primes in his art. I'll take the psychologists reporting on his abilities over your guys' bullshit detectors. (Your bullshit detectors are probably firing because of what Jason says about his abilities, but the sorts of abilities he's deploying are non-conscious and he should have no idea how they work. His explanations would be confabulations. Brogaard writes about this.)

He's obviously not really drawing fractals. Brogaard writes that they are "meticulously accurate approximations of mathematical fractals using only straight lines." So yes, he "bails out," but that doesn't mean he's not doing something savantish.

posted by painquale at 12:23 PM on July 25, 2011

*Fractals are a very specific kind of math formula. You can't actually accurately render a fractal on a computer screen or a piece of paper. There's a reason why fractal generators work with grids of pixels - you can't physically represent a fractal without telling the algorithm to "bail out" at a certain level of calculation and stop calculating more detail.*He's obviously not really drawing fractals. Brogaard writes that they are "meticulously accurate approximations of mathematical fractals using only straight lines." So yes, he "bails out," but that doesn't mean he's not doing something savantish.

posted by painquale at 12:23 PM on July 25, 2011

Sweet and gentle sensitive man with an obsessive nature and deep fascination for numbers and a complete infatuation with the calculation of PI.

posted by markkraft at 12:29 PM on July 25, 2011

posted by markkraft at 12:29 PM on July 25, 2011

*Did you guys read the Brogaard paper? He can apparently predict vectors for primes in his art. I'll take the psychologists reporting on his abilities over your guys' bullshit detectors.*

I've read the paper.

I've hidden prime numbers and Fibonacci sequences and other recursive or generative math in my art as well. It's seems to be rather inherent when playing around with geometric or math-based art. Prime numbers are aesthetically pleasing when conveyed visually. The numbers I choose for step-and-repeat patterns and the scaling/skewing values between iterations are intentionally chosen.

People have been embedding things like Pi, the Golden Ratio and prime numbers in art for centuries, if not since the dawn of art. The Golden Ratio in particular has been used in composition for a long time to calculate an interesting visual center. Look at the fantastic tiled mosaics of a mosque. Or the arrangement of idols in a Buddhist temple. Many so-called "primitive" pre-historic art attempts to convey "entoptic visions" from shamanistic psychedelic experiences - which are also arguably often directly related to math and even fractals.

Which brings us back to synesthesia. I know exactly what he's talking about because I've taken psychedelics and I've experienced the same things. It's qualitatively the same thing - you can see math everywhere. In the foam of bubbles in the kitchen sink, in the branching of trees, in the splitting of atoms and how subatomic particles move and interact, in the topological complexities of membranes. It's not an uncommon thing at all, in fact it seems to be fundamentally involved with how we're able to visualize symbology and formal systems in our minds, and how we think about and explore things like math.

The only unique thing here is that he's suffered a traumatic brain injury that gives him easier access to these mental states, which is illuminating to scientists who study the mind because it challenges their erroneous assumptions about how the brain works.

Which in my estimation the brain doesn't work in the linear, concrete ways that classical philosophers and psychologists want it to work. It works with fuzzy math and fractal-like constructs because nature is fuzzy and fractal-like, but follows predictable rules. We've evolved to find useful information in that noisy, fuzzy natural world, things that stand out and contrast from the fractals and noise that surround us every day.

Sure, I think that what he's seeing and trying to describe is valid, but I still think he's mis-using the terms "quantum" and "fractal", and that Brit Brogaard doesn't actually know what a fractal is, either. The drawings he's creating are very much

*not*really fractals. Fractals aren't that geometrically simple. They change and morph via recursion, and what you and I see as a 2D "fractal" is really just a cross section or focal plane of a much more complex object that's better represented in three or even four dimensions. They're just less interesting to look at, because a 3D fractal represented as a 2D plot is just a featureless blob since you can only see the surface or boundary limit.

I'm not doubting he's gained savant-like abilities from his head trauma. I'm doubting the accepted scientific definition of "savant". We all naturally have and use some of these savant-like abilities every day just by being conscious.

You can even experiment with some of these sensations and fascinating processes yourself by way of an sensory deprivation tank or the Ganzfield experiement. (Ignore the parapsychology part, just replicate the sensory isolation.) Or you could eat mushrooms or acid, or meditate until you're tripping. Same difference, really.

posted by loquacious at 1:11 PM on July 25, 2011 [5 favorites]

There should be some kind of license to use the word "quantum" to describe any of your work.

Maybe you should have to read the Feynman Lectures or something.

posted by odinsdream at 1:27 PM on July 25, 2011 [8 favorites]

Maybe you should have to read the Feynman Lectures or something.

posted by odinsdream at 1:27 PM on July 25, 2011 [8 favorites]

*I know exactly what he's talking about because I've taken psychedelics and I've experienced the same things. It's qualitatively the same thing - you can see math everywhere. In the foam of bubbles in the kitchen sink, in the branching of trees, in the splitting of atoms and how subatomic particles move and interact, in the topological complexities of membranes. [...] The only unique thing here is that he's suffered a traumatic brain injury that gives him easier access to these mental states*

It phenomenally seems to you that you see all this stuff. But do psychedelics actually make you better at calculation? Do they make the user able to solve math problems with Kim Peek/Rain Man speed? I'm skeptical. JP's not special for making drawings that use mathematical patterns. The claim that his drawings are exceptionally accurate geometric representations of exceptionally complex equations. He's not just tossing a couple of recursive elements into a piece of art; he's building images that using algorithms that are so heavy-duty that normal people like the rest of us could not do without a ton of computer aid. If that's true, that's really cool, and I don't see any reason to think it's not true.

(I don't really see your objection to calling his drawings "approximate fractals," which seems to be a well-defined term.)

*We all naturally have and use some of these savant-like abilities every day just by being conscious.*

That's still an open question, hence the Dehaene/Brogaard debate.

posted by painquale at 1:41 PM on July 25, 2011

*He's not just tossing a couple of recursive elements into a piece of art; he's building images that using algorithms that are so heavy-duty that normal people like the rest of us could not do without a ton of computer aid. If that's true, that's really cool, and I don't see any reason to think it's not true.*

Point taken. I'm not out to approximate pi in an unusual way or anything.

I do think this post is interesting and good, but there's a lot of hubris around the artist's own claims and as worded in the post. I nearly choked on my coffee when I read "including hand-drawn approximations of fractals, the first time anyone had ever done so."

This hubris is reflected in the prices of his art, but that's not uncommon in the art world, either. If he actually sold a geometric line drawing (and not a small amount of woo) for 100k I'll admit I'm jealous.

People have been doodling "fractals" - in particular, various kinds of Sierpinski foams - since long before telephones were invented.

*But do psychedelics actually make you better at calculation? Do they make the user able to solve math problems with Kim Peek/Rain Man speed? I'm skeptical.*

Be skeptical, by all means. I have seen people do really intense things with math and/or programming and/or logic in the fugue-state of a psychedelic experience, but they were mathematically minded to begin with.

What I'm describing is more akin to the mental math someone does when catching a ball. When you catch a ball you're naturally calculating a lot of complex, dynamic and time sensitive math. Sure, you're not going to be able to call out the formulas and real numbers that describe the arc of the ball as you're catching it, or the complex geometry of your arm and body moving to catch the ball, much less measure the velocities (paging Heisenberg) - but you still caught the ball. And we do and understand and use this kind of math in our heads all the time.

So, we all have this innate, natural grasp for math, and this really shows up for a lot of people when they take psychedelics. It's like you get to observe and sense the math underlying your own sensory perceptions, like you can suddenly see the texture and artifacts of the codec algorithm driving your own senses. And then you can observe how that naturally interacts with the math and geometry all around you.

Transcribing those internalized symbologies into real words or formal system symbols that aren't merely thoughts is where the savant part really comes in, though.

Last: He is arguing from a position that states that there's no such thing as a circle, or by definition, a true curve, and that's how he's approaching his "proofs" as they were. As others have pointed out there have been others throughout history that have done this and approximated pi with what is more or less trigonometry.

I argue there's no such thing as a straight line in nature or anywhere in the universe, outside of a symbol or a mathematical abstraction. Take a laser pointer and beam it into the sky, then wave it. You're not waving around a straight line, that stream of photons "bends" and behaves just like water from a garden hose. Even the individual photons will have bent and curved paths in the presence of gravity. The shortest path between two points in reality is almost always curved.

Space is curved, man. Space is curved.

posted by loquacious at 2:14 PM on July 25, 2011 [4 favorites]

*But do psychedelics actually make you better at calculation? Do they make the user able to solve math problems with Kim Peek/Rain Man speed? I'm skeptical.*

It sounds like a relatively simple experiment to conduct, given that all that is needed are a willing mathematician, a suitable psychedelic, and some prompting stimuli.

posted by aeschenkarnos at 2:54 PM on July 25, 2011

*It sounds like a relatively simple experiment to conduct, given that all that is needed are a willing mathematician, a suitable psychedelic, and some prompting stimuli.*

Man, I'd love to see that experiment, but it would probably be more effective with someone who has had prior experience with psychedelics. But you could run the experiment both ways.

Anecdotal: I once babysat for a pretty good programmer on his first trip. 30 minutes into it at first onset of effects he was scribbling C code out in longhand on pads of lined paper, and didn't stop for hours. I can't tell you if the code was any good but he kept shouting things like "SO MUCH FASTER THIS WAY" and "MY GOD, WHY DIDN'T I THINK OF THIS BEFORE?"

I can't speak for pure mathematics but psychedelics have a long history and deep roots with programming.

I would wager that everyone here has benefited from it and used concepts, application or code that was either written or conceived under the influence.

posted by loquacious at 3:11 PM on July 25, 2011 [2 favorites]

Yeah I don't even know enough to be able to tell if this is BS or not and I just came in here to say that YOU ARE ALL EDUCATED STUPID, but this discussion is really interesting so thank you.

posted by zoinks at 3:19 AM on July 26, 2011

posted by zoinks at 3:19 AM on July 26, 2011

*Sure, you're not going to be able to call out the formulas and real numbers that describe the arc of the ball as you're catching it, or the complex geometry of your arm and body moving to catch the ball, much less measure the velocities (paging Heisenberg) - but you still caught the ball. And we do and understand and use this kind of math in our heads all the time.*

That's a funny example to pick, because it's a case where we don't actually perform that much computation. Studies have shown that people trying to catch a ball, amateurs and professional ballplayers alike, use a relatively simple heuristic: keep the ball in the center of your visual field. We don't actually compute the arc.

But the particular example's not essential to what you're saying, and the computations involved in keeping the ball in the center of the visual field are non-trivial, so point taken.

posted by painquale at 12:21 AM on July 27, 2011

I disagree, painquale. What you're citing is cybernetics, we use a feedback loop to make corrections. But many routine tasks require more than feedback. I recall reading a science paper that analyzed how dogs caught a flying frisbee, they were basically doing algebra to calculate how much they had to accelerate to catch the flying target. Feedback would only provide accurate corrections if everything was moving at a constant speed.

I'd put it in terms of a more common human task. I first thought about this when I was merging onto a freeway in LA. You're at a dead stop, you get a green light, then you start moving and look for a potential opening slot to merge into. How fast do you have to accelerate to be in position to merge into that spot and match the traffic speed? Sure you can make corrections as you get close. But unless you do a very complex calculation, instantly, you won't even get close enough to make the corrections.

posted by charlie don't surf at 8:50 AM on July 27, 2011

I'd put it in terms of a more common human task. I first thought about this when I was merging onto a freeway in LA. You're at a dead stop, you get a green light, then you start moving and look for a potential opening slot to merge into. How fast do you have to accelerate to be in position to merge into that spot and match the traffic speed? Sure you can make corrections as you get close. But unless you do a very complex calculation, instantly, you won't even get close enough to make the corrections.

posted by charlie don't surf at 8:50 AM on July 27, 2011

I know that not all tasks work this way, but catching balls appears to. I was citing the study discussed here. Dogs figuring out how much to accelerate might work by entirely different principles.

posted by painquale at 10:25 AM on July 27, 2011

posted by painquale at 10:25 AM on July 27, 2011

Jason Padgett discussed by a philosopher of math in a paper about blind mathematicians and symbol manipulation.

posted by painquale at 9:43 AM on July 28, 2011

posted by painquale at 9:43 AM on July 28, 2011

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This image is purported to be the first accurate visual explanation of Einstein’s theory of relativity, Jason is now being consulted with regard to applying this insight for the purposes of developing a “fractal fusion reactor” which may one day provide a clean source of energy....absolutely pegs my bullshit detector.

posted by jcreigh at 8:36 AM on July 25, 2011 [36 favorites]