Brain Injury Turns Man Into Math Genius 208
mpicpp sends in the story of Jason Padgett, a man who developed extraordinary mathematical abilities as the result of brain trauma when he was attacked outside a bar. "Padgett, a furniture salesman from Tacoma, Wash., who had very little interest in academics, developed the ability to visualize complex mathematical objects and physics concepts intuitively. The injury, while devastating, seems to have unlocked part of his brain that makes everything in his world appear to have a mathematical structure 'I see shapes and angles everywhere in real life' — from the geometry of a rainbow, to the fractals in water spiraling down a drain, Padgett told Live Science." "He describes his vision as 'discrete picture frames with a line connecting them, but still at real speed.' If you think of vision as the brain taking pictures all the time and smoothing them into a video, it's as though Padgett sees the frames without the smoothing. "
No story here, move along (Score:5, Interesting)
Can someone explain to me exactly what is so marvelous about what this dude can supposedly "see"?
A google search reveals a history of his story popping up from time to time - probably whenever he can find a venue to promote himself, and whenever sites like Slashdot get duped into posting about him - but I found nothing that describes anything that he's actually able to intuit about math since this injury other than a bunch of crap about how he can 'see mathematical patterns' now. Awesome - so how about parlaying that into any statement that demonstrates any extraordinary grasp of math? Because in all my searching, I haven't found this dude to have ever said anything that anyone couldn't easily just make up.
I also found this comical link to "End of Pi Found" on some Physics forum:
http://lofi.forum.physorg.com/... [physorg.com]
Not sure if it's the same guy but it was posted by a Jason Padgett who says he is a "math/physics student in Washington state", and the Jason Padgett in the article is supposedly from Tacoma, Washington. Note that the post was from 2008 and the article that Slashdot has linked to describes Padgett as a "sophomore in college". Some math genius - still a sophomore in college 6 years later!
Slashdot, why do you waste my time with this crap?
I swear, Slashdot editors are worse than the patent office; they don't do even he smallest amount of verification before rubber stamping what is presented to them and pushing it out.
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I was going to post something like this but less involved. This dude is being called a savant for no reason, as he does not actually inhibit any savant-like skills, or really any skills at all. The only concrete detail I was able to find is that he once drew a pattern of triangles in a circle.
Re:No story here, move along (Score:5, Insightful)
You mean other than going from a party boy furniture salesman to a student of mathematics specializing in number theory?
Savantism doesn't mean an ability practically nobody else has (though it can be that), it is an ability that is out of context for the person who has it.
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Well, I mean, we never see people make significant life changes after traumatic events. That's why no one converts to Christianity in prison, why middle-easterners don't radicalize after their family is blown up, and why the term "near-death experience" is meaningless.
wait
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It is somewhat less common to develop a talent or aptitude for something they didn't have before, such as math.
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And he went back to school majoring in math. RTFA
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Well, we do tend to like the things we're good at more than the things we aren't.
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Savantism is an ability beyond that which is expected in the majority of the population, and also without any special instruction or education in the subject matter. It's great that this guy got his life on track and is getting himself educated, but unless he's already capable of doing advanced number theory in his head, he
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If you chose IT because physics was beyond you (personally, not humans in general), but one day you slipped on a floppy, hit your head on the edge of a server, then when you woke up you exclaimed "So THAT's what Einstein was saying!", then yes. Otherwise, no.
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I see Matt Damon's character in Good Will H
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Correct, he specializes in number theeory.
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And he is correct under the conditions he states along with that.
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He doesn't specialize in jack shit.
Isn't a more polite expression for this santorum?
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I was also wondering how much this seeing ability contributes to actual, productive math ability. The visions described remind me of what, erm, some people see when on acid.
I'm particularly interested in the idea, being mathematically minded myself, and I believe my ability to conceptualize things in many visual dimensions is an important factor. Nevertheless, there is rarely a direct translation from my pictorial musings into hard and solid math. Visualization helps you get new ideas, but it's implement
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My understanding is that advanced maths becomes almost exclusively symbol manipulation. I could intuit a lot of physics stuff and easily attach equations to concepts but when it came to the quantum stuff, it was a totally different story. That could have just been the way it was taught though.
Re: No story here, move along (Score:2)
Looks like his human graphics card was fried. :)
I guess calling yourself math and physics intuitive is a good way of coping with 8th graphics and no 3d driver
Re: No story here, move along (Score:2)
*8bit. Auto correct on phone made it an 8th.
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I don't know about fried but that was my thought. the injury cross linked his normal "cpu" and vision "GPU" basically using his normal vision processing as a massive floating point processor. Not unlike using your GPU to mine bit coins or do other massively parallel processing.
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Mining bitcoins in your head just by looking, now THAT would be a savant skill worth having.
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No one else does it, it's another way to look how parts of the brain function.
Acquired savant syndrome is an interesting subject.
I wouldn't call a guy who sees angles and connected shapes a math genius, but it is interesting and unique,
Re:No story here, move along (Score:4, Insightful)
Re:No story here, move along (Score:4, Informative)
The neuroscientists who have been studying his brain seem fairly convinced he's not making it up. Though calling him a "math genius" doesn't necessarily seem warranted (at least not yet... maybe it's a case where formal study will allow him to apply his abilities more specifically?), I don't think they would diagnose him with what they're calling acquired savant syndrome without some evidence.
Maybe read the book? Even the top negative review seems to give weight to his claim:
http://www.amazon.com/Struck-G... [amazon.com]
Re:No story here, move along (Score:5, Informative)
No, the media calls him math genius because he calls himself a math genius. Also, he believe PI has an end.
from the neurologist's preliminary report:
We studied the patient JP who has exceptional abilities to draw complex geometrical images by hand and a form of acquired synesthesia for mathematical formulas and objects, which he perceives as geometrical figures. JP sees all smooth curvatures as discrete lines, similarly regardless of scale. We carried out two preliminary investigations to establish the perceptual nature of synesthetic experience and to investigate the neural basis of this phenomenon. In a functional magnetic resonance imaging (fMRI) study, image-inducing formulas produced larger fMRI responses than non-image inducing formulas in the left temporal, parietal and frontal lobes. Thus our main finding is that the activation associated with his experience of complex geometrical images emerging from mathematical formulas is restricted to the left hemisphere.
Re:No story here, move along (Score:4, Interesting)
Under the conditions he specifies, Pi does have an end. He makes it clear he means as seen in the physical world where it is bound by the Planck length. He may or may not realize that mathematicians prefer to have as little as possible to do with the physical world, at least professionally.
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In the physical world, its expression (pi is always constant, of course*) is also affected by gravitational curvature and possibly other effects.
*For some values of "of course"
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In the physical world, 355/113 is a close enough approximation that almost nobody owns a physical instrument precise enough to need anything better.
And 355/113 is even easy to remember. One one three under three five five.
I've never understood why 22/7 gets so much admiration.
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Decimal fractions were not always as familiar to people as they are now. I think the shift mostly occurred in the 60s and 70s with metrication and increasing use of digital calculating devices (calculators and computers)
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No. None of them do. Most of them repeat the information about being mugged.
But there isn't a single one of those that specifies HOW he is a "genius" of any kind.
Can he look at a formula and intuitively draw it?
Can he look at a drawing and intuitively give the formula for it?
The simplest question on his "genius" is still unanswered. WHAT does he do that is "genius" level? HOW is it "genius" level?
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You're misinterpreting my response. I very specifically said I agree that there's no evidence that he's a math genius, at least not yet. GP seemed to imply that he was making *everything* up though. Or maybe I misunderstood him too. All I'm saying is that his claimed ability to see things differently than everyone else seems to have credence.
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Moreover, if he can intuitively draw a formula, or derive a formula from a drawing, that does not constitute mathematical genius. He's not proving anything. It may be a remarkable ability, and it may be useful, but it doesn't sound like mathematical genius..
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I also found this comical link to "End of Pi Found" on some Physics forum:
http://lofi.forum.physorg.com/ [physorg.com]...
*SPOILER ALERT*
It's a '4'.
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One might gain an artistic appreciation of his drawings but it is difficult to view this as Mathematics.
The real story here is that he convinced someone at Houghton Mifflin Harcourt, to publish a book about him.
I don't doubt that he experiences visual phenomena, perhaps indistinguishable from hallucinations. Although such a unique perspective might conceivably give him an opportunity to understand math in a new way I'm skeptical this occurred. I'm afraid he has no more insight than a nautilus has into th
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"Can someone explain to me exactly what is so marvelous about what this dude can supposedly "see"?"
He sees dead people, all the time.
Re:No story here, move along (Score:4, Funny)
"Can someone explain to me exactly what is so marvelous about what this dude can supposedly "see"?"
He sees dead people, all the time.
So does a mortician. Big deal!
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Seconded.
There are 24 paragraphs in the first link. The ONLY mention of ANYTHING about his mathematical "ability" is in paragraph 9.
That's a "savant"? How many kids in high school understand pi?
Re:No story here, move along (Score:4, Informative)
How many kids in high school understand pi?
An elite few. Most people simply memorize equations and procedures; understanding never comes into it.
But still, I'd be impressed if this guy actually did something, like solve an unsolved problem. Sadly, these popular math 'geniuses' and child 'geniuses' never seem to do a damn thing that's truly notable.
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Sadly, these popular math 'geniuses' and child 'geniuses' never seem to do a damn thing that's truly notable.
Perhaps except Terrence Tao; a famous math prodigy, who also became an incredibly successful mathematician, "Such is Tao's reputation that mathematicians now compete to interest him in their problems, and he is becoming a kind of Mr Fix-it for frustrated researchers. "If you're stuck on a problem, then one way out is to interest Terence Tao," says Charles Fefferman [professor of mathematics at Princeton University].". Also Erik Demaine, who finished PhD and became a professor at MIT at 20; he has a less imp
Re:No story here, move along (Score:5, Informative)
I don't know if the guy is full of shit or not... but, I did my own google search.
I found that:
1. He wrote a book that was well received about his injury, though complaints were that it was overly wordy. There were several people that claimed to be mathematicians that reviewed it and said his area of specialty was fractal geometry and that he was so specialized it was uninteresting to them. He was basically obsessed with 1 aspect of geometry.
2. He is an artist, and makes Fractal art. Not that his stuff is that incredible but I doubt a furniture salesman could pull this off. http://fineartamerica.com/prof... [fineartamerica.com]
3. Here's photos of him. One includes his doctor: http://www.struckbygenius.com/... [struckbygenius.com]
4. That doctors name is Darold Treffert who appears to be am expert on Savant Syndrome. http://en.wikipedia.org/wiki/D... [wikipedia.org]
So it appears to me that the guy actually did develop some Savant abilities. I don't know if he got them from an injury or not. But it appears that those abilities are so specialized that they may not be useful in an academic sense. If he can visualize incredibly complex geometries but can not, for example, do long division, his skill wouldn't really lead him to write a lot of papers.
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1. Those aren't fractals.
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They look more like spirographs then fractals.
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He did not necessarly develop any ability (Score:3)
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As far as I know, that art link does not contain anything that a furniture salesman could not pull off. The drawings don't seem to have any connection whatsoever to their scientific, nonsensical names, and the only thing he seems to do is to draw intersecting lines from and to the vertices of polygons.
This does not really seem like a savant ability.
Injury unlocked scamming part of brain (Score:5, Funny)
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I don't think the amazing thing is what he can see or can't so, or even what is math skills are or aren't.
The intriguing part (to me) is the mechanics of the brain changing so drastically after an injury. From the little information I've read - his injuries weren't much more than a concussion - yet it's completely changed some functions of how his brain processes information. That's truly amazing to me - and leads me to more questions but mainly these two: Was this ability there all along and somehow was un
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Seems like we could probably stop at about 187 digits, really. The radius of the observable universe in planck lengths (call it X) is about 2.7*10^61, which makes the observable volume (4*pi*X^3) about (8*10^184)*pi cubic planck units. The value of the 186th digit of pi (after the decimal) should only affect the final volume by about 0.7 units; going much beyond that seems unnecessary :)
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To be even more dramatic, while the planck length determines the ultimate resolution, you only need 39 digits of pi [numberphile.com] to cal
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What does the size of the observable universe have to do with anything? Talk about a completely arbitrary limit. We have reason to believe the universe is far larger than what we can observe (and in fact are losing more of the matter of the universe beyond that barrier at every moment), and for practical purposes 5-10 digits is plenty. Neither of those have anything to do with the decimal expansion of number proven to be irrational and non-repeating.
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Re:A "Feyn" place to end Pi (Score:5, Insightful)
Practically, the end of Pi is around 760-some digits [wikipedia.org], where you start to sound like Herman Cain [youtube.com]. At that point, diameters won't be more than a Planck length off.
If you're using it for the geometry of the physical world, then you'd be correct. Fortunately however, Pi is used for far more than measuring the physical world.
Re:A "Feyn" place to end Pi (Score:4, Informative)
Indeed. And if you define pi as the smallest positive real number whose cosine is -1, the Planck length becomes immaterial.
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It's considerably smaller than that.
63 decimal places can calculate the circumference of the observable universe to an accuracy of one planck length.
I can't think of a single practical application that would have any need to calculate a distance that large to that level of precision.
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It's considerably smaller than that.
63 decimal places can calculate the circumference of the observable universe to an accuracy of one planck length.
I can't think of a single practical application that would have any need to calculate a distance that large to that level of precision.
To build my full scale working model of the universe of course how else are you going to build your turing oracle.
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Yeah, I considered adding this to my post as the only practical application but my guess is that even if you wanted
to simulate the entire universe that you would take shortcuts and never need that precision.
On a somewhat related note if we are currently living in a simulation and the microscopic stuff is only fully
simulated when examined closely that might explain certain quantum effects like wave particle duality.
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I can't think of a single practical application that would have any need to calculate a distance that large to that level of precision.
How about to win a bet? I seem to recall some famous maths or science guy winning a bet as to what the 100 kazillionth digit of Pi was.
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Did you even realize that you had Godwinned the thread at this point? ;^)
Re:A "Feyn" place to end Pi (Score:5, Funny)
ridiculous, That only applies to numbers in base 10
Just imagine a number system of base-pi, or possibly base-rad. Of course, then people would be debating how many digits "10" should be approximated to for useful work (like counting your fingers).
Re:A "Feyn" place to end Pi (Score:5, Informative)
You cannot because it's not possible. A 'base' is the number of unique symbols in the number system. You can't have partial symbols; you can have 3 symbols for base 3, and 4 symbols for base 4, but you cannot have 3.1415xxx symbols for base Pi.
You might as well ask what it would be like to have a "base yellow" number system or a "base CmdrTaco" number system. Meaningless.
Wrong, you can have non-integral bases, including base Pi [wikipedia.org]. Your positions each represent Pi, Pi^2, Pi^3 etc
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It's weird, but everytime I read interesting stuff about entropy and information density, "e" pops up somewhere. Weird number.
Re:A "Feyn" place to end Pi (Score:4, Informative)
You cannot because it's not possible.
To say such a thing, you don't understand what maths is truly about on a very fundemental level. I don't mean this in a bad way. Most people don't because despite the supposed maths eduation one gets they omit this important point. I didn't until very recently.
Maths isn't about "the rules" it's about YOUR rules. You set the rules, and you can set them to be whatever you like. There are generally three results from such an activity:
1. The rules are inconsistent.
2. The rules are trivial.
3. Some interesting patterns emerge.
(3) is what maths is about. You pick some rules and see where they lead you. The thing is rules are not as passive as they seem. Sometimes once you pick some basic rules, the patterns build and build and build. Sometimes they join up to other patterns.
A good example is complex numbers. i is not a real thing. It's just an invention. You can essentially say: I wonder what happens if we have this number i such that i*i=-1. Let's say we'll keep the other rules we know and see what happens.
The result is incredibly rich. Of course, there is no real numer i, such that i*i=-1, but that just plain doesn't matter.
There are others too. Smeone asked what happens if we have a nonzero numer e, such that e*e=0. I believe those are called dual numers. They're neat but do not have the quite astonishingly all-pervasive richness of complex numbers.
Likewise with frational powers. You can't multiply a number by itself half a numer of times, or a negative numer of times. That makes no sense. However, you can take the integers and replae them with fractions, real numbers, complex numbers, matrices and so on just for shits ang giggles and see what happens. Naturally if you're working form integer powers as the premise you need to make sure when they degenreate to simple integers you haven't broken your own rules.
All the rules you know and have seen for such things are merely choices. They are presented as facts because they have by far the most useful and interesting consequenes. But, they're not really facts at all, just choices. It's also nice in that in many cases, it's the most natural way to see what happens when non-integers are used for example as powers.
This even happens to the extent that the cherished fact 1+1=2 is no fact at all. You get interesting things too when 1+1=0, for example and when 2+2=1.
So back to number bases. You can have fractional bases simply beause there's no one to tell you you can't. You an if you want: that's the beauty of maths. The question is, can you figure out a way to make it work?
THAT is maths.
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Well thanks for the well though out response.
I guess it really comes down to what question is being asked.
I believe that most people think of "base" as the number of symbols that can be used in a "standard math system" using symbolic representations that can be written and operated on using the same "rules" as in base 10 math, but with a different number of symbols.
It is true that you can define the rules however you want, so we could even define a system where "base CmdrTaco" has meaning, because we could
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I guess it really comes down to what question is being asked.
Indeed. Bear in mind that a lot of maths starts asking silly/funny/strange questions just for the hell of it. Galois invented modular arithmetic in 1832. It's very useful in things like cryptography and error correcting codes, but it didn't become useful in a practical sense until well over 100 years later.
I believe that most people think of "base" as the number of symbols that can be used in a "standard math system" using symbolic representations
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Thank you again for your response, very interesting. And I mean that sincerely, and did also in my previous reply. I feel a little better educated for having read your posts and that's a rare thing on these forums :)
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so you would have an enumeration system where you can't enumerate. I think you miss the definition of symbol somehow. maybe your harddisk also has half a bit at the end.
Re:No story here, move along (Score:5, Funny)
Says the 6-digit to the 3-digit user ...
Correlation != Causation (Score:3)
Perhaps the karaoke did it?
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Perhaps the karaoke did it?
Nah, I can't see a positive outcome from that kind of brain trauma.
Tomorrows headline.. (Score:5, Funny)
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retrophrenology at it's finest!
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retrophrenology at it's finest!
So it's not the bumps, it's the divots?
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Dozens killed or severely injured trying to learn maths.
The White House will make a public announcement that they're looking for the irresponsible person than unleashed weapons of math destruction on impressionable American youth.
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MMA Fighter/Math Teacher (Score:2)
EOM
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Yeah, it's a bit of an out-lier in the spectrum of brain injuries. All I got from mine are ataxia and diplopia which are things I can't see anyone wanting.
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Dozens killed or severely injured trying to learn maths.
...Gives new meaning to "rack you brain" for the answer.
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Dozens killed or severely injured trying to learn maths.
...Gives new meaning to "rack you brain" for the answer.
And apparently I didn't hit my head hard enough before I posted that.
Life imitates art: Phenomenon (Score:4, Interesting)
Re:Life imitates art: Phenomenon (Score:4, Funny)
Doo - Doo - Do Do Do.
Phenomenon
Doo - Do Do Do.
Uh... (Score:5, Insightful)
Padgett dislikes the concept of infinity, because he sees every shape as a finite construction of smaller and smaller units that approach what physicists refer to as the Planck length, thought to be the shortest measurable length.
So, the bang on the head didn't help him improve his abstract thinking after all. How can someone be an "aspiring number theorist" and dislike the concept of infinity? That's like being an aspiring blacksmith and disliking the concept of tempering carbon steel.
the many fragments of infinity (Score:2)
He strikes me as being more like David Helfgott and less like Rachmaninoff.
To a large degree in mathematics, infinity is used to invoke the limiting configuration of an unbounded process (where there is always a next step). This isn't precisely the same thing as believing in infinity itself, or any of its many discrete fragments.
Meaning in Classical Mathematics: Is it at Odds with Intuitionism [arxiv.org]
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I had a friend who once interviewed R. Buckminster Fuller for his college newspaper, and got into an argument with Fuller over geometry. That took chutzpah, but my friend was on solid ground: Fuller claimed that lines couldn't really intersect because the bits that touched would have to somehow interfere with each other.
Clearly this visualization-based dislike of intersecting lines didn't hamper his use of the *abstraction*, otherwise Fuller couldn't have functioned as an architect.
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Agreed. And Planck lengths are physics. Mathematics is a useful tool in physics and things in the real world must agree with physical laws (or those laws must be changed [or qualified]) but mathematics is so much more than physics (cue XKCD strip)
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There are a fair handful of constructionists (aka finitists, or number theorists who do not like infinities) who would care to disagree.
Although I'm not a constructionist, I am related to one by birth, and nearly always find something off-putting about mathematical arguments that rely on infinities. Sure, they're fun to play with, but reasoning about them means you're essentially being fast-and-loose with time, and I've not been convinced that's OK.
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I don't buy the thermodynamic argument. That's an epiphenomenon (i.e., correlation not causation).
Basic mathematics does not consider time. Nor does it really consider sequential ordering properly until it deals with the notion of state, State begets the field of Computational Theory. Before a proper wrangling of the ideas at the core of Computational Theory (as embodied in Turing Machines, for example), there was a horrific thrashing-about that was particularly inelegant, such as the attempts in First
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Now, when you talk about infinity, you are effectively saying that results from Computational Theory are being computed by a machine that takes zero time to get from one state to the next. Nothing in the physical universe takes zero time, and so infinity is considered to be ill-supported by Nature. That's the crux of the Constructionist objections.
And here I was thinking that some of the most beautiful knowledge in mathematics stemmed from the fact than unlike with trivial mechanical or computational/enumerative reasoning, proper mathematics is able to formulate finite-sized arguments about infinite objects. And you're saying that there are evil people out there who want to take the fun out of it? That's really naughty of them.
Now why should mathematics be beyond time?
Because artificial limitations are useless? What if we find that space isn't continuous, will you call for abolishing real nu
I too dislike infinity (Score:2)
Infinity isn't a number; you can't add, multiply, nor divide with it. The only legitimate use I find for it, other than communicating with non-mathematical folks, is as a shorthand for unbounded, eg limit of f(x) as x tends to infinity. I suppose you could say that infinity could be used as an answer to "what is the cardinality of the set of natural numbers", but aleph_0 works too and is unambiguous as to which of the many infinities you mean.
Some people say that [sum from i=1 to i=infinity of 3*10^i] = inf
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Infinity is a placeholder, a word that describes any one of many distinct extensions of finiteness. Think of "infinity" like a variable, "x" that can take many values. Depending upon the value it takes in any given application, it has some properties. In a different application, it has other properties. For example, it can mean the point at i
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Is he truly a math genius? (Score:3)
The revenge of the geeks (Score:2)
I bet this is a geek conspiracy to lure football players into self-injury considering an upcoming math exam.
Finally... (Score:2)
I remember... (Score:2)
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Apparently all you need to teach math with is a baseball bat.
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Being a math genius does not imply you know how to teach.
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Apparently you can turn a jock into a nerd by damaging his brain? Suddenly I understand college football.