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Brain Injury Turns Man Into Math Genius
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. "
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/...
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.
Perhaps the karaoke did it?
love is just extroverted narcissism
Dozens killed or severely injured trying to learn maths.
All I got from a brain injury was a giant cerebral meningioma about a decade later.
Isn't this the plot of the 1996 John Travolta vehicle Phenomenon ?
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.
Ezekiel 23:20
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 :)
This symptom is similar to the problem of a video card with faulty memory.
Practically, the end of Pi is around 760-some digits, where you start to sound like Herman Cain. 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.
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
EOM
love is just extroverted narcissism
I would define someone as a "math genius" if they're able to solve previously unsolved problems, and publish results in major, refereed mathematical journals. Has he been publishing papers since his injury, or at the very least, has he been doing well on university level math exams? Nothing in the article seems to suggest this, so I do question the headline.
If I can be modded down for being a troll, can I be modded up for being an orc, or a balrog?
Apparently all you need to teach math with is a baseball bat.
love is just extroverted narcissism
I bet this is a geek conspiracy to lure football players into self-injury considering an upcoming math exam.
Can I find this bar?
I've been there, and like when I go back. Visually .. it's like lines, a grid is over everything and you know momentum and velocities without need of display.. I drempt the mathematics equation which I understand dictates my life.. in fact. The simple function .. y = 1/x. I added a dimension and connected the two at y=0. .. simulate .. those well enough for public interaction (given the correct support.) And likely most of the rest of his brain will become available in time and work.
Simple.. but in my dream!
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It's the very male brain. I know it well.
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For him, it's likely all that's left for now.. depending on other factors he is likely high Autism level for things like sympathy. Not completely devastation, he can learn to work with what he has to
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I wish him, and all well.
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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).
Being a math genius does not imply you know how to teach.
I should use this sig to advertise my book ISBN-13 : 978-1501515132.
Beer turns me into a love machine....
Probably the writer of the book is the person who convinced the publisher to publish the book. Unless he was that guy too.
Indeed. And if you define pi as the smallest positive real number whose cosine is -1, the Planck length becomes immaterial.
His math is unchanged, but it *damaged* the ethical part of his brain and now he EXCELS at marketing and con-artistry and I heard he is now going to law school!
Priest: "Universe from nothing, no laws of physics, sped up time"+ huge discrepancies. Creationism? No. Big Bang Theory
Yeah, the world is flat after all and we understand 100% of everything right now. Nothing new will be discovered and we will never be wrong.
Did you even realize that you had Godwinned the thread at this point? ;^)
I sense some sarcasm in this post, somehow...
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.
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.
---Saying gnome 3 is better than windows 8 not so much a compliment as it is damning with light praise.
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] = infinity. To them I say, [sum from i=1 to i=infinity of 9*10^i]/[sum from i=1 to i=infinity of 3*10^i] = 3, but what is infinity/infinity? So long as you leave your unboundedly large numbers as their formulaic description, you can do maths with it.
Don't waste your vote! Vote for whoever you want, unless you live in a swing state it won't matter anyways
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.
world was created 5 seconds before this post as it is.
Any consistent set of rules creates a valid form of mathematics.
There have been mathematicians and philosophers interested in a kind of mathematics limited to finite processes. That sort of mathematics probably has uses - after all computer calculations are always a finite number of steps.
His dislike of the infinite implies, to me, that he's relying on some unconscious processes for his intuition and those processes have limitations - that doesn't make them or what they create uninteresting.
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.
Rampant carbon sequestration destroyed the Dinosaurs' tropical paradise. I'm here to help repair the damage.
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. Your positions each represent Pi, Pi^2, Pi^3 etc
As said in another post he was a math sophomore. The "furniture salesman" is a red herring, what is important is that he had studied math. Not to put him "down" but he does not appear as interesting once you realize that it is something he studied in university.
C. Sagan : A demon haunted world:
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visit randi.org
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.
SJW n. One who posts facts.
Knock some sense into you! I foresee lots of brain injuries heading into finals week. Kids please don't try this at home.
Apparently you can turn a jock into a nerd by damaging his brain? Suddenly I understand college football.
Is there anything not directly pi-related (i.e. not something like "I wonder whether or not the digits of pi are random" or "look how many digits of pi this computer can calculate") in which it's actually usefull to have more than a few hundred digits of pi? Just curious, not being sarcastic.
I suspect that this is more common than people think. Most of us don't let on because of the type of ridiculing seen right here on SlashDot.
At a young age I had a brain injury. As a result I lost something that is probably best described as what you are.
I was also given a medication that was in research at the time. That appears to have sped up my brain, they think by increasing the rate of transmission of nerve impulses.
Losing that part of me I gain a lack of cohesion which might be thought of an odd gain to you. But that freed up other parts and forced me to cope with the world in other ways.
I don't think in language. In fact, years later I was shocked to learn as a teen that people do think in language.
In part I think of things in part very much like he describes but with a lot more mathematics and more than just mathematics.
I have separate parts that think in terms of probabilities, geometries and calculus as well as what might be equated to a database system. I have two separate language processing systems. I have perfect sensory memory - that is a mixed blessing.
When I'm all functioning together, or at least enough of me, you don't know I'm any different than you.
When I'm not I avoid interaction with other people. I've setup my life carefully so I can control this.
I have never knowingly met someone else who has this but I suspect that is because those of us who are different from the norm don't tend to display it, rather we hide it because as children we learn how brutal normals are to anyone who is different. My IQs for math, memory, logic and language are off the scale. I'm careful not to show that but to keep my display persona within the range of 'bright'. That way the villagers don't try to burn me at the stake.
I strongly suspect that there are many people like this.
I remember reading an article about the information density in different number bases. Having a larger base, say base 10, allows you to write a big number with fewer digits, like 1022. While having a smaller base, base 2, would take more digits, 1111111110. By multiplying the number of symbols by the number of digits needed (something like that, it was a while ago I read about this) you were able to figure out how efficiently you can represent numbers in any base. It turns out that the most efficient base is between 2 and 3, actually it is base e that comes out as the most efficient base to use. Here is a link with possible references to this question.
-- ssoorrrryy,, dduupplleexx sswwiittcchh oonn.. -Quote found on actual fortune cookie.
It's weird, but everytime I read interesting stuff about entropy and information density, "e" pops up somewhere. Weird number.
Therefore, by the (faulty) logic you're using, you're just a cow with a keyboard - osu-neko (2604)
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.
To be even more dramatic, while the planck length determines the ultimate resolution, you only need 39 digits of pi to calculate the circumference of the observable universe to within the width of a hydrogen atom.
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.
--- Most topics have many sides worth arguing, allow me to take one opposite you.
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 make the rules be whatever we want.
But nobody actually means that when they talk about "base N" because it's kind of pointless. Why even ask the question about what it would be like if we could have "base N" if the answer is, "it would be however you want it to be".
Therefore, I believe that you have misinterpreted the question, by applying the most liberal possible interpretation to the concept of "base".
I believe an analogy would be if someone asked you "who was the first president of the United States" and you answered "James Bond". And then you explained your answer by saying "Oh I assumed you were asking about who the first president of the United States was in the invented universe I made up in my mind". I mean sure, if we can interpret any question in the most liberal sense possible, then any answer is possible to any question, and that's kind of pointless.
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.
You appear to be assuming that a number system must consist of discrete objects (such as fingers) that can be reorganized in interesting ways. That's using integers, but that's only one way to look at the universe.
If, for example, you went with base yellow, you'd have a very rich number system, which for humans would be an instantly comprehensible Real number system stretching from Red to Violet, with Yellow as the base point. You'd really be basing it on temporal frequency, which would have all sorts of neat results that you wouldn't have to define after the fact, because they'd be a built-in part of the system. So for example, you could say "It's going to be this colour orange out today" and people would know exactly what temperature you were talking about -- in fact, we already use "heat graphs" because they're so much better at conveying quantifiable information in some situations than decimal numbers.
However, if you've settled on a base of Yellow (think white balance in photography), then you can also use this system to measure differences in weight and even discrete numbers of objects, albeit in a more abstract sense.
Another place you can see this is in an analog clock. Sure, it's got either roman or decimal numbers on it usually, but you can also think of it as a representation of either Pi or Rad, and the full circle lends itself much better to this than to dividing it up into an infinite number of discrete slices. So when we say "It's ten o'clock" we're actually making a flawed approximation to the actual time, based on the best accuracy we can make with a decimal number system. Using this argument, you can say that using a number system to track time isn't possible, as you can't accurately represent the passage of time with integers. And yet we do it every day.
The language systems you use (including number systems) heavily influence the way you think and see the world around you. There are some cultures in the world that don't have words for certain objects and concepts -- they get along by using the other concepts to approximate the missing one, or they just don't think about that concept in the first place.
By painting the box that says "a number system's base must be integral" you are severely limiting the way you observe the world around you.
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 that can be written and operated on using the same "rules" as in base 10 math, but with a different number of symbols.
Pretty much. I believe what you're referring to is generally a "standard positional number system", or more specifically, everything that doesn't fall into the borad definition of having an integer base of greater than 1 is generally referred to as a "nonstandard positional system".
But nobody actually means that when they talk about "base N" because it's kind of pointless. Why even ask the question about what it would be like if we could have "base N" if the answer is, "it would be however you want it to be".
Indeed. If one doesn't stick to standard naming, then people get confused and there's little point in confusing people for the sake of it. I'm prepared to say that base-N (where N is an integer gerater than 1) follows exactly the quite simple and elegant rules one expects. Likewise if someone's talking about a "number", I'll generally assume they're talking about probably an integer or a real number unless they specifically say otherwise.
Anyway, I think my point didn't come across clearly. My point is that things like fractional bases and fractional powers don't inherently amke sense. It's not that you can't do them it's that you haven't invented a way to do them. In this sense you can do whatever you like as long as you invent a way. For number bases, you generally want it to have certain properties:
1. If you plug in an 10 instead of a fraction, it really ought to look like base 10, otherwise it's basically inconsistent and not interesting. Likewise for all other integers > 1.
2. You need to be able to represent all real numbers with your system otherwise it's not much use and only works "properly" for integers (except perhaps for the odd degeneracy).
3. You probably don't want to have special cases (if number is an integer do this else do that) because that's horrible, inelegant and unpleasant, and almost certainly not very interesting.
4. You probably want it to be able to work with all the things that normal number bases work (e.g. algorithms) automatically and without having to change them.
Once you have done that, there are two probable paths:
1. You invent the same thing that everyone else works on. This is quite easy to do for non positive integer powers. In this case you'll eventually find the names everyone else uses and avoid confusion.
2. You invent something new. To avoid confusion, you'll need to give it a different name.
So back to number bases. It turns out it's interesting if you simply pick the number of symbols as floor(base)+1. Base 2, 10, ... etc still work perfectly. Multiplication algorithms work fine with no modification. So does addition up until you have to perform a carry at which point it you have to generalise the carry algorithm to suit. An example.
If you have base pi, then the you'll have 3 symbols like base 3 (0, 1, 2), and the digits will be: ..., pi^2, pi, 1. So to compute pi * pi you'd find the representation in base pi. This satisfied by 10: 1 lot of pi + nothing else.
pi^n, pi^n-1,
We're not in modular arithmetic, so using the normal multipliction algorithm, we get: 10*10 = 100.
Looking back in the table of what each digit means, we get pi^2, so it's consistent with how we expect a number base to work.
SJW n. One who posts facts.
from personal experience there may be some slight truths in it although most the stuff I've seen on him (came across before this article) looks like he's full of shit. I have diagnosed aspergers, I am high functioning but have savant traits and way above average IQ and it initially became apparent as a small child. I was born at 27weeks @ 2lb1oz and in hospital for 6months at birth, due to mistake of junior nurse who did something she wasn't qualified to do (feed me) my lungs got filled with milk (the tube was supposed to go in the other tube ;) ) and I stopped breathing for 7 to 8min. There is record of all this and parents confirmed they were told there would likely be damage to my brain due to way above the oft quoted 4min barrier as well as optic damage from the oxygen given.
So it seems the accident may have been the trigger for it although a lot more at play. The traits seem to run in minor form through one side of family all of whom are educated to high degree in maths/engineering/science and work in such fields as well as extensive hobbies within them but I am unusual in it is very exaggerated in me.
I am able to visualise mathematical and scientific theories in a way but it isn't as he describes. It is more like the same appearing object to sense organ but the conceptual object linked to it tends to have the physics etc of it linked in so I notice things naturally just seeing stuff that many wont without deeper thought. I found my studies easier due to this but it isn't special since anyone can train to do it it just doesn't seem to happen naturally in many cases. The seemingly intuitive nature is just deep familiarity and many many people have that.
I remember this movie; it didn't end well.
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 :)
the report of a woman in Perth, Scotland who started to speak with a French accent after a brain injury or a stroke (or both). She could not speak French, she just had ze aczent. She sounded good not at all like the Now Legendary TV show "Allo, Allo" (cultural oblique reference, sorry.), it was difficult not to laugh when she was interviewed on the radio.
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