Ramanujan's Deathbed Conjecture Finally Proven 186
jomama717 writes "Another chapter in the fascinating life of Srinivasa Ramanujan appears to be complete: 'While on his death bed, the brilliant Indian mathematician Srinivasa Ramanujan cryptically wrote down functions he said came to him in dreams, with a hunch about how they behaved. Now 100 years later, researchers say they've proved he was right. "We've solved the problems from his last mysterious letters. For people who work in this area of math, the problem has been open for 90 years," Emory University mathematician Ken Ono said.
Ramanujan, a self-taught mathematician born in a rural village in South India, spent so much time thinking about math that he flunked out of college in India twice, Ono said.'"
Died at 33 (Score:3)
Just imagine the contributions he might have made if he had lived. Such a shame.
It's just a hunch, but I have a feeling, unlike say technology, that mathematics is one of those fields where discoveries aren't always inevitable. Either someone thinks up of some things or they don't.
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So what is the significance on these functions? Are they useful for anything?
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Yes, they help minimize passing on the Math gene to the next generation.
Flunked out of college twice (Score:5, Interesting)
Re:Flunked out of college twice (Score:5, Insightful)
Probably a lot of pot.
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Re:Flunked out of college twice (Score:5, Funny)
I wonder what would happen if US colleges (or even earlier in our educational system) let students have free reign, and really specialize.
We'd have a bumper crop of PhDs in Call of Duty: Black Ops.
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I wonder what would happen if US colleges (or even earlier in our educational system) let students have free reign, and really specialize.
If you don't want a liberal arts education, don't go to a liberal arts college, although some will let you design your own curriculum as long as you meet some basic requirements and get the department head(s)'s approval.
And there are plenty of highschools that focus on specific areas of study: they're called "magnet" schools.
You can also find magnet programs within normal highschools, which allow students to focus their studies on one subject.
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1. Why it benefits them.
2. How to find out who it might benefit.
3. How to make it available to those who might benefit.
As opposed to saying "make a choice on which college you attend" (which for many many students is restricted by past academic performance and financial caste) and letting the students who don't end up at schools that give students that kind of reign.
One approach i
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It is called M.I.T. [mit.edu]
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They do let students specialize - students are free to take any course they want (as long as the prerequi
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Actually, there are some universities that penalize you for going beyond a certain number of credits when working toward your BA/BS (if I remember correctly, Univesity of Texas at Austin is one of them, but my memory might be failing me). Which would prevent someone (outside of double majoring) from taking too many courses outside their area of specialization (major).
That said, as someone who has recently (within the last two years) started working on their college degree(s) part time while maintaining a c
Re:Round them out (Score:2)
Not really buying it.
If you got a kiddo with a 150+ IQ, your lectures on Gilgamesh will be wasted. End Of Story.
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I wonder what would happen if US colleges (or even earlier in our educational system) let students have free reign, and really specialize.
You can, if you want. I spent a lot of time outside my class work studying things that interested me. Why didn't you?
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If they're lucky, they might learn to spell "free rein" (yes, that particular euphemism is derived from stagecoaches/wagons, rather than kings/queens).
Now that the obligatory grammar nazism is done, the main effect would be to produce people who couldn't communicate their ideas effectively enough to be taken seriously - it's all very well to come up with a revolutionary idea, but if the paper
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Let's face it. The kinds of ideas that were rolling around in Ramanujan's head can not be communicated in a language other than math. Ramanujan's "problem" was that his interest in number theory was greater than anything being discussed in his other courses. Also, he had the problem that he needed to support himself by tutoring others as a source of income, which only added to his "problem".
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let students have free reign
Young people do need guidance. Complete freedom can lead nowhere too. The real challenge is to recognise what each person's mind is most talented at, and what they're naturally attracted to. The intersection between talent and enjoyment is a good place to find guidance. We don't do anywhere near enough to recognise kids' individual talents. We go about education *too* uniformly and I think that misses a lot of opportunity.
Re:Flunked out of college twice (Score:4, Informative)
Why do you think we have such advanced technology? Because people specialise in very narrow fields. A person doesn't have infinite capacity to learn and invent. They also don't have infinite time, or any method of instantly transferring knowledge.
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An engineer who never had to take a biology class never looks to nature for a simple solution and keeps banging his head against the wall studying more and more about solutions that have already been tried.
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As the AC also said right now some of the best ideas in engineering are coming from studying nature.
Why are plant cells so efficient at harvesting light and how can we duplicate that ability?
The real trick about advanced technology it is driven by material science and nature does somethings incredibly awesome.
Re:thought across those areas (Score:2)
Hi AC,
I know about four sentences of a whole lot of stuff. It's like it's a party game, you can drop a key word or two, but the min any actual specialist asks you a question, you're hosed.
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There's room for both. Put a few "sythetist" type thinkers in with of a whole bunch of specialists and you've got a pretty amazing combination. Some people are better suited to specialty, while others excel at being a "jack of all trades". We obviously can't all be a DaVinci but those who are really make an impact.
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I wonder what would happen if US colleges (or even earlier in our educational system) let students have free reign, and really specialize.
Then maybe the US would continue to rein over the rest of the planet indefinitely.
Or until a year later, their narrow minded specialization became obsolete, with the new graduating class.
I studied communications:
vacuum tubes, teletype, rotary switches -- all the modern stuff of the time. Even had 2 weeks of transistor theory, a promising new technology, suitable mostly for portable radios at the time.
Because of those unwanted "required" electives I took philosophy and logic (totally of no use in electronics), although some of it applied to math in a nonsensical way.
And then the world ch
The summary is incorrect (Score:2, Informative)
Ono's team did not prove the Ramanujan Conjecture. It was proven a long time ago, in 1974 by Deligne as part of his proof of the Weil conjectures
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The summary is fine, it's just not very specific. A conjecture of Ramanujan's was proved, and it was one appearing in his final letter to Hardy.
The conjecture most often referred to as the "Ramanujan Conjecture" was something he had published 4 years earlier.
Re:The summary is incorrect (Score:5, Informative)
The summary is actually referring to other conjectures from his notebooks and other notes, not 'the' Ramanujan conjecture as proved by Deligne, so the summary is not really incorrect, just misleading. It should be noted that these other conjectures are in fact not unusually important and certainly not even close to the Weil conjectures, but are nevertheless interesting.
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Let me guess, the curtains stayed?
misleading summary (Score:2)
The summary suggests that Ramanujan wrote down some results that were conjectures until now. He wrote down many results, few if any on his deathbed, and most of them have already been verified for years, though some were still open until recently. Apparently the actual article is about the closing of the last few ones only.
Re:deathbed (Score:2)
I'm lost, he apparently wrote a bunch of stuff on his deathbed and sent it all to Mr. Hardy.
Flame-bait summary? (Score:5, Insightful)
Whenever I read submissions like this, I wonder why they put a sentence like "genius in flunked out of ...". Unless the area they were a genius in was the same one he/she failed at, it seems kind of flame-bait - trying to start an "school is useless - look at these outliers" discussion.
Ramanujan was brilliant at mathematics, and there is no denying that. But like any school/college, his was made for the average person. Sure, it would be great if education was tailored to each individual's aptitude. But we don't have a good way of finding out what that is directly yet. Instead, we throw a bunch of subjects at students, and they figure out where there relative strengths are. And they focus on one or two areas where their natural aptitude lies (or more realistically, where their job prospects and abilities/interests combine to give "best" results; best being chosen by the student. Some may chase money, others fame, others just want to solve interesting problems - applications/paycheck be damned).
And discovering outliers early is hard when the teachers themselves are not much better at their subjects than the students. If some kindergarten student started using calculus for loading of building blocks, it won't be much use if her teacher doesn't realize that what she is doing is phenomenal (especially since the child will have her own notations/symbols). Obviously, that is an extreme example, but the point remains - outliers will have a tough time in the current system.
Alternatively, we can let everyone do what they find interesting, but a majority of students will just spend time doing "fun" things like sports - which is not necessarily bad. But as long as we have the current system where you starve if you can't hold down a job doing "productive things", I think the educational system prepares most people for such a world.
Outliers are great - and can help speed up society's progress significantly. But at the end of the day, they are just that - outliers. If you design a system to help the outliers, most people (myself included) would wind up getting a very bad outcome - because most people aren't phenomenally skilled at anything (and no, being the best me I can be doesn't cut it). And if you have a lot of starving deadbeats on the street (instead of the mediocre, but holding down a job majority) I expect society to completely break down - and that won't help the outliers either.
Flame-bait comment. (Score:2)
Whenever I read submissions like this, I wonder why they put a sentence like "genius in flunked out of ...".
Let's look at the sentence in question: "spent so much time thinking about math that he flunked out of college in India twice" -- and you went off on a many-paragraph rant, when the only things that the sentence showed were that he was more interested in mathematics (some might rather say obsessed with) than the baseline, and perhaps that the school system was not set up to handle him. It does not contain an indictment of the school system, and only you thought it did, then went off on a massive rant about
Not only that (Score:3)
But there's value to a well rounded education. In part because it lets you work with others and function in society better. While some great works are done almost solely by an individual (like the Principia) most are done via collaboration.
Also it allows you to see things more cross-domain. Knowledge of things in more than just one area can let you see connections that you might otherwise miss, and to see applications for things that otherwise might just seem to exist in a vacuum.
Hyper-focused education is
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There is also value in a single driven focus is there not? I mean, Einstein wasn't known as a rounded scholar. Most of the most brilliant people in their fields pretty much just got past the other worthless classes on their path to greatness.
People who constantly defend college are just as bad as those who constantly attack it. Some people seem to think that college is the only path to greatness, of course that's probably because it's the path >they chose. I personally went to college, graduat
There is no greater human inspiration (Score:3)
Ramanujan is pretty near the top of my list of most admirable humans. His widely encompassing spirituality, the incredible way he developed his own native ability, and his focused obsession which hindered his college learning, are all themes that resonate strongly with me. The story of his life is at once a triumph of the individual human spirit and a tragedy of the life of one of the very finest of us being cut short.
Re:Guy was so smart it's scary. (Score:5, Interesting)
Obsessed, and smart.
He had a mathematician's mind, sure. Probably not much brighter than what we consider reasonably bright and particularly attuned for maths. But what he had that sets us apart, was a raging obsession. The kind of demon that consumed Newton and possessed him to calculate pages of logarithms and Tesla to study from dusk 'til dawn and further, without respite.
Re:Guy was so smart it's scary. (Score:5, Informative)
Ramanujan is a totally different ball game. Completely self thought, from a book of identities and formulae. He found a sort of Cliff notes for the BA in Math in England. He assumed that is the way to present mathematics. Just the final result without any deriviation or proof. Did not know what was already invented and well known. He reinvented the wheel so to speak so many times. Almost all the major math break throughs of the previous century, he reinvented all over again, independently. Think about it. One century of mathematicians original work completely reinvented by this lone clerk toiling away in colonial India working as a harbor master's assistant. He presented his inventions without any proof or even a hint of how it was arrived at. Most of his first letters were rejected as some crackpot's ravings by math professors in England. Hardy was the only one who saw that among all the well known identities, that were being presented as new inventions, were real gems never seen before. He invited Ramanujan to England and the rest was history.
A special tit bit: BTW he and I both have the same ancestral temple, that of Lord Oppiliappan at Kumbakonam, Tamil Nadu, but his favorite god was not Oppiliappan, but Nama Giri Devi, the ancestral god of his mother's family. I wish we were related. His personal life was very sad. Died at age 30. His wife was left as a destitute and ended up working as house maid.
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A special tit bit: BTW he and I both have the same ancestral temple, that of Lord Oppiliappan at Kumbakonam, Tamil Nadu, but his favorite god was not Oppiliappan, but Nama Giri Devi, the ancestral god of his mother's family. I wish we were related. His personal life was very sad. Died at age 30. His wife was left as a destitute and ended up working as house maid.
It would usually only be a tit bit if you are referring to one of the gods with 8 or 10 breasts or something like that. In most other cases, it would be a tidbit ;-).
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titbit was a bowlderization of tidbit from what I was aware, but you are right that the American version is a bowlderization of the British version.
tidbit
c.1640, probably from dialectal tid "fond, solicitous, tender" + bit "morsel."
Online Etymology Dictionary, © 2010 Douglas Harper
which I give more credit to than Merriam-Webster which can only manage a
Origin of TIDBIT
perhaps from tit- (as in titmouse) + bit
First Known Use: circa 1640
At least a probably sounds more authoritative than a perhaps.
That said
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One, the word is bowdlerisation and two, they work the opposite way round.
You don't have a clue what you're talking about, do you?
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Newton was very much after glory and fame. Became an MP, attended the House of Lords, (but never delivered a speech ever), got himself appointed as the Controller of the Mint and excessively obsessed about priority and credit.
Where did you get that bit of information?
BTW logarithms were calculated by John Napier, not Newton.
This statement seems unnecessary and implies that Newton was found of taking credit for other people's work. Newton's accomplishments are huge - even his work in the Royal Mint.
Yes, Ramanujam was great, but why put down Newton's reputation to exalt Ramanujam?
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Actually, he was unusually gifted in mathematics and certainly much brighter than the average mathematician, at least in terms of raw power and intuition. Evidence of this can be found both in his work and in the comments on him by G.H. Hardy, the eminent English mathematician who helped Ramanujan come to England and who collaborated with Ramanujan for years.
Re:Guy was so smart it's scary. (Score:5, Informative)
Probably not much brighter than what we consider reasonably bright...
From what evidence did you draw this conclusion? I'm not personally qualified to assess Ramanujan's brilliance (and neither are you, I suspect), but G.H. Hardy, the western mathematicion who worked most closely with Ramanujan, certainly was. What did he think? "I have never met his equal, and can compare him only with Euler or Jacobi." [usna.edu] By all accounts, Ramanujan's abilities went way, way beyond "not much brighter than what we consider reasonably bright". He possessed one of the most gifted mathematical minds in recent history.
Re:Guy was so smart it's scary. (Score:5, Interesting)
Probably not much brighter than what we consider reasonably bright and particularly attuned for maths.
Give a reasonably bright math graduate an entire lifetime and he is unlikely to be able to reinvent all the math that Ramanujan reinvented due to not knowing it already existed, nor invent all the new math stuff that Ramanujan came up with. Ramanujan did all that in only 32 years.
The merely obsessive would get stuck in ruts or fruitless paths. Ramanujan came up with tons of stuff.
The way his mind works is pretty different:
He was sharing a room with P. C. Mahalanobis who had a problem, "Imagine that you are on a street with houses marked 1 through n. There is a house in between (x) such that the sum of the house numbers to left of it equals the sum of the house numbers to its right. If n is between 50 and 500, what are n and x?" This is a bivariate problem with multiple solutions. Ramanujan thought about it and gave the answer with a twist: He gave a continued fraction. The unusual part was that it was the solution to the whole class of problems. Mahalanobis was astounded and asked how he did it. "It is simple. The minute I heard the problem, I knew that the answer was a continued fraction. Which continued fraction, I asked myself. Then the answer came to my mind," Ramanujan replied.
This is not the "normal" savant rapid addition/multiplication sort of stuff.
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I am not so certain.
Do consider the reasonably bright math graduate. Take away from him the want or need for leisure, and instill in him a burning desire to do nothing but study and think about maths. Now just push his intelligence a little higher than the rest of the reasonably brights.
And then consider the implication that actively thinking about math all of the time changes your brain structure and makes you more intelligent.
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Re:Guy was so smart it's scary. (Score:5, Insightful)
So, because he ended up losing his mind, that invalidates all his accomplishments?
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Problem is, if you're off your guns just a little, you get dropped by the Genius Envy crowd and then you're just cooked.
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There's likely also a strong correlation between running and wrist injuries. Nevertheless, running and having a wrist injuriy don't have much to do with each other and the latter doesn't help you with the former.
Re:Guy was so smart it's scary. (Score:5, Interesting)
Newton later turned to alchemy, and was obsessed with disproving the trinity.
Re:Guy was so smart it's scary. (Score:5, Insightful)
Actually, Newton was an alchemist foremost. He only did physics and calculus to help with his alchemy.
And no, alchemy was not the crackpot gold-seeking they teach it was in history class. Promises of gold were and still are what gets you the funding. Alchemy was a larger discipline concerned with truth about the world, a kind of philosophy 2.0 that finally recognized the need for empirical data and experiment; the most advanced worldview up to that point. Later, as it progressed, physics and chemistry were branched out from it, other parts merged into medicine, philosophy and humanities.
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Another way of putting it: all the stuff we remember Newton for was for him a fun hobby project. Not only was alchemy a big focus of his, he also played around with religion and magical ritual (as did several other British academics in his time).
Same story with Rene Descartes, a couple generations earlier: His focus was first and foremost on his philosophical works, the algebra work (including inventing exponents and analytic geometry) was just for fun.
It gives you an idea of how ridiculously smart these gu
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In Newton's day there was little distinction between alchemy and science. It is incorrect to presume that Newton was principally an "alchemist". This can be seen that his work outlining the existence of the infinitesimal calculus was done prior to most of his work in alchemy. In fact, his alchemy is inconsequential to the essential nature of his significant contributions to science, except perhaps that his careless handling of mercury probably hastened his death.
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Whether your conclusion is correct has nothing to do with whether you're a quack. It could very well be that acupuncture helps, but that doesn't make Qi a real thing. It could be that cold fusion is possible, but that doesn't mean that the guys who claimed to do it last time were right. Many things could be, and what makes one a quack is how you get to your answers, not whether you got to the right answer. Put another way, homeopaths aren't quacks just because it's possible to cure many of the diseases they
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A way to define Qi would be 'the thing that makes acupuncture work'. Since acupuncture works, there must be something to make it work. Thus, empirical proof. If you go and practice some certain schools of meditation or martial arts, you will also find first-hand proof of this something.
Getting to the root cause has not been that much on the agenda of the eastern worldviews. Unlike the western world, that seeks to identify causation, the eastern cultures have more interest in correlations. In the center of a
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This is nonsense. By this definition, if it turned out that acupuncture worked because of fraud, then you would say that qi actually exists (and that it consists of fraud).
If Bigfoot turns out to be a guy in a costume, does that mean Bigfoot exists? It does if you define Bigfoot as the creature that appears in Bigfoot photos.
Common sense says that "qi exists" means that 1) something makes acupuncture work, and 2) it's at least somewhat l
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I have to wonder whether most people today understand that the alchemists had it right all the way, that elements can indeed be made into other elements.
Alchemists also believed the philosopher's stone (which was the thing they believed would turn base metals into silver and gold) could also heal all forms of illness, prolong life, create perpetually burning lamps, transmute common crystals into precious gems, revive dead plants, create flexible glass and create golems.
One of the extremely long list of stupid things they believed in turning out to be possible through means that they'd never envisioned does not make alchemists "right all the way."
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Alchemists also believed the philosopher's stone (which was the thing they believed would turn base metals into silver and gold) could also heal all forms of illness, prolong life, create perpetually burning lamps, transmute common crystals into precious gems, revive dead plants, create flexible glass and create golems.
Let me just translate these goals into modern language: resources, health, lifespan, energy, money, death, materials, army. These days we believe that nanotechnology will solve all of these problems. Or will it be biotechnology? Gene technology? Drones? IT? MMT? Every time we open a new frontier of understanding into the world, we try to use it to solve our problems. This is why we do this progress thingy. Hoping that the next big thing will solve the problems is no more stupid now than it was then. It is a
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Forgot the one very important thing. Golems represent not only the army, but also automated production, that is, a post-scarcity society.
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Her friends call her Edwina.
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Newton spent most of life working on Alchemy--far more than he did on Physics or Mathematics. He didn't turn into a crackpot, he was one from the start.
So...what was your point?
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Alchemy was all there was. Physics hadn't been invented yet.
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Re:Guy was so smart it's scary. (Score:5, Funny)
noodles?
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bah, posting to cancel a mistaken mod. Sorry about that.
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I suggest reading Hans Camenzind's "Much ado about almost nothing". It pretty much recounts Tesla the way he really was. His only "paramout" work of practical importance was in multi-phase power transmission and generation. He devoted the latter part of his life thoroughly to crackpottery, defrauding his investors along the way.
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Re:He tapped on to his full potential (Score:4, Insightful)
I suspect that you're quite wrong. The man was a mathematical prodigy. I don't think it was a matter of choice at all, but rather some sort of unique wiring
Re:He tapped on to his full potential (Score:5, Insightful)
There's no way to know because he's dead, but there's certainly a body of evidence suggesting neurological differences between genius level mathemetic prodigies to suggest that a poor young man from an Indian village who literally taught himself 100 years worth of mathematics was in possession of cognitive abilities beyond the average person's.
The amount of grey matter is an obscenely crude way to measure intelligence. What I find interesting is your need to make the man average and ordinary. Does the possibility that some have greater cognitive capacity than others bother you?
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There's no way to know because he's dead, but there's certainly a body of evidence suggesting neurological differences between genius level mathemetic prodigies to suggest that a poor young man from an Indian village who literally taught himself 100 years worth of mathematics was in possession of cognitive abilities beyond the average person's.
The amount of grey matter is an obscenely crude way to measure intelligence. What I find interesting is your need to make the man average and ordinary. Does the possibility that some have greater cognitive capacity than others bother you?
Or maybe he was just more motivated than average. How many people would want to spend all their best moments in life on math?
Best moments of life (Score:5, Funny)
I have to say that some of the best moments of my life were calculating the area under the curve by tactile measurement.
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I did quite well in math by almost any measure, but I wouldn't say I'm anywhere near the level Ramanujan achieved at. Sure, I read books on math and such and didn't get out much, but I wouldn't have called myself a particularly hard worker. For the most part performing a few standard deviations above my peers in my areas of talent was fairly effortless. No doubt for me to achieve at a world-class level would have required considerable effort, but for most people no amount of effort would have made that p
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I can believe this. Intelligence isn't an absolute value. Sure, you can take a whole bunch of measures and add them up, but the fact is that your brain is a complex organ capable of doing all kinds of things, and it can do all of them to varying degrees.
I'm married to somebody who is fairly intelligent, but due to a recent stroke she went through a period of time where her vocabulary was all of about 20 words. Now she struggles but does fairly well verbally, but still struggles with written language. Ho
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If you actually attempt to read Ramanujan's work, it becomes obvious pretty quickly that there is more than just motivation involved in his genius. Check out some of his generating functions if you don't think this is true and honestly ask yourself "could I have thought of this"? There is absolutely nothing "obvious" to the rest of us mere mortals, about why his incredibly complicated equations should be so incredibly accurate.
I personally doubt his inspiration came from God, and suspect it derives from a
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Well, maybe it's luck. Much of it could be.
We all have strategies we approach problems with, in maths and puzzles as in life. Some strategies are better fits for certain sorts of problems than others. To some degree you can change your mental strategies, but once you're set in them, it becomes an expensive proposition. Like assumptions, methods are hard to change once you've built a lot of genuinely useful stuff on them. Maybe we have different aptitude for certain strategies, but it may also be affected by
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Indeed -- From study, it seems that Albert Einstein's brain may have better enabled him to make his discovery's on the workings of space and time.
“Although the overall size and asymmetrical shape of Einstein’s brain were normal, the prefrontal, somatosensory, primary motor, parietal, temporal and occipital cortices were extraordinary,” said Falk, the Hale G. Smith Professor of Anthropology at Florida State.
“These may have provided the neurological underpinnings for some of his visuospatial and mathematical abilities, for instance.”
-- http://www.examiner.com/article/differences-albert-einstein-s-brain-may-explain-his-genius
Not all brains are the same and when extraordinary ability is granted to such a narrow focus such as mathematics, I would have to guess that the cause would have a physical cause rather than simply "putting his brain to use more than 99.9999999999% of us"
Re:He tapped on to his full potential (Score:4, Insightful)
So your argument is just as silly as those "you can do anything if you just try hard enough" bullshit cliches.
If you think it's so simple, go ask the top athletes/musicians why they aren't all number one despite most of them spending much of their life training, practicing etc. You think it's because they lack willpower to push themselves to their limits? They're not trying hard enough?
I may not know my exact max limits, but I know that no matter how much I try I am never going to run as fast as Usain Bolt, and I'm never going to be as good at math as Ramanujan. Thinking otherwise is foolishness or hubris even.
I'm all for people trying to improve themselves and others, but I'm against spreading bullshit. The world would be a better place if more humans fully realized and admitted how crap they were, but still persisted in helping and bettering others despite their limitations.
Re:He tapped on to his full potential (Score:5, Interesting)
The grey matter in between your ears contains similar amount of chemicals as the ones inside the head of those so-called "prodigies".
So if I put your brain in a blender, it should work the same afterwards right? Silly argument.
Unless it is proven that that deceased Indian math genius suffered from some acute type of "savant syndrome", I seriously doubt his brain has any "unique wiring" of any kind.
Perhaps not unique in that you'd see a difference on a brain scanner at the macro level, but I think it's more about being wired right or wrong. Look at people playing chess, the poor players aren't making any less of an effort but they're just overlooking moves or forgetting what paths they have and haven't explored or miscalculating because they don't see the piece is pinned. Your average player has an early botched Pentium and flaky non-ECC RAM, the grandmasters an Xeon with RAS features and ECC RAM. They very rarely think wrong or remember wrong, of course there's also training but I think it's also a lot what you're given from nature's side. It doesn't help if the same number of neurons are firing if in one brain it only leads to noise and nonsense and in the other to answers and solutions.
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He said exactly the opposite. He said: the wiring is important. O_o
No, just reading comprehension fail on your end. The post I replied to by Taco Cowboy clearly argued it wasn't and that it is only a "will" to use your full mind.
Re: He tapped on to his full potential (Score:3, Insightful)
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The man was a mathematical prodigy.
Einstein was a mathematical prodigy. We preserved his brain for post-mortem study and it is unquestionably different from the average brain.
How much was the thinking shaping the brain and how much was the brain shaping the thinking isn't something we can determine, but his brain was definitely different. And, like Ramanujan, he had a reputation for never ceasing to think.
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The only difference between Srinivasa Ramanujan and 99.99999% of the human race is that he opted to use his brain power as much as it could be sustained.
If only you were lucky enough to have a brain half as good as his, you'd realise that your hypothesis was a load of utter bollocks.
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Srinivasa Ramanujan was given a brain, a brain that is not that different from the one we have in between our own ears.
There's another comment in this thread with a link to Harvard that says you're wrong. According to the article, creative people's brains aren't normal. They're closer to the brains of madmen. And yes, it applies to me as well, I'm nowhere near normal.
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It is a testament to Ramanujan's genius that when W. H.Hardy, who was himself an extraordinarily gifted mathematical genius, was asked what his greatest contribution to mathematics was, he replied "discovering Ramanaujan".
Let's face it, our brains may look like Ramanujan's, but at a molecular and inter-neuronal level the similarity ends. One only has to try to work through Ramanujan's work to quickly understand this first hand.
Anyone know where the results in the article have been or are being published an
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Or gently shaking his head in confirmation.
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Unless you're a doctor or a lawyer, your Indian degree is less than worthless.
Hmm... nice choice there - especially since doctors and lawyers can't generally practice in other countries based on their Indian degrees. On the other hand, a lot of Indian engineers (or engineers from most countries) can take up jobs wherever they get the opportunity. Bitter much?
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2 + 2 = 5, for very large values of 2 [straightdope.com]
You lose, Robin.
From the original "2 + 2 = 5 for SUFFICENTLY LARGE values of 2"
Simple to prove, with a question: "how large a cup does it take to hold 2 heaping cups of flour taken twice from the barrel?"