"Student: How can one realize his Self-nature? I know so little about the subject. Yasutani: First of all, you must be convinced you can do so. The conviction creates determination, and the determination zeal. But if you lack conviction, if you think ‘maybe I can get it, maybe I can’t’, or even worse, ‘This is beyond me!’ - you won’t awaken no matter how much you do zazen."

When I came across this quote, I was struck by its relevance to one of Eliezer Yudkowsky’s ‘beisutsukai’ posts about finding the successor to quantum mechanics, “The Failures of Eld Science”.

I meant to write an essay on how interesting it is that we intellectually know that many of our current theories must be wrong, and even have pretty good ideas as to which ones, but we still cannot psychologically tackle them with the same energy as if we had some anomaly or paradox to explain, or have the benefit of hindsight. The students in Eliezer’s story know that quantum mechanics is wrong; someone with a well-verified observation contradicting quantum mechanics knows that it is wrong (replace ‘quantum’ with ‘classical’ as you wish). They will achieve better results than a battalion of conventional QMists.

But nothing quite gelled.

“—for over thirty years,” Jeffreyssai said. “Not one of them saw it; not Einstein, not Schrödinger, not even von Neumann.” He turned away from his sketcher, and toward the classroom. “I pose to you to the question: How did they fail?” Brennan didn’t jump. He deliberately waited just long enough to show he wasn’t scared, and then said, “Lack of pragmatic motivation, sensei.” “The Manhattan Project,” Brennan said, “was launched with a specific technological end in sight: a weapon of great power, in time of war. But the error that Eld Science committed with respect to quantum physics had no immediate consequences for their technology. They were confused, but they had no desperate need for an answer. Otherwise the surrounding system would have removed all burdens from their effort to solve it. Surely the Manhattan Project must have done so - Taji? Do you know?” Jeffreyssai chuckled slightly. “Don’t guess so hard what I might prefer to hear, Competitor. Your first statement came closer to my hidden mark; your oh-so-Bayesian disclaimer fell wide… The factor I had in mind, Brennan, was that Eld scientists thought it was acceptable to take thirty years to solve a problem. Their entire social process of science was based on getting to the truth eventually. A wrong theory got discarded eventually - once the next generation of students grew up familiar with the replacement. Work expands to fill the time allotted, as the saying goes. But people can think important thoughts in far less than thirty years, if they expect speed of themselves.” Jeffreyssai suddenly slammed down a hand on the arm of Brennan’s chair. “How long do you have to dodge a thrown knife?”

— They didn’t know that they were looking for a better theory.

The students in this story have the incredible advantage that they are starting from a wrong theory and know this for certain, and not merely suspect or hold as a general philosophy-of-science principle ‘there’s probably a better theory than the current one’. This gives them several things psychologically:

the willingness to scrap painfully won insights and theories in favor of something new and saves them from spending all their time and effort patching up the old theory.

I know in the past when I’ve tried my hand at problems (logic puzzles come to mind) that I am far more motivated and effective when I am assured that there is in fact a correct answer than when I am unsure the question is even answerable.

And a quick note to those who think I’m echoing Brennan: I am, here, but my point differs in that I don’t think it was a matter of ‘training’.

I think if you abducted all the old greats, gave the necessary experimental data, and gave them a few months to produce the new theory before they were dragged out to the shed and shot, then they could do it just as well as these students. It’s all about motivation.

It’s not a matter of competency at paradigm shifts, if you will; it’s accepting that one needs to happen now and you are the one who needs to do it. But there’s no normal way to convince a scientific community of this; isn’t it true that most new paradigms fail to pan out?

From “Class Project”:

Jeffreyssai took a moment to look over his increasingly disturbed students, “Here is your assignment. Of quantum mechanics, and General Relativity, you have been told. This is the limit of Eld science, and hence, the limit of public knowledge. The five of you, working on your own, are to produce the correct theory of quantum gravity. Your time limit is one month.” Ordinarily, at this point, I would say: “Now I am about to tell you the answer; so if you want to try to work out the problem on your own, you should do so now.” But in this case, some of the greatest statisticians in history did not get it on their own, so if you do not already know the answer, I am not really expecting you to work it out. Maybe if you remember half a hint, but not the whole answer, you could try it on your own. Or if you suspect that your era will support you, you could try it on your own; I have given you a tremendous amount of help by asking exactly the correct question, and telling you that an answer is possible.

http://lesswrong.com/lw/qr/timeless_causality/

http://www.coordinationproblem.org/2010/04/neurological-freaks-and-the-drive-to-excel.html

Claude Shannon once told me that as a kid, he remembered being stuck on a jigsaw puzzle. His brother, who was passing by, said to him: “You know: I could tell you something.” That’s all his brother said. Yet that was enough hint to help Claude solve the puzzle. The great thing about this hint… is that you can always give it to yourself.

–Manuel Blum, “Advice to a Beginning Graduate Student”

After working as a statistician in Seattle, he [George Dantzig] wrote in 1939 to Neyman, whose papers had interested him, and an assistantship was arranged for him at Berkeley. This story from that period is a classic: During my first year at Berkeley I arrived late one day to one of Neyman’s classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework – the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o’clock, Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: “I’ve just written an introduction to one of your papers. Read it so I can send it out right away for publication.” For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them. [from Albers 1994, More Mathematical People: Contemporary Conversations]

–Tales of Statisticians, E Bruce Brooks 2001

“In the Hebrew University, it [the story about Dantzig] is told about Avinoam Mann.” –Daniel Moskovich

“At Princeton, it is told about (who else) Jack Milnor. The result is the ‘Fary-Milnor’ theorem, on the total curvature of a knotted curve (there is an Annals paper to back up the story…)” –Igor Rivin

“The version I heard was that Milnor was late to class, and copied down several (open) problems written on the board that he thought were homework. At a later class he says, ‘That homework was hard! I only got 2 of them.’” –Jonas Meyer

“Paul Cohen used to claim that the Bergman kernel was discovered this way (by Bergman).” –Dan Ramras

“The Huffman code story I heard is that in an information theory class, Huffman had a choice of writing a term paper or taking a final. His term paper was the discovery of an algorithm for finding optimal binary codes (i.e., Huffman codes).” –Peter Shor

–MathOverflow

Ron Graham, pg105: Harvard mathematician Persi Diaconis, who has collaborated with Graham many times, describes him as “a remarkably accomplished mathematician. Ron is always willing to help a struggling student or a colleague. He never leaves you hanging. He’s a genius, but a nice genius.” Diaconis remembers giving a talk about joint research that he and Graham had done. He ended his talk by saying “This problem is still unsolved.” At that point, Graham, who was in the audience, stood up and gave a solution on the spot. The audience, thoroughly impressed, burst into applause, an unusual outpouring of emotion for a group of mathematicians. Benoit Mandelbrot, pg 224-226 MP : Kleinian groups and iterates of rational functions were reputed to be highly technical mathematical topics. When and why did you become involved? Mandelbrot : In 1976, after I had read Hadamard’s superb obituary of Poincaré (which everyone will soon be able to read - and should read - in an American Mathematical Society book on Poincaré). This obituary made it apparent that my work should be extended beyond the linearly invariant fractals, to which I had restricted myself up to that point. Indeed, the limit sets of Kleinian groups and of groups based upon inversions are fractals also; the latter could be called self-inverse. This forthcoming extension of self-similar fractals was mentioned in a last-minute addition to the 1977 Fractals, and then I set out to work, namely to play on the computer in order to acquire a “hands-on” intuition. The payoff comes very quickly, in the form of an explicit construction algorithm for the self-inverse limit sets. It took me longer to ascertain that, to my surprise, I had solved a problem that had stood for one hundred years. pg258: John von Neumann took classes from Pólya at the Eidgenössische Technische Hochschule in Zürich. Pólya recalled that he once remarked in class that he thought a certain conjecture was true but he had not been able to prove it. A few minutes later the young von Neumann raised his hand and announced that he had a proof. He went to the board and explained it. Pólya agreed that it was correct, but he later remarked, “After that I was afraid of von Neumann.” Robbins, pg291-292: It was in the Navy, in a rather strange way, that my future career in statistics originated. I was reading in a room, close to two naval officers who were discussing the problem of bombing accuracy. In no way could I keep from overhearing their conversation: “We’re dropping lots of bombs on an airstrip in order to knock it out, but the bomb impacts overlap in a random manner, and it doesn’t do any good to obliterate the same area seventeen times. Once is enough.” They were trying to decide how many bombs were necessary to knock out maybe 90% of an area, taking into account the randomness of impact patterns. The two officers suspected that some research groups working on the problem were probably dropping poker chips on the floor in order to trace them out and measure the total area they covered. Anyway, I finally stopped trying to read and asked myself, what really does happen when you do that? Having scribbled something on a piece of paper, I walked over to the officers and offered them a suggestion for attacking the problem. Since I wasn’t engaged in war research, they were not empowered to discuss it with me. So I wrote up a short note and sent it off to one of the two officers. In due course, it came to the attention of some mathematical research group working on the problem. However, I had no clearance to discuss classified matters, so there was a real communications problem: how were they going to find out my ideas without telling me something I shouldn’t know? (What I shouldn’t know was, in fact, the Normandy invasion plans.) Well, in some mysterious way, what I had done came to the attention of Marston Morse, and he saw to it that my note reached the right people. Shortly afterward, S. S. Wilks , then editor of the Annals of Mathematical Statistics, asked me to referee a paper by Jerzy Neyman and Jacob Bronowski (author of The Ascent of Man) on this very same problem. I recommended rejecting their paper as “a rather unsuccessful attempt at solving a problem that is easily solved if it’s done the right way, and here’s how to do it.” Wilks wrote back that he had to publish the paper because Neyman was one of the authors. But he also wanted me to publish a paper on what I’d written to him. So, after the war in Europe ended, there’s an issue of the Annals containing the paper by Neyman and Bronowski, followed immediately by my paper which, so to speak, says, “Please disregard the preceding paper. Here’s the solution to the problem that they can’t solve.” That was my first publication in the field of statistics. But even then I had no idea that I would become a statistician. What I had been doing was not statistics, but some rather elementary probability theory.

–Mathematical People: Profiles and Interviews 2008 (ISBN 978-1-56881-340-0), edited by Albers

One of the interesting consequences of the use of three-dimensional intuition is that the field of low-dimensional topology has advanced in a way that is significantly different from other branches of mathematics. One is expected to “see” results in this field, and once the result, or partial result, has been “seen”, it requires no further discussion. I do not wish to criticize this approach. I have myself “seen” several results in this field, and believe them to be as correct as any other mathematics….Once, at a seminar, one of the world’s best low-dimensional topologists was presenting a major result. At a certain point another distinguished topologist in the audience intervened to say he did not understand how the speaker did a certain thing. The speaker gave an anguished look and gazed at the ceiling for at least a minute. The member of the audience then affirmed “Oh yes, I hadn’t thought of that!” Visibly relieved, the speaker went on with his talk, glad to have communicated this point to the audience. Such is truth in mathematics.

–“A credo of sorts”; Vaughan Jones (Truth in Mathematics, 1998), pg 216-218

We recently reported on a game played at the closing dinner at last December’s Chess Classic. During this dinner at Simpsons in the Strand they stage a now traditional simul by the players of the Classic against the guests. Most tables have one or more strong chess players whose job is to guide rather than direct. One particularly high-powered table had Rachel Reeves, MP, the Shadow Chief Secretary to the Treasury, who was a UK U14 girls champion, Professor Vinayak Dravid, a leading nanotechnologist from the University of Chicago, the Indian High Commissioner Rajesh N Prasad, Jo Johnson MP, brother of Boris, and Frederic Friedel. Their advisor was Garry Kasparov…After the game some of the simul masters said Kasparov had perhaps been too generous with his advice during the game. But he vigorously denied this: “Before the critical sacrifice I said one word: ‘wow!’ Fred immediately jumped up and started to analyse with Rachel, and they worked out the sacrifice together, in less then a minute.” He then proceeded to recount the story about his 1996 game against Anand in Las Palmas, given above, and how at the time it had become clear to him that a single bit of information, passed on to a player at the right moment, could have a decisive influence on the course of a game. “If Fred was allowed to come in and signal ‘now!’ in the critical position I would have worked out 20.g4 and played it!” That’s right, it often needs just one bit of information – ‘now!’ – to change the result of a game.

–“A history of cheating in chess (4)”, Frederic Friedel 2000

…deriving a theorem on the blackboard, Wiener in his intuitive way . . . skips over so many steps that by the time he arrives at the result and writes it down on the board, it is impossible for the students to follow the proof. One frustrated student . . . tactfully asks Wiener if he might show the class still another proof. . . . Wiener cheerfully indicates, “Yes, of course,” and proceeds to work out another proof, but again in his head. After a few minutes of silence he merely places a check after the answer on the blackboard, leaving the class no wiser.60

–F. Conway and J. Siegelman, Dark Hero of the Information Age (New York: Basic Books, 2004), pg83 (this anecdote has been told a number of times about Wiener, and I believe some other mathematicians as well)

…S stands for secret; you can keep it forever—

Provided there’s no one abroad who is clever.

–Edward Teller, “Atom Alphabet”

In the problem of decoding, the most important information which we can possess is the knowledge that the message which we are reading is not gibberish. A common method of disconcerting codebreakers is to mix in with the legitimate message a message that cannot be decoded; a non-significant message, a mere assemblage of characters. In a similar way, when we consider a problem of nature such as that of atomic reactions and atomic explosives, the largest single item of information which we can make public is that they exist. Once a scientist attacks a problem which he knows to have an answer, his entire attitude is changed. He is already some 50% of his way toward that answer. In view of this, it is perfectly fair to say that the one secret concerning the atomic bomb which might have been kept and which was given to the public and to all potential enemies without the least inhibition, was that of the possibility on its construction. Take a problem of this importance and assure the scientific world that it has an answer; then both the intellectual ability of the scientists and the existing laboratory facilities are so widely distributed that the quasi-independent realization of the task will be a matter of merely a few years anywhere in the world.

–emphasis added; pg124-125, Norbert Wiener, The Human Use of Human Beings

Weiner was correct: given the knowledge that atomic bombs were possible, it is possible to invent one using the open literature. pg 39–40, MacKenzie & Spinardi 1995

Even without such publications, much could be inferred from relatively elementary physics. As long ago as 1946, it was reported that a “Midwestern teacher of high-school physics” had used the information contained in the Smyth report successfully to calculate the size of an atomic bomb (Friendly 1946, p. 3; see Smith 1970, p. 84). Since then, there have been reports that “undergraduates at Princeton and MIT have drafted roughly feasible atomic weapon designs, drawing only from unclassified documents” (Harvard Nuclear Study Group 1983, p. 219), as had scientists awaiting security clearance at the nuclear weapons laboratories (Hersh 1991, p. 155).

The Guardian on the Nth Country Experiment

Today his experiences in 1964 - the year he was enlisted into a covert Pentagon operation known as the Nth Country Project - suddenly seem as terrifyingly relevant as ever. The question the project was designed to answer was a simple one: could a couple of non-experts, with brains but no access to classified research, crack the “nuclear secret”? In the aftermath of the Cuban missile crisis, panic had seeped into the arms debate. Only Britain, America, France and the Soviet Union had the bomb; the US military desperately hoped that if the instructions for building it could be kept secret, proliferation - to a fifth country, a sixth country, an “Nth country”, hence the project’s name - could be averted. Today, the fear is back: with al-Qaida resurgent, North Korea out of control, and nuclear rumours emanating from any number of “rogue states”, we cling, at least, to the belief that not just anyone could figure out how to make an atom bomb. The trouble is that, 40 years ago, anyone did. …They would be working in a murky limbo between the world of military secrets and the public domain. They would have an office at Livermore, but no access to its warrens of restricted offices and corridors; they would be banned from consulting classified research but, on the other hand, anything they produced - diagrams in sketchbooks, notes on the backs of envelopes - would be automatically top secret. And since the bomb that they were designing wouldn’t, of course, actually be built and detonated, they would have to follow an arcane, precisely choreographed ritual for having their work tested as they went along. They were to explain at length, on paper, what part of their developing design they wanted to test, and they would pass it, through an assigned lab worker, into Livermore’s restricted world. Days later, the results would come back - though whether as the result of real tests or hypothetical calculations, they would never know…Eventually, towards the end of 1966, two and a half years after they began, they were finished. “We produced a short document that described precisely, in engineering terms, what we proposed to build and what materials were involved,” says Selden. “The whole works, in great detail, so that this thing could have been made by Joe’s Machine Shop downtown.” Agonisingly, though, at the moment they believed they had triumphed, Dobson and Selden were kept in the dark about whether they had succeeded. Instead, for two weeks, the army put them on the lecture circuit, touring them around the upper echelons of Washington, presenting them for cross-questioning at defence and scientific agencies. Their questioners, people with the highest levels of security clearance, were instructed not to ask questions that would reveal secret information. They fell into two camps, Selden says: “One had been holding on to the hope that designing a bomb would be very difficult. The other argued that it was essentially trivial - that a high-school science student could do it in their garage.” If the two physics postdocs had pulled it off, their result, it seemed, would fall somewhere between the two - “a straightforward technical problem, but one that involves some rather sophisticated physics”. Finally, after a valedictory presentation at Livermore attended by a grumpy Edward Teller, they were pulled aside by a senior researcher, Jim Frank. “Jim said, ‘I bet you guys want to know how it turned out,’” Dobson recalls. “We said yes. And he told us that if it had been constructed, it would have made a pretty impressive bang.” How impressive, they wanted to know. “On the same order of magnitude as Hiroshima,” Frank replied.

While still disputed, as it hinges on whether the German physicists were as morally blind & culpable as they appeared, the German atomic bomb program was stalled by erroneous calculations that tons of uranium would be required for a critical mass rather than 5-10kg; but when they were captured and learned of the successful bombing of Hiroshima on 1945-08-07, the Farm Hall transcripts indicate that with just this knowledge, Heisenberg was able to find his error by 1945-08-14 and calculate that a more accurate figure was 14kg. This was still off by 2x but far more feasible than tons.

To put it at its most elementary, while observing others riding bicycles does not enable one to learn the skills of the cyclist, it nevertheless shows that cycling is possible. Knowing that older brothers or sisters have learned to ride can encourage younger siblings not to conclude from early failures that the task is impossibly hard. …The confidence—indeed overconfidence—of wartime Anglo-American physicists (including Continental refugees) in the ease of development of a nuclear weapon does not seem to have been widely shared by their French, German, or Soviet colleagues, and the governments of the last two countries were unconvinced prior to 1945 that the task was feasible enough to be worth the kind of resources the Americans devoted to it (see, e.g., Holloway 1981; Goldschmidt 1984, p. 24).24 Trinity, Hiroshima, and Nagasaki were dramatic demonstrations that the task was not impossibly hard, and this proof (as well, of course, as the perceived threat to the Soviet Union) explains the sudden shift in the USSR in 1945 from a modest research effort to an all-out, top-priority program (Holloway 1981). As we have seen, the British test explosion in 1952, although no threat to France, contributed to the latter’s weapons program by suggesting that developing an atomic bomb was easier than had previously been assumed. Likewise, the Chinese explosion in 1964 showed other developing countries that the atomic bomb was not necessarily the preserve solely of the highly industrialized world. Furthermore, profound questions over the feasibility of early hydrogen bomb designs helped delay the American move from an atomic to a hydrogen bomb (Bethe 1982). By contrast, all subsequent hydrogen bomb programs could proceed with confidence in the basic achievability of their goal, and, in words used in another context by a group of weapons designers (Mark et al. 1987, p. 64), “The mere fact of knowing [something] is possible, even without knowing exactly how, [can] focus … attention and efforts.”

http://lesswrong.com/lw/g75/psa_please_list_your_references_dont_just_link/87f1?context=3

One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can’t, almost surely you are not going to. Courage is one of the things that Shannon had supremely. You have only to think of his major theorem. He wants to create a method of coding, but he doesn’t know what to do so he makes a random code. Then he is stuck. And then he asks the impossible question, “What would the average random code do?” He then proves that the average code is arbitrarily good, and that therefore there must be at least one good code. Who but a man of infinite courage could have dared to think those thoughts? That is the characteristic of great scientists; they have courage. They will go forward under incredible circumstances; they think and continue to think. …So before I left, I told all my friends that when I come back, that book was going to be done! Yes, I would have it done - I’d have been ashamed to come back without it! I used my ego to make myself behave the way I wanted to. I bragged about something so I’d have to perform. I found out many times, like a cornered rat in a real trap, I was surprisingly capable. I have found that it paid to say, “Oh yes, I’ll get the answer for you Tuesday,” not having any idea how to do it. By Sunday night I was really hard thinking on how I was going to deliver by Tuesday. I often put my pride on the line and sometimes I failed, but as I said, like a cornered rat I’m surprised how often I did a good job. I think you need to learn to use yourself. I think you need to know how to convert a situation from one view to another which would increase the chance of success.

–Richard Hamming, “You and Your Research”

But there was a datedness to the problems, a preoccupation with Euclid, and Newton, and exercises in mathematical physics - a sphere spinning on a cylinder with the candidate asked to establish the equations governing its motion, or a problem based on Carnot’s Cycle in thermodynamics, and so on. They demanded accuracy and speed in the manipulation of mathematical formulas, a shallow cleverness, perhaps, but not real insight. And not even stubborn persistence; a proof demanded by a Tripos question couldn’t be too long or too involved; so you learned to look for that hidden Tripos twist. During one Tripos exam, a top student - that year’s Senior Wrangler - observed a less capable candidate making short work of a problem over which he agonized. Must be a trick, he realized - and went back and found it himself. The personal qualities encouraged by the Tripos, J. J. Thomson would make so bold as to suggest, made it excellent training - for the bar.

–The Man Who Knew Infinity

More often, computers help discover interesting patterns in data, about which mathematicians then formulate conjectures, or guesses. “I’ve gotten a tremendous amount out of looking for patterns in the data and then proving them,” Billey said. Using computation to verify that a conjecture holds in every checkable case, and ultimately to become convinced of it, “gives you the psychological strength you need to actually do the work necessary to prove it,” said Jordan Ellenberg, a professor at the University of Wisconsin who uses computers for conjecture discovery and then builds proofs by hand.

http://www.wired.com/wiredscience/2013/03/computers-and-math/all/

They’d [Yang-Mills or non-Abelian gauge theories] been invented in 1954 and were the last and least understood entry in a short list of what came to be considered the only possible descriptions of fundamental particle interactions. Erick explained the defining basics but told me that nothing was known about their consequences and that many of the most famous senior particle theorists had gotten seriously confused about them. (The list of such notables included Dick Feynman, Shelly Glashow, Abdus Salam, and Steve Weinberg.) And now it seemed that no senior physicist wanted to discuss them; their ignorance and confusion were too embarrassing. …It turns out there was one brave soul, [Nobelist] Tini Veltman, who never gave up on Yang-Mills theory, and, with his best-ever grad student, [Nobelist] Gerard ’t Hooft, cracked the case in 1971. I think it worth noting that I, personally, know of no one who claimed to understand the details of ’t Hooft ’s paper. Rather we all learned it from Ben Lee, who combined insights from his own work (that renormalization constants are independent of the choice of ground state in such theories), from hitherto unnoticed work from Russia (Fadde’ev and Popov on quantization and Feynman rules), and from the simple encouragement from ’t Hooft ’s paper that it was possible. (It is amazing how much easier it can be to solve a problem once you are assured that a solution exists!)

“The dilemma of attribution” by H. David Politzer; Nobel Lecture, December 8, 2004

“The (Almost) Secret Algorithm Researchers Used to Break Thousands of RSA Keys”

At first glance this seems like the whole story. Reading through their paper more closely, however, reveals something strange. According to the authors, they were able to run the entire computation in a matter of hours on a single core. But a back-of-the-envelope calculation suggests that it should take years to compute GCD’s between 36 trillion pairs of keys, not hours. So how did they do it? The authors hint in a footnote that at the heart of their computation is an asymptotically fast algorithm, allowing them to bring the running time of the computation down to nearly linear; but the actual description of the algorithm is kept a secret from the reader, perhaps to guard against malicious use. Within just months of the paper’s publication, though, follow-up papers had already discussed various approaches in detail, both presenting fast algorithms (see this paper and this paper), and even showing how to use GPUs to make the brute-force approach viable (see this paper). There’s probably a lesson here about not bragging about things if you want them to stay secret.

“During race, I am going crazy, definitely,” he says, smiling in bemused despair. “I cannot explain why is that, but it is true.” The craziness is methodical, however, and Robič and his crew know its pattern by heart. Around Day 2 of a typical week-long race, his speech goes staccato. By Day 3, he is belligerent and sometimes paranoid. His short-term memory vanishes, and he weeps uncontrollably. The last days are marked by hallucinations: bears, wolves and aliens prowl the roadside; asphalt cracks rearrange themselves into coded messages. Occasionally, Robič leaps from his bike to square off with shadowy figures that turn out to be mailboxes. In a 2004 race, he turned to see himself pursued by a howling band of black-bearded men on horseback. “Mujahedeen, shooting at me,” he explains. “So I ride faster.” His wife, a nurse, interjects: “The first time I went to a race, I was not prepared to see what happens to his mind. We nearly split up.” The DVD spins, and the room vibrates with Wagner. We see a series of surreal images that combine violence with eerie placidity, like a Kubrick film. Robič’s spotlit figure rides through the dark in the driving rain. Robič gasps some unheard plea to a stone-faced man in fatigues who’s identified as his crew chief. Robič curls fetuslike on the pavement of a Pyrenean mountain road, having fallen asleep and simply tipped off his bike. Robič stalks the crossroads of a nameless French village at midnight, flailing his arms, screaming at his support crew. A baffled gendarme hurries to the scene, asking, Quel est le problème? I glance at Robič, and he’s staring at the screen, too. … Over the past two years, Robič, who is 40 years old, has won almost every race he has entered, including the last two editions of ultracycling’s biggest event, the 3,000-mile Insight Race Across America (RAAM). In 2004, Robič set a world record in the 24-hour time trial by covering 518.7 miles. Last year, he did himself one better, following up his RAAM victory with a victory six weeks later in Le Tour Direct, a 2,500-mile race on a course contrived from classic Tour de France routes. Robič finished in 7 days and 19 hours, and climbed some 140,000 feet, the equivalent of nearly five trips up Mount Everest. “That’s just mind-boggling,” says Pete Penseyres, a two-time RAAM solo champion. “I can’t envision doing two big races back to back. The mental part is just too hard.” Hans Mauritz, the co-organizer of Le Tour Direct, says: “For me, Jure is on another planet. He can die on the bike and keep going.” And going. In addition to races, Robič trains 335 days each year, logging some 28,000 miles, or roughly one trip around the planet. Yet Robič does not excel on physical talent alone. He is not always the fastest competitor (he often makes up ground by sleeping 90 minutes or less a day), nor does he possess any towering physiological gift. On rare occasions when he permits himself to be tested in a laboratory, his ability to produce power and transport oxygen ranks on a par with those of many other ultra-endurance athletes. He wins for the most fundamental of reasons: he refuses to stop. In a consideration of Robič, three facts are clear: he is nearly indefatigable, he is occasionally nuts, and the first two facts are somehow connected. The question is, How? Does he lose sanity because he pushes himself too far, or does he push himself too far because he loses sanity? Robič is the latest and perhaps most intriguing embodiment of the old questions: What happens when the human body is pushed to the limits of its endurance? Where does the breaking point lie? And what happens when you cross the line? …Winners [of the RAAM] average more than 13 miles an hour and finish in nine days, riding about 350 miles a day. The ones to watch, though, are not the victors but the 50% who do not finish, and whose breakdowns, like a scattering of so many piston rods and hubcaps, provide a vivid map of the human body’s built-in limitations. …The final collapse [of RAAM competitors] takes place between the ears. Competitors endure fatigue-induced rounds of hallucinations and mood shifts. Margins for error in the race can be slim, a point underlined by two fatal accidents at RAAM in the past three years, both involving automobiles. Support crews, which ride along in follow cars or campers, do what they can to help. For Robič, his support crew serves as a second brain, consisting of a well-drilled cadre of a half-dozen fellow Slovene soldiers. It resembles other crews in that it feeds, hydrates, guides and motivates - but with an important distinction. The second brain, not Robič’s, is in charge. … His system is straightforward. During the race, Robič’s brain is allowed control over choice of music (usually a mix of traditional Slovene marches and Lenny Kravitz), food selection and bathroom breaks. The second brain dictates everything else, including rest times, meal times, food amounts and even average speed. Unless Robič asks, he is not informed of the remaining mileage or even how many days are left in the race. “It is best if he has no idea,” Stanovnik says. “He rides - that is all.” …In all decisions, Stanovnik governs according to a rule of thumb that he has developed over the years: at the dark moment when Robič feels utterly exhausted, when he is so empty and sleep-deprived that he feels as if he might literally die on the bike, he actually has 50% more energy to give. …In this dual-brain system, Robič’s mental breakdowns are not an unwanted side effect, but rather an integral part of the process: welcome proof that the other limiting factors have been eliminated and that maximum stress has been placed firmly on the final link, Robič’s mind. While his long-term memory appears unaffected (he can recall route landmarks from year to year), his short-term memory evaporates. Robič will repeat the same question 10 times in five minutes. His mind exists completely in the present. “When I am tired, Miran can take me to the edge,” Robič says appreciatively, “to the last atoms of my power.” How far past the 50% limit can Robič be pushed? “90, maybe 95%,” Stanovnik says thoughtfully. “But that would probably be unhealthy.” Interestingly - or unnervingly, depending on how you look at it - some researchers are uncovering evidence that Stanovnik’s rule of thumb might be right. A spate of recent studies has contributed to growing support for the notion that the origins and controls of fatigue lie partly, if not mostly, within the brain and the central nervous system. The new research puts fresh weight to the hoary coaching cliché: you only think you’re tired. …Researchers, however, have long noted a link between neurological disorders and athletic potential. In the late 1800’s, the pioneering French doctor Philippe Tissié observed that phobias and epilepsy could be beneficial for athletic training. A few decades later, the German surgeon August Bier measured the spontaneous long jump of a mentally disturbed patient, noting that it compared favorably to the existing world record. These types of exertions seemed to defy the notion of built-in muscular limits and, Bier noted, were made possible by “powerful mental stimuli and the simultaneous elimination of inhibitions.” Questions about the muscle-centered model came up again in 1989 when Canadian researchers published the results of an experiment called Operation Everest II, in which athletes did heavy exercise in altitude chambers. The athletes reached exhaustion despite the fact that their lactic-acid concentrations remained comfortably low. Fatigue, it seemed, might be caused by something else. In 1999, three physiologists from the University of Cape Town Medical School in South Africa took the next step. They worked a group of cyclists to exhaustion during a 62-mile laboratory ride and measured, via electrodes, the percentage of leg muscles they were using at the fatigue limit. If standard theories were true, they reasoned, the body should recruit more muscle fibers as it approached exhaustion - a natural compensation for tired, weakening muscles. Instead, the researchers observed the opposite result. As the riders approached complete fatigue, the percentage of active muscle fibers decreased, until they were using only about 30 percent. Even as the athletes felt they were giving their all, the reality was that more of their muscles were at rest. Was the brain purposely holding back the body? “It was as if the brain was playing a trick on the body, to save it,” says Timothy Noakes, head of the Cape Town group. “Which makes a lot of sense, if you think about it. In fatigue, it only feels like we’re going to die. The actual physiological risks that fatigue represents are essentially trivial.” … Fatigue, the researchers argue, is less an objective event than a subjective emotion - the brain’s clever, self-interested attempt to scare you into stopping. The way past fatigue, then, is to return the favor: to fool the brain by lying to it, distracting it or even provoking it. (That said, mental gamesmanship can never overcome a basic lack of fitness. As Noakes says, the body always holds veto power.) …The theory would also seem to explain a sports landscape in which ultra-endurance events have gone from being considered medically hazardous to something perilously close to routine. The Ironman triathlon in Hawaii - a 2.4-mile swim, 112-mile bike ride and marathon-length run - was the ne plus ultra in endurance in the 1980’s, but has now been topped by the Ultraman, which is more than twice as long. Once obscure, the genre known as adventure racing, which includes 500-plus-mile wilderness races like Primal Quest, has grown to more than 400 events each year. Ultramarathoners, defined as those who participate in running events exceeding the official marathon distance of 26.2 miles, now number some 15,000 in the United States alone. The underlying physics have not changed, but rather our sense of possibility. Athletic culture, like Robič, has discovered a way to tweak its collective governor. …“I find motivation everywhere,” Robič says. “If right now you look at me and wonder if I cannot go up the mountain, even if you are joking, I will do it. Then I will do it again, and maybe again.” He gestures to Mount Stol, a snowy Goliath crouched 7,300 feet above him, as remote as the moon. “Three years ago, I got angry at the mountain. I climbed it 38 times in two months.” Robič goes on to detail his motivational fuel sources, including his neglectful father, persistent near poverty (three years ago, he was reduced to asking for food from a farmer friend) and a lack of large-sponsor support because of Slovenia’s small size. (“If I lived in Austria, I would be millionaire,” he says unconvincingly.) There is also a psychological twist of biblical flavor: a half brother born out of wedlock named Marko, Jure’s age to the month. Robič says his father favored Marko to the extent that the old man made him part owner of his restaurant, leaving Jure, at age 28, to beg them for a dishwashing job. “All my life I was pushed away,” he says. “I get the feeling that I’m not good enough to be the good one. And so now I am good at something, and I want revenge to prove to all the people who thought I was some kind of loser. These feelings are all the time present in me. They are where my power is coming from.” …Robič talks about his plans for the coming year. He talks about his wife, whose job has supported them, and he talks about their son, who is starting to walk. He talks about how he will try to win a record third consecutive RAAM in June, and how he hopes race officials won’t react to the recent fatalities by adding mandatory rest stops. (“Then it will not be a true race,” he says.) In a few months, he’ll do his signature 48-hour training, in which he rides for 24 hours straight, stays awake all night, and then does a 12-hour workout.

–“That Which Does Not Kill Me Makes Me Stranger”, New York Times

“Don’t tell me what you can’t do. You don’t want to. That’s understandable; it’s crazy, asking strangers you’ve only just met for money. But don’t confuse what you’re unwilling to do with what’s impossible to do. If you want to go, raise your voice and ask them, ‘Who’s willing to give me money to go to the next seminar?’ Or sit down.” …He swallowed, thinking it over. I don’t know what would have happened if he’d sat down; I’d like to say that the seminar leader would have said, “You made an honest choice” and walked away, but probably not. It was, after all, about the money. But no, Salesman Guy said, in a wavering voice, “Will anyone give me money to go to the next seminar?” There was a long, uncomfortable silence. Then someone reached for his wallet. “I’ll give you $10 towards it.” That broke the ice. Next, a woman got her purse open and said, “I’ve got $20 to spare.” And lo, once asked, the entire room started pulling out cash until he had enough to go, all fully donated, and wham, he was in. And then the next person who wanted to go but was even broker than Salesman Guy stood up and asked, and the next person had to go out into the hall and ask est employees and volunteers for cash, which was even more embarrassing, but they got it. Everyone who wanted to go got their cash that day. (And a lot of people remained seated, or just said “no.”) I was both squicked and enlightened. Because the cash clearly went towards est’s benefits - but the guy was also absolutely right about reasonable efforts. We live in a culture so bound by what most people are willing to do that we often take them as hard limits - “I can’t do more than that,” we say. “I’ve done the best I can.” But it really isn’t. It’s just the best we’re willing to do for right then. When I was running and got my side-stitch, I really thought that I’d put 100% into it. But the truth was that I hated running, and I hated exercise, and I was putting maybe 20% of myself into it. If I was being chased by a bear, suddenly I’d find new reserves within me. And though I hated math homework, and thought that the grudging half an hour I did was really balls-out for math homework, I’d forget how many hours I’d spend memorizing PAC-Man patterns. After that, I realized where my real limits were - they were way up there. And maybe I could stop telling myself and others that I did my best. I didn’t. Not even close. I did what I thought was reasonable. Sometimes you don’t want reasonable.

–“On Reasonable Efforts”, Ferrett Steinmetz

I have always thought that one man of tolerable abilities may work great changes, and accomplish great affairs among mankind, if he first forms a good plan, and, cutting off all amusements or other employments that would divert his attention, makes the execution of that same plan his sole study and business.

–Benjamin Franklin’s Autobiography

http://lesswrong.com/lw/uo/make_an_extraordinary_effort/

http://lesswrong.com/lw/un/on_doing_the_impossible/

http://lesswrong.com/lw/2p5/humans_are_not_automatically_strategic/

“DIY Diagnosis: How an Extreme Athlete Uncovered Her Genetic Flaw”:

“Take Rodney Mullen. He’s a real genius,” she says. Mullen is not a figure from science or medicine. He is, in fact, a legendary skateboarder, famous for inventing mind-blowing tricks that previously seemed impossible. One of them is actually called the “impossible”. “He executes these movements that defy reason, films them, and publishes them on YouTube,” Kim says. “And inevitably, within a few weeks, someone will send him a clip saying: This kid can do it better than you. He gave that trick everything he had, he’s pulling from all of his experience, and here’s this kid who picks it up in a matter of weeks. Because he learned that it’s possible to do that. Rodney just acts as a conduit. He breaks barriers of disbelief.”

Mark Xu