As a physics student, I found that I could solve most of the problems simply by looking at derivations and listening carefully to my reactions to the equations. A soft voice inside me would say, “No, that term just doesn’t seem right. Go and find out what went wrong there.” Or, “Ah, these terms hang together and the result feels right. It must be okay.” And it almost always worked out. My piano teacher would do the same when playing an unfamiliar piece of music. She could play it just by making sure it sounded right.
Were these just party tricks? Or was a more fundamental process going on?
The answer is in my favorite study from the field of expertise and expert performance; like the best research in this field, it teaches us general lessons about how one reaches high performance in almost any domain, whether music, chess, poker, mathematics, or teaching.
The study is by Fernand Gobet and the late Herbert Simon, winner of the 1978 Nobel Prize in Economics. They wanted to measure the relative importance of analysis (calculation) and perception (insight) in expert performance. And they thought of a beautiful measurement based on objective data. ["The roles of recognition processes and look-ahead search in time-constrained expert problem solving: Evidence from grandmaster level chess", Psychological Science 7:52-55 (1996)]
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Their subject was Garry Kasparov, chess champion of the world for 15 years (1985-2000). As world champion, he often demonstrated his skill by playing a “simul”: games of chess against several masters and grandmasters simultaneously. Kasparov would have to rotate between games. As soon as Kasparov reached a board, his opponent on that board had to make his or her move. Kasparov would then think for roughly 20 seconds before moving on to the next opponent and game. In contrast, his opponent would think for 3 minutes, until Kasparov’s return from cycling through the other games (typically six others).
At 20 seconds per move, Kasparov mostly used his perception and judgment of chess positions rather than his ability to calculate chess variations (the “I take, he takes, I take, etc.” kind of thinking). Thus, simultaneous chess is a real-life laboratory for measuring the value of perception. How well did Kasparov play, in comparison to his normal strength when playing at the usual tournament rate of 3 minutes per move? His normal strength at the time was 2750 on the Elo scale of chess skill. (To give a feel for the Elo scale, a beginner would be rated about 1000, an average tournament player is rated about 1600, a master is rated at 2200 or above, and a grandmaster is usually above 2400.)
The amazing result: At the rapid “simul” pace, Kasparov performed at a rating of 2650: higher than all but half a dozen players in the world! In other words, most of his world-class expertise comes from how he sees and looks at the chess board, not from his calculation ability. The traditional picture of the chess master as a calculating prodigy is bogus.
This unexpected result explains my (lack of) success playing chess against a friend in college, Adam Lief, who at the time was a very strong master. To make the games even remotely interesting, Adam started with less and less time, eventually reaching 30 seconds to make all of his moves while I had my 5 minutes for all my moves. In my best effort at those odds, I managed, in one game, to get Adam on the run. As I was gloating to myself, he paused for a longer think. As his time was running out, I sensed victory, even if it would come from Adam’s running out of time. After an eternity (7 seconds), he sacrificed his queen and announced “mate in 6″, i.e. that I would be checkmated in 6 moves even if I played perfectly.
Adam had only 5 seconds total for all his moves, so I thought, “I’ll just move fast, so that he doesn’t have time to think while I think, and might then not manage the checkmate.” Bad choice. With my first move, I made a mistake. Adam instantly announced “mate in 2.” And so vanished my victory, the only time I managed to even come close—even though Adam barely even had time to move his piece and hit his chess clock, let alone study the board. For the master, perception and insight are king!
This idea, as I will discuss in a subsequent post, explains the insanity of most mathematics teaching.
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Is there any research on the transition from “calculative thinking” when someone is a beginner to “intuitive/perceptive thinking” when that person becomes an expert? Does engaging in intensive “calculative thinking” sufficient to build the intuitive muscles? Or is it more complex than that?
One thing I would be very interested in knowing is understanding the decline in the efficiency of this transition with age? That is can ‘older’ people still master arts like mathematics, music with sufficient practice?
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It’s a combination of practicing calculation and learning the theory. Here’s one analogy – it’s possible that someone could advance from beginner to concert pianist based solely on practicing pieces and learning more songs – start with Twinkle Twinkle Little Star, work your way through the Mozart minuets, and eventually you’re ready for the Rachmaninoff concertos. That said, I doubt many pianists have actually been able to do that. Musical patterns on the keyboard tend to make more sense when the student has training in scales and arpeggios. It accelerates the learning when you have that theoretical side to back up the rote calculation, and this is the same for chess. Students learn strategic fundamentals like opening principles (take the center, develop knights/bishops before rooks/queen) and endgame technique (outside passed pawns, bad vs. good bishops). These ideas are like scales, and they complement and reinforce the tactical side of chess. I suppose some gifted chess players can figure these ideas out, but they’re more commonly learned through study and instruction.
I was thinking the same thing Krish.
An example might be martial arts. Beginners struggle to remember the list of body movements necessary to strike and block, and it seems far too slow to be of any use in a real emergency. But with time those movements become easier and easier, finally becoming instinctive so that all calculation and memory disappears and the body simply knows what to do.
…Or at least so I’m told, I never got that far! But it seems reasonable that a chess champion would begin calculative and become instinctive, responding instinctively to different patterns as they appear on the chess board. Fascinating stuff.
speed golf suggests that it’s not only chess where performance doesn’t drop as much as one might expect when put under time pressure.
This doesn’t in any way dispel the notion that chess masters are calculating prodigies. It tends to confirm that calculation often occurs without conscious computation.
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It seems to me a lot of calculating (of the she takes, I take variety) must have taken place behind the scenes during individual practice. The insight can only come after hours and hours of analysis. When you watch Kasparov play “simul”, you are seeing the end result of a lifetime of study. I don’t think Kasparov started out learning to play chess using just perception. But you make an interesting point, experts are so good that what they do becomes intuition or second nature.
After 30 years of playing the cello off and on, I no longer make the mistake of leaving out sharps or flats. I used to have to check the key signature, but now I infrequently play wrong accidentals because I hear (intuit) the notes a split second before I put my fingers down. Still have many years to go before I become an expert though!
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Right on. Here’s my math lesson on fractions: “There aren’t any fractions…. It’s just made up.”
Intuitive understanding is not the way our school system is structured, but it should be. Paul Hewitt writes physics books designed to bring out intuitive understanding in students. (Does a big rock fall faster than a small rock? Imagine that the big rock is just a bunch of small rocks flying in formation.)
I claim vast but entirely intuitive knowledge of etymological matters and probably annoy Fred Shapiro’s postings followers, but some thing just ring right, and some just don’t. I’ll go to the mat on many matters for which I have absolutely no objective evidence. In these matters “experts” have no sway with me.
But I also claim vast but entirely intuitive ignorance, or that is, I don’t feel anything I have heard rings right…thus a smooth and unrippled fabric of ignorance stretch before me, and I am a pain in the butt in the presence of people who claim to know. Example: Global Warming.
I suspect a similar phenomenon in language acquisition as well. Fluent individuals understand the language “automatically,” whereas non-fluent individuals first convert it to their primary language.
As inferred to in this article, a key skill to succeeding in chess is pattern recognition–developing as effective as possible in as few moves as possible. A good chess player has developed complex patterns of recognition on the board where they can instantly perceive how different pieces on the board can support or mount attacks with other.
Most people struggle so much with chess because they think the whole game is about calculating a perfect execution of a checkmate rather than playing for positional and developmental strength.
Examples of basic patterns chess players come to recognize: effective use of pawn structures to break gridlock, how to effectively develop in as few moves as possible, the importance of knights in closed games and bishops in open games, how controlling the centre can open attacking opportunities, effective development of rooks, effective use of the king was a defending piece during the end game, etc……..
The list is endless. A good player is able to identify these patterns, but most critically, evaluate in any given situation which set of strategy from these patterns is the most effective to achieving victory. That’s the really hard part.
An alternative possible explanation as to how Kasparov won is shown in this video of Derren Brown, playing 9 simultaneous games including grandmasters:
http://www.dailymotion.com/video/x8a6st_derren-brown-beats-9-chess-players_videogames
He basically played them off against each other.
Certainly he would not have been able to play at 2650 using that trick. He’s known for getting 100% scores in simuls.