Wildly Different Knowledge Levels

This is a topic I’ve wanted to write about since 7 years ago but was too lazy to find a good concrete example until recently.

The gist:

  1. Imagine three people of varying degrees of knowledge in a particular area: A is a random person with zero knowledge, B is someone with real amateur knowledge, and C is a professional. You pose a yes/no question. There are weird situations where A and C agree on the same answer, but B disagrees. Someone (B) who is definitively smarter than a layperson in one area might, with good reason, disbelieve what experts in the field consider the objectively right idea.
  2. In the above case on social media, person A might have no good argument or makes the default argument. B thinks they are pretty smart, and posts the standard reply to A. Then C makes a much more nuanced argument why B’s argument is wrong, and A is actually right. However, B doesn’t really understand or doesn’t read C’s argument, assumes C is just another dumb A and just repeats their flawed argument of why A is wrong.
  3. Also, is C actually right??? What if there is someone smarter, D, who agrees with B and figures out the nuanced response to C’s nuanced answer? Most people arguing on the internet are just A and B, and their arguments don’t even make sense compared to the real debate between C and D.

The most provable example of (1) is in chess. If you could see 3 moves ahead rather than 2, you would play a better move almost all of the time. But here is a weird exception. In the position below, should White capture the d5 pawn with the knight?


What players of increasing skill level might think:

  • A: “Who is a knight? What is a knight? Why is a knight?” [No]
  • B: “So knights move in an L-shape, so I can take the pawn, and taking pawns is good…” [Yes]
  • C: “If I take the pawn, then Black’s knight will take back and I lose a knight for a pawn, which is bad.” [No]
  • D: “Black’s knight is pinned, so if I take the pawn and Black’s knight takes back, then my bishop will capture the queen, which is really good. So that is a free pawn for me as the Black knight cannot take back.” [Yes]

In fact, winning a queen is *so good* in chess that, in almost all cases that end with one side losing a queen, it is a waste of time and mental energy to calculate any further. And yet…

  • E: “The knight pin is only a relative pin. Yes if I take the knight then Black will lose a queen after capturing back the knight… but wait! After losing the queen, Black can play a bishop check (Bb4+) and win White’s queen. After all the trades, Black is up a minor piece.” [No]

(For the chess enthusiast, the line is 1. d4 d5 2. c4 e6 3. Nc3 Nf6 4. Bg5 Nbd7 5. cxd5 cxd5 {diagram} 6. Nxd5 Nxd5 7. Bxd8 Bb4+ 8. Qd2 Bxd2+ 9. Kxd2 Kxd8 and Black is up a knight for a pawn.)

The weird thing is that player C is clearly better than B, but ends up with the correct answer only because of luck. Based on their thought process, C didn’t understand what was truly going on in the position, but rather, just happened to calculate a convenient number of moves ahead and stop. Weirder, D, who calculated more steps ahead than C, would play an objectively bad move here that C would have avoided! In some sense, D is just unlucky that they stopped calculating at the wrong level!

In addition, it happens that the “number of moves to look ahead” gap between D and E is quite large. In fact, the number of moves (using “ply” or “half-moves” in the chess term) to look ahead was:

  • A: N/A
  • B: 1
  • C: 2
  • D: 3
  • E: 6

We’ll come back to this later, but if this were an analogy for how society views something as knowledge increases over time, we could be at a plateau for a long time between D and E, thinking that we have the answer figured out, but in fact have the wrong answer.

Let’s replace the chess question with a more real-life one, say “Is the climate warming?

  • A: “I read online that it’s true so it’s true.” [Yes]
  • B: “You can’t just believe what you read on the internet. Plus it was really cold yesterday.” [No]
  • C: “One data point doesn’t define a trend. If you look at long-term graphs of temperature published by X, they go up over time.” [Yes]
  • D: “What is source X, is it reputable? Also, what about a long-term temperature graph going back hundreds of years–weren’t there unusually warm periods in the past as well? [No]
  • E: “Yes but not as drastic as the current warming period. And source X is the vast majority of scientists…” [Yes]
  • F: (If you’ve been on the internet before, you can imagine how this continues…)

If you see a twitter post where someone says a few words saying global warming is false, you often have no idea if they are person B (who might not be that smart) or person N (who is very smart but has maybe stopped at the “wrong” level).

If you see two strangers debating on the internet without any context, it might be non-obvious how far they are down this argument chain and how much they’ve thought about it. This is compounded by how most internet posts & comments so brief that you can’t really see any nuance.

Similarly, this is how popular debates can make one side look bad even when supported by all the facts. In the chess example, if C and D went on a public debate, D would win, yet C’s view is the objectively correct one. And on a larger network like Facebook or Twitter, you have people from all over the knowledge spectrum–though probably concentrated in the As and Bs–so any “debate” on such a medium is pointless. You can consider a twitter chess “debate” where E actually says the correct answer but doesn’t have room to post the full variation (or the energy to do it for the 1000th time), and then the various D’s of the world point out why E is wrong, thinking that E is just another A or C.

To pull the chess analogy even further, the knowledge gap between D and E makes this even harder. If E could teach D to think not 3 moves ahead, but 4 or 5 instead, D would still have the same wrong answer as before. They would need to think ahead 6 moves to realize E is right. Maybe once someone gets to think-5-moves-ahead, they think that’s sufficient for everything and stop calculating further.

A converse situation arises if you are a person at knowledge level E, and you run into someone who seems to disagree with you. You might be so used to teaching people to go from D to E that you assume they are arguing from the level of D. However, most people who are in D’s camp might be at knowledge level B. In chess, explaining the D-to-E step to someone at B might not make any sense. It could even make things worse, as from B’s perspective: “Someone is saying nonsense and also disagrees with me, therefore I should update my belief to be even stronger.”

Look for the context. Know what level you’re at.

If you disagree with someone, know that they might be thinking much further ahead, and you might not even know what the real debate is.

Talent Is Overrated

“Talent” is a word that is tossed around all too often, whether for top musicians or businessmen, or even just a person who creates popular Youtube videos. The idea of talent is in nearly every case taken for granted. As a young member of a very supportive family and community, I had heard the saying myself many times. But is talent a correct or even useful explanation for high-level performance?

Talent Is Overrated

I recently read a very intriguing book by Geoff Colvin. It was really a lucky buy—I was actually reading through reviews of Josh Waitzkin’s The Art of Learning, when the ever-so-omniscient Amazon Recommendations pointed me to a bizarre and blatantly absurd statement: Talent is Overrated.

With a plethora of examples, data, accumulation of research, and forcible writing, Colvin argues convincingly that the source of great performance in just about every field is best explained not by reference to the mysterious force known as talent, but by sheer amount and direction of deliberate practice.

My Personal Experience

First, a line from Colvin (193):

Their parents made them practice, as parents have always done, though it’s interesting to note that in these cases, when push came to shove and parents had to make a direct threat, it frequently played off the student’s intrinsic motivators. So it wasn’t “If you don’t do your piano practice we’ll cancel your allowance,” but rather “we’ll sell the piano.”  Not “If you don’t go to swimming practice you’ll be grounded Saturday night,” but rather “we’ll take you off the team.” If the child truly didn’t care about the piano or swimming, the threats wouldn’t have worked.

I was one of those kids who was, regarding the piano, totally immune to such a threat. As I wrote earlier, I absolutely dreaded playing the piano, and would have loved to see the piano disappear and find a bunch of cash in its place. But what I lacked in interest for the piano I made up for in my interest in chess. From 2003 to 2010, I competed in more than 70 rated chess tournaments. But looking back at the distribution of tournaments, I found that the majority of them occurred between 2003 and 2006, with one resurgence in 2008 [data]. It would be accurate to say that my tournament frequency was very closely correlated to how much time I spent on the game outside of tournaments in practice. As if to confirm Colvin’s thesis, here are my regular and quick rating graphs:


When the frequency of tournaments, and thus training, increased, my rating climbed. And when the frequency of tournaments and training decreased, my rating stagnated or declined. This seems to support the dedicated practice model argued in Colvin’s book. The performance in a given time period seemed to be determined by the amount of training in the same time period.

But what about compared to others? I am hardly an expert player, but my very first rating  after my first tournament, 1372, was in the 96-97th percentile of scholastic players at the time. By contrast, the current US chess champion Hikaru Nakamura, whose current USCF rating is a whopping 2834, started at a provisional rating of 684, an unimpressive statistic. However, he has played in 439 rated events over a period of 17 years, which is a hell of a lot more effort than I had ever thought about spending on the game. Thus even when you have an “advantage,” such as having a starting rating of 1372 versus 684, thinking of it in terms of talent is useless. If you do not follow it up with the necessary amount of work, the advantage will assuredly disappear.

There is a third point, to truly put the nail in the coffin of the talent model. In a two year span from 2006 to 2008, my rating stopped improving in the 1700s. Excuses aside, I simply didn’t practice the game much. But one thing I think could have happened is what Josh Waitzkin described, from Colvin (197):

The most gifted kids in chess fall apart. They are told that they are winners, and when they inevitably run into a wall, they get stuck and think they must be losers.

I don’t think it takes a gifted kid to run into the wall and get stuck (the 1372 initial rating was actually in part due to luck, as my first few tournaments were counted out of order, and a tournament that I had done really well in was incidentally the first one counted). For those two plateau years, I did feel the way that Waitzkin forewarned. I thought the high initial rating meant something special, i.e. talent, and that the 1700 plateau meant I was doomed. This thought process in terms of talent condemned me mentally to not advance. Even though I was still fairly high rated in my age group, I stopped practicing and reading as much, and as a result did not prepare myself adequately for tournament events. This caused my rating to drop.

How to Be a World-Class Performer

Colvin’s thesis works for far more than just chess. He applies it to the violin, piano, football, players, business, investment, management, art, teamwork, and just about anything, all while citing tremendous amounts of evidence for his claims. For music, the obvious counterexample is Mozart, yet early in the book Colvin disposes of this myth, as well as that of Tiger Woods. Mozart, for instance, had my years of intense, expert training starting at an early age, and Tiger Woods swung his first club at age seven… months, also trained by his father.

Another result of years of deliberate practice is the ability for an expert to see complex patterns that would completely elude an average person. A professional tennis player can return a serve of a ball traveling at a speed so high that a normal human should not even have time to react. Yet they are normal in this sense. But they don’t watch the ball, they watch their opponent’s body movements instead, and know approximately where the serve is going to land (or whether it will fault) before the racket even hits the ball. Similarly, a top stock trader can see signs that the average trader does not even consider to be relevant. A top manager sees the critical signs more so than an average one. And a master chess player can memorize an entire chess position in seconds and reproduce it perfectly, while the average person can recall only five or seven pieces. Most notably, this is not from better general memory, but by extensive training to be familiar with certain positions and patterns, so that they read a position by words instead of letters.

I would most certainly recommend this book to anyone. It breaks the shackle of “talent,” which although is a warm, comforting hope, it is no more than that, a beloved superstition with little evidence, and which discourages so many from even attempting something because they believe they “don’t have talent” or “divine spark” for it. But as it has repeatedly occurred, looking back at the backgrounds of top performers give little or no indication of any talent early on, but rather, what is common to all of them is an immense amount of training and dedicated practice. Perhaps this is the even more fascinating hope, that the world is within reach to everyone.

Two Pawn Swindle

I’m generally a fast player, and although this is a disadvantage in that I make plenty of careless mistakes, it does mean I rarely get into time trouble. The following is one of my favorite games. It’s really less of a comeback than it is an extraordinarily lucky swindle.

Li, Sean (1383) – Haley, Connor (1754)

Texas State Scholastic. 2/23-24/2005. Round 7 (final).

My opponent’s rating of 1754 was rather intimidating at the time, but I had just beaten a 1640 and a 1700 in rounds 5 and 6 respectively. I had 5 points; winning this game would put me at 6 points out of 7.

1. c4 c6 2. g3 Nf6 3. Bg2 d5 4. b3

4. Black to move

A somewhat unusual opening.

4… e6 5. Nc3 Be7 6. d3 Qa5 7. Bd2

7. Black to move

The only reason I take note of this position here is that this is exactly the same position as my game after my 7th move two rounds earlier in the same tournament. I won that game against a 1640, so I thought it was pretty good for me that this game was proceeding the same way. At move seven, however, my previous opponent played 7… Bb4, whereas Haley played 7… Qd8, a more conservative move.

7… Qd8 8. e3 0-0 9. Nf3 Nbd7 10. 0-0 Rb8 11. Qc2 Re8

12. White to move

12. e4 dxe4 13. Nxe4 Nc5 14. Nxc5 Bxc5 15. b4

15. Black to move

15… Be7 16. Rfd1 Qc7 17. Bf4 Bd6 18. Bxd6 Qxd6

19. White to move

19. Rab1 e5 20. d4 e4 21. Ne5 Bf5

22. White to move

Black’s position is superior.

22. h3 h5 23. Rb2 Rbd8 24. c5? (This move is a positional mistake—now the d4 is very weak.) Qe6 25. Kh2

25. Black to move

e3 26. Qe2 exf2 27. Qxf2 Be4 28. Re2 Bxg2 29. Qxg2 Qd5 30. Qxd5 Nxd5

31. White to move

At this point it’s fairly grim for White. The Black knight is threatening the pawn on b4 and a fork at c3, and White’s pawn on d4 is weak.

31. Rb2 Nc3 32. Rdd2 Ne4 33. Rdc2 Rxd4 34. Nc4

34. Black to move

White is a pawn down, and Black controls the center.

Rd3 35. g4 hxg4 36. hxg4 Rg3 37. Rg2 (37. Nd6! threatens the rook on e8 and the knight on e4, which guards the g3 rook. This would have won at least the Exchange.) Rxg2 38. Rxg2 Rd8 39. Re2 Rd4

40. White to move

40. Na5 Rxb4 41. Nxb7 Rxb7 42. Rxe4 Rb2+ 43. Kg3 Rxa2

44. White to move

Here is the critical position. Black is in severe time trouble. White is two pawns down, but swindles the game. 🙂

44. Re7 Kf8? (44… Ra5 would have won for Black.) 45. Rc7 Ra6 46. Kf4 f6 47. Kf5

47. Black to move

47… Ra5? (This gives up the c6 pawn without a fight and leaves the rook passive.) 48. Rxc6 Rb5 49. Ke6 Rb8 50. Ra6 Re8+ 51. Kd6 Rd8+ 52. Kc7 Ke8 53. Rd6 Ra8

54. White to move

White now trades the rooks and easily wins.

54. Kb7 Rd8 55. Rxd8+ Kxd8 56. c6 a5 57. c7+

57. Black to move

Kd7 58. c8=Q+ Kd6 59. Qd8+ Ke6 60. Qxa5+ Kf7 61. Qc7+ Kg6 62. Qf4 Kf7 63. g5 Ke7 64. Qe4+ Kf7 65. g6+ Kf8 66. Qe6 1-0

The game was G/75; each side started with 75 minutes, and there was a 5-second delay on each move. At the end, my opponent had run out of time, while I had 51:07 remaining. With this win, I had 6 points, and tied for second place; this is the best I have ever done at a Texas State Scholastic.

Full game (contiguous): 1. c4 c6 2. g3 Nf6 3. Bg2 d5 4. b3 e6 5. Nc3 Be7 6. d3 Qa5 7. Bd2 Qd8 8. e3 0-0 9. Nf3 Nbd7 10. 0-0 Rb8 11. Qc2 Re8 12. e4 dxe4 13. Nxe4 Nc5 14. Nxc5 Bxc5 15. b4 Be7 16. Rfd1 Qc7 17. Bf4 Bd6 18. Bxd6 Qxd6 19. Rab1 e5 20. d4 e4 21. Ne5 Bf5 22. h3 h5 23. Rb2 Rd8 24. c5 Qe6 25. Kh2 e3 26. Qe2 exf2 27. Qxf2 Be4 28. Re2 Bxg2 29. Qxg2 Qd5 30. Qxd5 Nxd5 31. Rb2 Nc3 32. Rdd2 Ne4 33. Rdc2 Rxd4 34. Nc4 Rd3 35. g4 hxg4 36. hxg4 Rg3 37. Rg2 Rxg2 38. Rxg2 Rd8 39. Re2 Rd4 40. Na5 Rxb4 41. Nxb7 Rxb7 42. Rxe4 Rb2+ 43. Kg3 Rxa2 44. Re7 Kf8 45. Rc7 Ra6 46. Kf4 f6 47. Kf5 Ra5 48. Rxc6 Rb5 49. Ke6 Rb8 50. Ra6 Re8+ 51. Kd6 Rd8+ 52. Kc7 Ke8 53. Rd6 Ra8 54. Kb7 Rd8 55. Rxd8+ Kxd8 56. c6 a5 57. c7+ Kd7 58. c8=Q+ Kd6 59. Qd8+ Ke6 60. Qxa5+ Kf7 61. Qc7+ Kg6 62. Qf4 Kf7 63. g5 Ke7 64. Qe4+ Kf7 65. g6+ Kf8 66. Qe6 1-0

Oldest Record

Earlier I decided to devote part of this blog to chess. I thought I would begin with my oldest game that I still possess. This happens to be the first-round game of the 2003 Houston Open in my 6th grade, in the scholastic section; the tournament was actually my eighth rated tournament, but I do not have my notation sheets from any of my first seven.

I would like to bore the reader with a history of how I started chess, but then again, it would be boring. I learned how to play in 4th grade; my first rated tournament was in 5th grade. Because that was in early 2003, and because the United States Chess Federation (USCF) was just starting its online player rating tracking system, there were a few minor bugs—in my case, my “first” tournament was actually the third I played in, the 2003 Texas State Scholastic from March 1-2, 2003 (I wish I had the games from this tournament), and this gave me a provisional rating of 1372, which was fairly high to start with.

I don’t know how, but on October 11, 2003, my listed rating at the Houston Open was still 1372 (it should have been 1304). My first round opponent was Joseph C. Wong, at the time rated 853. (Just after the 2010 Texas State Scholastic, my rating is 1806 and his is 1951.)

Li, Sean (1372) – Wong, Joseph (853)

Houston Open, Scholastic. 10/11/2003. Round 1.

1. e4 e5 2. Nf3 d6 3. Bc4

3. Black to move

The game begins as the Philidor Defense.

3… h6 4. d4 Nc6 5. dxe5 dxe5 6. 0-0 Bd6 7. Nc3 Nf6 8. Re1 0-0 9. Nh4 Bg4 10. f3 Bc8 11. Nf5 Bb4

12. White to move
12. White to move

At this point I decided to sacrifice the dark-squared bishop for two pawns with 12. Bxh6, intending 12… gxh6 13. Nxh6, but I did not anticipate 12… Bxf5. White finishes this combination down a piece for two pawns.

12. Bxh6 Bxf5 13. Bxg7 Kxg7 14. exf5 Bxc3 15. bxc3 Qxd1 16. Raxd1 Rad8 17. g4 Rxd1 18. Rxd1

18. Black to move

After a number of exchanges, Black has the upper hand.

e4 19. g5 Nh7 20. h4 exf3 21. Kf2 Ne5 22. Bd5 Rd8 23. Bxf3 Rxd1 24. Bxd1 f6 25. g6 Nf8 26. Ke3

26. Black to move

Here Black plays the unfortunate 26… Ng4+, which just loses a knight.

26… Ng4+ 27. Bxg4

27. Black to move

White is is two pawns up and clearly winning after this.

Nd7 28. Bh3 Nb6 29. Kd4 c6 30. Kc5 Nd5 31. c4 Nc3 32. a3 Na4+ 33. Kd6 c5 34. Bg2 b6 35. Kc7 Nb2 36. Bd5 Nd1 37. Kb7 Ne3 38. Be6 Nxc2 39. a4 Ne3 40. Kxa7 Ng2 41. Kxb6 Nxh4 42. a5 Nxg6 43. fxg6 Kxg6 44. a6 f5 45. Bxf5 1-0 (for non-chess players, this means Black resigned)

So, this was not exactly a special game (and the rating gap is huge), but it has symbolic meaning for me.

Move list (contiguous): 1. e4 e5 2. Nf3 d6 3. Bc4 h6 4. d4 Nc6 5. dxe5 dxe5 6. 0-0 Bd6 7. Nc3 Nf6 8. Re1 0-0 9. Nh4 Bg4 10. f3 Bc8 11. Nf5 Bb4 12. Bxh6 Bxf5 13. Bxg7 Kxg7 14. exf5 Bxc3 15. bxc3 Qxd1 16. Raxd1 Rad8 17. g4 Rxd1 18. Rxd1 e4 19. g5 Nh7 20. h4 exf3 21. Kf2 Ne5 22. Bd5 Rd8 23. Bxf3 Rxd1 24. Bxd1 f6 25. g6 Nf8 26. Ke3 Ng4+ 27. Bxg4 Nd7 28. Bh3 Nb6 29. Kd4 c6 30. Kc5 Nd5 31. c4 Nc3 32. a3 Na4+ 33. Kd6 c5 34. Bg2 b6 35. Kc7 Nb2 36. Bd5 Nd1 37. Kb7 Ne3 38. Be6 Nxc2 39. a4 Ne3 40. Kxa7 Ng2 41. Kxb6 Nxh4 42. a5 Nxg6 43. fxg6 Kxg6 44. a6 f5 45. Bxf5 1-0

The full game in animation:

Chess Blogging

I’m an amateur chess player (I’ve won money from tournaments, but that hardly qualifies me as professional), and thought to add some chess stuff to my blog. The reason? I just played in the Texas Scholastic (Feb 20-21), which will probably be my last major scholastic tournament. Over the years I’ve had quite a few interesting games (mostly at non-scholastic tournaments, particularly in Vegas and Philadelphia), and thought I would share some of them here.

I’m still trying to find a good way to post chess games into a blog. Because I am using WordPress.com instead of self-hosted WordPress, plug-ins are not going to work. And WordPress does not have a native chess reader as it does for math (LaTeX typeset).

Here are a couple options I found.

For simplicity we shall consider the game 1. f4 e5 2. g4 Qh4#. Chess players should recognize this as the Fool’s Mate, the shortest possible game—Black checkmates on the second move. The first option is to simply take screenshots at critical points and have the reader visualize the rest. (This isn’t too hard for serious players.)

For example:

Diagram 1

This board is rendered by Apronus.

The second option is an animated gif:

Diagram 2

This software is by Caissa, as the watermark suggests. However, the gif image sequence is impossible to pause, and furthermore, it is difficult to analyze a specific position on the board.

In Chess Circle there is a thread about publishing chess games into a blog, but I did not find it particularly useful.

Perhaps I’ll use a combination of animated gifs and normal images. The gif will give the overview of the game while still images will focus on key positions.