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?

chess_trap_2

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.