“The boy has high intelligence. You see, he plays chess so well.” 

Then, what is intelligence? 

Intelligence equals the ability to memorize and to search all possible pathways

When playing a board game with a computer, which side do you expect to win?

Maybe you have played a kind of board game five. The board contains 15 lines crossing another 15 lines. The player who use black chessman go first and then the two players put chessman in turn on the board. The side who first forms a line containing five consecutive chessman will win. It is popular in China and Japan, many people like it and there are professional players.

Figure 1. the black side wins

Two

The game is interesting but a little complicated. Now let's consider a similar but simpler game two. The side who first form a line containing two consecutive chessman will win. We will begin our analysis on intelligence by this simple game.

Before the game, the following assumptions are needed for analysis:

1. Both sides are rational. Rationality here means: (1)Eachstep is the best under current condition and under the whole game processing, i.e., making his own chessman first form five consecutive line. (2)Both sides know clearly that the other is rational too.
2. At most 1000 steps are available for each side. After that the game ends up with a tie.
 3. The board is unlimitedly large.
4. The two sides are Bob (black) and Jane (white).

Now the game begins. Let’s see what will happen. After simple thinking, Bob will find wherever he puts the chessman, he will win in hissecond step. Also, Jane finds that wherever she puts her chessman, she will lose. Then, before the game, the result is clear. 

Oh! It is uninteresting! Yes, but let's spend more time thinking the following question: what really the both sides have thought before the game?

--Bob:IfI put it in Cc (Figure 2), then because Jane is rational she will put her chessman at Cb, Dc, Bc or Cd. If she chooses Cb, I will put my 2nd chessman at Dc; If she chooses Dc, I will choose Cd. If she chooses Bc, I, Cb; If she Cd, I, Dc. Then I win. Anyway, I win.

Bob's thinking stops here because he is rational and will not waste his energy. Anyway, he wins. During such thinking, he only uses 5 ifs. 

Jane’s thinking is almost the same as Bob. She knows she will lose under any conditions.
Figure 2. Bob wins at the second step

 

Three

Now comes to three: the side who first forms a line containing three consecutive chessman will win. Again, let’s see how Bob thinks: (We assume he has not the concept of symmetry)

--Bob: If I put the first side at Cc, then Jane will put it at Cb,Cd,Bc or Dc.If she occupies Cb, then I will occupies Dc(or Bc). Then if he occupy Ec, and I occupies Bc and wins; If he occupies Bc, I occupies Ec and wins.

He will also thinks if Jane puts her first chessman at Cd,Bc and Dc. He finally find he will always win. OK, he stops. Let’s calculate it: he use 1+4*(1+2)=13ifs.

It is much more complicated when it comes to 4. Also, we can calculate he will use at least 105ifs. But it is interesting that after a long time think (he have to consider all possibilities to win the game), he finds the game end up with a tie because Jane is rational. Can you imagine how many ifs when it comes to five?

Yeah, the game becomes interesting when it comes to 4. But it is not the case if two rational persons play, because the result is decided before the game and they even need not play. Then why it is popular? The reason lies in that no person in the world can be so rational that he can calculate all the possibilities.

Figure 3. Bob wins at his third step.

Computer plays

 

OK, replace Jane with a very powerful computer (we can give it a name Power) that it can calculate all the possibilities. How about if Power and Bob play? Suppose Bob is the best player in the world.

 

OK, let’s do the following imaginary experiment: Bob and Power are playing such a game in a room without others, and a tester will judge which one is the human being just by looking at the screen, on which shows the process of the game. Question is: can the tester distinguish which side is the human being? He can’t because the two sides are both more rational than him. If the two things can’t be distinguished, then we say they are identical. So, Bob's intelligence equals Power’s powerful ability to memorize and to search all possible pathways to win the game.

It is interesting tothink something about our brains, but just thinking isn’t enough. I hold a belief that explanations to all behaviors, intelligence included, can be found in molecular or even atomic level. Experiments on molecular level should receive much attention to explore the world of brain.