0:03

Now, I want to show you another example to describe the same concept in a different way.

This example consists in a game.

So you have to play a game.

And this game is called the game of 15.

Let's see how this game works.

In the game of 15, the pieces for the game are the nine digits: one,

two, three, four, five,

six, seven, eight and nine.

Each player takes a digit in turn,

and once a digit is taken,

it can't be used by the other player.

The first player to get three digits that sum to 15, wins.

So, here is a sample game.

Player A takes eight.

Player B takes two.

Then A takes four,

and B takes three.

A takes five. Now a question.

Suppose you are now to step in and play for B,

what move would you make?

So, stop here for a moment,

and think about what will be your next move.

1:22

Now, let's play a different game.

This one is the children's game called tic-tac-toe,

I suppose many of you are already familiar with this game. How does it work?

Well, players ultimately plays I'm not, or the symbol O,

or a cross in one of nine spaces arranged in a rectangular array,

like the one that you see in the image.

Once a space has been taken,

it can not be changed by either player.

The first player to get three symbols in a straight line, wins.

Now, suppose player A is X and B is O,

and the game has reached the state that you see in this image.

A question for you. Suppose you have now to step

in and play an O for B, what move will you make?

Once again, I'll give you a few seconds to think about it.

2:19

So, you may have noticed that the second game is easier to play than the first game.

Is even easier to describe.

Right? So, it turns out that these two games are exactly the same.

And this concept is called problem isomorph,

an idea that is been developed by Nobel Prize winner, Herbert Simon.

If you look at this array,

this is the array that I have shown to you to describe the tic-tac-toe game,

and I put the numbers that we used in the game of 15 in the cells of this array.

Now, if you think about it,

playing tic-tac-toe and the game of 15,

is exactly the same thing.

Because every time you are able to fill out a row,

a column, or a diagonal,

the sum of the numbers is 15.

But again, playing the game in tic-tac-toe is much easier than in the game of 15.

Why is that? Once again,

because in the second example,

in the second game,

we have some visual representation that helps

us store some of the information in the world,

rather than having all this information in our mind.

And ultimately, this makes reasoning about the problem much easier.