Puzzles compress the experience of insight into miniature, letting us watch understanding take shape in real time. Computer scientist Cristopher Moore argues that while AI can brute-force its way to a correct answer, only humans experience the leap from confusion to clarity that marks real insight, replacing mechanical search with an elegant path. As AI makes knowledge ever cheaper and easier to look up, Moore warns that we risk losing the habit—and the reward—of struggling toward answers ourselves.

What is understanding?

Artificial intelligence produces images that look like reality, and text that looks like thought. We all know that it merely recombines its training data to produce its responses, and yet this ability to recall and remix human knowledge produces amazing results.

Debates rage about whether AI understands what it says. But what does it mean to understand? What does it mean to have an insight, a realization about something? What is the nature of that “Aha!” moment when you suddenly grasp what was mysterious before?

Puzzles are understanding in miniature. Solving puzzles, designing them, and posing them to each other lets us create and navigate worlds of pure insight—worlds where “Aha!” experiences are central.

We can use puzzles as a philosophical playground to think about the nature of insight, and compare human and artificial approaches. And we can explore what understanding means to us as human beings—both when we struggle toward it ourselves, and when we share it with each other.

Puzzle #1: The magic square

Figure 1. Steps toward the magic square. We use symmetry to conclude that if the center is unique it must be 5, and parity to place the even digits in the corners. Then everything is easy to fill in.

Here’s an example. Ancient Chinese, Indian, and Persian mathematicians discovered that you can arrange the digits 1 through 9 in a three-by-three square so that every row, every column, and both diagonals sum to 15.

The fact that such a thing exists is lovely and mysterious, and these “magic squares” were sometimes ascribed occult powers. But how can we find one? Let’s pose this for ourselves as a puzzle. You might enjoy working it out for yourself. I’ll be over here.

The first thing you might notice is the symmetry of the problem. If we rotate a magic square by 90 degrees, or flip it top-to-bottom or left-to-right, it remains a magic square. The only part of it that doesn’t move is the center.

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We can use puzzles as a philosophical playground to think about the nature of insight, and compare human and artificial approaches.

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 Now suppose I give you the hint that there is essentially only one solution—that every magic arrangement is the same except for rotations and flips. That means there is one number which always has to be in the center.

We can find that central number using another kind of symmetry. If I subtract each digit from 10, replacing x with 10–x, the magic square stays magic—do you see why? We can think of this as reversing the order of the digits, counting from 9 down to 1 instead of 1 up to 9.

Combining our symmetries, if x is the digit in the center, we must have 10–x=x. But that means that x is 5, and we have our first digit. If you intuited that the 5 ought to be in the center since it’s midway from 1 to 9, you have the right idea.