Saying AIs are “just math” is like saying humans are “just biochemistry.”

Strictly speaking, an AI isn’t “just” math. It’s a physical machine whose operations can be described mathematically. If that machine has outputs that can be read by humans, or if it has outputs that are connected to robot bodies, then it is just as capable of affecting the world as you are (using “only” bioelectrical signals inside your brain).

Compare:

For more on this subject, see Chapter 6.

Mathematical operations can represent ideas that aren’t intuitively “mathematical.”

Multiplication, addition, taking maximums, and other mathematical operations can be used to represent things that (from a human perspective) have nothing to do with math.

It’s a lot like how the 1s and 0s that computers send to each other can encode letters. 1s and 0s can even encode things like pictures.

1s and 0s aren’t limited to encoding pictures of things that look cold and blue-tinted and mechanical. They can also encode pictures of beautiful flowers under natural lighting. 1 and 0s can encode things that are beautiful, that are warm and gentle; they can encode things that exalt the human spirit.

It would be a fallacy of composition to say that encoding a picture into 1s and 0s meant that the picture had to be about something numerical or robotic. It would be like saying that a human brain is made of neurotransmitters with names like “norepinephrine,” and therefore human beings ought to only end up thinking about chemistry or only be good at reasoning about neurotransmitters and binding sites.

And while it’s cool that an endless variety of things can be built out of extremely simple parts, there isn’t anything ineffable or magical about how this process works. You could study a bit and learn how pictures of warm, beautiful flowers can be encoded into 1s and 0s until it didn’t even seem surprising. Compare the errors of vitalism.

Sometimes, yes, we don’t know all the rules for how something adds up, and then the step from simpler things to complicated things can feel very mysterious, and can in fact surprise us. But when we do understand how a complicated thing is made out of simpler parts, it ends up feeling as straightforward as building a model racecar out of LEGOs. When you can see how it works, it’s all there in the blocks.

The same is true for neural networks. We don’t understand how the complex behavior of modern AIs arises from such simple parts the way we understand binary image formats and LEGOs. We don’t even understand the “psychology” and “neuroscience” of AIs as well as we understand how the molecules and chemicals in a human neuron add up to human thought. That doesn’t mean the knowledge isn’t there or can’t exist; it just means that we don’t have it yet.

Even without understanding why AIs work, humans can train them to play good chess. With enough parameters and arithmetic operations, we can train AIs to the point where they start talking like a person. You could say that the complicated patterns animating an AI to talk are “just math.” But it’s not “math” like questions on a high school math quiz. It’s “just math” in the same way that a complete human brain is “just chemistry.”

Mere chemistry landed on the moon. It invented nuclear weapons. It built the world as we know it today. It might be hard to see how the simple chemicals of the human brain did all those things, but they did them all the same.

AI is no different. Somehow, even though we don’t fully understand how AIs work internally, we were able to “grow” AIs that can write poetry, compose music, play chess, drive cars, fold laundry, do literature reviews, and discover new drugs.

Being “made of math” didn’t stop AIs from doing those things. So why should it stop AIs from doing another, more complex set of things tomorrow? Where do you draw the line, and how do you know to draw it there? Mathematical operations, it turns out, are sufficient for doing quite a lot more than many people expect.