Tom Griffiths

And then the book is really about three threads of thinking, right?

So one is logic.

One is sort of foundations of neural networks, which I sort of characterize in terms of spaces, features, and networks, right?

So thinking about

thoughts as corresponding to a point in space, and some of the mathematics that we use for thinking about spaces, like calculus and so on, being a tool for then thinking about how thoughts work.

And then the third thread is this thread of probability theory, which I think each of them is very helpful and sort of complementary to the other in explaining various aspects of how thinking works.

For probability theory, the origin that I focus on in the book is this 18th century idea where really the radical idea is that probability theory could be applied to thought.

Before that, people had been developing probability theory as a mathematical theory.

And it was a mathematical theory that applied to things like gambling games.

So you see this in the very earliest origins of probability theory.

The best example we have is like Girolamo Cardano, who was a mathematician, but also an addictive gambler.

And so he really wants to know for his recreational and financial reasons,

how to think about the outcomes of rolling dice or these probabilistic events.

And so he works out the mathematics of how to do that.

And the next moment that we see in the origins of probability theory is Blaise Pascal doing something similar, trying to solve a gambling problem and from that developing some of the foundations of probability theory.

But that was a theory of what happens when you roll dice.

The innovation that comes with Bayes was saying, well, maybe this mathematical system that we have, this set of axioms that characterizes some mathematical object,

also characterizes another thing that we're interested in.

It's not just what's going on with dice.

It's also what's going on inside our heads when we change our beliefs.