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Donald Knuth is one of the greatest and most impactful computer scientists and mathematicians ever. He is the recipient in 1974 of the Turing Award, considered the Nobel Prize of computing. He is the author of the multi-volume work, the magnum opus, The Art of Computer Programming. He made several key contributions to the rigorous analysis of the computational complexity of algorithms. He popularized asymptotic notation, that we all affectionately know as the big-O notation. He also created the TeX typesetting which most computer scientists, physicists, mathematicians, and scientists and engineers use to write technical papers and make them look beautiful.

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So you refer to people, including yourself, who gravitate toward a kind of computational thinking as geeks, at least I've heard you use that terminology.

It's true that I think there's something that happened to me as I was growing up that made my brain structure in a certain way that resonates with computers.

So there's this space of people, 2% of the population, you empirically estimate.

That's been fairly constant over most of my career.

However, it might be different now because kids have different experiences when they're young.

So what does the world look like to a geek?

What is this aspect of thinking that is unique to, that makes a geek?

In the 50s, IBM noticed that there were geeks and non-geeks, and so they tried to hire geeks.

And they put out ads for the paper saying, if you play chess, come to Madison Avenue for an interview or something like this.

So what is it that I find easy and other people tend to find harder?

1 is this ability to jump levels of abstraction.

So you see something in the large, and you see something in the small, and you pass between those unconsciously.

So you know that in order to solve some big problem, what you need to do is add 1 to a certain register, and that gets you to another step.

And below the—I don't go down to the electron level, but I knew what those milliseconds were, what the drum was like on the 650.

I knew how I was going to factor a number or find a root of an equation or something because of what was doing.

And as I'm debugging, I'm going through, did I make a key punch error?

And this idea of being able to see something at lots of levels and fluently go between them seems to me to be much more pronounced in the people that resonate with computers.

So in my books, I also don't stick just to the high level, but I mix low-level stuff with high-level.

And this means that some people think that I should write better books, and it's probably true.

But other people say, well, if you think like that, then that's the way to train yourself, keep mixing the levels and learn more and more how to jump between.

The other thing is that it's more of a talent to be able to deal with non-uniformity, where there's case 1, case 2, case 3, instead of having 1 or 2 rules that govern everything.

So it doesn't bother me if I need, like an algorithm has 10 steps to it.

Each step does something else that doesn't bother me.

But a lot of pure mathematics is based on 1 or 2 rules which are universal.

And so this means that People like me sometimes work with systems that are more complicated than necessary because it doesn't bother us that we didn't figure out the simple rule.

And you mentioned that while Jacobi, Boole, Abel, all the mathematicians in the 19th century may have had symptoms of geek.

The first 100% legit geek was Turing, Alan Turing.

I think he had, yeah, a lot more of this quality than any, just from reading the kind of stuff he did.

So how does Turing, what influence has Turing had on you?

Well, okay, so I didn't know that aspect of him until after I graduated some years.

As an undergraduate, we had a class that talked about computability theory and Turing machines.

And it sounded like a very specific kind of purely theoretical approach to stuff.

So when, how old was he when I learned that he had a design machine and that he wrote a wonderful manual for Manchester machines, and he invented all subroutines, and he was a real hacker, that he had his hands dirty.

I thought for many years that he had only done purely formal work.

As I started reading his own publications, I could feel this kinship.

And of course, he had a lot of peculiarities.

Like he wrote numbers backwards because, I mean, left to right instead of right to left because it was easier for computers to process them that way.

He would write pi as, you know, 9514.3, I mean, okay.

I mean, he had trained himself to do that because the computers he was working with worked that way inside.

Trained himself to think like a computer.


Speaker 0: So you refer to people, including yourself, who gravitate toward a kind of computational thinking as geeks, at least I've heard you use that terminology.

Speaker 1: It's true that I think there's something that happened to me as I was growing up that made my brain structure in a certain way that resonates with computers.

Speaker 0: So there's this space of people, 2% of the population, you empirically estimate.

Speaker 1: That's been fairly constant over most of my career. However, it might be different now because kids have different experiences when they're young. I'm just saying.

Speaker 0: So what does the world look like to a geek? What is this aspect of thinking that is unique to, that makes a geek?

Speaker 1: This is a hugely important question. In the 50s, IBM noticed that there were geeks and non-geeks, and so they tried to hire geeks. And they put out ads for the paper saying, if you play chess, come to Madison Avenue for an interview or something like this. They were trying for some things. So what is it that I find easy and other people tend to find harder?

And I think there's 2 main things. 1 is this ability to jump levels of abstraction. So you see something in the large, and you see something in the small, and you pass between those unconsciously. So you know that in order to solve some big problem, what you need to do is add 1 to a certain register, and that gets you to another step. And below the—I don't go down to the electron level, but I knew what those milliseconds were, what the drum was like on the 650.

I knew how I was going to factor a number or find a root of an equation or something because of what was doing. And as I'm debugging, I'm going through, did I make a key punch error? Did I write the wrong instruction? Do I have the wrong thing in a register? And each level is different.

And this idea of being able to see something at lots of levels and fluently go between them seems to me to be much more pronounced in the people that resonate with computers. So in my books, I also don't stick just to the high level, but I mix low-level stuff with high-level. And this means that some people think that I should write better books, and it's probably true. But other people say, well, if you think like that, then that's the way to train yourself, keep mixing the levels and learn more and more how to jump between. So that's the 1 thing.

The other thing is that it's more of a talent to be able to deal with non-uniformity, where there's case 1, case 2, case 3, instead of having 1 or 2 rules that govern everything. So it doesn't bother me if I need, like an algorithm has 10 steps to it. Each step does something else that doesn't bother me. But a lot of pure mathematics is based on 1 or 2 rules which are universal. And so this means that People like me sometimes work with systems that are more complicated than necessary because it doesn't bother us that we didn't figure out the simple rule.

Speaker 0: And you mentioned that while Jacobi, Boole, Abel, all the mathematicians in the 19th century may have had symptoms of geek. The first 100% legit geek was Turing, Alan Turing.

Speaker 1: I think he had, yeah, a lot more of this quality than any, just from reading the kind of stuff he did.

Speaker 0: So how does Turing, what influence has Turing had on you? In your way of thinking?

Speaker 1: Well, okay, so I didn't know that aspect of him until after I graduated some years. As an undergraduate, we had a class that talked about computability theory and Turing machines. And it sounded like a very specific kind of purely theoretical approach to stuff. So when, how old was he when I learned that he had a design machine and that he wrote a wonderful manual for Manchester machines, and he invented all subroutines, and he was a real hacker, that he had his hands dirty. I thought for many years that he had only done purely formal work.

As I started reading his own publications, I could feel this kinship. And of course, he had a lot of peculiarities. Like he wrote numbers backwards because, I mean, left to right instead of right to left because it was easier for computers to process them that way.

Speaker 0: What do you mean left to right?

Speaker 1: He would write pi as, you know, 9514.3, I mean, okay.

Speaker 0: Right, got it.

Speaker 1: 414.3, on the blackboard. I mean, he had trained himself to do that because the computers he was working with worked that way inside.

Speaker 0: Trained himself to think like a computer. Well, there

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Donald Knuth: Alan Turing was the First 100% Geek | AI Podcast Clips