Turing machine

The team's most striking connection related the same version of the pigeonhole principle to one of the first theorems that students encounter in introductory complexity theory courses.

This classic banger of a theorem, as IBM's Marco Carmosino describes it, sets a lower bound on the amount of time required for a type of theoretical computer called a single-tape Turing machine to determine whether a string of zeros and ones is a palindrome.

So does it read the same forward and backward? Li, Chen, and Oliveira used reverse mathematics to prove that within PV1, this palindrome lower bound theorem is equivalent to the pigeonhole principle.

Chen says if you told him this, he wouldn't believe it because it sounds very ridiculous.

But I think what I was trying to do was just understand, like, if you think about these more mathematical abstract sides of the field, fundamentally, like, you don't need computers to do that work, but how important is the existence of these machines to that side of the work, like conceptually? And one reason you might say, "Well, it's not really about computers," is that the people who first started to think about these questions from the theoretical side, in many cases, they weren't motivated by the possibility of building computing machines.

Like Alan Turing, who came up with this famous model of computation called the Turing machine, was trying to think about how human mathematicians work.

Defining the human mathematician also as a computer-

Right.

Then, yeah, two games I don't have much to talk about.

Turing Machine I got recently, and it's a game I have already...

It's the only game I think I've learned digitally and played digitally before... having it and I think it's a blast it's a simple game that is really hard to get your head around it the first time because it's a logic game where you have some conditions and you're trying to figure out the code and just how the conditions work in the machine it's a bit it's a bit weird to get your end around and I totally remember that because I tried to teach it to my wife this past weekend and it went horribly wrong And I realized, yeah, I remembered, yeah, I was like playing six or 10 games of these in PGA, not understanding what was happening until I got it.

And then it's simple.

Nice.

Yeah, definitely we'll look into that one.

And then going to the next, that I already talked about, Turing Machine, which the game doesn't really tell you much, just tells you that the game is based on an analog machine that Alan Turing invented to crack codes from the Nazis, but it doesn't really tell you more, but it made me go search.

and find out some horrible things, that not only Alan Turing was responsible for ending the war, because he cracked the Enigma codes and they were able to listen on the Nazis, and that way that was really important to end the war, but also that Alan Turing was gay, and after the war was over, the British Empire castrated him, chemically.

And of course, that view initially seems very naive because the machines of the time did one particular thing, like a sewing machine is just good for clothes.

So the thesis was really rather implausible until the development of the idea of the Turing machine, Alan Turing's idea of an ideal digital computer.

Because what's special about that is that now you have a multipurpose problem solver, a device that can be reprogrammed to do just about anything that can be reduced to a set of instructions.

And of course, that then makes you think, well, Could it be that a human being is essentially an organic realization of a Turing machine, right? The Turing machine seems versatile enough, maybe that's really all there is to us.

And in the background, the big target though is just any version of materialism that wants to say that we're nothing but an arrangement of physical parts.

Great.

Turing was trying to define what computation actually is.

He invented the theoretical concept of a Turing machine, a machine that reads and writes symbols on an infinite tape according to a set of rules.

This is the conceptual blueprint for every computer on Earth today.

And Turing asked a fundamental question: Is there a universal algorithm, a master program that can look at any other computer program and predict whether that program will eventually finish running and halt, or if it will get stuck in an infinite loop forever?

I was on my way to Lafayette to a job at a healthcare company.

I listened to Republican talk radio and a red DJ started talking about this basically, uh, uh, Turing machine that was able to produce human tech and write social media stuff.

And I was like, that is BS.

Like, I cannot wait to get to work.

You gain this like super general, easy to, to code, you know, program.

But because of that, you have to flip bits, right? The, the Turing machine, it's all these bits and that's, that's why, you know, you end up needing all this memory and Micron stock's going up, right?

[laughs]

Um, because you know, they're, they're bottlenecked on basically, you know, to make things go faster, you can parallelize it and, and flip bits and, and it's a super general thing.