Episode 152 - Computational Breakthroughs: Advances in Ramsey Theory and Quantum Computing
Max and Maryam discuss the theory of computation and the recent breakthroughs in Ramsey Theory by a team of young mathematicians and in Quantum Computational Complexity. Other topics include Graham's number and the halting problem.
Links
Quanta Magazine: Undergraduate Pushed Frontier of Graph Theory
theconversation: Quantum Computing Breakthrough
Related Episodes
Episode 146 with Tai-Danae Bradley on Quantum Mathematics
Episode 102 on Induction and Ordinals
Transcript
Max Sklar: You're listening to The Local Maximum Episode 152.
Time to expand your perspective. Welcome to The Local Maximum. Now here's your host, Max Sklar.
Max Sklar: Welcome, everyone. Welcome. You have reached another Local Maximum, a new year of The Local Maximum. Today I have—I'm joined by Maryam today. Maryam, how you doing?
Maryam: Doing great. Good to be back.
Max: Thank you for helping me ring in the new year. Aaron will be back very soon. But I'll just give him a break in the first week of the new year. Regardless of when we are recording this. We’re kind of traveling forward in time a little bit and it is now the first week of 2021. So I feel really good about that. I don't know about you.
Maryam: 2020 feels good to be in the rearview mirror. Definitely. Not to say that this year's going to be easy.
Max: When this comes out. Oh yes. But yes, we all know that. Sure.
So, as this goes out, we’ll be starting the first week of 2021. This is when my plan that week in terms of The Local Maximum, is to just look at all the guests that I want to have this year and just start shooting out emails. And what I would do in the past, which wasn't really that good, maybe it was okay, was I would kind of be worried about emailing someone too big and wanting to write the perfect email and then ending up not doing it. You know what? I'm just going to send, like ten, kind of whatever, good, but not perfectionist emails to a bunch of really good guests and see what I get. And I'll do that the first week of 2021. AndI'll have you on, I'll do a solo show, I'll have Aaron on. And by the time I get emails back and get some interest, I think we'll have some really good guests on the lineup. I don't know who yet. But that's my plan.
Maryam: Sounds like a really good plan.
Max: Yes, I think it's the best—no, maybe not the best plan I've ever come up with but it’s pretty straightforward. I mean, no, it's a good plan. It's not like a brilliant plan. But it's a good plan.
Okay, so we are not slacking off today. I can tell you about this. What did I say? We can't bullshit through this one. That's for sure. Yes, because we've got some breakthroughs in—we're talking about some breakthroughs in mathematics. it's sort of related to, both of them are related to computing today. So, I know you wanted to talk about some of these topics. So I'm excited to talk about it, we’ll sort of stretch the limits of what we know and what we can explain. We're going to try the best we can, folks.
But today, we're going to start talking about Ramsey theory. And also, it's my understanding that someone—I want to say some kid, he's 21 years old, came up with some new results in Ramsey theory as an undergrad, which is pretty impressive. Is it not?
Maryam: Yes, super, super impressive.
Max: Yes. So first of all, most people listening don't know what Ramsey theory is. So tell us what that is.
Maryam: So Ramsey theory is a field of mathematics, part of combinatorics that focuses on patterns in large structures, like, even if you have randomly generated this large thing, you can expect certain structures in it. And that's kind of the basis of Ramsey theory.
Max: So those structures I understand, they're like, they're graphs, they're like points and nodes, right?
Maryam: They can be graphs.
Max: Oh, they don't have to be?
Maryam: The specific part of Ramsey theory that we'll be talking about today has to do with graphs, but they don't have to be. Ramsey theory, there's aspects of it that are also around numerical sequences. So you have like a bunch of numbers in a sequence, it doesn't matter what the numbers are. If you assign a certain color to each number, Ramsey theory has taught us that there are certain patterns that you can expect once the sequence gets large enough.
Max: Right. So there are certain things that must happen after a certain period of time.
Maryam: Yes.
Max: Yes. So I always find it interesting, like the phrase structure, that we throw around a lot in mathematics. What do you see as the essence of structure, like what is a structure?
Maryam: Yes, I feel like it's just that it's one of those like, words that you just throw out.
Max: I know, it just occurred to me, I've been using it for years.
Maryam: Yes, it could be, I feel like it's just ways that we group numbers or group things together.
Max: Yes, could be any way that we group data.
Maryam: Not to be confused with mathematical group, a mathematical structure.
Max: No, but like a structure and data is really any way we relate things to one another, which is really just like the nature of information.
Maryam: Yes.
Max: So and the nature of knowledge basically. So, okay, so who is Ramsey? I assume that's a person.
Maryam: Yes. So Ramsey theory is named after the mathematician Frank Ramsey. He's an English, or he was an English mathematician, but not just a mathematician. He was a philosopher, a mathematician and an economist, and made major contributions to all three of these fields before he died at the age of 26.
Max: Whoa, there's a lot of those like, Galois is one that I know.
Maryam: It's amazing what some people do at such a young age.
Max: Yeah, what some people can do.
Maryam: Not me.
Max: That’s how I feel. Well, it's very rare. Well, the other guy who we're talking about today is also very young. So this seems like whoa, yes. And then now it makes me feel like I'm over the hill, and so I'm in my 30s. I don't know. And for in terms of Ramsey theory. But actually, there are some results like, well, Graham's number, I'll talk about a little bit, where I believe when Graham came up with that he was a little bit older.
So okay, so what's your interest in Ramsey theory? When did you first hear about it? And in what context were you interested in it?
Maryam: Yes, I first heard about it in graph theory course in my undergrad. So it was taught by my favorite math professor, John Mackey. And I think he brought it up because it was a personal interest. So when he was getting his PhD in math in ‘94, his PhD thesis was on Ramsey theory. And he actually use computers to find new, lower bounds for a bunch of what we call diagonal, Ramsey numbers. And that's what his paper is also about.
Max: Yes. Oh, so can you give an example of those, like, what would be in a diagonal Ramsey number?
Maryam: Yes, so we've talked about Ramsey theory. We haven't talked about Ramsey numbers yet. So a Ramsey number—because there's two numbers that come as input. So let me describe it. I'm going to describe it the way that John Mackey originally described it to us. So let's say you're at a party. Now, a lot of math problems start this way. But let's say you're at a party.
Max: Yes. But a lot of computer science problems start this way.
Maryam: It’s true.
Max: Yes. But it usually ends up like sorting people into tables, or something like that, or shaking hands. I don't know.
Maryam: This one, you know graph theory? I learned about it in graph theory. So it's all about relationships.
Max: It doesn't say whether the people, the party will get along or have good conversations, but they do certain things. They do certain mathematical handshakes to each other. At least they know how to do that.
Maryam: Sometimes it's marriage.
Anyway, Ramsey number, is it? Okay, if we are at a party, either everyone—either between two people, they're either total strangers, or they've met before. So the diagonal Ramsey number for three means, how big does a party have to be before you have a group of three people who either all have already met, or are all strangers?
Max: Right. So it sounds to me like you need both requirements for it to be interesting. Because if you say, “Well, I want three people who have all already met.” Well, that could never happen. It could be that like, no one was ever met. And if I want three people who are total strangers, well, it could be that that could never happen because it could be that everyone you've ever invite will all be total strangers to everyone else. Just be all newborn.
But if you have both of those requirements in there, like either you have a group that have all met each other say group of three, or a group of four, or a group that's all total strangers to each other, then at some point, one of those is going to have to happen.
Maryam: Yes. Yes.
Max: Okay. Cool.
Maryam: And the answer is six.
Max: Six? For three and three?
Maryam: Yes, for three and three, the answer six. You’re guaranteed to have three total strangers or three acquaintances, if you have six people at your party.
Max: That's interesting because you would think that you could set it up so that maybe everybody, every group, you kind of know one person and someone else is a stranger, and so on and so forth. You wouldn't think it would be guaranteed that there'd be a group of three that all know each other. But keep in mind, it's any group of three. So you as a party participant might not be in that group. So there has to be kind of some way of doing that.
Maryam: Yes, exactly.
Max: Okay. Interesting. So, I'm guessing just because I know the nature of sequences here, when you move that three, number up to four or five, six, that this thing grows pretty fast.
Maryam: Yes. So we know that the Ramsey number for four is 18 and the Ramsey number for five is unknown. All that we know—you would think okay, five, that's such a small number, we certainly know this.
Max: At least go to like 3, 18 to like, I don't know, 1024 or something. That's a fast moving sequence.
Maryam: It is a small number. It's not that big of a number. So we had bounds. We know the number is between 43 and 49.
Max: Wow. So it must be so hard to check these then.
Maryam: Exactly. This field, it's really grown with computers. These checks have become done via algorithms.
Max: If you think about it, like you have 43 people at a party? Well, I don't know. Checking every group of five, is that really that hard?
Maryam: It's not checking every group of five. It’s the edge, all the edges, like going through all the possibilities for whether the person knows each other or not.
Max: Oh, yes, all the possible graphs. So that's like, that's like 2 to the 43rd. Yes, that's bad. And I'm sure—well, 2 the 43rd, you really can't do. But I'm sure there are ways, there are symmetries they could find to make that much smaller.
Okay. Yes. So all right. So seems like fun math problem, but why don't you give us example of why there's like research into this. Is this just sort of, of pure interest? Or is there some kind of application?
Maryam: Yes, I feel like there have to be some implications for having the knowledge that for certain groups are going to be there. But I don't know what those are.
Max: Yeah, well, it certainly pushes—Ramsey theory certainly pushes computer science research forward. And it's always very interesting to learn, like where the frontier of knowledge is right now. So what is the most recent development by, I believe it's Sah and Sawhney?
Maryam: Yes. So as you hinted at earlier, Sah is very young. Sah’s only 21 years old. And Sawhney also is—I mean, they're both recently graduated from undergrad and when they made this discovery, they were undergraduate at MIT. And yes, it kind of echoes Ramsey’s own youth.
What's really impressive about is that they're both undergrads and this isn't the only discovery that they've published many papers together and formulated many proofs together that are kind of pushing mathematics forward to the point where if they had a PhD, like they have done professor level work as undergrads.
Max: Yes. That is pretty impressive. So, what can you tell us about the thing that they came up with, like is this something we can kind of grasp?
Maryam: So they have come up with an upper bound formula for any diagonal Ramsey number. So if you input, if you say like Ramsey number n wherein n is some number they have a formula for an upper bound that is better than the previous formula for the upper bound.
And not only that, but their specific formula is—it has pushed the boundary. It's like pushed the bounds of what is possible to do with the current focus of research. So If you were to make a better bound, you would have to use a totally different approach to developing the formula than what has been used before.
Max: What kind of bound is it? Is that something we could even get into? Or is that going to be hard to like, to state in an audio format?
Maryam: It's going to be hard to state.
Max: So it's not like, “Hey, the diagonal Ramsey n is like, no larger than n squared or so,” well we know it's bigger.
Maryam: Like e to the something, but it's not so easy to say over audio.
Max: Yes. Okay. So, I mean, I'll try to post links to that on localmaxradio.com/152. Anything else that you could say about this?
Maryam: For me, like, I was super excited about this, because Ramsey theory—I just find it very beautiful. Just to—I feel like math. Math could teach us so much about the world and like, this is something where we know there's just patterns and randomness, like even in the most random things, there are patterns.
Max: Something has to happen.
Maryam: Exactly, exactly. So for me personally, when this came out, it struck me because I've always thought Ramsey theory was beautiful.
Max: Yes. Well, so this reminded me of a concept in graph theory, I think it's related to Ramsey theory called Graham's number. And what I really liked about that number is that you always have kids fight over who could come up with the largest number, until you come up with like, infinity, oh, yes, infinity plus one. But if you don't allow infinity, then you could keep on making up larger and larger numbers.
But for a time Graham’s number was the largest number ever found, obviously, you can always come back with Graham's number plus one. But with the rule that it has to be legitimately useful for something. And Graham's number is so enormous that it can't be represented as a number as we normally would, it can’t even be represented by scientific notation.
You think that most physical constants, most things you want to measure in the physical world can be measured by scientific notation. Even when you're talking about sets of things still. But sometimes in the mathematical world, you really go beyond that, you need something called Ackermann functions, which is related to computations, not even complicated programs, but just programs that use a lot of loops and recursion to try to get it so that this machine, you can actually write a very short program that counts up to a very, very astronomically large number, it will never get there.
But you could write a program that does that. And so, Graham's number has to be kind of expressed in that way. But the problem that it's talking about is actually pretty simple. My understanding of it is that you take a hypercube—all right, people are already going to say hypercube, that's already blowing my mind. But no, but if you think about it, the sides of a hypercube, think of a binary digit, like 100101010, whatever. And then, and let's say they're, like 30 digits, that's a vertex on a 30 dimensional hypercube. And then, as you change one digit, you're moving along the sides of the hypercube. So you could kind of, if you change two digits in a hypercube, if you flip them back and forth, you could kind of form a square, right?
And so basically, what Graham's number says—and so, if you imagine, like just a three dimensional hypercube, like, which is a cube. A square could be the face of a cube, or you kind of cut through the cube diagonally, and you get like two points on two opposite sides. But really, what you're going to do is you're going to look at all the different vertices in that hypercube. And you're going to color them either red or blue. And essentially, one of those square slices is going to have to be either all red or all blue as soon as the hypercube gets huge, or if you'd like to think of it as the number of bits, the number of digits gets really, really huge.
Turns out the upper bounds that Graham came up with, the best he could do is Graham's number, which is this huge, huge, huge, huge thing, which is pretty crazy. Like you think once you state the problem—and I know probably all you listening, if it's the first time you've heard it, you might want to go and kind of look it up. But it's simple enough where you're “Okay, this should be a simple number, like, okay, if it's not 12, maybe it's 1000.” But no, it's this crazy number. And it's really, always interesting and rare when a number of that enormous complexity is actually used in a real world problem like that. That's simple. I mean, maybe make up a complicated problem.
Maryam: Yes, I feel like a lot of times in math. Instead of having a number like this, if you would just prove that it wasn't infinite. It would be like a yes, no. Not a yes, and it's because it's this number, or less. You would have like a bound this big.
Max: Yes, I'm sure that the actual number, which I don't think they found yet is much smaller than Graham's number. But, not only can you prove it's not infinite, but he does have a bound. So, and I suppose it's just constantly taking—I don't even want to speculate on how he got to that bound. But obviously, the way I imagined it is, he just saying, “Okay, take every possibility here, take every possibility there.” And then when they all kind of line up in almost a program that approximates this crazy, recursive thing, if that makes any sense.
Maryam: Yes, makes sense.
Max: Okay. All right. So now we're going to try a third story that is going to blow your mind, just to start off this year with—I think we're having trouble kind of wrapping our heads around this. I know I am.
Maryam: I definitely am, you’re not alone, Max.
Max: Allright, I'm not starting 2021—I could go talk about something that, like Bayes rule again, that I could do, like, I know like the back of my hand, as they say. But we're not starting with that in 2021, we're really trying to push the limit here.
Okay, so it's this another breakthrough that has occurred in the theory of computation. And this time it has to do with quantum computers. Now, I don't know. So, first of all, there's the famous problem P=NP. And I feel like I'm a little bit more that's not quantum computers, that's regular computers. I feel like I am a little bit more comfortable with explaining that. So why don't I try that first, you could correct me, or you tell me...
Maryam: Embellish.
Max: If you have a better way to explain. Yes, embellish. But we'll start with that. Because that I have a pretty good idea in my mind of what it is. So P is programs. First of all, not everything is computable. That's one interesting fact of computer science is that there are some problems that are real problems, that have real answers, like they could be yes or no, that literally, you can prove that it's impossible to build a machine or essentially computer program that does that. The most famous one being the halting problem. It's not just the most famous one, it really is. You use the halting problem as the proof, kind of. But basically, to determine if any other, you want to write a program that reads another program. And determines whether it will halt or not, or whether we'll get into an infinite loop.
Now, you could write something that reads code and can tell you whether it halts. Most of the time, I actually think it's, it's quite possible. But you could always write code that tricks it. That's the sort of way the proof goes. So not everything is computable. But then there are things that are computable. But it's kind of impractical to compute. So it takes—we would say exponential time, or even super exponential time where it would take till the ends of the universe to compute, even if the whole universe were turned into a computer or something like that. So one good example of exponential time algorithm. I'm trying to think off the top of my head.
Maryam: Solving a Ramsey number or finding a Ramsey number.
Max: Yes, finding a Ramsey number. That would be a good one. And so then there are ones that are solvable in polynomial time, which is more—I mean, here's a good one that's exponential, right? I mean and this is a very simple one, right? If you want to take a binary number or even like a decimal number, and then turn it into a series of ticks.
So for example, if I want to take the number 316 and turn it into 316 ones. That’s actually exponential time. Because if you think about it, you can write a huge decimal number very easily, and then it would be impossible that you would have the space to store all those ones. So that's actually kind of a simple one. And that's actually what you would kind of use on a small scale, like, exponential time is no big deal, if you have very small inputs, even a 316 is no big deal. So if you have small inputs, but what happens is in those exponential time algorithms, as you want bigger and bigger inputs, it becomes untenable.
Whereas polynomial time, I always laugh at this, because it has come up several times, whenever I use the term polynomial, or Aaron uses the term polynomial. They don't want to hear about polynomial. We don't want to hear that. It just means that it's less than exponential like, it could grow very fast still, but just not that fast. So is that a good primer?
Maryam: Yes, yes.
Max: Okay, so let's say polynomial time is easier. And then that’s P. And then there's NP, which is stuff that is verifiable in polynomial time, a good example of that would be let's suppose I have a thousand digit number and it's the product of two primes. So each of those primes, maybe have five hundred digits, find those two primes that make up. Factor it, that multiply to get that bigger number. That’s a really, really hard problem.
But once you give me those two five hundred digit numbers, piece of cake for a computer to store five hundred digit number, a piece of cake for a computer to multiply it together. Even if you, a human, wanted to spend all day you could do it. And you can verify that very fast. So it's verifiable in polynomial time. And then it hasn't been proven that verifiable—that NP is not equal to P. Although it's suspected that it is not because there are problems that just seem like, you'll never be able to solve in polynomial time, but I could give you the answer, and you can verify it pretty easily.
Maryam: Yes, but it would be a really easy way to become a millionaire, all you have to do is prove that it is one of these two things—
Max: It's one of the millennial problems.
Maryam: Yes, yes. Okay, it’s one of the millennial problems.
Max: So we've got polynomial time, exponential time, things that are computable, things are not computable. Sometimes the rules are frustrating, but I think with classical computers, we all kind of know what the rules are.
But now, people are starting to research quantum computers. I don't think you and I are going to have access to a quantum computer anytime soon. This is my impression. But anyway, all of these rules seem to get thrown out the window and start to become wacky and unintuitive. And I don't know if it's just like, before I studied computer science, maybe the classical rules were unintuitive. But this stuff just seems crazy.
Maryam: It's definitely hard to wrap your head around.
Max: Right, right. And so I've even looked at, kind of, researched this article, which is—there's a breakthrough in quantum computational research. And now instead of P=NP or P≠NP, it's actually proven that MIP*=RE. And so it's like all right, so let's, let's try to break that down a little bit.
Maryam: Yes. What do these things stand for?
Max: Right, so RE is actually pretty simple. It's recursively enumerable, that's all computable problems. Right? Okay, so there's something that quantum computers can do with any problem that is computable. So it sounds like—we're not talking about the halting problem and stuff but we're still talking about very, very hard problems. And MIP*is multi-prover interactive proofs.
The best that I can understand as to what's going on, and I would love to get like a quantum computer expert on the show to talk more about this. But what I understand about what's going on is that these interactive proofs is that—it's not just verifying something, you're kind of going back and forth. You’re like a classical computer and you're going back and forth with a quantum computer who has an answer and they're trying to prove to you that something is true.
And so if you could question them, and then like probabilistically determine that they're correct in a reasonable amount of time, then something is interactively provable. MIP means you're questioning multiple quantum computers, I think. And MIP* means that those multiple quantum computers are allowed to communicate with each other via an entangled particle. Don't even get me started. Right. So that's crazy. So you actually are using this, like Einstein’s spooky.
So what's an entangled particle? It means that something happens to a particle in one place and then instantly, it means that a particle in another place is a different way. But it's not exactly, Einstein called it “spooky action at a distance,” but from what I can tell, it's not exactly action. It's almost like one of those quantum decisions where you don't know what it is until you observe it. And so once you observe it, it was like the other one was always like this. So it's a little bit mind-bending, I think. How do you understand it?
Maryam: I don't really. I’m not a physics person. Like, all right, sure.
Max: What are we going to do if they require all software engineers to program in quantum computers? Or are we just like, truck drivers, where this is not going to be a problem until way after we are done with our careers?
Maryam: Who knows? I'm hoping, like, I'm secretly hoping, because there's some equivalences with set theory and quantum thinking, I'm hoping that that will help me in this, like, awkward future. But who knows?
Max: Yes, no, I mean, it's quantum thinking, that's a good way to put it. Like how can you think in terms of quantum computing? Because it's really alien to us, who are used to writing code.
So anyway, what this is saying is that—and then, for these interactive provers. Again, I'm having trouble wrapping my head around what the exact application is, but it could be cracking codes, it could be search, could be like a Google type thing. It could be some very complicated type search. So it could be very efficient searches of databases, or something like that. You could search the whole internet, maybe.
So if you're talking about MIP, or it could be like searching Ramsey numbers. It says that if you're doing these multi-prover interactive proofs, I think we said that it comes down to exponential time.
So okay, so it's not like you get all these problems in polynomial time, in which case, it could decrypt everything and blah blah blah blah. But at least get it down to exponential and not like a super exponential, that's what I think is going on. And that's any solvable problem can be done in exponential time. So that's pretty crazy. So beyond exponential, once you get into the quantum computers, you don't have to worry about it anymore. Almost is what this is seems to be saying. This is such hot off the press stuff.
Maryam: As we were doing research about this, first of all, have you ever tried to just Google MIP?
Max: This is not what comes up.
Maryam: No.
Max: It’s not some of those search terms where it's like something really bad comes up, but it's totally like, other computing things come up that's like not even related.
Maryam: Like, I think it's multi-integer programming or something. Yes, there are other terms that have similar names. Yes, there's not a whole lot of good explanations for things on the internet.
Max: Because it's so new.
Maryam: Yes. So new.
Max: Yes. So let me let me quote from this article: “It seems obvious that communication between provers…” And they're talking about the quantumly entangled bit, so it's not necessarily communication, I should point out. “...that it seems obvious the communication between the provers can only serve to help the provers coordinate lies rather than assist the interrogator in discovering the truth.” The interrogator is the one that is trying to verify. “For that reason, nobody expected that allowing more communication would make computational problems more reliable and solvable. Surprisingly, we now know that MIP*...”, That star is the quantum entangled particle. “...equals RE. This means that quantum communication behaves wildly differently to normal communication.”
And we said that before. Because an entangled bit, you can't really communicate very well, or at all with an entangled bit. You're not really sending information. It's just if my bit is one way, I know that your bit is the other way. But we don't really communicate like that.
Maryam: Yes, but even this like, tiny thing makes a huge difference in terms of complexity.
Max: Yes, yes. So I'm still trying to wrap my head around this, like, what are problems that these machines that we'll be able to solve that we would have trouble solving right now?
So I hope it's not encryption right away because that would be a big problem. And it looks like so far, it's not. But is it better search? Is it some type of AI we could build that is perhaps more flexible than kind of the deep neural networks we have now? That's where I'm like—I don't know yet. And I think we need to do more research.
Maryam: Yes, I think it'd be really interesting. Could be very interesting. I don't know, just thinking about—so we know from this that at least some problems are going from super exponential to exponential. There could be things that are going from exponential to the polynomial as well.
Max: That's true, too. I mean, without being P=NP. Yes, no, that's absolutely true. From my understanding, it's been very difficult to get quantum computers to factorize numbers at scale. And I don't really know why that is. If you look at quantum code, it looks like something from an alien civilization. I mean, look, maybe someone would say that about some machine learning code.
Maryam: I don’t know, have you ever wrote Perl?
Max: Yes, I wrote Perl once and I remember somebody laughing at my code being like, “How on earth does anyone understand this?” I probably wouldn't have been able to understand it, if I didn't read it, if I didn't write it. Because it's just like stars and parentheses and pluses.
Yes, I know what they do. But then it just looks like a random jumble of them.
Maryam: Add symbols, too.
Max: Maybe what is needed is sort of someone to come in. Because there's a lot of, not disdain, but there's not enough emphasis sometimes in this research put on simplifying the language in which all these things are expressed. And sometimes that's the most important thing. Sometimes that's what actually makes this stuff useful. I mean, that's what programming languages are all about. Right? If you think about it, research into better programming languages has increased the efficiency of software engineers, who knows? By leaps and bounds. I mean, imagine considering Python and Scala, we were using Assembly or something.
Maryam: When Grace Hopper first suggested using more human language for programming, people laughed at her.
Max: Really? And so what was the argument against it?
Maryam: I think it was about like, “These technical types aren't going to learn these words,” or like, “Why change something that we already understand?”
Max: Our people are machines already.
Maryam: How would this help?
Max: Yes. Well, I mean, it's hard to change. I mean, I even feel it myself, like I hate learning something new. If someone says, to learn a new language. It took me a long time to get on board with Python, for crying out loud. Well, it's always hard to learn, because it's like, well, “Where do I start?” and what. So it's—I can imagine even at the beginning, where...
But really the, like, even in mathematics, like the terminology that you use is very important. There isn't really that deep of an insight, say, going from Roman numerals to Arabic numerals that we use today. Huge difference in terms of how fast you're able to do things. I mean, I guess there is an insight. But it's a huge difference in terms of how fast you're able to solve problems. And so I feel like the language of quantum computers needs to be made more intuitive to humans. And I don't hear anybody in the quantum space talking about that.
Maryam: Yes, that would be a really beautiful, great thing to do. I feel like, when it comes to software products, like we have people focused on UX. But in the scientific and mathematical community, there's no UX person.
Max: There absolutely should be—in a pure mathematics department, there should be a UX person.
Maryam: You heard it here first.
Max: Yes. No, no, I'm serious. All right.
Maryam: I agree.
Max: Yes. Okay. So I feel like we touched on some themes today. First theme is that yes, it's 2021, folks. We're not messing around.
Second theme is that in terms of just basic computation, there's still so much stuff to be discovered that is actually going to reverberate quickly through the world of computing into I think real world implications, even Ramsey theory. Just like the idea of you go from like complexity theory, into quantum computing, into all this. I feel like it kind of flows into AI. What problems can we solve fast?
Maryam: Yes. And to think like what's the point of this? Like what can we do from it?
Max: Yes, yes. And but I think that the theme today is that computation is still an active field. And it's fascinating for anyone who wants to dip their toes into it.
All right, Maryam, any last thoughts from you before we wrap up?
Maryam: No, I really enjoyed getting a platform to talk about Ramsey theory. I never thought that would happen. So it's been an exciting day for me.
Max: Yes, that's a good way to start the year. All right. So Maryam, thank you so much for coming on today. Thanks for your time.
Maryam: Thank you, too.
Max: And for being my sometimes fill in co-host. And maybe we'll do it again sometime. And yes, have a great week, everyone.
Maryam: Happy New Year, everyone.
Max Sklar: That's the show. To support The Local Maximum, sign up for exclusive content and their online community at maximum.locals.com. The Local Maximum is available wherever podcasts are found. If you want to keep up, remember to subscribe on your podcast app. Also, check out the website with show notes and additional materials at localmaxradio.com. If you want to contact me, the host, send an email to localmaxradio@gmail.com. Have a great week.
