Science & Technology Q&A for Kids (and others) [Part 145]

Hi, guys. Welcome to another episode of Science and Technology Q and A for Kids and others. I do want to say that this is my effort to try and give explanations of things you might have wondered about, about science and technology. And not terribly technical things, but things where perhaps the things I know or the things I've thought about might be relevant. So please ask questions about things that are kind of. They might be in textbooks, but they're not. Or things you wondered about. How does this work? What happens with whatever. These are good things to ask. I see a number of questions here that are saved up, many of which are a little hard to answer without letting, like, demoing things, which I'm not doing in these sessions. Well, I see a question here about a piece that I wrote called why Does Biological Evolution Work? A minimal model for biological evolution and other adaptive processes. I just wrote that a week or so ago. I can try and talk a little bit about that. Let's. Let's talk about kind of biological evolution, what it is and why it works. So we don't know how life started on Earth. Big question. It's what is life? There isn't a particularly clear definition of what life is, other than the particular example of life that we have here on Earth. The particular example of life that we have here on Earth has a lot of very specific characteristics. It has DNA, the molecule that records kind of genetic information, records essentially the program for how to make an organism. It has specific chemistry that determines about how proteins, the molecules that are sort of assembled to make the organisms, how those are set up, all those kinds of things. There's pretty specific sort of chemistry and physics for the particular way that life is constructed on Earth. So we don't really know what the general notion of what life might be like is. We know, for example, that one feature of life that got discovered very early in the history of life on Earth, the Earth is about 4.6 billion years old. The earliest examples of life are from maybe two and a half billion years ago. So for the first billion years or so of the Earth's existence, there probably wasn't any life on it. And it was also a rather inhospitable place, kind of hot, different atmosphere than we have today, lots of different characteristics than Earth as it is today. But the thing that started off one of the sort of earliest discoveries of life on Earth was the idea of having separate organisms. One thing that could happen is you have sort of chemical processes going on that are kind of like growing and doing things and so on, and they're kind of a bit lifelike, and it's a great big single organism. But then what became early, we don't know when, what sort of got invented with the idea of let's have lots of separate organisms. Let's have a critter that is created, it replicates, it produces other organisms, then it dies, and then its children, its children's children live on, so to speak. This idea of kind of modularizing life, having these kind of blocks of chemistry and physics that correspond to life and having them be separate as separate organisms. And this idea of things being modularized has been used over and over again in life. For example, we're made of maybe 100 trillion cells, individual cells. Each of those cells has its own sort of separate characteristics interacting with other cells. Within those cells, there are organelles which are again, kind of separated pieces that kind of have their own existence independent of the rest of what's going on. So this idea of things being sort of organized into definite kind of modular pieces, that was a very early idea in the history of life on Earth. And another idea, we don't know when it originated, is this idea of kind of the program, the genetic program for an organism. And once you have these separate organisms, there's. Well, what's the relation between these separate organisms? Well, one organism might split in two to produce two other organisms. Those two other organisms need to develop the same way more or less as the first organism. How does that get specified? Well, it has essentially a program. What is that program? It's a chemical specification of a sequence of units in this DNA molecule. And those chemical specifications are used through chemical processes that produce these molecules, proteins that then fold up in different shapes and fit together in different ways to make all the things that corresponds to a living organism as we know it. But then there's sort of a thing that would happen which is these programs, they change slightly every time. It's like you have the parent of an organism, and then you have. Let's say you have an organism which produces progeny by basically just splitting in two. So there's the sort of original parent is left over, and then there's a child that's sort of split off from the original parent. The it was later in the history of biological evolution that sexual reproduction, the idea of two parents to make a child, originated at the beginning. That wasn't how it worked. The so then this idea of, okay, you've got the child organism, and it has a program too, and its program is going to make it do what it does and make New child organisms and so on and keep going. Well, what happened probably by chance originally and later on it was sort of organized properly was that there was a small mutation in this program, a small change in the program. When the, when the child made a copy of the program to get its own version of the program, it wasn't precisely the same as the parents program. So then that led to that organism having slightly different characteristics. Okay, so then the big thing that sort of came in is the idea of natural selection, which is sort of a necessary and inevitable phenomenon. That is, let's say that the mutation that happened in the program caused the child organism to grow better and to then. And to take for example, less time to get to the point where it could have more child organisms and so on. And you have one mutation where that happens, another mutation where it grows more slowly and doesn't have as many child organisms. Well, clearly what's going to happen is the successful mutation with the more child organisms, so to speak, is going to win out because there'll be more copies of it and then the children of it will again make more copies of themselves. And so over time, there'll be just a total winning of, of the thing that has the characteristics that make it more successful at reproducing itself. And that's sort of the key idea of natural selection, is that whatever the environment is like, the organisms that are more successful and have more children will be the ones that you see more of, the ones that are selected for, the ones that become the dominant ones in kind of the history of these organisms. So the question is, okay, we're getting organisms that are somehow more successful. What makes organisms more successful? Well, it obviously depends on what it is the organisms are trying to do. And that is one thing the organism is definitely trying to do is not die, not die too quickly, have as many child organisms as possible and so on. Well, a thing that is completely not obvious is that successful organisms will be complicated. We are complicated organisms. We've got 100 trillion cells. We've got. Each of our cells is full of all kinds of chemicals that do all kinds of things. We've got all these different organs, we've got brains, we've got all kinds of complicated stuff. Why do you need such complicated stuff in order to do? Well, in the kind of struggle for life and natural selection, maybe the best thing to do would be to be a single celled organism and just replicate that single cell and don't make it too complicated. And there are plenty of organisms that indeed don't make it too complicated. If you look at the organisms that exist on the Earth, I mean, in the history of life on Earth there have probably been about a trillion generations of organisms. And in terms of the total number of organisms, I think there have been about 10 to the 40th, which is, let's see, a trillion trillion, trillion billion more or less organisms. So lots of individual organisms and most of those organisms are in fact tiny single celled organisms and things not big complicated organisms like us. But the question is, why did natural selection even lead to any complicated organisms having been produced? Why didn't it just stick with the simple single celled organisms that were replicating just fine and there's all kinds of slime all over the Earth from these organisms and they did just fine. And there are more of those and they're just more. And why make something complicated like a whole human that's got computers and is live streaming and all those kinds of things? Why not just have the simple bacteria and so on? Well, we don't know. But people like Charles Darwin, who kind of initiated this natural selection idea, people hadn't known before. So Charles Darwin wrote this book in 1859 called Origin Species. And sort of the very title of the book sort of is the big story there, that their species have origins. People have thought that the different species that exist of different kinds of birds and animals and birds and mammals and reptiles and all this kind of thing, that all these different species just had always existed in the history of the Earth. They didn't know how old the Earth was. They kind of thought these species just came into existence and there aren't ever new ones. And it's just they are what they are. There are probably around 10 million species that exist on the Earth. Species die out species, new species are created. What Darwin sort of emphasized was the idea that yes, new species can be created and that in this kind of gradual mutation of the thing changes a bit and it changes a bit and changes a bit, that eventually that process could lead to something which is a identifiably new species. And by the way, when their species are doing things like sexual reproduction, by the time there are two organisms that are different enough, they won't be able to mate with each other. And that means that you'll sort of be forced into these. That is one mechanism for kind of forcing things into separate species. So the thing that has. So Darwin, for example, sort of thought that somehow this natural selection process implies the creation of more and more complicated organisms. He didn't know how he Thought that there would be kind of a law of nature that just says it's an inevitable consequence of natural selection that you get more and more complicated organisms. In the 150 years since that time, nobody ever figured out definitively why that would be true. And so I've sort of been interested in that question. And the thing that I was looking at, I'd looked at it, like 40 years ago and didn't really make much progress. And then suddenly a couple of months ago, was working on a quite different project and realized that one could make progress on this. It's more fun if I show pictures, but I'm not going to do that here. You can look in the piece that I wrote. It has lots and lots of really cool, I thought, pictures. But the main point is we're looking at very simple computational programs, things where you just say, I've got a line of cells. Each one is white, red, or blue. And then I've got steps where I'm saying, this cell gets updated to be this color because it had a blue cell on one side and a red cell on the other, and it was white or something. And you just follow those rules. And they're not very many different cases that you have to specify to say what's going to happen in the red, red, blue case and the red, white, blue case and the blue, white case and so on. There are a bunch of different cases for three colors. There are 27 different cases that you have to specify what happens in each of those cases. So as my kind of approximation to mutation of genetic programs, it was like, well, just change one of those different cases, change the outcome in one of those cases. And so you start off doing that, and then you say, well, what's the criterion for whether it's a successful organism? Well, let's say the criterion is you started off from just one red cell at the beginning, then it makes a pattern, the pattern grows. And then let's say the pattern doesn't go on forever. It dies out, but only after a reasonably large number of steps, like, let's say 50 steps. So you say, well, make me a pattern that goes for as long as possible, but doesn't go forever. And from a particular program, then as you change that program, every time you make a little change in the program, you will end up with a different pattern. Sometimes those patterns will die out immediately. Sometimes those patterns will live forever, and sometimes those patterns will live for a limited time and then die out. So let's say that you say, well, I want the rules to Be such that the pattern lives for a bit longer, or at least no shorter than it did before, then I'll keep it. Otherwise, I'll reject it. I'll say it's selected out. Okay? So the surprise is if you do that, you can successfully, over the course of thousands of generations, effectively thousands of different mutation steps, you can end up with something where you have progressively longer lifetimes. And when you look at those longer lifetimes, you realize it went from lifetime 2 to lifetime 10 to lifetime 50 to lifetime 300 and so on. You look at the patterns that were actually produced in generating those longer lifetimes, and it's like, well, it had an idea for how to generate that pattern. Oh, it has this streamer that goes out in one direction, Then comes back, and it fills it in with a color and this and that and the other. And it does that a few times, and then they build up and then they die out. And you see, it kind of. It looks as if it had an idea for how to live a long time. It used that idea and, as you said, go make more mutations. And it was kind of figuring out, in some sense how to use that idea, how to build on that idea to live progressively longer until it eventually could live for a thousand steps or something. And the patterns you get are very complicated that live for a thousand steps and then die out. And it's very reminiscent of what you see in the fossil record, where you see organisms that lived 300 million years ago. And they're kind of simple, but they kind of have the beginnings of the idea of an eye, and then later on, they have more sophisticated eyes, or they have the beginnings of the idea of legs, and then they have more sophisticated legs and so on. It very much looks like the same kind of phenomenon happening. Of as you push the thing in the case that I was looking at to live longer, it has more and more elaborate mechanisms to let it be able to do that. So that's very reminiscent of what we see in actual biological evolution, where things seem to get more complicated, to achieve more. And by the way, what happens in this very simple model Is something just like the formation of species in the sense that there'll be a sort of a progression of mutations that discover how to live long by one method, and then a different set of mutations that build up a different way of living a long time. And so you get this kind of branching of these different cases that sort of reminiscent of the branching of the tree of life into the different kinds of cartilaginous fishes versus insects. Versus this versus that. So that's sort of the. What is not obvious is that you can take these rather simple rules and get them to successfully achieve the objective of, for example, living a long time before dying. It's not obvious that would work. And if you said, I'm going to sit down as an engineer and I'm going to design a rule that will work in this way, you will not succeed. The things, the inventions that are come up with are things that are very ornate and very kind of, oh, it just happens to work that way. Lots of pieces have to come together to make that work. They're not things that you would, by systematically saying, let me put in this piece, this piece, this piece, you would end up being able to make work. So I consider that an interesting way of understanding the phenomenon of biological evolution. The phenomenon that if you put enough effort and you try enough different, make enough different, try enough different things in this sort of progressive way, you can achieve a lot. Now there's sort of the question of, why does this work? Why can you go on and get to one place where you've achieved part of the objective and then you say, well, I'm going to tweak it some more, I'm going to change the program a little bit more. Then you get closer to the objective and so on. Why doesn't that process get stuck? Why is it the case if you imagine you're going over a mountainscape and you're trying to reach the know, the deepest valley or the highest peak or whatever, and you say, I'm always going to keep going up to reach the highest peak. Well, you could be on a local peak and it could be like, well, you can see the other peak, but you can't get to it because you'd have to go down before you went up. And in the case of our sort of models of biology, the going down would mean unsuccessful organisms which die out. So you'd never make it to the big peak. And so if you think about it in terms of mountains, you'd just say, you get stuck. You get stuck on a local peak, you'd never make it to the biggest peak. The thing that is wrong with that intuition, there are two things that end up being wrong with that intuition. The first thing that's wrong is when we think about mountains, we're moving around in two dimensions. We're going north, we're going west, whatever we're moving and we're saying, do we get to the higher mountain? In the case of these systems, we're looking at space that is hundreds of dimensional, thousands of dimensional, millions of dimensional. So instead of just being you can go north or south, east or west, there are a thousand different directions you can go that are all sort of moving around in this space of where you're at and what level of fitness of organism you can get to. So the thing to realize it's a bit unintuitive, is that when you're in a high dimensional space, you are not this thing about, oh, you get stuck on a local peak, there's much more likely to be a way down. In Dimension 300, there's a path that leads to the bigger peak, even though that didn't exist in Dimension 37 or Dimension 20 or whatever else. That's the first thing. The second thing is that there is a certain degree of randomness in the kind of fitness landscape. And that randomness is a consequence of the kind of computational character of these systems and probably a biology as well, that there's sort of an inevitable randomness. So as you are at a particular point in this landscape and you look around, it's kind of like things are kind of random as you look around you, it's not the case that everything is very organized and you've just got these walls and you're stuck in these walls, they're sort of random. And there are enough different directions you can go that between the randomness and the many different directions, there's sort of always a path up. And that I think is sort of why biological evolution works. And by the way, it's sort of a same problem when you do machine learning. You're trying to get some system to perform a particular function, to recognize, this is a cat, this is a dog, whatever else. And what you're doing is you're taking a system that is made, in that case with artificial neural nets or whatever else, where you've got all these numbers that specify how the system should behave. And you keep on trying to tweak these numbers to make the system do better. And it's again, not obvious that you can tweak that given that you are partially successful, that tweaking from partial success leads to better success. But the things that lead to the success of biological evolution, I think are the same as the things that have led to modern recent success in machine learning. And sort of the big intuitive surprise there is, you have to do a lot of work, you might have to do a trillion tests to find something that works better. It's not like, oh, we've done five possibilities, none of Them work better, we're done. It might be. It might be millions, billions of different things you have to do to find the thing that does better, so to speak. And in biology, I mentioned there are probably about 10 to the 40th organisms that have ever lived. That's a lot of organisms. That's a lot of things to try. And that's sort of, in a sense, why it's been possible to find things, even though there was sort of a narrow path to do it. But you didn't. There was a way to get there. It wasn't like you were completely blocked. And by the way, if you say, well, why don't you just try every program? I've done that a lot on computers. The problem is that the. Every program would be unbelievably much more. 10 to the 40th is kind of. Well, there are probably about 10 to the 80th atoms in the universe, for example. So 10 to the 40th is big. I mean, it's like, oh, I don't know. In the sun, there are about 10 to the 57 nuclei, mostly protons. And it gives some sense in a human, there are about 10 to the 26 molecules, roughly on the order of 10 to the 26th, 20 to the 27 atoms or something. It gives some sense of how many of these things there are. But if you said, well, what is the number of possible. Let's imagine that you were just looking at, oh, I don't know, a thing, where there are, let's say, 10 possible cases in the rule, and each one of those cases has 10 possibilities. Well, that right there is 10 billion possible arrangements. And when you say, and as you increase the number of, of essentially pieces to the genetic program, that increases exponentially, incredibly rapidly, and it's vastly, vastly larger than the number of organisms that ever lived, and so on and so on and so on. So this idea that you can kind of search around and find good situations, if you were really having to try every single possibility, you'd never get there. The surprise is that you don't have to try every possibility. You can go on this path where you're getting sort of partial success and then improving on that, and that that works. And that's sort of the surprise of biological evolution, that that works. And the second surprise is that in doing so, as you get to things that are more and more successful, that you end up building these more and more elaborate programs more and more elaborate. And they're not more elaborate programs, they're just more elaborate behaviors of Programs to achieve that success. There's a question here from Hula, what is convergent evolution? So convergent evolution is when sort of two different lines of evolution led to different kinds of organisms, but they both had the same idea about something. So, for example, wings might be a thing that I don't remember the evolutionary history well enough to know this, but it could be the case that wings for insects work in one way, wings for birds work in another, wings for mammals work in yet another, and that some of those inventions were separate but ended up with the same basic idea. And you see that quite often. For example, I know for eyes, our eyes evolved on a sort of separate branch from the eyes of various kinds of deep sea critters, like squids and so on. And you can kind of get a big clue that they evolved separately because their actual architecture is a bit different. They still have the same idea of you've got this thing that has light coming into it, and you have these molecules that turn the presence of light into an electrical signal that excites nerve cells and so on. That's the same idea, but the detailed architecture of how the thing is set up and where the different layers are is different. And that is a consequence of the fact that those two ideas got discovered separately, by the way, in these simple models that I have of biological evolution. You absolutely see this kind of convergent evolution stuff going on where the same idea kind of develops from two different kind of antecedents, so to speak. The yes, Harry is commenting. This is sort of different genotypes coming to the same phenotype. So the idea is the program underneath is the genotype, the genetic sequence. The thing you see, the actual constructed organism is what's called the phenotype. And so what one's saying is that in evolution, the genotype is what's mutating, the phenotype is what's being selected for. So there's kind of this computational gap between the program and the thing that got created from the program. And that leads to all kinds of interesting phenomena that have not been easy to understand without sort of the kind of foundational ideas about computation that, for example, I've been working on for a long time. And let's see, Let's see, Brady is commenting for suggested another experiment that could be done based on what I did in this piece that I wrote about biological evolution. Yeah, I mean, there's all kinds of cool experiments you can do about what kind of evolution you can achieve, what kinds of things these critters can learn to do. Effectively if you say select for this effect. So for example, I was selecting ones for ones that have the ratio of the maximum width that they achieve in their patterns to the maximum Height will be 3 to 1 or PI to 1. I tried both of those. And you can try all kinds of different things. And what you see is all kinds of different ways in which these rules, these toy organisms achieve their objectives. And the thing that's most striking to me is if you say, well, I think I know how it's going to do that. No, it will do it some other clever way that you never guessed it would do. And sometimes it's like kind of sticking out its tongue at you, so to speak, because it found a really simple way to achieve the objective you want to achieve. Like, for example, I wanted it to make a 3 to 1 ratio of height to width. And well, it managed to do that by just having a pattern that was a red cell, a blue cell, a white cell. And then it died out. And it's like, yep, that made three to one. I didn't think of that. It's kind of a trivial way. It wasn't what I was sort of hoping for. And so it was. So it outsmarted me in that particular case by doing something very simple, but in other cases by doing something very complicated where it's like, I had no idea that you could fit those pieces together to do that. Let's see. Peter asks, do you think life existed before it did on Earth? Oh, yeah, that's an interesting question. If you don't know how something originated, a kind of a little bit of a wimp out is to say, well, this wasn't really the origin. There was really another thing that was the origin of what we thought was the origin. An origin of the origin of what we thought was the origin. And you're kind of just running it backwards. So let's say life didn't originate on Earth. Let's say that life was delivered to Earth by some meteorite that delivered, you know, the first replicating organisms, self replicating organism to Earth and it then sort of took off from there and we were seeded, so to speak, by something from elsewhere in the universe, let's say. Well, then we could ask the question, well, okay, how did life originate on the thing we were seeded from? And you've got the same question again. Let's hope life originated on Earth because we have a much better scientific chance to figure out how it originated here than if it turns out we discovered it originated on a star far, far away. Where we don't get to visit the planet, at least anytime soon, and we have much less direct information. So the question of whether sort of life is how unique life is. It depends on how we define life, that there are complicated physical and chemical processes going on. For sure, that will happen. Even things that sort of replicate themselves are not too hard to find. I mean, for example, famous example is a flame. A flame. You have a flame that's burning here, and by golly, it will make something else burn. It will turn some other material into something that's a copy of the flame. Or we've certainly seen in computers the idea of computer viruses, malware, all these kinds of things where you have a program running on one computer and it makes a copy of itself, many copies on one computer, it starts spreading over the network to other computers. It's doing the whole thing that biological evolution tends to do. It is surviving by replicating more copies of itself. And even as people try and squash it in this way, it mutates, it sort of escapes that, and it manages to do something different. So this question of. So, I mean, there's this sort of question of how do we define life? And so on. And if we, for example, if we found on some, oh, I don't know, maybe on Mars, on the ice caps of Mars, maybe it'll be, you know, the oceans of Enceladus, I think, is one that. I mean, there are a variety of outer planet moons that have different kinds of oceans under sheets of ice and things like this where the environment could be a little bit similar to the environment on Earth. Similar enough that the physics and chemistry of life on Earth could be potentially adapted to those environments. Well, and let's say we find a critter that is sort of alive in the same way that things are alive on Earth and it has the same RNA and it has the same proteins and so on. And you say, well, was that sort of an example of convergent evolution, where this is the only way life can be, or was that something where one thing seeded the other? I would say there will be overwhelming expectation that one thing seeded the other. The chance that these particular molecular structures are the only way to make something that replicates itself in a sort of lifelike. I think that's just no way that that's the case. So. But this question of whether there's sort of whether one can transport life from one planet to another, for sure one can on meteorites and things like that, whether the chance of, you know, the meteorite that came from this planet managed to get to that planet, and the little spores that were on that meteorite survived, and the meteorite happened to land in a place where they could take root and, and start replicating. Who knows whether that chain of circumstances ever actually happened or whether the probabilities were just low enough that it just like never happened. So, but I think this idea, often called panspermia, the idea that sort of there's life suffusing through the universe, there's life kind of being transported throughout the universe and kind of seeding planets hither and thither, I don't know, I'm not optimistic that that's a correct theory, but I don't think one can rule that out. And then of course, the question would be, if that's a correct theory and everything in all these different planets got seeded by the same life, how come there aren't? How inevitable is the evolutionary path? How inevitable is the things I've been saying about how you make more and more sophisticated organisms? And is it inevitable that on those million other planets that got seeded by the same panspermia seeding mechanism that, you know, did those million other planets all just get microorganisms and we're the only one where we were sort of crazy enough to make humans who send out spacecraft and so on. It's, you know, it's a long term mystery sort of why there aren't more sort of intelligent life things out there like us. I think that the biological evolution part is probably not the part to look at for why that hasn't happened. I think rather, and this is a long discussion, but rather my feeling is that the notion of sort of intelligence in the universe, as soon as you're more broad in your definition of what counts as intelligence, you've got things like the weather having a mind of its own and all kinds of things like this. And you realize that what we're really asking is how close is this sort of intellectual stuff in the universe? How close are the other minds in the universe to the, to our human minds? And are they close enough that we can kind of rep, that we can recognize them as minds, just as one human might recognize another human as having a mind, so to speak, are the things out there close enough, we wonder, you know, do cats and dogs have minds? Are they, how similar are they to humans and so on? I think I've talked about this at some length before. Let's see, there's a question here about what is the importance of biodiversity and ecosystems in biological evolution? You know, I had always Thought that you had to have sort of the competition between organisms to really have anything that was at all realistic for biological evolution. The model that I was just working on really just says, you're an organism. It's you against this general problem of, for example, how do you live longer? It's not you battling the other organism. You know, is there a more beautiful peacock? Is there a more successful, you know, woodpecker that can peck deeper or something? You know, it's. It's that it isn't so much a story of the competition between organisms as it is something that you can at least understand in its simplest form as a kind of a competition against nature, so to speak. There's a whole separate question of to what extent. I mean, this sort of segues into all kinds of ethics questions and so on. But there's this question of does it matter that there are lots of organisms, lots of different organisms? Does that matter to the production of the new great organism? Well, I don't think it's particularly clear. I think that it is the case that organisms do leverage what other organisms do. And ecosystems tend to be. In a sense, what we're dealing with is sort of a super organism of the whole ecosystem. The whole thing is evolving. And just like in us, we've got all these different types of cells, and between. The previous primates and us, there are probably particular kinds of cells, like certain kinds of nerve cells, for example, that might have changed their character since a couple of million years ago in biological evolution. But that doesn't mean that everything. We still have two legs, two arms and so on, just like a lot of our primate ancestors, two eyes, all those kinds of things. And a lot of those things work incredibly similar to the way that they do in our biological ancestors, so to speak. So there's sort of local innovation in particular types of cells and things like that, while the whole body plan and all that kind of thing doesn't really innovate very much. And I think it's probably the same with ecosystems that there can be sort of local evolution of, oh, this organism is like this amazing, you know, red and white striped organism and so on that has never been seen before. But most of the beetles and microorganisms and so on in the ecosystem are just the same as they were before. It's sort of the super evolution of the superorganism that is the whole ecosystem, and it is a feature of ecosystems, just as it's a feature of individual organisms that some cells die, some organisms die out, some species die out. It is sort of, there's an ongoing rhythm of sort of change that is sort of the natural way it works now, you know, you can say, well, let's change the change. And then we don't necessarily know what's going to happen. So, for example, if we say, even if this organism had a really, really hard time surviving to adulthood, we're going to give medical interventions to let it survive. So if it had traits that were really losing, traits that were things that caused it to really expect to die very quickly, but we kind of intervened to prevent that happening. We're changing the course of biological evolution. What biological evolution would have done is to select out those traits that cause the organism to die quickly and only the mutations to that organism that didn't have those bad traits, they would be the things that would survive and be propagated. And I think that's, you know, if we change that, then we're changing what happens now. Similarly, if we change the environment, we're changing the kind of criteria for are you a fit organism or not. Famous example, there was a kind of moth that had been sort of a whitish color and that was a good camouflage color on some bark of some kind of trees. And subsequently, as a result of industrial pollution, lots of the trees turned darker in color. And so did the surviving moths. As you know, the children of the children of the children, children of the moths. Every time there was a darker moth, it had a better chance to survive. So over the course of generations, the moths on average got darker and darker. That's sort of a famous example where sort of human intervention, so to speak, caused something. The fitness to tip in a different way in the natural environment and to lead to a different outcome. I think there's sort of a question of if you say, gosh, if you take out that species, we're toast. We'll never be able to evolve. The better, you know, the better bird or something. I think one would be hard pressed to make such a claim. And I think that sometimes one of the things to realize is that biological evolution is a brutal business and it's all about organisms dying and it's all about things sort of failing and being reborn and so on. And so though one may not like sort of ethically those things happening, but they are probably, they are the things that have to happen in order for biological evolution to make progress. And at least in many cases. And so when you say, well, you know, we're having an effect, we're building a city, we're doing this and that, and the Other you are changing the set of fitness criteria. Just like if the sun suddenly turned purple or something, we would change the criteria for success for organisms on the Earth, we're changing the criteria for success. Do we end up with a better set of species? Is it the case that the ones that are, you know, that have to survive in an urban environment, in a city or something, are ones that maybe there'll be some great discovery made by biological evolution that is the amazing kind of space faring type of bat or something that was only evolved because of the fact that it had to survive in a city with trains going by or something like this. So it's hard to know the consequences of these things. And the, I mean one has the general feeling that, I mean, I think from a general. How does one feel about it? I would say don't let those species die out. They're part of the great heritage of what's been achieved by all of the processes and computation and so on of life on Earth. It would be a terrible thing to have those species die out. But can I justify that on the basis of what will be the future of biological evolution? I doubt it. But in a sense, in the end, a lot of ethics is about how humans feel about things. And I suppose one of the things that I know, maybe a person like me who is into kind of creating information and so on, is one who's going to say, don't destroy that stuff. Don't let the endangered human languages die out. Don't let the endangered biological organisms die out. But that's much more of a. Can I justify that? Well, it depends on what one's trying to achieve. If one says, will we have the better organism? Will we have the successor to humans emerge as an organism that evolves from the birds or something? Will that. And then we have to ask, well, is that really what we want? I mean, let's say we knew that by doing this and this and this and preserving this interesting ethical question, preserving this line of development in. Oh, I don't know, let's pick a, pick something in, in tigers that, you know, in another million years there will be tigers who were smarter than the humans. What would we do under those circumstances? Would we say help the tigers, let's get more tigers, let's help them achieve their best objectives. Even though we know that at some time in the future the tigers will become more powerful than the humans and they'll just eat all the humans and that will be the surviving species, so to speak. What would we do under those circumstances? And I think many people would say, wait a minute, stop the tigers. You know, the humans are in charge. We get to say that. Other people would say, look, if the tigers have better potential than us humans just, you know, give everything over to the tigers, so to speak. I think it's a complicated issue. I think that, and this is, you know, typical of kind of ethical issues that there's no right answer, so to speak. If you have certain ground rules, like you say, one of the ground rules is the species shouldn't die out. Anything that makes the species die out is bad. Well, given that ground rule, you can work backwards and say don't let the tigers prosper type thing in that scenario. But it's, you know, it's difficult and you have to kind of. It's not. There's no obvious right answer. Let's see. I think I need to go soon. But let me see if I can address a couple of other. As comments here about, about life. Follow the water. Yeah, I mean water is a very special molecule. H2O is just has a lot of very special properties that are super useful for making life in the form that we have it. Whether one can imagine something just like life, that this functionally like life, whatever that means, has self replication, can mutate, can do this and that and the other without water, I'm sure it's possible. I am certain my life studying simple programs and what they do. If it's taught me one thing, it's taught me that given certain components, you'll never be able to foresee how those components can be put together to do things. They will always surprise you with kind of the, this, this sort of the components are being a sort of the that that you, you won't be able to foresee if you say I can't imagine a way this can work without water. Yeah, you may not be able to imagine it, but that absolutely doesn't mean it doesn't exist. And you know, many, many times I have thought, even recently when I was working on this piece about biological evolution, I thought, gosh, these programs, they're too simple. They'll never be able to do this. And then you actually try it and it's like, oh, I guess it can do that. I didn't think of that. Happens to me all the time. Even though I've been working on, working on these things for a long time. Hid asks, did microorganisms have teachers? Who is the Einstein of microorganisms? That's a good question. Whether microorganisms kind of what Learning there is in microorganisms, most of the quotes, learning is from natural selection. It's just like kind of you did the wrong thing, you and your progeny died out. And rather than learning with a brain where you have a memory that lasts for the lifetime of the organism, in sort of the earlier form of memory is, in the genetic program is the actual sequence of DNA that determines what, what you would get in what, what that, that's, you know, that, that determines what happens to the organism. The big innovation when organisms started having brains was the idea that you could remember things in your brain. And then the super big innovation for our species was and then we invent language that allows us to package up the things that we as individual organisms remember and go yak, yak, yak, and pass on those ideas, hopefully to other organisms that can then pass them on again and to allow kind of the ideas to kind of evolve and be passed on in kind of the way that in the past it was only genetic information that was being passed on, now we get to pass on ideas. That's in a sense the big thing of our species is being able to do that for abstract ideas. Now, I don't know how birds teach little birds how to fly, how beavers teach little beavers how to build dams, how there is presumably some communication and that there's some indication that there's communication of sort of how do you train the next generation about something? Some of these things are like the horse is born and immediately gets on its legs and can walk. That's something which is sort of a burnt in genetic feature. Whereas, and we humans, for example, have a long period when we can't do much, so to speak. And we in a sense have to get taught almost everything. It's kind of more of a blank slate than most organisms. We don't know how to walk without we have to be taught how to walk. We have to be sort of given examples to learn how to talk all those kinds of things. In a sense, perhaps one of our other achievements as a species is the fact that we do have flexibility because we are learning as an organism just with our brains, lots of kinds of things. They weren't sort of built in features where just by instinct, so to speak, we have to be able to do this. Rather it's something where we get to learn how to do it and so we can learn it in a different way. And so we can like learn different languages, we can learn different sort of things where, you know, one kid who grew up in the jungle or something is going to be really good at recognizing certain kinds of natural phenomena. The kid who grew up in an urban jungle is going to be really good at recognizing certain things about what happens in cities and so on, and those. And those things, you know, a lot of those things. It's a lot easier to learn when one's really young. Although I have to say, one of the things that's happened in recent decades is that as we've learned more about learning, I think it has become easier for us to know how to learn, even though we're not so super young. I mean, whether that's learning languages and being able to sort of visualize what you're saying and being able to sort of learn a better accent, so to speak, which is something easier if you're very young, but is something where as we learn more about how to learn, it becomes easier to learn even when the sort of the advantage of youth isn't there in the effort to learn. Let's see, just. I'm going to maybe end with one other question I saw here. Question from a kid from Harry here. If you put a lot of laser in one spot, would that create matter? Okay. The answer is no, but it's pretty subtle. Okay, so what is a laser? A laser is something that has kind of a concentrated lump or beam of light. And, well, what's actually happening in a laser light? You can think of light in different ways, but you can think of light as being a big stream of photons, little particles of light. And, you know, the light that I'm seeing right now is trillions and trillions and trillions of photons. So at any moment there'll be, oh, in a bright room, there might be a trillion photons that enter my eye every second and that I'm seeing that are causing me to be able to see what I see. So in a laser, what's happening is you're getting just huge numbers of photons all set up to all be just sort of in a blob doing exactly the same thing. So, for example, all the photons will be exactly. They'll make the same color of light. They'll be going in the same direction. They'll make a beam where they're all going in one direction. Okay, so you can have a laser. What happens in a laser is, well, you're just putting in more and more and more photons. And the way photons are set at work, photons really like to be doing the same thing as other photons. And so as you pour more photons in, they'll all kind of be wanting to form this beam together. And so what you end up with in a laser is very, very bright, lots of photons doing the same thing. And that can be. And so it can be a bright enough beam of light that even though you're shining it all the way to the moon, you'll still be able to get that light all the way to the moon. Photons along the way, some photon will hit an atom in a gas and it will get sort of thrown out of the beam and so on. But there'll be enough photons in this beam, enough intensity in this beam, that there'll be some of it that survives all the way to the moon and. And may be reflected back. The beam won't stay. It so happens that the details of how lasers work, that roughly, if you see a laser that you just have a little laser pointer or something, you're shining it across the room, It'll make a very small spot on the other side of the room. But the beam of photons, they more or less stay going in the same direction. The spot more or less stays the same size as you shine it further away, but they get a little bit further apart. And by the time you got to the moon or something, it'll be a couple of miles across, even if you started with just a very, very tiny, very intense spot. Okay, so you can have lots and lots of photons, very high intensity. Can you make matter from that? What is matter? Matter is things like electrons and protons and atoms and all those kinds of things as distinct from photons, which are what light is, is different from matter. Matter is the stuff that we can pick up, the stuff that makes the air. All of the things. Matter is ultimately made of atoms and molecules, and the atoms are made of things like protons and electrons and so on. So the question is, can you make those things out of light? Well, it's a bit of a subtle thing, because here's the story. The story is you can. You can make matter from photons, but the photons that exist in ordinary lasers don't have enough energy to make matter. So here's roughly how it works. So a photon, every photon of, let's say, light that is like red light, particular type of, you know, particular color of red, that photon is the same as every other photon that is a piece of red light. The only difference between those different photons is what direction they're going in. They'll go at the same speed, the speed of light. They're all Basically identical. Every photon that is a particular shade of red is identical other than what direction it's going in. Okay, but if we have a blue photon, photon of blue light, it's different from a photon of red light. And there are different kinds of photons that those photons, red light, blue light, and so on, they're distinguished by the energy of the photon. Each photon has a certain amount of energy. So, for example, we know about if you have a ball, you have 10 identical balls, and one of them you throw faster than another. Well, the ball that you're throwing faster has more energy, kinetic energy, than the ball that you throw slower. They're the same ball, same, they weigh the same, and so on. But one of them, you throw it faster, it has more energy. For photons, the notion of energy is a bit more subtle because all photons go at the speed of light. They have no mass, they go at the speed of light, but they have energy. And different photons can have different amounts of energy. What is that energy, so to speak? Well, that's. For that, you have to kind of drill into a fundamental theory of physics, which I think we now finally have. But that's a subtle question. What sort of fundamentally is the energy? But you can just say different photons, like red photons, blue photons, they have different energies. And the energy works in a bit of a different way for photons than it does for things like balls, because all the photons go at the same speed. So you're packing energy in, which is just something independent of the speed that the thing is going at. Okay, so the next thing to say is there are different kinds of photons. So there are. There are blue photons, red photons, There are photons of infrared light. There are photons that are radio in radio waves. There are photons that make X rays, there are photons that make gamma rays. All these different photons, the only thing that's different between them is that the energy of the photon is different. So, for example, visible light, there's a certain energy of each photon depending on whether it's red, blue, whatever else. Infrared, it's slightly lower energy. Radio, it's even lower energy. And so on. On the other side, you go to X rays, ultraviolet light, and then X rays. The photons have a higher energy. Okay, so, and you can make a photon which have any energy you want in our universe. Maybe there's a limit, but there are some very high energy photons knocking around our universe, produced by matter falling into black holes and being sped up and Emitting very high energy photons, things like this. There are places where there are photons that are high energy, which means they're not photons of light, they're not photons. They are photons that of X ray photons or gamma ray photons and so on, have higher energy. By the way, we can ask the question, can you make a laser for X rays? And the answer is, well, kind of. The X ray lasers are a story that in the 1980s 90s there was a lot of discussion about weapons based on X ray lasers. And it's very difficult to make an X ray laser. Probably one way to do it is to have a nuclear explosion and to take the energy from the nuclear explosion and concentrate it to make these X rays form something like a laser. So it's very exotic. It's not like the kind of laser that you have in a laser pointer for visible light. But so you can imagine making lasers for these very high energy photons, but it's really difficult to make those lasers. But what's special about these high energy photons? Okay, so, gosh, this is more difficult to explain than I thought. The so matter like electrons and so on. What's the relationship between that and things like photons? Well, here's the thing. Electrons, once you have an electron just sits there. I mean the electron can be attracted to something, it'll be pulled into an atom, things like this. But fundamentally an electron is a stable thing. So is a proton. People looked for, do protons decay? Do they sort of self destruct? And if they do, it takes more than 10 to the 31 years. The lifetime of the universe is about 4 times 10, is around 1.5 times 10 to the 10 years. And so the lifetime of a proton, if a proton does decay, it takes a lot longer than the lifetime of the universe to do that probably. Who knows, maybe it's completely stable. Okay, so a proton left to its own device would just stay as a proton electron. Same way there are. Okay, this is where it gets tricky. When you have an electron, there is also an anti electron. An electron is a particle, just sits there. It's very tiny. We don't know how big it is. Electrons seem to be of zero size in our theories of physics. They actually have some, some tiny, tiny size protons. We know how big they are. They're about a million billionth of a meter across. And, but, but they. Okay, so proton is what it is, is what it is. There are also antiprotons. There are protons that are the same as they're things that are the same as protons, but they have an electric charge that's the opposite of the electric charge of a proton. Okay, so you have antiprotons, anti electrons. They're called positrons. Those are examples of antimatter. And one of the things about antimatter is that you can take a proton and an antiproton, and if they crash into each other, they can produce. They can annihilate each other. The proton, the antiproton can turn into a pure collection of photons. They can turn into other things as well. But one of the things that they can turn into a proton and antiproton can annihilate into photons. And those photons will typically be pretty high energy photons because the proton and the antiproton, the very mass of the proton and the antiproton represents a certain amount of energy. And that energy is then transferred to the photons that get produced. So when proton and antiproton annihilate, they produce a bunch of. They can produce high energy photons. Okay, so then the interesting fact is you can run that in reverse. So instead of the proton, the antiproton annihilating into photons, or the electron, the antielectron, called the positron, annihilating into photons, instead of it going electron and positron goes to photons. The reverse also can happen. Photons can come together to produce an electron and a positron, or a proton and antiproton. But in order to do that, you need very high energy photons. You need photons whose energy is high enough that it basically has enough energy to produce the mass of the electron or of the proton. So famous formula from the history of physics, E equals MC squared, energy equals mass times the speed of light squared. That formula tells one kind of how much energy corresponds to a certain amount of mass. And the fact that you can sort of convert between mass and energy is a fundamental fact in physics. It's what allows one to get energy from nuclear reactions. It's what allows the sun to operate. It allows many different kinds of things. But one of the things it means is that that there is a sort of conversion between mass and energy. And so in this case, we used to have proton and antiproton. They annihilate into photons. Those photons have energy that corresponds to the mass of the protons. That is where you're taking that energy. Because total energy, it's sort of a rule of physics more or less true, at least as far as physics on the Earth is concerned that energy is conserved. When you have a certain amount of energy, you will end up with the same amount of energy. Now, energy can be converted from the energy of motion of a ball rolling or something to heat, which is also a form of energy. So that energy of actual organized motion can be converted into energy associated with heat. But nevertheless, there's a sense in which the total energy is conserved. That's true for everything on Earth. When we look at things about the universe as a whole, energy conservation is a bit more complicated. But for things at this level, energy is conserved. And so that means that if we have this proton and the antiproton that are packing a certain amount of energy because of E equals m C squared, then that energy ends up with the photons that they annihilate into. Well, again, we run it in reverse. Photons come together to have with enough energy that they can make electrons and positrons. They can make a proton and an antiproton. And so that's actually observed. You can have photon photon scattering. People have done these experiments where you have very high energy photons. They come together and they make an electron and a positron. It's not been done with protons and antiprotons, not with photon photon scattering, but we know it would work in principle. So with sufficiently high energy photons, you can make electrons and positrons. In other words, you can make matters. But whenever you're making matter from photons, you're always making the matter and the antimatter together. Now, those two things may separate out. So you may be able to get your bottle of matter and your bottle of antimatter, and they may live happily ever after. If the matter and the antimatter ever come together, they will interact and potentially annihilate each other. But you can go from high energy photons to matter. And it happens in photon, photon scattering, where two photons, two beams of intense. Well, it's kind of gamma rays. The beams cross and you get electrons coming out. And so that's a way in which you can get sort of intense. You can get the creation of matter from pure radiation, from pure sort of photon stuff, from pure light, like stuff. Okay. But the reason that doesn't work for a laser is that lasers, for visible light, those photons just don't have enough energy. You can have tons and tons of photons, gazillion photons, but each individual photon does not have enough energy. And the way it works is you have to have those individual photons have to come Together to make the electron the positron. And that's not possible for photons that have the energy of visible light. It's only possible for photons that have vastly higher energies. Sufficient these gamma ray photons sufficiently much energy that their energy can be used to create the mass of an electron and a positron. And by the way, that process happens in the early universe when the universe was very hot. That process was happening all the time. Photons were turning into electrons and positrons. Sort of. All the matter that we have today was ultimately made in that way. It was made from things like photons and photons interacting to make matters and also antimatter. For reasons that are only partly understood, There was a slight excess of matter over antimatter produced in the early universe, which is why matter is here now. It didn't all annihilate with antimatter. But that's kind of the idea is that you can have intensity of light, which is just a count of the number of photons. But in order to make matter, you have to have photons that have a certain energy and individual photons with a certain energy. Okay, so now you could ask if you were being difficult or something, or you could ask, why can you not take all those photons in a laser? Let's say you have a laser that has a total, oh, I don't know, a thousand watts of power or many a million joules of energy in a pulse and a laser pulse. Why can't you take all that energy in a laser pulse and somehow organize it to all contribute to making matter? How come the only, you know, I'm saying the individual photons don't have enough energy to make matter. But together, those photons, those trillions, you know, zillions of photons, together, they all together have enough energy. Okay, so why is it the case that you can't have the photons sort of work together to make matter? That's fairly subtle. The reason you can't do that, you don't do that is that photons don't interact much with photons. Photons are when there's an electric charge, like an electron has an electric charge, it interacts with photons. Light just like, oh, I don't know, in a radio, for example, it's. You're wiggling photon, wiggling electrons up and down by having voltage in a wire, and it's moving the electrical current up and down. And that wiggling is making those electrons emit photons that correspond to the radio waves you're generating. So there is an interaction between individual electrons and individual photons. It's the theory of quantum electrodynamics is the theory that describes the interaction of individual electrons with individual photons. Okay, so there's an electron which has an electric charge. As that electric charge makes it sort of have an effect on a photon. But photons don't have an electric charge. So photons, when two photons pass by each other, they just pass by. They don't interact. There's in a. In, to a very good approximation, photons are just completely. You can have, you can throw like in a laser, you can throw more and more and more photons in. There's an effect having to do with sort of the way that sort of the counting of photons works, that causes photons to effectively like to all be in the same state. But that's not by virtue of them actually hitting each other and interacting. That's by virtue of a different kind of effect that has to do with quantum mechanics, but it has to do with sort of the way that you count photons and things. It's a little different. It's not to do with actual. Two photons crash into each other and something happens. So when two photons sort of run into each other, most of the time absolutely nothing happens. As I mentioned, if you have sufficiently high energy photons, occasionally they can make an electron positron pair. Even ordinary photons, like photons of light. There is a phenomenon, it's called light by light scattering. There is an incredibly tiny phenomenon that will allow photons even of ordinary light to interact with each other. They don't. They interact with each other actually by creating not a real electron or positron, they create a so called elect a virtual electron positron pair. And that particles that they don't really exist. They only virtually exist for some trillion trillionth of a second or something, and then they disappear again. That phenomenon is another phenomenon from quantum mechanics that actually I just realized a few days ago how that kind of a very how that phenomenon really works in our models of fundamental physics. But any case, that phenomenon of light by light scattering is incredibly rare. And it's generally photons just don't interact with each other. So and by the way, the rate of light by light scattering increases dramatically as you increase the energy of the photons. So for visible light I would have to try to work it out. But it's the math of it. I think it goes like the eighth power of the energy of the photons. So I think your average laser probably no two photons ever interact in this way. They just, even though there are zillions of photons, they just. It's such a rare process, it never really happens. So the reason. So that means that in the, in the details of how this works, one photon interacts with one electron. It does what it does. You. There just isn't a way to get a whole collection of photons to all sort of act together to produce. Let me think how to explain this. Well, I mean, I can say what the, what the official. Oh, gosh, Yeah, the. Okay. In quantum field theory, there's a. Yeah, here's the reason. Okay, there's a. This is. Every time there's a certain probability for a, for example, a photon to produce a virtual electron positron pair, every time it's going to do it, there's a certain low probability that that happens. By the time you needed to have enough sort of enough photons all contributing to something to make your matter be produced, the chance of that happening is unbelievably small because the chance of any single photon interacting with a single electron is fairly small. There's a constant, the so called fine structure constant, 1 over 137 roughly. That sort of gives you a sense of the strength of interaction between photons and electrons. And so sort of every time you have, oh, am I going to interact, am I not? There's some small chance of interacting. If you say, well, actually I need a million photons to all interact with this one electron, the chance of that happening is absolutely incredibly infinitesimal. So the chance that all the photons could sort of get together to sort of add in the energy to one virtual electron is where it needs to be added in to make it produce a real electron. Positron pair is just infinitesimally tiny and it will never happen. Probably hasn't happened in the history of the universe. So in the end, it's actually quite subtle. And I mean, to really understand how this works, you have to kind of dive into quantum field theory and so on and dive into these things called Feynman diagrams, which are kind of this kind of ways to represent particles interacting with each other. They're just diagrams that show sort of lines for the history of every particle and how they interact and so on. So I suppose the simple answer is in order to make matter, you have to have photons with enough energy to achieve. To get to the. Okay, I should have explained. Electrons have a certain mass. Protons have a mass 1800 times bigger. Electrons are kind of the lowest they're the lowest mass particles that have an electric charge. In order to make things from light, in order to have interaction with light, you have to have an electric charge. And so far as we know, and we have pretty good evidence of this, the lowest mass particles in the universe that have electric charge are electrons. Now, could anything lighter than that? Well, neutrinos have a lower mass, significantly lower mass, but they don't have an electric charge. Could there be particles that have an electric charge that have still lower mass? The answer is basically no, because if the such particles existed, they would have been produced in large numbers in the early universe, and we'd still be swimming in them today. So it's pretty much impossible that we know experimentally that there can't be particles with masses that have electric charges that are masses less than electrons. So we couldn't. There is no particle we could make from sort of by the process of photons interact with an electric charge. Okay, the other little footnote here is, well, might photons interact with things that don't have electric charges? Photons kind of exist because of electric charge. They are, in fancy terminology, they're the gauge particles of electric charge. They kind of exist. The way we can understand why they exist, they exist to kind of communicate the presence of electric charge across the universe, so to speak. But could photons have an interaction with some other kind of particle that would be a lighter kind of particle with lower mass, so that two photons could actually, even photons of light could produce the particle? Well, not in the most immediate sense. There are little particles, they're called axions, that are a hypothetical theoretical particle that might exist. I'm a little bit skeptical that they actually do exist. And they have some kinds of interactions with photons. So you might have a chance with those kinds of particles, but they're not matter in the ordinary sense. Because axions, if they exist, which I'm skeptical about, would be things that don't. They're not things that, you know, make. That you can make, you know, pieces of metal out of or something. They're not. They're not the same kind of thing. So long answer to what you know, I have to say that it's. I. I do enjoy these. These questions that seem like they're, you know, why can't you have a more intense laser and make matter from? That is a perfectly sensible question. And the answer is pretty subtle. And I think that's always something that in areas of science which one has reasonably deep understanding of, it's usually possible to unravel these obvious questions, so to speak, but it's sometimes quite challenging and, for example, that particular question, to kind of, to illuminate that question, as we just saw, we have to touch on a bunch of different areas of physics to see how that works. And there are even some places where sort of the, the explanation is, is really quite, quite elaborate. And, you know, I, I didn't fully describe how the quantum field theory story works from that, but, but to really get that, I think, think I can do it, but I think it, it goes fairly deep into, into talking about what's known about how the formal theory of quantum fields works. All right, I should wrap up there. Thanks for your questions, and I look forward to talking with you another time. Bye for now.