Science & Technology Q&A for Kids (and others) [Part 133]

Hi, everyone. Welcome to another episode of Science and Technology, Q and A for kids and others. And I see a variety of questions that have accumulated here. So let me try and take a few of these. There's a question here from Jimmy. Could we be inside a black hole? Can biological life survive inside a black hole? Well, so first of all, what is a black hole? A black hole is something where there's so much gravity that even light can't escape from that area. So what happens is, when you have the Earth, for example, if you shoot a rocket up from the Earth, if you don't shoot it up fast enough, the gravity of the Earth will just pull it back and it will cross, crash down on the Earth again. If you shoot it faster than 25,000 miles an hour up from the Earth, it will escape the gravity of the Earth. It goes fast enough, it has enough momentum that it can break away from the gravity of the Earth and just go off into space. Every different kind of object, depending on its mass and how big it is, will have a different escape velocity. So, for example, the sun has an escape velocity maybe 100,000 miles an hour. Our galaxy has an escape velocity of, I think, about a million miles an hour and so on. But what happens is, if there's enough mass in a small enough volume in a small enough sized object, the escape velocity eventually becomes higher than the speed of light. So that means, because it seems to be a fact about physics, there are some footnotes to this that come out of our. Our new models of physics. But basically, nothing gets to go faster than the speed of light. And so if you have something where the escape velocity is the speed of light or larger, that means that even light, even something which goes as fast as light can't escape. So that means that there's this region of space where anything that tries to get out or we sort of pull back in and can never escape. So, in particular, in a black hole, there's this thing called the event horizon, which is this place in space where it turns out that any light that originates inside the event horizon will always get pulled back inside and will never escape. And everything outside the event horizon can escape. And it was very confusing to people when black holes were first kind of thought about the equations that describe the structure of space time, the equations of general relativity that were invented in 1915 by Albert Einstein. Those equations kind of describe how mass and energy deform the structure of space time. And that deformation of the structure of space time is what leads to gravity. As soon as you kind of change the shape of space. You change kind of the shortest, the ways that things go on shortest paths. By deforming how those shortest paths go, it's deflecting how sort of objects move through space. And that's kind of has the effect of, is the thing that leads to the force of gravity. But in any case, those, the equations of general relativity implied that you could get these funny singularities, these funny sort of one over zero type things going on. And people were very confused. Actually, Robert Oppenheimer was one of the people involved with this in the 1930s to early 1940s, trying to sort of unravel what was really going on in these cases where there were These kind of 1/0 infinity type singularities in the sort of structure implied for space time. And people at first thought that when you have this event horizon, that if you were in a spacecraft that was kind of falling towards a black hole and you went through the event horizon, people sort of thought, oh, something terrible is going to happen at the event horizon. Turns out that's not true. Turns out you wouldn't even notice going through the event horizon. The only thing that would happen is that the signals you send out, you wouldn't know. You'd be waiting forever and ever for as you get close to the event horizon, a signal you send out is kind of pulled back a bit. So it takes longer to get out than you might expect. But eventually you might send some signal out to some other spacecraft or planet or whatever and eventually somebody might reply and you get, get the signal back. What happens as you go inside the event horizon is that the time for your signal to reach its destination becomes infinite. You'd never get an answer back. You wouldn't get, you wouldn't. Your signal would never, would never be able to reach the sort of the sender. But you wouldn't notice as you go through the event horizon. You wouldn't really notice anything bad happened. It would only be if you waited for signals to come that you'd sent out to come back. They wouldn't ever come back. So this question was, what's it like to be inside a black hole? Well, as you pass through the event horizon, nothing much happens. It's only kind of in the long view of history that you would realize you were now kind of nothing you said could ever be heard outside, so to speak. But then as you sort of, you're sort of falling into this black hole. Now there's a bit of an embarrassing feature about black holes which is the mathematical theory that describes Black holes kind of tells you how event horizons work and things like that. They don't really tell you much about what happens inside the event horizon. In fact, as far as the mathematics is concerned, it doesn't really matter if there's anything inside the event horizon. Well, pretty much anything inside the event horizon. In reality, a black hole is formed when a massive star collapses and is pulled by the force of its own gravity into this tiny area. And that produces enough kind of mass and a small enough volume that you get larger than speed of light escape velocity and you get a black hole. But so inside the event horizon of a black hole, you would normally, you would think in physically that what would happen is what the way it will be formed is that there's a collapsed star and there's all kinds of stuff from the collapsed star inside the event horizon. But because you can't find out what's happening inside the event horizon from outside the event horizon, because no information about what's inside can get out, you don't really know there's a collapsed star inside. You might know from the past that, oh yeah, we saw the star, it was collapsing. Now, now that must be what's inside this event horizon. But you can't know that from just seeing the event horizon of the black hole. So that's, that's sort of a. So in the mathematics of what goes on, the structure of the event horizon and all those kinds of things is quite independent of what's inside. It could be this, this, you know, there could be this whole civilization that's going on inside. They could be, they could have a whole, you know, it could be the thing that's this shape. It's that shape. It doesn't matter outside, it all just looks like this kind of sphere of event horizon. Well, it's even more bizarre than that because in the usual mathematical theory, there can just be vacuum inside the event horizon, with one exception. There has to be some kind of puncture in the structure of spacetime. There has to be a single point at which the structure of spacetime has changed. A single point at which, for example, the curvature of space time becomes infinite. Now, in our models of spacetime, things are not nearly as pathological as that. In our models, there's this kind of network that represents the structure of space. And space is ultimately composed of these just individual points related by the edges in this network. And so when we say that what happens when you make an event horizon, for example, is certain features of that network or actually certain features of the way that Network progresses through time work in a certain way. And what happens at the center of the black hole where you have this singularity in space time, in sort of the traditional view of space as a continuous thing, the only way you can deal with that is to say there's a hole punched out of space time, where there just is no space time there. It's just an infinitesimally small hole. But there's a hole. So in our models, it doesn't quite work that way. You could have something much more structure. You can actually see the structure of the network is different as you get in towards the singularity at the center of the black hole. But one feature of that singularity is, for the simplest kind of black hole at least, is that time stops. So in our model of physics, what's happening time is this sort of progressive computation of the state of the universe, the next state of the universe, the next state of the universe always being computed from the previous state. And sort of structurally, what's happening is you have this giant graph. And at every step, all the different pieces of this graph are being rewritten. And so sort of the progress of time is the progressive rewriting of this graph. And everything in the universe is a feature of this graph. Every electron, every whatever, they're all just features of the structure of this graph. And so time is this progression of sort of the rewriting of this graph. Okay, so what happens at these singularities? In the simplest kind of black hole, non rotating black hole, in the simplest kind of black hole, what happens is time just stops. So what does that mean? It means that at the center of the black hole, there are pieces of the network where no more rewrites apply. There isn't another rewrite that gets done. It just stops. So it's, it's. If, if you were sort of part of that, it's kind of like your mind just stops running, your brain stops running. You, you won't. It's not like, oh, I'm realizing I just froze. You don't realize anything. There's no thinking going on. There's no, there's no mind, there's no experience happening. It just. Time just stops. And in the. So what happens in the sort of traditional view of things is the spacecraft that fell through the event horizon eventually is led into that singularity at the center of the black hole, at which point time stops. And it always, after a limited time, the spacecraft always ends up at that singular point at the center of the black hole. In our models, it's a bit more Explicit what happens. But the end result is at some moment, time is frozen. Nothing ever happens anymore. So you don't know what happened because time is frozen for you as it's frozen for everything else. So in this question of can you sort of lead a happy life inside a black hole? Well, up to a point. Eventually you die, so to speak. Eventually there's no more kind of, there's no more experience that happens. That's the case with the simplest kind of black hole. With the other kind of black hole, you get a more bizarre thing still in rotating black holes that effectively are rotating. So the thing I just described is called the space like singularity. There's another kind of singularity called the timelike singularity, where instead of time stopping, effectively space has stopped. What does that mean? It means that normally in space you can move back and forth, you can move around, there's extent to space. But in a time like singularity, there is no extent to space. Space is infinitesimally small. And you are sort of trapped in this infinitesimally small region of space where all that can ever happen is the same thing keeps on happening over and over again through time. And that's kind of a different. So there time is infinite, but space is infinitely small. So that's a different kind of singularity that can happen. But in both of these cases, it's kind of not like you notice anything really bad happened because you don't get to notice anything, because your mind is kind of frozen at that point. But in terms of can there be a sort of, if you, after a limited time, everything comes to an end. Now for our universe could be the same thing. It could be that in our universe we expand for a while and then gravity pulls back the expansion of the universe and eventually it goes crunch in a big crunch. That doesn't seem to be the path that our universe is on. Based on the speed at which the universe is expanding and other kinds of things we can measure, it seems like we're just going to get to the point where we're just eventually coasting and going, and we're neither going to speed up in our expansion, nor are we going to sort of turn around and crush down again. But if we did, it can still be the case in both scenarios that you can end up with a situation where again, for the whole universe, time eventually ends and where sort of we keep going for a long time and then eventually it's all over and time has ended. The possibility where the universe just sort of expands forever at an Increasing rate. You can get into a situation where it expands forever, but the rate increases. And eventually everything gets so far apart that, at least in the traditional model, so far apart, that kind of nothing very interesting can happen anymore. I actually, now that I think about it, in our models, it would not really work that way. It would not be the case. That would be an approximation. And if you look below that approximation and you look at the actual structure of spacetime, there will still be features of the actual structure of spacetime. It won't be the case that the thing has become sort of uniform and boring. And in fact, in our models, again, even with the sort of the big crunch scenario, again, it won't get as. It won't get the same way as it does in kind of the older models of physics where the thing just sort of compresses to a point and there's nothing more going on there. It's a little bit more structured than that. So that's a little bit of a discussion about could we be what's inside a black hole? Can things survive in a black hole? The answer is yes, but only for a finite time, typically. But we are, you know, our universe may only survive for finite time as well. And there's an awful lot of time before, you know, let's say our universe survives for a trillion years. We're about 14 billion years in, and we can lead happy lives for an awfully long time even if the actual lifetime of the universe is quotes only a trillion years. So we're kind of existing in what one can think of as kind of a. We might think we're existing in sort of the transient before the real outcome of the universe is known. I don't think in our models, for example, this idea that things become very different when the universe is either crunched down or gets very big or whatever else. It's a little bit of a subtle thing because what it means to an observer like us today, you know, we're roughly a meter tall, give or take one and a half meters tall, whatever it is. And to an observer like us, if we imagine what the universe might be like when it's crunched down or it's really big or whatever we say, oh, that. That doesn't look very interesting. That looks like nothing. Nothing that we can kind of engage with. But that's because we're a meter and a half tall or whatever, and we have certain things we can measure. If we imagine sort of projecting the future of humans, not really humans are very likely, you know, a trillion years from now. And we say, well, what do we sense then? Well, we're probably not a meter and a half tall and made up with, you know, biological molecules and things like this. And with a different kind of observer, the structure of the universe as it might exist at that time in the distant future can be perfectly exciting and interesting, even though to an observer like us, it isn't interesting. So it's. There's the same. Is true a lot of these different kinds of things. The question of, is there kind of a. What's one's impression of what's going on? Well, it depends on what one is like as an observer. Let's see. Oh, boy, a lot of black hole questions. All right, let's take a look at some of these. Des asks, would something trapped in the space between the event horizon and the singularity eventually be able to escape black holes? The things I explained, there's actually more to the whole story of black holes. And one thing that happens is quantum mechanics leads to yet more bizarre effects around black holes. In our models, it gets a little bit clearer what's going on, but it's a bit complicated to explain. In our models, there are many different paths of history for the universe, and that's what kind of corresponds to quantum mechanics. And what happens in a black hole is there's an event horizon for things moving through physical space. There's a different. What one can call entanglement horizon for things. For sort of things that correspond to different paths of history. And there's a slightly longer story to explain the picture. But essentially what the. Well, the end result is when you think you formed a black hole where nothing can escape. There's sort of quantum mechanical things going on that allow things to escape. And in the. If you wait sufficiently long, you'll end up with the sort of. The thing where no black hole ever really formed being what comes out. So one way that one sees that is with Hawking radiation, which is a quantum mechanical effect, which kind of a picture of what's going on is in the vacuum. In quantum mechanics, there are continually particle antiparticle pairs being formed and being destroyed again at every moment everywhere in space. Space is full of particle antiparticle pairs. They form, they do get destroyed. They form, they get destroyed all the time. And smaller and smaller scales, et cetera, et cetera, et cetera. In our models of physics, that is really the. There's this giant network, and particles are features of that network. And so as that network gets updated, you can think of those updates in terms of particles getting formed, particles getting destroyed. But in the end, it's just a network getting updated. And that goes all the way down, Even below the level where you can kind of identify particles and antiparticles and things like that. So, in fact, in our models, it is the activity in this network that. That knits together the structure of space. If it wasn't for that activity, Two different places in space Would have no relation to each other. There wouldn't be any sense in which these things were connected. In which we could imagine motion that goes from one to the other and so on. So, in any case, this idea that there's kind of this continual particle antiparticle formation. Or continual sort of updating of this network. That one can think of in terms of particles and antiparticles Happening in the universe Around a black hole, Kind of a typical picture would be that these particle antiparticle pairs Getting formed. And what happens if, let's say, the antiparticle Falls into the black hole? It gets formed, and then it's going to annihilate again. But before it annihilates again, the antiparticle falls through the event horizon and can no longer escape again. So that means that the particle is just left hanging on its own. And that emerges As a piece of radiation Coming out from the black hole. Because its partner that it would have annihilated with, Again, got trapped inside the. Inside the event horizon of the black hole. So that's a kind of a sort of radiation that emerges from black holes. And eventually it will sort of mine the mass of the black hole. And eventually all of it will turn into radiation. That's a kind of a strange picture of what's going on, I think a better picture, which is a little bit harder to understand, Perhaps it all has to do with, let's see, as you get to the event horizon of a black hole. Two. Yeah. This is where things get kind of complicated. In terms of what you feel like as you're falling into a black hole Versus what folks outside of it think you're doing. So what happens is, if you're falling into a black hole, you're just going along and you're thinking A certain amount of times elapsing. It's not too much, et cetera, et cetera, et cetera. But to an observer far away, you seem like you're slowing down and slowing down and slowing down. You know, what if you had a clock that was ticking on your spacecraft. And somebody was observing the ticking of that clock from Far away, far away from the black hole. It would be as if that clock was ticking slower and slower and slower and slower and slower until eventually you just freeze. To an observer on the outside, you just freeze sort of at the surface of the event horizon. So for you, you're like, oh, I just fell into the event horizon. To an observer outside, it's like, well, it's an infinite amount of time. The, the observer is stuck, the, the spacecraft is stuck at the event horizon. And that's kind of the flip around of the fact that when you send a signal out you, it is a, a limited time for you, but that time, it's sort of an infinite time for the outside world. And that's kind of why your signal never actually gets out, so to speak. It's why, for example, in black holes, where it's term invented in the 1950s, 60s I guess, by an American physicist called John Wheeler. In Russian physics, black holes were called frozen stars because of this effect that as you kind of get to the outside, it looks like sort of everything freezes. So, okay, that's what happens. So to an observer on the far outside, it freezes at that level. Now there's another bizarre thing that can happen, which is that when you think about these different threads of history that originate, that exist in quantum mechanics, the big thing that happens when we so the universe looked at sort of from outside the universe. There are many paths of history in the universe. But to an observer embedded inside the universe like us, our minds are also branching, just like the Universe is branching into many parts of history. So we have this question of what does a mind that's branching think is happening when observing the Universe that is itself branching? And we have the idea that definite things happen. So it's as if in our minds we're conflating together all those different paths of history. It's a non trivial fact that we don't get lots of confusions and inconsistencies by conflating those things together. But we conflate those things together. And that's kind of how we go from the sort of underlying quantum many possible paths of history to the definite things happen kind of kind of situation. Well, the ability for us to knit those paths of history together and conclude that something definite happens shouldn't be taken for granted. And in fact, what happens at the entanglement horizon, as we call it, around a black hole. And this is part of things that have emerged from our physics project, understanding all of this stuff that at the entanglement horizon, what happens Is that an observer can no longer knit together in finite time all of these different paths of history. Just like one can't kind of connect, one can't send signals out and so on, one also can't kind of come to a definite conclusion about which path of history one was on. So it's as if for us, we can say, yes, we're going to conflate these parts of history. We're going to say a definite thing happened. But to an observer at the entanglement horizon around a black hole, the entanglement horizons are probably outside of the event horizon at that. When the observer reaches that, they get to the point where they can no longer sort of form a classical thought. They can no longer conclude with any definiteness what happened. And I think that's what's going on. When one looks at kind of a black hole that sort of forms, but sort of one is, if one's an observer right there, one kind of isn't really sure it formed because one can't form the sort of classical thought to know what happened. And eventually the black hole has disintegrated again. And it's like, well, I don't really know what happened because I couldn't really form a classical thought to know what happened. And that's roughly the picture of what goes on there. Let's see. Christian asks about the stopping of time in a black hole. Is this the case also for string theory? So there is a. One of the things that was discovered actually by a friend of mine, when was it, 20 years ago, maybe, was that in string theory, there's a way to sort of. If you think about the analog of a black hole in string theory, there's a way to understand the properties of a black hole in terms of the structure of strings. So maybe I should explain what string theory is and how. How strings work. Let's see, String theory has a weird, weird history because it's basically had three different epochs where the same mathematics was used for three completely different purposes. So it's rather confusing as you start talking about it. But in a first approximation, let's talk about how string theory works. So in theory of. In quantum mechanics, for example, one of the things one wants to talk about is how do particles behave? What's a particle, an electron, a photon, a quark? These are particles that have. Where we have this sort of picture that there are all these many parts of history, we have this way of representing what is the sort of amplitude, roughly probability for a particle to be found in different places in space and so on. In the end, what happens for these particles is that one has certain rules for how particles can move through space. So these things called wave equations, for example, and different kinds of particles obey different wave equations. Like an electron obeys a thing called the Dirac equation, which is just some mathematical equation which describes how sort of the amplitude of these different paths of history which assign different positions to the electron, how that amplitude evolves through time and in space. And for example, a photon has a different wave equation that it satisfies. They're different because the particles are just, they have a different intrinsic spin and that kind of the spin determines kind of which kind of wave equation they satisfy. But so there's kind of this theory of how particles work in terms of these wave equations. And if you look in space, the particle, an electron, for example, in traditional physics, not in our models, but in traditional physics, an electron is a point particle. It has absolutely no extent. It's infinitely small. Same with a photon, same with a quark. A proton, for example, it's pretty big. A proton is measurable size. We know how big it is. An electron, so far, as any experiment has shown so far, the electron is infinitely small. In our models of physics, the electron is not infinitely small, but it's really, really small compared to anything that we can measure with particle accelerators and so on today. So an electron is essentially a point particle in space. If we look at it through time, it traces out what one can call a world line. If one just says, if one looks at sort of imagine space is two dimensional and we just make a stack of configurations of space going down in the third dimension with time, then the path of a particle will just be a line in the space time structure. So particles make lines in space time. And okay, so that's a fine thing. So now the question is, well, what if we had something that wasn't a point particle? What if we had a bigger object? What if we had something that was extended somehow in space time? Well, for many, many years, there were was a lot of difficulty understanding what that could possibly be like, because a lot of the rules about quantum mechanics and relativity and so on, they get very, very confused when you deal with extended objects. I'll give you an example of how things get confused. You've got an extended object, you've got an arm and the arm, it's an extended thing, it's swinging around, but it's a rigid arm kind of swinging around in space. You say, let's make a longer and longer and Longer arm, but it's rigid. Well, eventually that arm, the tip of the arm, if it gets long enough, will be going faster than the speed of light. But that can't happen. That's not how things work. So then you have to say, well, what happens to this arm? Well, the answer is, in reality, it can't be rigid. The mechanical forces that were built up to make the tip of the arm go as fast as the speed of light are such that the arm could never stay together. If it's made of metal or made of atoms or made of some carbon nanotube or whatever it's made of, there are infinite forces that get developed and the thing could never stay together. So you can't think about an extended object that's kind of like a long arm or something rigid thing that doesn't end up being compatible with relativity theory. And people had a lot of difficulties seeing how do you deal with extended objects. Okay, so it was realized that you could have a kind of a string that was an extended object in space, that kind of where sort of the pieces of it sort of all go at the speed of light. And this string, just as a particle traces out a line in space time, a string traces out a world sheet in space time. And so then the question is, well, okay, that's well and good. Can we make that? Can we make kind of a wave equation like thing for that string that's kind of moving at the speed of light and the pieces of it are moving at the speed of light and so on? Can we make something a consistent kind of wave equation like thing? And this is where things got complicated and people realized that, well, actually, no, you couldn't really quite do that. But there was this cool thing that happened if the universe, if space happened to be 26 dimensional or in some cases 10 dimensional, then it did work out that you couldn't get. See, what ended up happening was that inevitably, as the string moved through space time, there would be kind of features of the string that move faster than the speed of light. That turned out to be an inevitable feature. But somehow that, because of the way the mathematics works out in, let's say, 26 dimensions, the sort of, the things that lead to those kind of faster than the speed of light pieces, they somehow cancel out. And so it's like, well, maybe actually the universe is 26 dimensional and maybe those extra 24 dimensions or so, 22 dimensions or whatever, maybe, or 23 dimensions, depending on how you're counting things. Maybe the reason we don't see those Is that those dimensions are curled up really small and that all that happens is that in those dimensions it's kind of like that time, like singularity I was talking about earlier. In those dimensions, space isn't really extended. Space is just curled up. And it's only in the three dimensions of ordinary space that it's extended and we can move around. So that's kind of the. That's sort of a basic picture of kind of the setup. Now. There are a lot of details about this and about different kinds of strings and different kinds of the strings that like to live in 10 dimensions. And in 26 dimensions, the strings that correspond to kind of a bit like a generalization of a photon versus the strings that correspond to a bit like the generalization of an electron. There's this idea of supersymmetry. So, gosh. Well, you know, there are things that are symmetrical. Like you take a sphere and you rotate it and however you rotate it, it's always going to look like a sphere. If you had a cylinder instead, well, you can rotate the cylinder around its axis. But if you turn the cylinder not around its axis, it's not the same thing anymore. So there's lots of kinds of notions of symmetry like that. One of the more interesting kinds of symmetries, that is a. Well, there are symmetries that are associated with kind of the, the features of, of particles and so on. For example. Well, let's see in. Well, there are cases where. Well, for example, particles versus antiparticles. You can think there's sort of a discrete symmetry transformation instead of with a sphere where you can turn it to any angle. You could say, well, let's say we've got a square, for example, and we can reflect the square as it's a discrete thing with that discrete transformation. Or we can turn it through 90 degrees with that discrete transformation. It turns into itself again. Well, there's a similar kind of thing with particles and antiparticles. You can kind of apply charge conjugation, turn a particle into an antiparticle, apply it again, the antiparticle turns back into a particle again. And when I say apply, I just mean consider applying it. There's no machine that will apply charge conjugation. There is a machine that will turn something, so to speak, through a certain angle. But there isn't these kinds of things that these so called internal symmetries, they're not things where a machine like that can make that transformation. It's actually a little bit more subtle than that because the interaction this is a subtle mess about how gauge theories work and so on, but let's not go down that particular rabbit hole. But there is this idea of supersymmetry in which things that are like photons, which sort of turn into things that are like electrons, just as sort of a particle could turn into its antiparticle. So there are these transformations that turn one of those into the other, and that's they kind of relate things like photons to things like electrons. And kind of that story plays into the kind of string generalizations of things like electrons and things like photons. And that makes a very lovely theory that has a lot of very interesting mathematical properties. We kind of suspect that in the end, certain features of that theory correspond to features of our models of physics. And there are, let's see, it's kind of a question of, boy, this is complicated. Well, in our models of physics, we talked about how there's this kind of giant network that's progressively getting rewritten according to certain rules. But in the most general case, you can use any rule you can imagine. You can just apply all these different rules. You make this thing we call the ruliad, which is this kind of entangled limit of all possible computational processes. And the tricky thing is that we are embedded in this ruliad. We are observers within the ruliad observing the ruliad. And that sort of self observation when we are observers with certain properties causes us to believe certain things about what we observe. And the things we believe correspond to laws of physics. But the way in which we kind of parse out what we're observing in this kind of entangled limit of all possible computations, there are different ways to parse that out. We could say, well, there's this state of the universe and then there's another state of the universe at a successive time. There are particular rules for the universe that are being followed. There are these different rules followed, There are different possible rules we can follow, and so on. There are different ways to slice up the ruliad. Our guess is that string theory corresponds to an approximation to one way to slice up the ruliad. And that this, when I talked about these kind of compactified dimensions and so on, that's a particular kind of way to sort of arrange the things in the ruliad so that we can organize them to kind of compress the amount of information associated with them, so that we can kind of say, oh yes, we can see what's going on. It's not just this big complicated mess. And our guess Is that there are certain conditions about how in order to get consistency in the way that slicing works that correspond to these things that lead to these implications about particular dimensions and string theory and so on. That's sort of still somewhat of a guess. And there's lots of mathematical physics to work through to see exactly how that works. Boy, this got kind of complicated. Let's see. Okay, Technic is asking a rather technical question. What are the implications of a naked black hole? One without an event horizon? Okay, so I mentioned that in the center of a black hole, in the traditional view of physics, there's sort of an infinitesimal point punched out of space time. Now, normally you can't tell it's there because it's hidden behind an event horizon. And people have believed that there would be no naked singularities, that it wouldn't be possible to set things up so that you could form the singularity but not form an event horizon. Then it was discovered maybe 15 years ago that there is an elaborate procedure where you can essentially carefully orchestrate what happens in space time so that you form a singularity, but you carefully avoid forming an event horizon. Now, there's a lot of tricky aspects to this because event horizons are really. You don't know whether you formed an event horizon until an infinite time has passed. They're really a story of infinite time. It's an infinite time question. They because you could say, well, I didn't really get an event horizon. Just if I waited long enough, I'd be able to get through. It's an infinite time question whether an event horizon is formed. And this question about whether you can form this thing which has no event horizon and just a singularity. It seems to be the case that the formation of a naked singularity is something similar to making something of zero temperature. So normally you have all these molecules bouncing around in a material, and if you try and reduce the temperature, what you're trying to do is make all those molecules. You're trying to just stop every molecule. You're trying to do something where you pick every molecule and you stop it. And there are different ways to do that, more in bulk. But what's known. The third law of thermodynamics, basically, is the statement that there's no way to get to absolute zero by a finite number of steps. Every time you've kind of you've stopped one molecule where you've got to stop another one, you've got to stop another one, Et cetera, et cetera, et cetera. There's no way to, with sort of, in my way of thinking about this, with sort of finite computational effort to stop all the molecules, you'd have to sort of predict where every single molecule was and zap everyone to stop it. Well, I think the same thing happens with the formation of naked singularities, but that basically it's the same kind of thing that you'd have to be able to break out of kind of all the computational complexity of the structure of spacetime to be able to carefully orchestrate things so that you wind up with this pure naked singularity. And so I think what happens is that in space time, you have all the sort of bubbling around of all these rewritings of this network and so on, and you'd have to kind of orchestrate it so that you just carefully navigate things so that you have exactly the right set of rewritings so that you have this pure place where time stopped and there's nothing sort of around it. And the claim is that you can only do that. You can't do that with a finite amount of computation, that you'd have to kind of be dealing with every individual atom of space separately and sort of computing how it works. The problem is we're embedded in the universe, so the only way we get to do those computations is by using the stuff of the universe to do it. And so we never get to have enough computational ability to be able to sort of untangle things to the point where we can get to that naked singularity. So that's. My guess is that it's kind of like in thermodynamics, like the inability to get to something like absolute zero. You similarly can't get to a thing where just in the universe at large, there's a place where time stopped. And you can kind of, I mean, it's, you know, and you can sort of get to it, so to speak. Now, even. Even when you imagine a place where time stopped, you know, by the time you get to it, time has stopped for you, so you never get to get out of it. So it's all a bit. Bit difficult to. To untangle. But I think that's the basic idea. Let's see. Marcus comments about when a black hole eats more stuff, it gets bigger. So where's the singularity? So the singularity is at the center of the black hole. The. In the traditional view of physics, it's a vacuum solution to the Einstein equations. The. The thing that. The most simple, simple description of a black hole. But what happens is there's this sort of place punched out of the universe right at the center and it's the, the, the sort of. Well, sounds very silly, doesn't it? They say there's an amount punched out of universe, but there can be more punched out of the universe, but it's still an infinitesimal point. The mass parameter of a black hole is a parameter associated with that thing that got punched out of the universe. It's kind of a weird setup in our models of physics. It's much cleaner, it's much more. There's a much more direct interpretation of the fact that the mass associated with the black hole has to do with essentially the activity of this rewrites in the network inside the black hole. So what's happening in our models is there's kind of the presence of a large amount of mass, is the presence of many rewrites. Space is being sort of intensely sort of bubbling around in a very intense way, getting knitted together in a very intense way. That's what mass and energy are. And that's what in the end, that a different mass of black hole is one where there's different amounts of that activity going on in the structure of space inside the event horizon. Let's see, Buildings comments that mass and matter and antimatter both have positive mass. So why doesn't Hawking radiation increase the mass of alcohol? Well, it decreases it because. Because whether you are emitting matter or antimatter, you're emitting positive mass. And so that, that comes off the kind of balance sheet of the black hole's mass. And you're decreasing the mass of the black hole because things are escaping away. Question of how small from Storin, how small can a black hole be? Well, we don't know. In our models of physics, black holes can be really small because they can be little features of space. So here's the thing that I suspect. I suspect that electrons are basically black holes and that an electron is essentially a feature of space time. Just as a great big black hole is a feature of space time. An electron is also just a feature of space time. It has nothing in it other than being kind of this lump of space time. It's kind of like in a fluid like water. You can have an eddy, just water circulating around and there's, you know, you can point to that eddy and say, oh, it moved around. But there's nothing in the eddy other than a bunch of molecules that happen to be kind of coherent, coordinated in the motion that they're going through. And that's what I think things like electrons are And I think there's a very close analogy between a black hole, where there's sort of this definite structure to space that forms the cement horizon and so on, and an electron, where I think there's also a definite structure to space. In kind of traditional physics, electrons are point particles where there's just no internal structure. I don't think that's right. I think there is internal structure. But one of the things that's interesting is that to the outside world, just like in a black hole, to the outside world, all you see is the event horizon. The event horizon is sort of featureless. And that means all you know about the black hole is things like what its mass is, what its effective angular momentum, spin is, and things like this. You don't really know. It's not like you can say, well, that's a black hole, that is this shape or that shape. No, they're all kind of the same. They're all this sort of perfect shape to the outside world. One of the things that's always been mysterious about electrons is that they all seem to be the same. It's kind of like there's only every electron in the universe seems like it's the same. They can have different energies, momenta, things like that, but otherwise they're all the same. They all have the same mass, they all have the same other properties and so on. And one of the more bizarre theories about why that might be the case theory that was circulating in the 1940s was the theory maybe there's just one electron in the universe, and maybe that electron is going forwards in time, then zipping backwards in time, then going forwards in time again. It's just sort of knitting through, and we are existing at a particular time, and the electron is just sort of zipping back and forth in time, and there's just one of it. Kind of like in computer science, you talk about Turing machines, where there's just one head, where activity happens. That might be the case with electrons. Turns out that theory doesn't really work. So you still are left with the question, why is there only. Why is every electron in the universe the same? Well, I think in our models that what's happening is it's kind of like you can say, well, I make a knot in a rope. I can make the rope in lots of different configurations, but it's a definite kind of knot. There's a definite structure to that knot. Even though the rope may have a slightly different form, when I kind of pull on the ends, I can see it's ultimately the same kind of knot. It has the same topological structure. And we suspect that that's sort of, in some sense why kind of all the electrons are the same is because even though their details might somehow be different, particularly inside some analog of an event horizon, they're at some sort of large topological scale. They are all the same. And so if you ask what's the smallest possible black hole? It might be that basically an electron is such a thing. But in any case, in our models of physics, you can have things like black holes on a pretty small scale, I think, that are pretty comparable to the distance the elementary length. A proton, for example, is maybe a 10 to the minus 15 meters, a million billionth of a meter across. But an electron is certainly smaller than 10 to the minus 20, 10 to the minus 21 meters. And in our models of physics, it's probably more like 10 to the minus 80 meters across. So very, very tiny. And the elementary length might be 10 to the minus 90 meters. So in a single electron, there might be 10 to the 10 sort of elementary lengths. In space, there might be all that structure inside an electron, which kind of suggests there might be some particles that are even smaller and lighter than electrons. And that's a separate story about what might happen there. But let's see, I think the. So in some sense, there may be little tiny black holes being it's, you know, the whole structure of space time. Just as there are little particle antiparticle pairs that are being formed all the time, you can kind of think about there being little sort of black hole, kind of anti black hole pairs being formed. That's kind of, you know, one way to describe the kind of bubbling around of space time. Now, you know what black holes is. There, for example, in the early universe, could there be a whole spectrum of black holes, a whole distribution of sizes of black holes formed? Almost certainly. The answer is yes. There was recently an experiment based on looking at the timings for pulsars and kind of watching gravitational waves that might have existed from the early universe kind of go through and affect different pulsars for, I don't know, 20 pulsars or something. And as the gravitational wave goes through, it changes the timing of the pulsar just slightly. And by correlating all those timings, you can get a sense of sort of primordial gravitational waves that might be sort of existing in the universe today. And that's a. But you can imagine a whole spectrum of black holes formed from in the early universe. Lucky asked, do you think it will Ever be possible to reproduce a black hole in a lab for practical research and experimentation? People there are all kinds of mathematical analogs of black holes that are quite easy to make actually in fluid mechanics and quantum mechanics and so on. They're analogs. But if you say, can we take a piece of space time and kind of curl it up to make a black hole? Well, maybe electrons are black holes, in which case we got plenty of them. I think sort of being able to make a black hole from in the most traditional kind of black hole, I don't see a path for being able to make that in a kind of a lab setting. That's probably just as well because even a very small black hole kind of going through the earth would make, you know, would wreak havoc on everything and the earth would just get sucked into the black hole and so on. So it's probably just as well that that doesn't seem to be, doesn't seem to be a feasible thing to do in the current universe unless it turns out the particles basically are black holes, in which case there's a whole different story. And the question of whether we will eventually be able to simulate. I mean, what we've been doing in recent times is simulating the structure of space time in our network models of space and seeing how black holes work in those in that situation and seeing how we can get very, very tiny black holes that we can simulate, you know, kind of on a laptop. And a black hole that has, you know, 10,000 nodes of space, 10,000 atoms of space in it. Absolutely, you know, ridiculously small compared to real black holes that make might have 10 to the 200 atoms of space in them. But we can see many features of sort of big black holes already at the, these black holes that are very tiny. That's a sort of laptop simulatable. And we can see these black holes merge, as we know they do about once a week in our universe and produce gravitational radiation. Etc. Etc. Etc. Let's see. Philip asks what is spinning in a spinning black hole? It's a can of worms. The, it's really just a mathematical parameter. When we talk about things spinning. The it's. As far as the actual black hole itself is concerned, it's just a mathematical parameter. But that mathematical parameter has a consequence and it has a consequence. It's a phenomenon called frame dragging. And what happens is. Oh boy, you guys ask me non trivial questions here. What happens is in a black hole there's a question of sort of where are the gravitational field lines? What, what, what effect does the gravitational field of a black hole have on a material object like a, like a, a drop of liquid, for example? Well, sometimes the. Let's see how to think about this. Well, essentially there are tidal forces just like there are on the Earth from the moon and the sun and so on that elongate, that drop that the. There's kind of. There's more gravity kind of on the inside and there's less gravity on the outside. And so the blob will kind of elongate. And roughly what happens is that in a black hole, so called Kerr solution to the Einstein equations, that has this, this spin parameter, usually called J in that solution, what happens is that instead of things being sort of symmetrically pulled in, they're kind of dragged so that they get, so that they get kind of. So they get. So it's as if they were kind of spinning around the black hole. It's actually a little bit more complicated than this. What happens is the paths for light rays end up. You can think about kind of plotting in space time the paths that light rays go. This form so called light cones where you can have light rays are produced at some point and they go outwards in space. And if you're plotting them with time, they go outwards kind of in a cone that you form a cone in space time. And so what happens is that cone gets tipped near a black hole. And the way it gets tipped is kind of like it's getting tipped different angles as you go around the black hole. It's sort of as if it's being dragged around as a black hole is rotating. But there isn't really. There's nothing about the black hole itself that's rotating. It just makes things around it rotate in some sense. Michael asks, can black holes have a charge? Can the effect of the charge propagate out of the black hole if photons cannot escape? The answer is black holes can have a charge just like they have a J parameter that is like an angular momentum. They can have a charge parameter. There's a thing called the Reisson and Nordstrom solution to the Einstein equations, which is a black hole that has charge. How does that work? Well, essentially what's happening is just as the gravitational field. So you could say if, you know, in my kind of picture of how a black hole works, where nothing escapes the black hole because there's nothing goes faster than the speed of light and the black hole sort of pulls back in things going even at the speed of light. You could say if you want it to be Difficult. Well, what about the gravitons that make up the gravitational field? Why aren't the gravitons pulled back into the black hole and just like everything else is pulled black into the black hole? Well, that's subtle. It's really this picture of things escaping from black holes and so on really isn't quite the right picture. Black holes are better thought about as just these features of the structure of space time. And that's just sort of a picture for how to think about them. And so, you know, just gravitons are not pulled back into the black hole and nor are photons in that at the type of photon that makes a static electric field just as. Okay, so a graviton, if you were to have a gravitational wave that, that started inside the black hole, it would get pulled back into the black hole just like a photon that starts inside the black hole gets pulled back into the black hole. But okay, now it gets a bit subtle because a static gravitational field, a static electric field, these are sort of formed from gravitons and photons, but they're formed from virtual gravitons and photons. And they don't have the same feature that you can kind of trace them in space and time. They're things that it's really how to think about this some level. It's a kind of a feature of quantum mechanics. But in there isn't the same kind of idea that there's motion of the photon. When you have a static electric field, you can think about the electric field as being associated with the exchange of virtual photons and virtual photons going from one charge to the other charge and so on. But it doesn't have the same character of being kind of a thing moving from here to there. This is kind of subtle and I'm not sure. I actually haven't thought about this with any clarity. Let's see how to explain this. I'm not sure I'm going to. I mean, in the mathematics of what goes on, it's rather. It's fairly straightforward. But I'm not sure there's a picture like this that really nails it in a good way that sort of connects these virtual particles that exist sort of independent of time with these things that have emotion that happens in time, so to speak. Let's see. Emirudo asks us kind of a history of science question. Why are they named black holes? Not after the people who found discovered this phenomenon. Well, you know, it took a long time for the. For this phenomenon to become clear. What the heck it was. And people really were confused. I mean, the original discovery that there was this particular solution to the Einstein equations came in 1916. But it wasn't until the 1960s that people understood kind of something about what the phenomenon of a black hole was. And that was a very slow process involving many different people and sort of a long progress of, of mathematical development. Let's see. Well, I, I think I almost ran out of time, but we've been talking about black holes all this time. We were kind of dragged into the, into the event horizon of a black hole or something. Let me just try and address a couple more questions. Aaron asks. We got a very different kind of question. Could lasers be used to display an advertisement or perhaps a clock or something else on the moon? Can high bandwidth Internet connections be bounced off reflectors on the moon? So the answer is you can see laser light that has been reflected from the Moon. In fact, the Apollo astronauts put lunar laser retroreflectors on the moon that have little glass spheres in them. Laser light falls on the reflector, gets reflected back. Here's the problem. Lasers. You shoot a laser from the Earth, the beam of the laser gradually spreads out. So even though it was a very intense laser that might have had a spot that was just a centimeter across on the Earth, by the time it gets to the moon, it'll be a couple of kilometers across. I think the best lasers right now, the spread by the time you get to the moon is on the order of a kilometer. So there's much less intensity in the light by the time you get there. If you could keep the laser light kind of, well, collimated, you know, really keep it together until it gets to the moon and then you're illuminating moon rock and you know the, well, if you hit the laser retroreflector, you'll get, you know, you'll get the laser reflected precisely back. But mostly you'll hit lunar regolith, just moon soil, so to speak. Moon rock. And that consists of these tiny little sand like granules. And when light hits those, it hits in one direction. And it's like many kinds of surfaces that aren't mirrors. It's a so called Lambertian reflector. Light comes in and the light that comes out is kind of spread in all directions. That's a typical thing. And the albedo of the moon, that is if you send in a certain amount of light, how much light comes back out is I think about 1/10. So you shine in a certain amount of light. The surface of the moon is pretty black Only one tenth of the light comes back out. You know, if you have a mirror, its albedo is one, because any light you shine on the mirror, if it's a perfect mirror, comes right back out again. And different materials have different albedos. The Moon is actually pretty, pretty, pretty black. But 1/10 of the light coming from the sun being reflected back to us makes the moon look bright in the sky at night. So what happens is that you have a laser, you shine it on the moon, you've got a two kilometer sized spot. It's hard to have enough intensity there to, to really be able to see anything from that. For example, with the naked eye, what limits the, the, the amount of how unspread a laser gets has to do with the, the way a laser cavity works. And let me see the, in a laser, you've got kind of light bouncing back and forth. And the way a laser works. The word laser stands for light amplification by stimulated emission of radiation. Roughly you have this cavity with mirrors at the ends and so on. And light is bouncing backwards and forwards in this cavity and it's gradually getting amplified through a process we can talk about. It's related to Bose, Einstein, condensation. There's this quantum mechanical process by which photons kind of like to all be in the same state. And you can kind of, you can do this phenomenon of stimulated emission where the presence of photons gets there to be more photons in the same state. But anyway, bottom line is you've got these photons bouncing backwards and forwards in this cavity that makes the laser. And the sort of best thing you can get is a single mode of the electromagnetic field. So it's like you have a string and you can pluck the string and you can get the string to have just sort of one peak in the middle between the places where you're holding it. Or you can have two peaks or three peaks or four peaks. Those are different harmonics. They make for a different frequency of sound. If you made sound from the string and so on. Well, it's the same kind of thing with light. You can have just sort of a single mode of light in the laser cavity. And that's the thing that will get you the best, the least spreading of laser light. But then the amount of spreading is determined by features of the cavity. And there's a certain inevitable amount of spreading. I mean the fancy math version of this, these are, I guess you can make so called Gaussian, Gaussian modes. And there's a certain spreading rate that is determined by the process of diffraction in light that determines how much the, the thing will spread out. And I don't know exactly what's involved in making. Maybe if you have a bigger cavity, you can make there be less spreading. It's kind of like a, like the reverse of a telescope where the spreading angle is proportional to the wavelength divided by the size of the telescope. So you can get a better, a more precise telescope by having a bigger telescope. There's less diffraction limit for the telescope if it's bigger. And I think maybe the same thing is true with lasers. So if you have a big enough one, maybe you can get the thing to spread less. But. So that would be the way of kind of doing skywriting on the Moon. I think at sort of nearer term, people think about putting things in Earth orbit and having things that re enter the Earth's atmosphere and burn up, just like meteorites burn up. But you can kind of, you know, release something from a satellite and you can have this whole kind of collection of pieces of dust that you can see as they enter the Earth's atmosphere, Because they will burn up and they will, they'll emit light as they burn up. And if you change the chemical constitution of those things, you can get, for example, different colors. And you could imagine that if you have sort of the satellite that's laying stuff out that you can kind of skyright in Earth orbit, so to speak. Actually, there was a company that was trying to make that work like six, seven years ago. Not sure exactly who you have to get approval from to write a big message in space because the sort of the airspace of a country, for example, doesn't extend infinitely far out. So there are various outer space treaties that I don't know exactly how they apply to advertising in space or exactly who would get upset if you start writing your ad in space, so to speak. Let's see. See. Well, I should probably. Oh. M. Rudo asks, if the Moon is responsible for tides on the Earth, can the Earth be responsible for movement of Moon dust? The answer is yes. The Earth raises a tide on the Moon just as the Moon raises a tide on the Earth. But the tide on the Earth, most of the tide on the Earth is obvious because there's water on the Earth and that water can actually be raised up on the side of the Earth nearer the Moon and it goes further away on the side of the Earth that's further from the Moon. There is also a solid tide on the Earth. That same effect of the squishing of the Earth happens to the solid rock of the Earth, but it's a much smaller effect than the tide that you can see in the liquid water on the Earth. On the Moon, The Earth raises a solid tide on the Moon. And so the Moon is continually kind of squished a bit by the tides that are raised by the Earth. Now there's a satellite of. Is it Jupiter or Saturn, which has strong enough solid tides associated with. I think it's a Moon of Jupiter. Now I'm going to show my lack of astronomy knowledge. I think it may be IO not sure that has strong enough solid tides that they actually produce heating in the Moon. And that heating produces volcanoes and all kinds of stuff. So you can have enough squishing from tidal forces to have those kinds of effects. But for the Moon, we don't have that kind of. The Earth doesn't have that kind of effect. If you ask the question, does you know, if you leave your footprint on the Moon, is it going to stay forever? Is it going to be there billions of years from now? The answer is. It seems that the answer is yes. It isn't the case that the little pieces of dust on the Moon move around. Now, there is an effect that the solar wind. There's a stream of particles, just like there's light that comes from the Sun, There is also a stream of protons and electrons that come from the Sun. And those things stream into the atmosphere of the Earth. They are ultimately responsible for producing things like the aurora. But on the Moon, they're continually sort of bombarding the lunar surface. Moon doesn't have an atmosphere. So all those particles just come crashing down to the surface. And that seems to kind of bleach the surface of the Moon progressively over time. It doesn't have the opportunity to move around actual particles of kind of Moon dust. But it does seem to sort of, in a sense, chemically or physically bleach those things. And so if you see kind of features of the Moon that have been created recently, like places where a spacecraft crashed into the Moon, there's a little crater. Over the course of a few decades, there will be sort of a bleaching that happens there. Well, you can tell that there was a. There was. So when the spacecraft crashes into the Moon, it exposes layers of Moon rock that have not seen the sun or anything for billions of years. And those turn out to be sort of a different color. But over the course of decades, they get sort of bleached back into the same color. So there is an effect like that, but it's not one that can, I think, move around the actual particles of moon dust. And so you put your footprint on the moon and unless some tourist comes and erases it, you know, it's going to be there for a really, really long time. Psy Comments Buying an ad that burns up upon re entry sounds incredibly wasteful. Well, you know, it seems like you might say buying an ad that disappears, you know, when you click somewhere else is also wasteful. You know, I think it's all about what people notice. And I suppose, you know, you would hope that the kind of the ad that says I don't know what the ad would be an ad for. I don't know what people advertise for these days. I'm not in that many venues where there's tons of advertising or if I am, I kind of block it out, which is terrible. But any case, but you know, if it, the, the classic will be buy coke or something. And I think one can be fairly certain that if somebody did a giant bicoke visible in the sky at night from all over North America, that people will be talking about that for a long time. They might be complaining about it for a long time, but they'd be talking about it for a long time for sure. So there would be. Even though it burnt up in a matter of 15 minutes or something, it would still be a subject of conversation for, for many years to come. Let's see. All right, maybe one or two more questions here. Stephen asks, would the tea dumped into the Boston harbor during the Boston Tea Party have affected the underwater ecosystem? It's an interesting question. I don't know how much tea they dumped in. I mean, let's assume it was a few crates of tea. So the question is, how dilute does that mean the tea gets in, you know, in, in the Boston Harbor? And the next question is, do fish like tea? You know, it's always a funny thing that different, different kinds of animals respond in different ways to, to chemicals. So caffeine, for example, I don't know what caffeine does to fish. You know, one knows that there's some weird cases, like some particular kind, you know, like cats, I think, do very badly with Tylenol, I think, because the kidneys of humans kind of filter that out of our bloodstream. But that doesn't work with cats. And so it gets to some kind of poisonous level, I think. But you know, even with things like spiders, you can feed them all kinds of different drugs, caffeine or some other kinds of drugs. You can see they make different shaped webs depending on what you know. Even though they have very, very tiny brains, the effect of the brain function, the effect of neuron firings and things associated with those different chemicals is enough to make them make completely different sort of whether they, you know, you can make. A drunk spider will make a weird looking web, so to speak. So I don't know what, what, what tea does to fish in any concentration. One thing that's very confusing is that usually you would think with a dilute enough concentration it's just not going to have any effect. But we know that there are some chemicals, some drugs. I think LSD is a notable one where just a single molecule can have an effect on something. I don't actually know how that works now that I think about it, because a single molecule can have an effect on a single synapse and a single connection between nerve cells, but we've got 100 billion of those. And so, you know, how that has a more global effect is a more complicated story. I suppose it may be something a little bit like the story of black holes and things where you can have something where there's sort of a propagating effect from that one place where there's an effect. But so, you know, this question of, well, how diluted does the tea have to be before the fish no longer care that there was tea dumped in the ocean? I don't know the answer to that. And it may not be that the dose response for whatever is in tea will be any kind of sort of linear dose response, you might say. See, another thing that happens a lot with drugs with pharmaceuticals of various kinds is there's a nonlinear dose response. If you take, you know, one tenth the recommended dose, it might do absolutely nothing. It doesn't do 1 10th as much as if you take the recommended dose. It's nonlinear and it's not often not very well understood why that happens. You know, examples of why that can happen are things like, well, if you put enough of those molecules in, you'll eventually block everything. You know, you'll block a whole pathway. You'll prevent anything from being transported through some cell membrane or being, you know, participating in some reaction. But if you only bl 10% of it, there's still enough that can get through that. Whatever process it was that was the big process that was happening can still happen. And you know, if it's some immune response or something, there's still enough immune cells that can get through until you block 100% of doesn't really work. And so that that's how you can have sort of a non linear dose response. You have to put enough in that you get to the point where you're blocking 100% and blocking anything less than that really doesn't have much of a qualitative effect. And so that's how you can end up with these nonlinear dose response kinds of curves. And so I don't know whether that happens for the kinds of things which are in T. And I also don't know to what extent there are ocean currents and there's sort of a continual swirling of the ocean and I don't know how quickly there's mixing of water into different parts of the ocean. I mean, I know that in general there's quite rapid mixing between throughout the oceans of the Earth. I mean, the famous example of this was when nuclear tests were done in the Pacific Ocean in the 1950s. They produced tritium radioactive isotope of hydrogen, which kind of substituted for the hydrogens in water in the Pacific, in a few of the water molecules in the Pacific. And within just a few years you could detect tritium in water all over the Earth. So there was enough mixing between the different water in the ocean and the Pacific and in every other kind of water on Earth that would occur. I have to say that the tritium was generated in the 1950s bomb tests, has pretty much all decayed away by now. When I was a kid, the amount of tritium that was sort of said to be in a typical piece of water was higher than it is today because of that effect. A very weird phenomenon. Let's see. I think Capa is asking, how would biologists test for this? I'm not sure that this might be the effect of some molecule, caffeine or something on a fish. You know, I think that. Does it affect the brain? Well, you can start making measurements from about the, the, the firing of individual neurons or you can just see what a fish does and you can say, you know, you have a, a fish maze or something. And how does the fish go through the fish maze? Or how does the, you know, you, you see certain behavioral aspects of fish and you see how much effect it has. It's not an easy thing to measure really. All right, maybe one more question here. One from Frost. Why are the elements on the Earth not more homogeneous? Why are there areas and mines abundance with certain metals? Is the heterogeneity of elements increasing or decreasing on Earth? Is it the same for other planets, other galaxies? Interesting question. I've been curious about this question. In fact, I've been curious enough, I've asked a bunch of geologists and astrogeologists this exact question. So I can tell you some sort of distribution of world. Expert answers kind of converging on one thing. In fact, one version of this question that I've asked is, could there be a golden asteroid? You know, people say, well, we can go mine minerals, metals, whatever from asteroids, but different asteroids will have different metals in them. And I've asked, you know, could there be an asteroid that's all gold? Answer is probably not. So I think what people generally believe. So first point is, why are there like gold mines on Earth? Why is that? You know, gold has a rough abundance of 1 part in 10 billion of all the atoms in the universe. It's like one part in 10 billion. Well, all the atoms that near us, it's one part in 10 billion of gold. But in the Earth, there's a lot of concentration of gold into particular places on the Earth, you know, particular places where we make gold mines. So gold, like all heavy elements, is pretty much has to be made in supernovas, exploding stars, or processes related to those. What happened in the very early universe, mostly the universe was just hydrogen and helium, the just individual protons making hydrogen or helium nuclei. Roughly the universe is one quarter helium, the rest is hydrogen. And then there's a trailing amount of other elements, some which were made in the Big Bang. In the early universe, the heavier elements, particularly ones past iron in the periodic table, are pretty much all made in exploding stars. And so the fact that we have things like gold on our planet is a consequence of the fact that our sun wasn't a first generation star. There were other stars that lived and died before the Sun. I mean, the sun has a 10 billion year lifespan. We're at about the 4 billion year point in that lifespan, about halfway. There are other stars, particularly bigger stars, that live only a few million years, like Betelgeuse is one such star near us. And so there are stars that kind of come and go, that produce supernovas, produce heavy elements. That's where all the stuff, all the gold that we have came out of some other star that exploded at some time in the past. So when the Earth was formed, what happened is that there was this kind of region of dust and so on that was gradually being pulled together by gravity. It formed an accretion disk, it was spinning around. That's how we ended up with planets kind of more or less in a plane, all orbiting around in the same direction. It formed this disk and different parts of it would clump into a planet, another planet and so on. Well, depending on lots of details about the density of things and this and that and the other, exactly how far out they were in this disk. How did things get sort of vacuumed up by one thing that was kind of a massive object that was pulling in other massive objects? I think in the end the Earth as it was formed is this kind of giant amalgam of different kinds of objects that were formed at different distances out from the sun and so on, and whose orbits were not just circular, but whose orbits were more complicated. And things would gradually sort of crash into each other and all make themselves into this big blob of stuff. Now then what happened is, well, the Earth, it's the fact that the Earth is kind of a clump together of all these different pieces that I think is the first step in making it not heterogeneous. Now the second thing was perhaps a little bit confusing is when the Moon was formed. The current best theory for how the Moon was formed is something very bizarre. It's kind of a two step thing. It's well, first the Earth was formed and then some other little thing crashed into the Earth. And it's, you know, a thing maybe a little bit smaller than Mars or something crashed into the Earth. And that kind of disrupted the Earth a lot. And it made the Earth kind of, you know, turn liquid and so on. And then another kind of that, that ejected this big piece of stuff from the Earth which wound up then forming into the Moon. And actually the Moon, unlike the Earth, the Moon is not very homogeneous. The Earth is reasonably, if you look at the gravity of the Earth, you have a spacecraft going around the Earth, it kind of orbits at more or less the same height all around the Earth. The Moon. That's not true. One side of the Moon is denser than the other side. There's kind of a. It's like the Moon is two things that got stuck together. And that's probably from this big splat that happened when the Moon was formed, or at least that's the theory of it. So the Moon really has a very inhomogeneous, is two very inhomogeneous pieces stuck together. The Earth probably melted at one point and then refroze again. It's still molten and the core of the Earth is still molten. And probably there are sort of detailed processes associated with the motion of the molten core of the Earth and so on that had a different effect for some, depending on the densities of materials and things. Like this. And eventually there are chemical processes that will tend to concentrate things in one place rather than another. So in the question of whether that's true, if we go mining on the Moon or we go mining on Mars, we find the same kind of, oh, there's a tantalum mine here, and so on. That's an interesting question. Actually, I have not specifically asked that question. Whether the big splat Will have had an effect on the homogeneity of the Earth, I don't know. And the fact that the Earth has a liquid core might have an effect. Mars does not have a liquid core. The Moon does not have a liquid core. Well, Mars might have a tiny one, but the Moon doesn't seem to have one at all. And that's something we know. Just like from earthquakes on the Earth, we can tell that when there's one place on the Earth where there's a big earthquake, we can see how the seismic waves Propagate through the Earth. And we can see that in the core of the Earth, there's something liquid, because different kinds of waves go through liquids, Then go through solids. And so on the Moon, there are little moonquakes that happen. They're smaller than earthquakes. But we can see from that that there doesn't seem to be anything that. It seems to be that they propagate through the Moon As a solid object. So that's kind of the story of. So I'm guessing it's an interesting question. I'm sort of guessing, in first approximation, they'll be mining on Mars like there's mining on Earth. Second approximation, it might not be the same because of the big splat and things like that. And it might very well be that. And some of these planets and moons that get continually sort of squidged by tidal forces and so on, they may have kind of separated out different materials and different minerals and so on in different ways. Good question. As you can tell. I thought it was a good question because I've asked it of a bunch of people trying to get to a definitive answer. But I'm telling you the best I know so far. All right, I got to go to something for my day job, but thank you for a lot of interesting questions, and I hope people found that interesting, and look forward to chatting with you another time. Bye for now.