Science & Technology Q&A for Kids (and others) [Part 143]

Foreign. Welcome to another episode of Science and Technology, Q and A for kids and others. And I see we have a bunch of questions here. And I noticed there's one about the upcoming eclipse in the US Next Monday. And I'm supposed to know something about this because I wrote this book about predicting the eclipse, which you probably still find now, but you can find online versions of this easily. So there's a question here about what's kind of an elementary explanation of eclipses, why they happen, how you predict them, and so on. So let me see how I can do at that. So the basic point is an eclipse happens when the Moon is in front of the sun as viewed from where you are on the Earth. Now, there's lots of things moving. The Earth is moving around. The sun goes around the sun once a year, the Moon is going around. The Earth goes around the Earth in one lunar month, about 28 days. So you might think if the Moon is going around the Earth, the Earth's going around the Sun. Every time the Moon goes around the Earth and gets in between the sun and the Earth, there'd be an eclipse. What we know happens when the Moon gets between gets so that it's sort of between the Earth and the sun is we have a new moon. New moon being when the face of the Moon that we see from the Earth is not lit up by the Sun. So if the moon, if the sun was illuminating the Moon and then the light from the Moon came to the Earth, then. Then the Moon looks lit up, so to speak. But if the sun is sort of behind the Moon when viewed from the Earth, then the Moon will not look lit up, so to speak, from the Earth. By the way, when light from the sun falls on the Moon, the Moon kind of looks lit up relative to the rest of the night sky because the rest of the night sky is dark. But actually only about a tenth of the light that falls on the surface of the Moon is actually reflected back to us. The Moon is actually quite gray and dark. But relative to the night sky, which is completely black, it looks very brightly lit up, so to speak. So, okay, so every lunar month there's a new Moon. Question is, why is it the case that there isn't an eclipse every lunar month? That is, every time the Moon goes around the Earth and goes between the Earth and the sun, why doesn't it block out the Sun? Well, the basic reason is that the orbit of the Moon is tipped about 5 degrees, about that much. From the plane in which the Earth orbits the Sun. It's a little bit complicated. The geometry of this is a bit complicated. But the Earth is going around the sun and the Moon is going around the Earth. But the Moon is not going around in the same plane as the Earth is orbiting the Sun. The Moon is tipped at a 5 degree angle. So most of the times that the Moon is sort of between the Earth and the sun, so that the side of the Moon pointing towards the Earth isn't sort of seeing the sun, most of the times that's happening, the Moon isn't lined up between the Earth and the Sun. The Moon is kind of up above the plane in which the Earth is orbiting the Sun. And so you can sort of still see the sun sort of underneath the Moon in a sense or above the Moon. The Moon just isn't in the right plane to obscure the Sun. So actually it's kind of tricky because every so often, every, oh, what is it, 27, let's see, 20, 28.7 days maybe the Moon is in fact in the right plane to be between the Earth and the sun. And every 27 days the moon is in the position between the Earth and the Sun. So those two things. So it's going around and every so often it's in a place to be between the sun and the Earth. Every so often it's in a place that's in the plane that would actually obscure the sun from the Earth. But those two things don't usually happen at the same time. One of them's happening every so called synodic month, which is the time it takes the Moon to go around the Earth, so to speak. And every Draconic month is it passes through the so called plane of the ecliptic, the plane that the Earth makes when it's orbiting the Sun. So the fact that the draconic month and the synodic month don't line up because the orbit of the Moon is at an angle. That's why we don't see an eclipse every lunar month. On Jupiter, for example, its biggest moon, Ganymede is really close to to being in the same plane as the one in which Jupiter orbits the Sun. And so from Jupiter there is an eclipse produced by Ganymede every time Ganymede goes around Jupiter, which is, I think every couple of weeks. And in fact, most of the big moons in our solar system are orbiting close to the plane in which the planet orbits the Sun. I think Iapetus moon of Uranus, right, is, is another one that's fairly big and not in the plane in which its planet orbits. The Sun. But most of the big moons in our solar system are kind of lined up. And presumably that's because when the planets were formed, there was this big kind of disk of material, and some of it turned into moons, some of it turned into planets. But our moon was probably formed in a slightly complicated way through a collision of a sort of Mars sized asteroid with the early Earth that then caused the Earth to become liquid and a piece of it broke off and formed the Moon and so on. So it's a slightly more complicated story. And that presumably explains why our Moon is at a 5 degree angle. But the end result of all of this is that the conditions for an eclipse don't happen every lunar month. They only happen when these two kind of two things line up. And turns out that if there has been a time when the Moon is precisely between the Earth and the sun to make an eclipse, then you can go a certain number of periods of the Moon going around the Earth, a certain number of periods of the Moon going up and down between in the plane of the ecliptic. And those line up every, what is it? Every 19 years, I think, which is roughly every 19 years, 19 years, 11 days, I think. And that corresponds to a thing called the Saros cycle. And roughly every 19 years, 11 days there'll be, I think, 244 draconic months and 232 synodic months. And so at that point, the position of the Moon is basically the same as it was one saros cycle ago. So 19 years, 11 days roughly ago. So if there was an eclipse at that time, there'll be an eclipse another 19 years later. So the eclipse that we are seeing is one of a series of eclipses that started around the year 1500. And every 19 years since then there's been an eclipse. When things line up in this way, and the sequence that we're on I think goes on to about 2500 A.D. keeping on going every roughly 19 years. Well, so that's what sort of. When the configuration of the Moon and the sun is such that we get an eclipse, the now we can ask, well, where does the eclipse actually land on the Earth? And that's a tricky question. And one thing that happens is you don't exactly get a repetition every 19 years, 11 days or whatever. There are sort of other factors that come into play at about the one part in a million level. And those gradually cause that repetition do not precisely occur. So that's why this sort of Saros series of eclipses separated by that amount of time doesn't go on forever. It eventually gets sort of out of alignment and no longer happens. But during that series, the place where the cone of shadow that comes from the moon intersects, the Earth gradually moves across the surface of the Earth. So the eclipse we're about to see goes across the U.S. but the next eclipse in this series will be quite far to the, will be somewhere over, I guess probably over Asia. And I think this one is moving to the south, so it'll be more southern. That'll be the next sort of 19 year repetition of this eclipse in this series. And what happens is the precise position that the eclipse will be on the surface of the Earth depends on how the Earth is rotated and exactly sort of how it aligns with days that occur and so on. When you see the eclipse, there's this place where the whole sun is, is covered relative to your position on the Earth. If you move away from this region of totality, the so called umbra, you get to a place where only part of the sun is covered. So you see a partial eclipse. The region where the sun is completely covered by the moon, it moves on the surface of the earth at between 1,000 and 2,000 miles an hour. And mostly as a result of the Moon moving in its orbit and not aligning anymore, that sort of cone of shadow is moving as the moon moves around in its orbit. You know, I realized that in trying to explain this, it introduces quite a few concepts that are a little bit complicated. I mean, the other question would be why is it the case that the Moon as seen from the Earth just fills the disk of the sun? It's about half a degree of angle that is the size of the Moon as seen from the surface of the Earth and the size of the sun as seen from the surface of the Earth. It's completely coincidental. These match over time. The Moon is slowly moving a little bit further away from the Earth and it'll be a while before it really is out of whack. And we really don't see eclipses by while. I mean, hundreds of millions of years at least. And the dinosaurs will have seen eclipses pretty similar to the ones that we see today. The Moon hasn't moved that far in its orbit. It's kind of remarkable that in, let's say, 100 million years, that sort of the Moon is still moving in this very kind of organized way around the Earth. And it's a very precise kind of thing. And so it so happens that we kind of have a pretty big moon relative to the size of our planet. And the distance that it is away is such that it just lines up and just covers the disk of the sun. So that's a little bit of kind of why the eclipse happens and why it doesn't happen every month and why eclipses are quite rare. At any given time, there may be 20 or 30 of these different Saros series going on. So there'll be an eclipse that happened sometime in, I don't know, 1700 or something, and there's a repetition of that eclipse that might happen in 2026, let's say, and a repetition of some other eclipse that started in the other series of eclipses that started in, let's say, 1500 that happens this year and so on. So at any given time, the 20, 30, whatever of these Saros series that are active of eclipses, sort of being repeats of earlier eclipses in that series. And I think the things that can happen, the moon can be a little bit further away from the earth, Which will mean that it doesn't quite cover the disk of the sun. And so then you get an annular eclipse where you can still see sort of a rim of sun around the moon. The eclipse we're about to have is a, is a proper total eclipse. You can sort of measure the amount of eclipsing by the fraction of the area of the sun or that the moon covers. And I think this one is like 2%. The moon is 2% bigger than the disk of the sun when it's sort of in position for the eclipse. And for an annular eclipse, it might be a few percent less than the size of the disk of the sun. So you still see a rim of sun around the moon. So there are various things that happen in a total eclipse. So if you're seeing it, and first of all, you can typically see if you're in a place where, for example, on high ground, you can see the shadow of the moon kind of coming towards you as the sort of eclipse approaches. And then one thing that's a funny effect are things called shadow bands that are occasionally seen. I happen to see them in the 2017 eclipse. They're kind of this. A few minutes before the total eclipse happens, everything seems to shimmer. And you see this kind of. You look at the ground and it's kind of shimmering. And you say, I can take a video of this. And you try and take a video and the video doesn't come out. It's kind of one of those conspiracy theory like things. You can see it with your eyes. But typical videos of it don't show it. And presumably that's because of some complicated effect about light diffraction and so on. But the, the cause of these shadow bands Is probably something to do with the fact that the sun, the light from the sun is coming through kind of the air, which is rapidly cooling as it no longer has sunlight falling on it. And that causes motions in the air that cause changes in the way that the light moves through the air and so on. And that's presumably what causes these shadow bands. But that's one of the effects that one can see. Also, there's a tremendous habit for the. The animals around which might be chirping or making other noises. They're pretty quick to decide nights happened. We're going to sleep and become very quiet, which is kind of interesting. How quickly they kind of switch to it kind of gives us a lesson for us humans that probably, you know, when we were sort of the way we were originally built, it's just like if it's night, we go to sleep. We've kind of modified that with artificial light and so on. Well, let's see. Okay. There's some other questions about eclipses. Lola asks, is it possible to view an eclipse from space? The answer to that is yes. If you're in low Earth orbit like the International space Station is, you'll see an eclipse that looks pretty much just like it does on the ground. You're not far enough away from the Earth for it to make much of a difference. It's just like being on a very tall mountain. One thing you can potentially do is if the eclipse is moving at, let's say, a thousand miles an hour across the surface of the earth, then the question can you chase the eclipse? And I think there were eclipses where the Concorde, which could go at maybe 1200 miles an hour, could almost chase an eclipse and could keep one in the region of shadow for a while. Anything in Earth orbit is going too fast, and so it will presumably be in the region of eclipse For a short time and then move out of it. Actually, it's an interesting question. How long the iss, for example, is in a region that has that eclipse before it moves out of the cone of shadow. If you're further away from the earth, well, from deep space, let's say from the position of the moon, you can absolutely have a situation in which you're in a position where the Earth will eclipse the sun from where you are. So from the position of the moon, or even from much further away than the position of the Moon, because the Earth is pretty big compared to the Moon. The Earth can cover the disk of the sun relative to where you are. So that's another phenomenon. And I think that some. Well, the satellites of Mars, for example, Phobos and Deimos, are, I think, too small to cover the disk of the sun, even from Mars on Mars, because Mars is further away from the Sun. The disk of the sun in the Martian sky is smaller than. Significantly smaller than it is in the sky of Earth. But those satellites are just probably little captured asteroids, little tiny pieces of rock, and they don't cover the disk of the sun from there. Ganymede on Jupiter, for example, is big enough, and Jupiter is far enough away. And the numbers work out so that it does cover the disk of the Sun. I think it's about three times the size of the disk of the sun from Jupiter. And same happens with some other big moons in the solar system. Let's see. Golagaz asks, why does the Moon always show the same side to the Earth? Why is that? What happens is the Moon probably at one time was rotating just like the Earth rotates on its axis to give us days. The Moon was probably rotating too. But over time, the Moon got locked so that it. As it rotates, its period of rotation is exactly aligned with the period with which it rotates the Earth. And the reason that happened is the. Well, the Moon is what produces tides, ocean tides and so on on the Earth. The main effect for producing ocean tides on the Earth. And it does that by essentially elongating the Earth by pulling the water that's closer to the Moon, close, even closer to the Moon. And the water that's further away goes even further from the Moon. And that kind of elongates the Earth and actually doesn't just the force of gravity from the Moon doesn't just pull the water on the Earth. It actually produces a solid tide in the Earth. It actually distorts the Earth a little bit. And similarly, the Earth distorts the Moon a little bit. And that tidal deformation ends up being something that will sort of dissipate the angular momentum, the tendency for the Moon to spin around over time. That deformation will make the Moon tend to get locked so that it is rotating. It rotates on its axis at the same speed as it rotates around the Earth. And that's why the Moon gets locked with just one face to the Earth. Happens in other places, too. Like the planet Mercury is locked like that as far as the sun is concerned. So the planet Mercury has just one side that is constantly pointing towards the sun and getting really hot, and the other side is pointing away from the Sun. That type of kind of locking of the rotation period with the rotation period on the axis with the rotation period around the sun or around a planet for a moon is a pretty common phenomenon. And it happens. Well, let's see, it happens most dramatically when. What causes that to happen more than. I mean, I think it's a combination of how much you can deform the body that's rotating around and probably some other factors which I'm not immediately able to figure out. But it sometimes happens, sometimes doesn't happen, but it's happened for the Moon with respect to the Earth. And actually the Moon more or less shows us the same face all the time. And so that means the far side of the Moon is sort of away from the Earth. And by the way, the far side of the Moon gets a lot more meteorite craters, so it gets a lot more meteorites hitting it. So the far side of the Moon is much more full of craters than the near side of the Moon. And that's because the near side of the Moon is kind of protected from many meteorites, because those meteorites would get captured by the Earth before they hit the Moon. But if they're coming from sort of the far side, then they'll hit the far side of the Moon and never get deflected by the Earth. Well, there's another effect, which is so called librations of the Moon, where it almost keeps the same face to the Earth, but it's wiggling back and forth a bit. And that's something that's comparatively difficult to compute, but it's something that's an effect that one can see. Let's see. Ryan asks, how are orbits in the solar system so stable over time? Well, presumably in the first few hundred million years of the solar system, maybe the first billion years of the solar system, there were probably a lot of things that weren't terribly stable. There were probably lots of other planets in the solar system. I don't know, maybe 25, 30 planets, whatever it is. But over time, many of those planets had orbits that were unstable. They either got progressively. They either eventually got ejected from the solar system instead of wandering around in interstellar space, or perhaps they crashed into each other and sort of liquefied each other or maybe produced fragments like asteroids or something like this. So it's not really known in detail sort of what that. What, what was happening in the very early solar system. All we know is what survived to today about eight big planets and so on and lots of minor planets and all that. And it's the. In a sense, the reason the solar system is stable at some level is because all the parts that were unstable disappeared a long time ago. And what's left over is the parts that were stable over billions of years and are here for us to see, so to speak. Now, if you ask, could there be a little tiny instability that develops that gradually over the next 10 billion years, eventually causes, let's say, some two planets to crash into each other or something like that? The answer is yes, that's possible. People have tried to simulate kind of the behavior of the solar system over long periods of time. It's pretty difficult to do, partly because there can be these very tiny effects that gradually build up and become important. And the sort of gradual migration of planets into and out of further and closer to the sun and so on, and other complicated effects, it's pretty hard to work out. And it can be the case that what started as a very tiny change could be something that. That eventually leads to instability. And, you know, so it could be the case if one somehow was able to push the Earth in some way. You know, somehow you. Well, some big impact, for example, happened on the Earth and it got pushed in some direction maybe that would eventually lead to instability. I mean, we certainly know there's an experiment done even quite recently on an asteroid, asteroid called Bennu, which in I think the year like 2150 or something is due to go between the Earth and the Moon. It's due to become the asteroid that will get closest to the Earth. And if calculations are right right now, it'll miss the Earth and we'll probably be able to. Well, whoever's around at the time will probably be able to see it in the night sky pretty easily. But if sort of calculations are wrong or if it gets pushed in the wrong direction, even with a small push right now, that asteroid could end up, for example, hitting the Earth, which would cause a big effect. But that's something where sort of a pretty small change could over a period of time, have a large effect. I think it has to be a fairly big change to have an effect over the course of 150 years or something. If you were to make a small effect and then wait 10 million years, it could be a very small effect that will gradually build up to be a large effect after 10 million years. Let's see. So it's been a long time question. By the way, that was a big deal in the 1800s people wondering, is the solar system stable? And trying to work out from the sort of mathematics of gravity pulling on planets and so on, would that lead to the solar system always staying stable or eventually becoming unstable? Was very hard to work out. It's only with computer calculations that one can really do anything along those lines. And over the last, I don't know, 30, 40 years, it's been gradually getting to the point where, yes, we can predict it. We know it's stable for a million years, 10 million years, maybe 100 million years. Gradually, that period where we can sort of compute stability has been getting longer. Let's see. RSM asks, I wonder if it would have any effect if the Moon did rotate with respect to the Earth. I don't think it would have much effect on the Earth. I think it, for example, even the time of eclipses is only affected at one part in 10 million, I think, by the shape of the Earth. The Earth is not a precise sphere because of its rotation around its axis. It bulges out at the equator, and it bulges out by, I don't know, a few miles relative to its 6,000 mile, 6,000, 8,000 mile radius. And I think. So there's small bulging at the equator from the Earth. And, for example, even when it comes to all the detailed things that have to line up for eclipses, that's not a very big effect. So for the Moon, if the Moon was rotating on its axis, I would expect it to have a similar kind of. Well, I think it does have some equatorial bulge, but it's less than the Earth. The only thing one might say about kind of the Moon rotating on its axis and things about what happens to the Moon is I think if it was rotated on its axis, I think it would have more deformations. In other words, I think it's been set up now so that it is minimally deformed as it orbits the Earth. I think if it was rotating on its axis, it would have deformations. And those deformations, they're sort of solid tides on the moon changing its shape. And that would probably. Well, I know that. Oh, gosh, which is it? Is it IO or one of the other moons of Jupiter? I think it's that one. I'm not sure has strong enough tidal deformations that it actually sort of opens fissures in the surface of the Moon and produces all kinds of volcanic activity and things like that. And one might imagine that an extreme version of that on the Moon would lead to kind of. The Moon is unlike the Earth, which is liquid Inside, the Moon is solid inside. And there are tiny Moonquakes, but they're nothing compared to earthquakes. And those Moonquakes, I think, come from deformations of the Moon associated with gravitational effects from the Earth. But I suspect those would be bigger if the Moon was not tidally locked into this, showing only one face to the Earth. But I don't know of other. And so that would probably. I don't know how much effect it would have on the tides on the Earth, for example, if the Moon was rotating on its axis, I don't think terribly much. The monk comments. If the Moon was spinning fast, it would probably have a liquid core still. Maybe so. I think that. I mean, that depends on all of this question about. About deformation. Because the reason the Earth has a liquid core is there are really two effects that make the Earth hot inside. One is it didn't cool down yet from when it formed. And the Earth is a pretty good insulator. It doesn't let heat out. So the heat from when the earth was formed 4.6 billion years ago, there's still a bunch of heat from when it was originally formed. That's effect number one. Effect number two, there are radioactive elements, elements where the nucleus of the atom eventually explodes, so to speak, but it takes it a long time to do it. And elements like uranium. It can take it billions of years for the nucleus of the atom to explode and produce energy. And there's enough uranium, for example, and other radioactive elements, presumably in the center inside the Earth, that every time one of those explodes, it puts a certain amount of heat into the Earth. And I think these days, people think that the effects of remnant heat, heat left over from the formation of the Earth, and heat produced by radioactive decay is more or less equal. So both those effects are going on now. I suppose the Moon will also have heat from radioactive decay. And I don't know. I suspect the Moon is much smaller than the Earth. The surface area of the Moon is about the size of the US So the Moon is maybe a hundredth the mass of the Earth. So the time necessary for the heat to diffuse out from the center of the Moon is much less than it is for the Earth. And so it can kind of cool off and solidify more quickly. And I think Mars, for example, may have still some small liquid core, but nothing very large. It's also smaller than the Earth. Let's see. Gosh. Natanan asks, if the Moon were to be broken apart, leading to a debris field, what would happen to the Earth? Well, the thing you ought to realize is whatever effect broke the Moon apart is introducing lots of energy and momentum into the Earth Moon system. So whatever did that, that will have an effect on, for example, when the Earth orbits the sun, the Earth is much heavier than the Moon, but as it orbits, it's kind of doing this dance with the Moon. And the thing that is really following the elliptical orbit around the sun is the center of mass of the Earth Moon system, which is something where if you were kind of to take the Earth and the Moon and you were to put them on a balance beam or something, and you were to say, where do they balance? Where is the place where there is sort of. If there was no Moon, it would sort of balance from the center of the Earth. But because the Moon is there, the balance is slightly away from the center of the Earth. And it's that place where there's sort of balance that's the one that follows the electrical orbit around the Sun. And so if you kind of were to get rid of the Moon, that the position of that point would move. If you were to. If the Moon were kind of. If the debris from the Moon, if the Moon just had cracks, you know, if the Moon was basically in the same place, but it had a great big crack and it was in two parts, then I don't think that would have such a big effect. If you take the pieces of the Moon and you spread them as a ring around the Earth, for example, then then you would have a bunch of effects. And I don't know exactly what they would be. But assuming that if you blew up the Moon, very hard thing to do. But if you blew up the Moon, the force of blowing it up would throw some fragments towards the Earth. But if you just gradually sawed the Moon in half without generating any momentum for the fragments, they would just sit there and be some tidal deformation effects and things like this, but nothing much would happen. But if you have something which sort of blows up the Moon and sends fragments hurtling towards the Earth, then those things will hit the Earth and so on. But if the things are sort of left in the same position as the Moon, they'll just orbit just like the Moon is orbiting. If the. I mean, we know something about how asteroids of different sizes impacting the Earth, what effect that has. The asteroid that hit the earth 65 million years ago near the Gulf of Mexico and was responsible for kind of presumably finishing off the dinosaurs. I mean, it was fairly dramatic. I think we have some fossil record of one afternoon just suddenly bamboo this thing hit. It produced Lots of tidal waves. It threw a bunch of dust into their upper atmosphere which caused the sun to be blocked out for probably a year or two, which made things very cold on the surface of the Earth. And the tidal waves I think went, certainly went across the US from the Gulf of Mexico and so on. So big effect. And there are different things that happen at different sizes. I don't know how big. If you have something the size of Mars hitting the Earth, it would liquefy the Earth as probably it did four point something billion years ago when as the current theory goes, the moon was formed. I mean if you had something that big hit the Earth, the whole Earth will be sort of will turn liquid. But we know that that was coming a long, long, long time before it arrived. So I don't think we have to worry too much about it. I mean one might worry that one day there'll be one of those planets that escaped the solar system and just sort of wandering in interstellar space and you know, it might hit us. But we know that a long time in advance. And also the, the probability of that, the chance of that happening is incredibly low because space is really big and these planets are very small compared to the sort of the size of space, so to speak. It is, it is true that in, well, what probably happened 65 million years ago is that it being cold for a year or two was not good for the non internally regulated cold blooded reptilian dinosaurs, so to speak. And maybe it was better for the little mammals that were around at the time and which had independent, were warm blooded and had sort of independent regulation of their temperature. I mean I kind of, I think in, in modern times, you know, if the Earth was, if the sky was blotted out for a year, it would get very cold or at least fairly cold depending on exactly how much dust there was and so on. And lots of crops wouldn't, wouldn't work. I don't think, you know, it would be bad, but it wouldn't work wipe out our species at least. It would probably have all sorts of bad effects on lots of other species. But it's worth remembering that if you just look at mammals, I don't know how much effect it would have on the cockroaches and things like this. But you look at mammals, we are, what is it, 40% of the biomass of mammals on the planet. Most of the rest of it is farm animals that we keep. There's only a pretty small part of it that is wild animals. A little bit, a little bit of a Strange fact. But you know, we're the main, we're the main ones who would have, on whom it would have an effect. And we have a habit of doing things like being inside and being able to generate electricity other ways. I mean, I suppose photovoltaic electricity wouldn't be any good if there was this kind of, there was this kind of dust layer that blotted out the sun. You know, back in the, oh gosh, the 80s, I suppose 1980s people worried that if there was some nasty nuclear war with lots of nuclear explosions on the Earth, that that would similarly throw dust into the upper atmosphere and create what was referred to as a nuclear winter. I think that theory largely fell out of favor. Sort of a model for that was the dust storms on Mars, sandstorms on Mars. And I think that was on further study of those, it, I think became clear that that isn't what would happen. See other questions here. Well, Chat is asking, is predicting eclipses harder than motions of planets or comets? Yes, it is harder because the overall motion of a planet or a comet, you have to get a lot of things right to know exactly whether this thing will line up with that thing to produce an eclipse. So to predict the orbit of a planet or the moon to enough precision, if you predict it to enough precision, yes, you can figure out whether there will be eclipses, but you have to get it to very high precision or you'll just get it completely wrong and you'll say there is going to be an eclipse or there isn't going to be an eclipse and you can see that it's definitively wrong. If you get the position wrong in the sort of fifth decimal place, then it's less noticeable. If it doesn't cause there to be an eclipse when there shouldn't have been, or no eclipse when there should have been type thing. So it's more difficult from that point of view because it's more obvious when you're wrong. Let's see, there's a question here about very different topic. Can LLMs do math? So LLMs, large language models, are AI systems. ChatGPT is sort of the most famous LLM. There are now a bunch of others work in fairly similar ways. And the role of a large language model is to kind of learn from lots of examples of human language from billions of pages that one finds on the web and places like that, to sort of learn the patterns of human language and be able to extend them. So, you know, classic case would be, I don't know, something like. The moon keeps the Same face to thee. Blank. What's the next word? Well, if you looked up, the moon keeps the same face to thee on the web, I'm sure you find lots of instances of that sentence. And the next word is always earth. So the LLM as it tries to sort of learn from the content of the web, is it's going to sort of conclude that statistically the chances are the next word is earth. And the thing that is surprising is that if you get the LLM to predict the next word, then the next word, then the next word, and so on, to write a whole essay for you, what's surprising is that the essay that comes out can be something that sort of keeps a thread of sense to it and doesn't just kind of, yes, that word fits with that word, but it doesn't really keep going and make any sense. And the fact that it's possible to go far beyond what the things that it could sort of know from having seen examples on the web, the fact that it sort of generalizes from, from what's been what it's seen on the web to produce kinds of streams of text that are reasonable with respect to us reading them, that is a very surprising thing. Nobody really expected it. And that's the thing that we sort of discovered happens with ChatGPT. Well, my own guess is that the reason that that surprise thing happens is because there's more regularity and in human language than we had really recognized, and that there are patterns that you can sort of determine by just looking at lots of language that can allow you to sort of construct, keep constructing things and have something that sort of continues to make sense. Well, that. So, so kind of the. How does it actually work? How does it make those predictions? It's based on a neural network. And what is that? Well, something where you have, in a computer, you have a bunch of neurons, artificial neurons. Each one has a number associated with it. And what's happening is that you're kind of going through. You have a series of layers of neurons, each one with a number associated with it. You start off with a whole bunch of numbers from the top layer of neurons. And. And then you're going through and you're figuring out the numbers for the next layer of neurons, the next layer of neurons, the next layer of neurons, until you eventually get to the output layer. How do you figure out the numbers for the successive layers? Well, you have connections between neurons. So one neuron, a particular layer is connected to lots and lots of neurons at the previous layer. And it's A piece of essentially arithmetic that it does, it says, let's look at the values of the neurons on the previous level layer and let's multiply those numbers by weights, sort of connection weights. Let's just add up all those results from multiplying the values of the neurons on one layer by the weights associated with the connections, add them all up, and then let's say is that number, let's say larger than 0 or smaller than 0 or a little bit more. There's a so called activation function which, which kind of says based on the size of that sum, what should the new value of the neuron at the next layer be? So you just do that a whole bunch of times. And so, for example, I think the original ChatGPT had about 200 billion connections, a few million neurons in about 400 layers. And so what was happening was, so what happens? So you take the text that you've got so far, you turn that text into numbers. So for example, you might pick common words and you might say a, the is the number one, a potato is the number 712. And then sometimes you break words up and say just the thing that says ante as a prefix to a word might be 914 or something. So every token, every piece, every word or piece of a word gets a number. And you've got this. And those numbers are what's fed into the first layer of the neural net. And then the neural net then goes through and those numbers ripple through the neural net, multiplying by weights, getting to the next layer, going on, et cetera. And one of the things that was figured out is just how those neurons are connected up. There's so called transformers, which are kind of ways of connecting these neurons up, where a particular, where there's kind of a sort of a flow to the thing. And you kind of know there's a sequence of tokens that you put in and you're kind of looking back at a whole bunch of a certain context window of tokens back in this kind of block of text that was put in. And so you take all of that stuff, you grind it all up as it goes through this neural net, and at the end you generate a number, a probability for each of the possible tokens. And so that gives you a probability for what the next word should be. Should the next word be earth or should it be elephant? And it might be that it says probability 0.99 that it's Earth, 0.0001 that it's elephant. And then the thing that's actually writing the essay has to say, oh, well, I'll pick the thing that's most probable, or I'll pick the thing that is. Usually I'll pick the thing that's most probable, and sometimes I'll pick one of the other ones. And it does that, puts down the next token and then keeps looping through it again and again and again. And that's kind of how the LLM writes out successive tokens and then successive words in its output. Now, how do you set up all these weights, all these numbers associated with the neural net? Well, you have to train the neural nets, and that takes lots of effort. And the idea is that when you start the neural net off, just got these neurons arranged, it's got these weights and so on, and they're just random. And so you feed in. The moon keeps the same face to thee. And that turns into a bunch of numbers inside the neural net. And out at the end of the neural net, it makes a prediction about what words should come next. And it says the next word should be porcupine. Let's say something totally random. But you know that the next word from the data that you have, from the examples of text that you have, you know the next word should probably be Earth. So you have to kind of feed back that information into this neural net to train the neural net to say, no, it isn't porcupine. Move to the word that's a bit a different word in your sequence of words that are specified by numbers. Move closer to the one that corresponds to Earth, move closer to the number that corresponds to Earth. And the really surprising thing that's not obvious it would work is you can just keep bashing this neural net billions, trillions of times, just saying, here's what the text should say. And you do that for, let's say, a trillion tokens of text. Here's what the text should say. Oh, you produced this. No, Change the weights in the neural net to make it closer to producing the correct thing. You keep doing that over and over and over again. And eventually the neural net gets to the point where it can correctly kind of reproduce the, in general terms, at least the sort of correctly continued text that you feed in. The big surprise is that the way it does that is something that sort of agrees with the way that we humans would do it. It's not obvious that would work that way. Probably the reason it works that way is because we humans have in our brains something that's very similar to this kind of neural net that we've set up in a computer to be the large language model. So that's kind of the idea that it's always predicting the next word and it's doing so by looking at the previous words and by knowing kind of what it learnt and generalized from the text on the web, let's say. Okay, so now let's say, can you use this to, for example, do math? Well, if you say two plus two equals what's going to be the next character? It's probably going to be a four. You can see that, you know, millions of times on the web. So if you're just sort of remembering, if you're trained from text on the web, yes, two plus two equals four, it's all good. However, if you say what's 1-728-439644 or something, that particular computation will never have shown up on the web probably. And so the question is then, how does the LLM know what to say next? Well, the question is, can it generalize from the fact that it's seen 2 plus 2 or 2 times 2 equals 4, 3 times 6 equals 18, whatever. It's seen some of those things over and over again. Can it generalize from those to multiply these two big numbers together? The answer is no. That's a different kind of thing. What's different about it? What's different about it is that when we built up math, we've kind of built this formalized way of describing things. When we think about math and arithmetic and things like that, there is sort of a procedure for working out what two numbers multiplied together are. But that isn't a just, oh, you remember roughly what happened and just write down the next digits. You have to go through and you have to have these sort of loops where you're going through and you're figuring out, oh, the next digit. Is this based on this? Based on that? You're actually sort of running this computation. That's not what the neural net does. The neural net is just trying to take what it learned and trying to say what's the next thing based on the things that I've learned. So it's not a very good fit for kind of things that are things like mathematical computation where you're more dealing with something that has a kind of this, oh, you have to actually compute and do a whole series of computational steps and kind of remember what came in the middle and so on. That's something computers find easy, but sort of computers as they have normally been set up, find, find comparatively easy. But it's Something that neural nets just don't happen to be set up to do. Now, there's a question. Could you sort of merge kind of neural net technology with the ability to compute things? The obvious way to do that is to have the neural net just get to the point where it says, okay, I've got these numbers to multiply, or I've got this algebraic computation to do, or something like this. Let me do what a human would do, which is use a tool. I mean, we've built the main tools that people use to do things like algebraic computation, Mathematica, WolframAlpha and so on. Let's just call WolframAlpha and ask it to do this computation. And more than a year ago now, we set things up so that AIs could use WolframAlpha as well as humans and Wolfram language as well. So that when the LLM gets to the point where it says, oh, yes, I've got this algebra thing to do, what it does is it produces a bunch of words because that's what it sort of trades in that says, call this tool, call the WolframAlpha API tool and do this computation. And then the thing that's kind of watching what the LLM next generates says, oh, that's a tool call. Let me go and actually do that computation. Bring back the result, tell the LLM, okay, the result is 17 or something. And the LLM then reads that as another piece of input and says, and writes out, oh, and the result is 17. So it's kind of doing what a human might do. It's sort of going outside of the story of just this pure neural net and actually using computation. And neural nets are a very inefficient way to. Even when it comes to precise knowledge of any kind, they have a terrible habit of kind of making it up because they sort of know what's roughly right. And it's kind of. I've seen something a bit like that on the web, you know. Oh, on the Web, I saw that the population of such and such a city was, well, I think it's some number of millions. But I'm just going to make up what the number is because it's kind of similar in its view of similarity to what it saw for some other city or something like that. It's a very different kind of thing from, let's actually look up the answer in, for example, our knowledge base and then know what the answer is and then be able to generate it. And similarly, it's a very different thing to be able to do these computations and explicitly compute them and get the sort of precise right answer the LLM is all about. Let me make it sound roughly right as a piece of language. And sound roughly right isn't something that when you're doing math, for example, is the typical thing that you want. I mean, you can, you know, if you hand in your math homework and it kind of looks roughly right, well, maybe somebody would get fooled. But if you actually look at it, it's like, well, that answer is wrong, so to speak. It's much less forgiving than things like human language where you say, I could say I'm doing a live stream right now versus I'm making a live stream right now, or I'm in the middle of a live stream right now. There's a bunch of different ways to say it. And a word off a word, slightly unusual, it doesn't really throw the thing completely off. But if you get that number as instead of two, you put 17, it's really wrong if you're doing something like math. And so sort of a raw LLM is not suitable for doing these mathematical kinds of things. And you can ask LLM to do even very simple things like balance parentheses have the same number of opening and closing parentheses. And up to the point where we humans could readily look at it and say, oh yeah, looks roughly right, you know, five parenthesis open, five closings, something like that, it'll do it right as well. But if you get a really long sequence of these things, it'll be, you might look at it and you might say, oh yeah, it looks roughly right, but if you actually count the parentheses, it'll be wrong. And that's pretty typical of what you can do with LLMs. Now, LLMs are very useful for lots of purposes. There are lots of purposes for which you want that kind of fuzzy linguistic interface to things. You don't want kind of the precision of a thing that's rather non human precision. But if you're doing things like math and so on and chemistry, all the things that have come up in the exact sciences, if you're doing sort of exact science, exact computation kinds of things, it's not good enough to just say, oh, it's roughly right. And so those are things that it so happens that we built the tools to broadly do those kinds of things over the last, I don't know, 35 years or so. And it's really nice to see that they sort of fit in so well with modern AIs and LLMs and so on, that the LLMs, if they are trained, not only if they're trained for. These are things that WolframAlpha can deal with. These are things. This is how you write Wolfram language, computational language. If they're trained on samples of computational language, if they're trained on typical WolframAlpha queries, they can know, oh, the thing that I've got to. Can be formed as a WolframAlpha query and then I can call that tool and get the result back to the LLM. And that's something you see a bunch of, bunch of services starting to use our technology to be able to kind of put the computation, put the sort of exact knowledge and computation into the LLM as something where you're calling this tool to inject that computational knowledge into the LLM. But the sort of, left to their own devices, LLMs, it's sort of not doing these kinds of precise sort of towers of computation about the kind that you end up doing in mathematical computation, for example, is not what it's set up to do. Will it ever be? I think it's not a good fit for what it can do. Computation is in a sense a thing that is sort of ideally set up, sort of just following specific computational rules, doing them over and over again, having these precise rules. That's the thing that computers are well set up to do. Can one sort of weave computation into the insides of what a neural net is doing? Maybe to some extent there's a bit of a trade off between what is trainable, what you can sort of just say, oh, you got that wrong, make a tweak, make it a little bit better, and things where there's a lot of computation going on. Because the issue is if you just sort of fed the data through the neural net and something was wrong, you can kind of assign blame for what was wrong. And you could say, oh, it's that weight there. Just tweak that a bit and you'll make it closer to the right answer. But the problem is anytime you have serious computation going on, you've got some whole loop of operations and you've got this whole thing that's building up the, oh, make this tweak. And it's much harder to see what effect a tweak will have. So I think that that makes it sort of a trade off between what is, what's kind of readily trainable and what involves sort of computational depth. It's something, I mean, you know, I've been looking at this, we've been looking at this, other people have been looking at this. To what extent can you do those kinds of things? I. I think it is sort of a. You're, you're trying to fit together something which is a. A. It's like there's an easy solution. You just call these tools. Maybe there is a way that one will eventually be able to get sort of neural nets to limp better in, let's say, multiplying numbers together or something like this. But that's probably not the right solution. And in fact, neural nets in general are probably not the right solution. They're a good first cut because you can get them to work. But for example, when it comes to stringing language together, you have to go to an awful lot of effort and awfully much computational operations to know, oh, yeah, we ripple through. We use 100 billion weights. We compute with those to get the next word in our. We do 100 billion computations to get the next word that we're going to specify in our essay. Well, chances are that can be done unbelievably much more easily, because chances are there's lots of structure in the language that allows you to basically say, oh, we know kind of how. We know how words of this type fit together. And we just have essentially rules for how these words fit together. They're not precise rules. They might be rules that involve probabilities and things like this. But it's a much more direct thing than saying we'll form these words out of this kind of incomprehensible pattern of bits, an incomprehensible pattern of numbers that are the insides of the neural net. I mean, it's very difficult to tell what's going on inside the neural net, because all of your initial words, the essay you just wrote that was the prompt for the neural net, got ground up into all these numbers that are somewhere inside the neural net. And every neural net with every different training will have different detailed arrangement of where the numbers go and how things flow and so on. And that's just like probably every human brain has knowledge encoded in a slightly different way. But that's something where probably what we've learned from the success of LLMs is that there's a lot more structure in language than we knew. And we can directly use that structure, just like we can if we want to generate sentences that have correct kind of noun, verb, noun syntax, or we want to write something in some computer language that has the correctly balanced parentheses and so on. It's rather easy to write a program that uses sort of systematic computation to be able to work out how these pieces will be set up. Even though it's hard to get a neural net to do that, but it's very easy to get sort of a, a computational system to do it. And my guess is that a lot of that will be possible with, with human language. And we've got this giant clue from the success of LLMs in this, in this area. Long answer. There's a question from Gorgolo. When will the AIs start colonizing space? One could argue that's already happened. I mean, our deep spacecraft, you know, no humans have gone further than the moon. So everything that went further was sort of an AI, I think, you know, how many spacecraft will we be making a dent on the universe? Will we send out enough spacecraft? I think you have to have kind of the robotic factory using resources, you know, using resources on the moon or whatever that's making lots of sort of AI driven spacecraft that they're then going out into the universe. It's a little bit of a sort of hopeless effort, I suppose, because, okay, you have all these spacecraft going out into sort of vast universe. And it's amusing, it reminds one a lot of kind of the pyramids of ancient Egypt of somebody says, I want to be preserved for the afterlife or whatever and build a giant pyramid and then you'll sort of know I was here. And similarly, we can send out lots of spacecraft and it's like, yep, we were here for whatever that's worth. Let's see. SMO asks, when will we have large models of all sorts of other stuff with LLMs primary role being just interpreters between humans and tools? Well, I think that LLMs provide this linguistic layer where you can talk to it, you can kind of muddle around. And one thing that the LLMs can do, and we've done a lot of work on this, is generate precise computational language that then allows you to access all the things that can be done computationally. So that's a big use for LLMs. Now there are things that are other kind of sort of human like generalization of the kind that LLMs do for language you can do for other things like coming very soon is videos and being able to say these are the frames that happened in the video so far, what's going to happen next? And that's obviously relevant for sort of generating video, but it's also relevant for lots of things about sort of understand the world and understand what happens. If you pick this up, what will happen? Well, the system, the sort of behavior model system can predict that. And the Same be true that lots of stuff going on right now with robots and being able to know, oh, if I move this motor this much, what will actually happen? How will the robot move its arm and so on, what will happen to it picking up this particular thing? So that's, I think a sort of a coming soon kind of attraction is sort of robot control using, by having sort of learnt how the robot works and what the effect of moving this motor and that motor is by the same kind of training mechanism that's used for large language models, but now applied not to human language, but sort of physical things in the world. Sort of an interesting question when, under what circumstances this whole approach of neural nets is likely to work. I just made a bit of a study of that piece that I wrote called Can AI Solve Science? A few weeks ago. And the sort of the thing is that human like things, things that humans find it easy to do, the neural nets in our brains find it easy to do. And it's sort of not super surprising maybe after the fact at least that these artificial neural nets can also find those things fairly easy to do. And that's probably true of mechanical things that, you know, the things we choose to deal with in the world are things where our brains can have some prediction of what's going to happen. And so when we're dealing with those kinds of things, we can expect neural nets to also have some kind of prediction about what will happen. I think the general trend is what are the modes of, of dealing with the world that we have. There's language, there's audio, there's video, there's mechanical moving of things. These are some modes of dealing with the world. There are also things like social modes of dealing with the world. How do you interact with people in some kind of social setting and can that be learned? And I'm sure that is learnable by neural net kinds of techniques. So I think yes, it is certainly true. You know, the next generation of, you know, humanoid robots or something, you'll talk to them. That's sort of a large language model kind of story. And their behavior will be determined by some other model that. And then sometimes they'll do things which are not very human, where they're actually computing stuff, where they look at some pile of things and they try to and compute. How do we arrange these in a box? Well, you know, a human could do it maybe kind of heuristically moving this all out around. But we have powerful algorithms that let one just say, let's run combinatorial optimization on this thing and know we can arrange it in this and this and this exact way. So that's the story there. Hal is asking, can we look in the brain and find out what kind of transformers or other things we need in LLMs? You know, know, the history of that is not so spectacular. I mean, neurons were identified around 1900. The idea of neural networks arose in 1943 as something that came from sort of thinking roughly about brains. There are certainly many structures known in the brain, and people have tried to invent neural net architectures that are based on structures, cortical columns, all kinds of things that are seen in the brain. So far, those haven't been terribly successful. Now, it was a long road from the early neural networks to current neural networks, which are qualitatively extremely similar to the early neural networks, but they're a series of engineering tricks that were invented that were significant for this. So I think the idea of let's look inside some brains and get sort of clues about what to do for the engineering. So far, other than the original idea of neural nets back in 1943, hasn't been terribly successful. But it's not to say that it won't be in the future, particularly now that we have all these clues about how things work from the success of large language models. All right, I should wrap up there. So thanks for joining me and see you another time. And if you have a chance to see the eclipse, I hope it should be fun. I'm afraid that in many places around the US there's probably going to be lots of cloud, and I don't know what an eclipse looks like through clouds, I might discover, but it's cool when you see it kind of in a clear sky. All right, thanks for joining me. See you another time. Bye for now.