Science & Technology Q&A for Kids (and others) [Part 138]

Foreign. Hello, everyone. Welcome to another episode of Science and Technology. Q and A for kids and others. I think the last of 2023. So let's see. You know, I'm happy to try and answer questions that are like things you wondered about science technology that maybe should have been in some class that somebody could have taken at some time, but they either didn't take it or they didn't understand what people had to say. I'm happy to try and address those kinds of questions as well as kind of the, the more specific kinds of things. But let's see, Anti is asking, do we know enough of neurobiology to assert that the human brain works differently from machine learning or AI model? Well, at some level it obviously does because its underlying technology is different. The underlying technology of any kind of AI machine learning system is a digital computer, which is based on semiconductors and electronics and so on. Whereas the base technology for our brains is electrochemistry. And although it's still electrical signals, the electrical signals are generated and transmitted in different ways. It's also worth remembering that the kind of energy budget is quite different in the sense that for where and sort of time budget and so on. I mean, our neurons kind of fire every tens, some number of tens of milliseconds, so maybe 100 times a second or something like this. Whereas in a computer we're routinely having a billion operations per second. So the timescales are different by a factor of a million or so. The thing that our brains still very much have over computers is that it tends to be the case that most of the kind of components in a computer are idle most of the time, whereas in our brains, presumably most of the neurons are doing something most of the time. And we managed to get away with about 50 watts of power running our brains, whereas the typical computer. Well, I suppose actually it's an interesting question. I actually don't know the answer to this. If you ran a computer as slowly as our brains run, how much power would it take? And I suspect the answer is that if you redesign the computer to run as slowly as our brains run, that you could get away with using vastly less power than modern computers use to run that the million times faster than our brains. I think another feature of, well, another thing about our brains is that they are continually learning, whereas in current AI systems, one mostly has a time of training and then a time of actually running, or so called inference, inferring output from input, so to speak. And those are two separate things. Whereas for our brains those things are mixed together. I think that in terms of another thing about things like, well, a large language model or something like ChatGPT, it has the feature that the input comes in and it kind of trickles through a few hundred layers of neurons and then the output comes out and it says what the next word should be, and then the whole cycle starts again. And so the only way that the sort of feedback from what got generated to what will be generated next is through this kind of outer loop of, oh, this word got produced. Now the whole input contains that word as well. Let's ripple through the neural net again and see what comes out next. Whereas in our brains there are many more nerve fibers, our brains are not the same kind of feed forward architecture where it's just you start from sort of one end and then things percolate through and then you sort of use the output only in a kind of a small way to determine what the next input will be. More it's a kind of lots of two way connections and so on in our brains. So that's another difference. I would say that the thing to recognize is that one thing we learn from computers is this idea of universal computation, this idea that even though the detailed hardware of two computers might be different, the programs they can run can still be the same. And that means it becomes less important. What the detailed hardware is, what really matters, is what the structure of the software, the algorithms, the methods and so on are. And I think the same is probably true of brains that the details of whether some particular, The details of how particular neurons work, and the fact that we have all these different kinds of neurons and they have different connectivity patterns and so on, and the details of that is probably less important and that rather there are sort of global features of how brains generally work which are probably very much in common between modern AI systems and actual biological brains. I think I mentioned this before, but one sort of exercise that I've been wondering about recently is this question of, okay, so if our brains could be scaled up to run a million times faster, to have many more neurons than we actually have, we have about 100 billion neurons in our brains, each one of which has maybe 1,000 connections, maybe 10,000 connections. So there's perhaps something like 100 trillion connections in our brains and so on. That's as compared to in ChatGPT, at least the original version, there were about 200 billion connections in that system. But the question is, as you scale up the number of connections and the number of neurons and so on, how does that affect the capabilities that one has, and it's sort of a. An interesting and sort of interesting cautionary tale, I suppose that if you look at lower animals, they have smaller brains, and sometimes they have brains that are big because they just have lots of nerve fibers coming in from a very big creature, like a whale or something with lots of skin area and such like. But mostly they have smaller brains and they're able to do less stuff than we can do. So the question becomes, well, what happens if you scale the brain up? How much more stuff can you do? What are the qualitatively different things that become possible? I kind of think. I think I was mentioning this in another one of these live streams, that the fact that we humans have about 50,000 words in our languages is probably a consequence of the rough number of neurons that we have in our brains. And if we had many more neurons, we could deal with languages that have many more words in them. What consequence would that have? I'm not sure we would have more kinds of concepts that we would intrinsically know about. In a sense, the words in our language are the concepts that we intrinsically know about. And I suppose as you try and think about things, there's sort of this question of you're thinking about them in terms of concepts. If you had more concepts, it's sort of a more. You don't have to make as big jumps. And maybe it becomes easier to think about certain kinds of things because kind of the jump distance is smaller. Maybe there are more things that we can sort of see in the world, in the natural world, that we would be able to say, oh, I immediately know what that is, because it's part of our kind of concept space that we're able to have in a bigger brain. But, for example, the very fact that we have the idea of language with its sort of compositional structure and sub phrases and things like this, is that a consequence of the size of our brains? Is it different from what your average cat or dog would have just because their brains are smaller? Is there some threshold that we pass where we're able to have these sort of compositional languages, which have been pretty important for the progress of our civilization? And is there some other threshold we'd reach where something else happens that maybe we haven't yet imagined that is sort of the next level of intelligence capability? I'm not sure. I tend to think that it's like universal computation, that once you get above a certain threshold, you're there, you're finished. That's what the principle of computational equivalence that I developed back in 30 years ago or something now kind of suggests. It doesn't talk about. It talks about the overall computational capability of a system. It doesn't really address things that are more detailed about kind of the structure of meaning space and so on. Really the question of what happens when you compute things is different from what happens when you say, I think that's a meaningful concept and so on. This idea of sort of breaking the world into concepts that we can kind of stuff in our brains is a separate thing from asking sort of, what does it take to compute what happens in the world? And I think the. This question of sort of what happens? Are there other thresholds in kind of the way that we handle concepts and concept space and the idea of meaning and so on. I'm a bit skeptical. I think perhaps not. Perhaps it is more like universal computation where we get to a certain level and then we're done. But it's not obvious, and it's certainly an interesting thing to imagine what would happen, you know, what happens if our brains are sufficiently smaller than they are and we only can have 10,000 words in our languages rather than 50,000? It probably doesn't make much difference. What if you scale it down to only 100 words? That's less than even the smallest constructed languages have. And by the way, even in languages, you know, constructed languages with 200 words in them, there's a lot of nuance that you cannot communicate. There's a kind of a bulk. This is what I'm basically talking about that you can say, but when it comes to the finer details, you can't express those. And arguably that's the cat and dog situation as well. But the kind of the global I'm happy, I'm not happy type story is expressible in cat and dog language, but the detailed kind of philosophical discussion is not haveable in cat and dog language. And so I suppose the question then arises, okay, if you scale up the number of words and you can have sort of a more detailed discussion about things, what does that do for one? I suppose one example of a place where we get to see this a little bit is when you get specialized in some field, there's all this jargon you start using. And that jargon is different from the everyday language. So I don't know if you're in the medical field or something like this, you'll start talking with all this jargon, which does give you, in a sense, a finer set of gradations about what you're talking about than the common language does. And So I suppose that's perhaps a way to imagine what it would be like to be dealing with just vastly more words in one's everyday language is that one gets to make these finer gradations, these more, more detailed kinds of discussions. In a sense, one can think of this as what level when we think of human language, it is a kind of formalization of the world. We get to say table. And by that we mean a large class of things with four legs or have many legs that have flat surfaces and things like that. We don't have to go into all those details or point at a particular thing. We can more abstractly just say the word table. It's packaged that concept together. And I suppose the question then is as we package more concepts, we get to. Well, it's sort of an interesting issue. In some sense it gives us a bigger construction kit for figuring out both how to talk about the world and how to make things in the world or explain the world and so on. And I suppose in a sense, as we built our computational language, our Wolfram language system for, for instance, that's again what we're doing there, is to identify these kind of lumps of computational work that represent kind of these kind of computational concepts that are worth us kind of identifying and implementing. Actually, it's an interesting question there we're at the point where we have about 7,000 built in functions in Wolfram language that cover a very wide range of areas. And it's an interesting issue at what point it stops being learnable, at what point the number of functions is just too big that one can readily have one's arms around sort of everything that's there. I think this is the big difference between natural language and computational language is that in computational language one has a designer who is trying to sort of keep things sort of organized in a principled way, so that by learning the principle one learns a big swath of actual functionality. And of course, in Wolfram language, we're leveraging the meaning of things in English, where we're using English words to express things so you don't have to kind of learn everything from scratch. But I think that's again, with brains of the size we have, so to speak, there's a certain amount you can learn and a certain amount you can kind of maintain in your brain. And then beyond that, it's something where you're going to have to look it up every time type thing. And you've got to remember only sort of the higher level fact. I mean, in general, the story of lots of kind of modern education would be that learn those higher level abstract things, because that's what we've reached so far in the progress of our civilization. You only have to learn all the specific details when they have not been abstracted to something more general. And you might argue that you have a bigger brain, you have to abstract less. And perhaps in a sense, and by abstracting less, you get to make less general statements, you get to have less connections and analogies between different areas. So, okay, so that would be a downer for having the very big brain. The big brain where you have a million words in your language. Maybe you never have to abstract anything. Maybe you can always take each case as it is. You can say, oh yes, there are beavers and there are aardvarks and there are moles and there are this and that and the other. Everything has a separate word. We never have to aggregate these together and say, wait a minute, they're all mammals. Let's say we never have to do that aggregation. We can always just do it case by case. I suppose it's the analogy between what happens if you're doing mathematics with things like automated theorem proving, where you have a computer just grinding out sort of from detailed axioms of a mathematical system, you're grinding out kind of the mathematical results without a broader understanding. That's something that you can get away with. If you are a computer, for example, or if you are a brain that is big enough to store million, to deal with millions of words, you can get away with just saying, oh, there's this particular mathematical theorem and this one and this one and this one and this one and this one, and you never have to pull them together to make a more general kind of theory. So I suppose that's sort of an interesting point of view that the bigger the brain, the less you actually have to abstract, the less you have to make general statements. And that's sort of a thing one might say about AI as well. In a sense, if you've got a small AI, if you've got some small neural net, if it's going to make conclusions about lots of different kinds of systems, it has to have a model that kind of compresses the information about all those systems into something that will fit in that kind of AI brain. But on the other hand, it, if it's a giant AI brain that has quadrillions of different connections in it and so on, then it could just say, hey, I'm going to take, you know, I'm going to take this thing that I saw over here and that thing that I saw over there. I never have to kind of compress them into a model. I can always just take them case by case and just say, wait a minute, I saw that before. You know, a hundred years ago I saw that thing happen. Let me just make use of that thing that I saw happen before. I'm just going to say it's going to happen again now, rather than having to kind of aggregate together and make something that is a sort of a smaller, that's a true model for what's going on that says, you know, imagine that you were dropping sort of cannonballs off the Leaning Tower of Pisa back in the day, as Galileo did. And imagine that you were also dropping, I don't know, pieces of rocks from the, what is that place called the big Tower in Venice? You know, you imagine you, you're dropping rocks from one, cannonballs from the other, etc. Etc. Etc. And you could just say, I just remember what happens to the cannonball in this place, what happens to the rock in that place. I've got so much memory, I can just store all of those things. Whereas what actually happened was the science of mechanics got developed so that one could, with one model would just say, hey, doesn't matter if it's a cannonball or rock, if it's this tower, that tower, there's just a kind of a model that compresses all that information so that you can say what's going to happen in all these different cases. So in a sense that's what you are forced to do if you have a more limited brain, so to speak. And so maybe the trade offs just become slightly different. Let's see. Well, all right, I asked for general questions here, so I get one from Lola here. How would you begin an introduction to a chemistry course? You know, I have to say I'm always embarrassed that chemistry is a field that I never really learned as a kid. And I, to tell a story about myself in England, where I grew up, you know, there are these standardized exams you have to do at various times. And I think there was one that I did when I was like 14 years old about chemistry. And I really had not learned much at all about chemistry. And I, you know, night before I'm kind of learning all the stuff for this, for this exam. And I did just fine in the exam. I think I have a decent memory, so it's kind of an easy thing from that point of view. But I used to say that essentially all the chemistry I knew I learned the night before that exam. It's no longer quite true because as we built out chemistry functionality more from language, and as I've made use of chemistry in lots of different places, it's. I have learned more about it. But if you ask me, kind of typical high school chemistry of what happens when you mix this white powder with that white powder and put it in with this acid, and so on and so on and so on, I typically will not know the answer to those things. I would typically say, hey, you know what? WolframAlpha does a really good job answering sort of school chemistry questions. Ask it, because I don't know. But what would I say in sort of introducing the idea of chemistry? I think the first thing to say is that first thing to know is all matter is made up ultimately of atoms. And there are about 100 kinds of atoms. Hydrogen, helium, lithium, beryllium, boron, et cetera. The periodic table is the inventory of all the kinds of atoms that exist in the world. It's okay, footnote to that, as we go far out, we get past 92, the 92nd one of these. They're all, so far as we know, unstable. These atoms all self destruct in progressively, mostly progressively shorter amounts of time. We don't absolutely know that there isn't another one out there that that's stable, that could be made in the right kind of explosion of a star or something like that. But for most purposes, most of chemistry concerns itself with maybe 20 different kinds of atoms with sort of trace contributions from different obscure kinds. And in a sense, the story of chemistry is a story of given these limited set of building blocks of carbon and hydrogen and oxygen and nitrogen and so on, given these limited set of atomic building blocks, what can you make with those? How do those things stick together to make molecules? What kinds of molecules can you make then? What are the properties of those molecules? Those properties might be what happens when one molecule runs into another molecule? Does it react to rearrange the atoms in it to produce other molecules? Does it just bounce off? Does it not pay attention to the other molecule? That's one set of things. Another set of things are what are, in a sense the physical properties of those molecules? If you shine light on them, what happens to them? If you put them in shine radio waves on them, what happens to them? Those kinds of things, if you put these molecules together, and this isn't really chemistry so much anymore, you put these molecules together, do they make a solid? What are the properties of that solid? They make a gas. What are the properties of that gas and so on. But so one question is you've got these limited set of building blocks. Actually carbon and hydrogen, or even just carbon on its own, is a sufficient building block to make all kinds of things. And so what one's thinking about doing is taking for example, carbon atoms and putting them together. And one feature of atoms, atoms are an individual atom. The different kinds of atoms are slightly different sizes, but they're more or less the same size. They're all about a little bit less than a billionth of a meter across. So one question is what clumps of molecules will actually stick together. And there are particular arrangements that successfully stick together and others that do not. So for example, water, H2O, two hydrogens, one oxygen. That's a particular configuration of atoms that sticks together to make molecules. Sometimes you can have things which you can think of as a little bit like, you know, a. Well, one question is sort of how do the atoms stick together to make molecules? There are sort of two fundamental ways that happens, the so called covalent bonding and ionic bonding. One, ionic bonding is what happens when. Well, again, we're getting into more detail here, but when there's electric charges basically that are causing one atom to attract another atom. And that's what happens. I don't know, table salt, sodium chloride is an example of, of something which is where the atoms are ionically stuck together. But actually those atoms, you can have a sodium and a chlorine together and they're kind of like a molecule. But really when it's in solid form, that thing arranges itself in a giant crystal where you've got sodiums and chlorines and they're arranged in a certain, in an array. And that's kind of like one giant molecule in some sense, held together by these electrical forces. When you have something like water, what's happening there is the thing is being held together by the following fact. So within each atom there's a nucleus with protons and neutrons, and there's then sort of very big outside of the nucleus, very big and puffy. The nucleus is very tiny. Relative to this, there are electrons. And each kind of atom has a certain number of electrons. And what happens is when you put atoms near each other, what happens is that the electrons between the different atoms are kind of shared between different atoms. And that process of sharing electrons between different atoms is what leads to the fact that the atoms are sort of held together. You can't pull them apart because these electrons are kind of. Yes, I'm being shared between these Two different atoms. And the way that that sharing works depends in detail on what the arrangement of electrons is in each particular kind of atom. And so, in particular, One of the key facts about electrons is that when you are. If you try to put electrons in a box, for example, you'll find that the electrons, they. The first electrons you put in the box can have very low energy. They're just sitting there. As you try and put more electrons in, the electrons will never be prepared to be sort of in the same place in the same energy as the ones that were already there. They have this idea of the exclusion principle, which says that two electrons can't be sort of in the same energy level in the same place at the same time. And so that means that if you want to put more electrons in this box, they have to have progressively higher energies. And that box could be an atom. And what happens is that there are essentially these electrons that in order to put another electron into that atom, it is forced to be in a higher energy than the electrons that are already there. And what ends up happening is that the. The. It's again, a little complicated, but the. Roughly, what does it mean for the electrons to be sort of in the same place at the same time? Well, you can kind of think of the electrons as a bad picture is the electrons sort of orbiting around the nucleus. That's not a very good picture because nothing is moving through time like that. It's rather that there's kind of an arrangement of electrons that is as if it has. I'm trying to think how to explain this. The official terms are orbital angular momentum. But I think that's a very confusing term because that originally arose because the mathematics of thinking about kind of electrons in an atom, that was similar to the mathematics of thinking about planets in a solar system. At least that's the base of it. And so that has concepts like angular momentum of planets going around stars, and so on. And it's not quite the same type of very mechanical motion that you see. But what ends up happening is that in there are these different angular momentum states. And as you get to a higher angular momentum state, there are kind of more different directions in which the electrons can be stuffed in. And so that leads one to have these different arrangements of electrons where, for example, in a hydrogen atom where there's just one electron, it can just sit there. Helium atom, two electrons, okay? So it turns out electrons have this notion of spin, and the one electron can be in that one energy level. In hydrogen, as you go to Helium, you've got two electrons. And where do they go? Well, turns out they have the spin that can be either up or down effectively. And the two electrons in helium, one is an up spin electron, the other is a down spin electron. They can kind of hang out in the same state. By the time you get lithium, you've filled up this first shell, as it's called, of the kind of lowest energy configuration of lowest energy sort of place to put the electrons. And you have to put another electron out, sort of out away from that inner shell, and it's kind of hanging out on its own. And that's what happens in lithium, which has three electrons. Let's see, hydrogen, helium, lithium, beryllium, boron, so beryllium has four. And that can then get paired up. That negative electron can get paired up this, the, the next shell of electrons can have a total of, let's see, two L plus one. So that's three possible electrons in it. So what roughly happens is that these electrons are kind of in these atoms because of the exclusion principle, they're kind of, they're forced to sort of, they fill up these shells. And then once the shell is filled up, more electrons can't be in that shell. They have to be sort of outside of that. And so what roughly happens is that atoms where there are some electrons that are just sort of hanging out outside in the, not sort of well integrated into a shell, those tend to be more reactive atoms. They have more, those sort of outlying electrons have more tendency to be able to kind of sort of interact with and get exchanged and shared with other atoms. And so, for example, if you look at the periodic table, the idea of that is it's arranged so that the atoms that, the elements that correspond to that have sort of the same rough configuration of sort of spare electrons are arranged in the same vertical column. And so, for example, on the right hand side of the periodic table are the noble gases, which correspond to atoms where the shells are all filled up, where there's sort of no separate electrons hanging out. And those things, helium, neon, argon, krypton, xenon, these are all, they all exist as gases. And they have the feature that they don't interact much with anything because they just don't have these extra sort of outer electrons that can be exchanged with other atoms and so on. They just tend to hang out and, and sort of be on their own, so to speak. But I think the next question is, okay, so there are these atoms and they have these electrons, and the electrons can sort of, there can be a Certain number of electrons that are sort of available to exchange with other things. And that leads to this idea of valence, of sort of, how many other atoms do you want to be connected to? So, for example, carbon has valence of four. It kind of. Any carbon atom likes to be kind of connected. It likes to have bonds which are essentially shared electrons with four other atoms. So now the question is. Now it becomes a question of, well, what's the. You know, you've got carbon that has sort of four bonds for each atom. How do you arrange. What are the possible arrangements of carbon atoms? Given that each carbon atom has four bonds, how can you sort of make this construction kit of molecules made of carbon atoms where each one has these four bonds? And so you can draw graphs, networks, that say, okay, there's a carbon atom here, it's got these four bonds that's connected to another carbon atom and to another carbon atom and so on. And you can kind of make all these different shapes out of carbon atoms. And sometimes in typical hydrocarbons, very common kinds of chemicals, you'll have a bunch of carbons. And then maybe the hydrogen which has valence of one sort of the bonds from the carbon will stick out and they won't connect to another carbon. There'll just be a hydrogen hanging out there. So then there's the sort of combinatorial question of what, you know, given that you have, I don't know, 10 carbon atoms, for example, what possible arrangements are there that you can put these carbon atoms in? The answer is a lot. The number of molecules that you get. Oh, my gosh. What are they called? Isomers. Isomers? Yeah. The number of possible arrangements of a given number of, for example, carbon atoms grows very rapidly with the number of carbon atoms. So one arrangement might be all the carbon atoms are just in a line, and there's a whole sequence of hydrocarbon molecules that are just these linear chains with progressively more carbon atoms. Another possibility is that there can be something that's branched, where you'll have the backbone, and then you'll have one carbon atom instead of just having a hydrogen on the side of another carbon, and you'll make this branched molecule and so on. So the thing, in a sense, the story of chemistry can be thought of at least this part of chemistry, the story. And this is when it comes to things that involve carbon and hydrogen and oxygen and so on, that's the story of organic chemistry. When you're dealing with more, with things like metal atoms and things like this, you end up in other kinds of Atoms, that's inorganic chemistry. Organic chemistry is really this big story of all these different sort of arrangements you can make with this fairly limited set of possible atoms. And so how many are there? Well, there are big catalogs, chemical abstracts, a big catalog of these things. There may be 100 million types of arrangements of atoms into molecules that people have cataloged so far. And somebody found a use for it sometimes. Now the number that could in principle exist is infinite. You can just keep on tacking carbon atoms on, make bigger and bigger molecules. Sometimes just saying, oh, you can stick four carbons onto each carbon. It doesn't work out because, for example, let's say you try and make a tree where you're just having more and more and more carbons stuck on in this tree. Eventually there'll be so many carbons there they just wouldn't fit. They won't, because the carbon atoms have a certain size, you just won't be able to fit them in. So there are constraints like that, but in a first approximation, you're just making up these different possible graphs of networks of how the carbon atoms are connected together with the constraint of the valence of the carbon atoms and so on. So that's kind of. You construct these molecules. Another question is, well, what shape are these molecules? It turns out you can get a decent approximation to that just by thinking about these bonds that are these sort of shared electron pieces as like springs. And you can just think of the thing as kind of, it's got some sort of repulsion between atoms and they're pulled together with springs. It's very similar to the way that one typically lays out graphs when one's just trying to visualize a graph. That same general type of approach gives one some rough idea of what molecules look like. And one can be more precise if one has the more detailed kind of interaction potentials, the more detailed force laws between different atoms, one can make a more accurate view of what, for example, the three dimensional structure of a particular molecule will be. And for small molecules that are just made from a bunch of carbon and hydrogen, so on, one can get pretty good idea of what the molecule will look like when it gets to much bigger molecules. Things like proteins that, that might have millions of atoms in them and which have. It gets much more difficult to know how this molecule will fold up. And it's been a long term, kind of complicated issue how that works. And the shapes of proteins are really important for how they actually operate biologically. And that's been sort of the protein folding problem has been A long term problem that there's been a fair bit of progress on using AI methods in recent times. Maybe not quite as much progress as some people might hope for, but one can get a much better idea of how the molecule actually arranges itself, sort of based on sort of examples of how maybe 100,000 different molecules, where we know how they arrange themselves work. You can kind of extrapolate from that to other types of molecules. But so in a first approximation, that's what happens. Now when you, if you really want to say in tremendous detail how the molecules, how the atoms arrange themselves together to make a molecule, that's pretty hard to figure out. The first approximation of kind of this spring, like force laws and so on, that's pretty easy. And one can do that for pretty big molecules. But to do it really precisely using the equations of quantum mechanics and things like this, that's something which maybe for 100 atoms you can do maybe a little bit more than that now, but that's really hard to figure out. To do the quantum chemistry of figuring out exactly how the atoms are arranged in a molecule is pretty hard. But okay, so that's so. So the first step is what molecules can you make? The next step is, well, what happens when you have chemical reactions? What is a chemical reaction? A chemical reaction is 2, 2 molecules. In the end, what it is, is 2 molecules crash into each other and somehow they rearrange themselves. And what comes out is some number of other molecules. The molecules crash into each other, they sort of break apart, the atoms get rearranged into other molecules, and then the result is the products of the chemical reaction and the dynamics of how those molecules come together is truly complicated and it's poorly worked out. Even now the question of sort of what is possible, as in which molecules, which atoms can come out, given that these atoms went in? Well, the atoms are, you know, if you've got a sulfur atom that came in, there's a sulfur atom that's going to go out. And there's a lot that can be figured out. It was figured out 150 years ago or so now of kind of the just tracing which atoms go in, which atoms come out. That determines a lot about what chemical reactions can happen. Another thing that is important is sometimes the molecules are very, very tightly bound into a molecule. Sorry, the atoms are very tightly bound into a molecule and sometimes they're much more loosely bound in. If you take something that's loosely bound in and you rearrange it so that it's tightly bound in, there's energy that is dissipated by that process. If you're taking something where you've just sort of the thing is bouncing around and so on, and then you kind of lock it in place, you're dissipating some energy and doing that. And so that determines whether when the chemical reaction happens, when the molecules get rearranged, does it produce heat? Does it release energy that will cause the heat is in the form of motion of molecules. So it's releasing energy which goes into making the molecules sort of wiggle around more. Or is it using up energy to get the molecules? Do you have to ram the molecules together with lots of energy to get them to possibly stick? Maybe the molecules tend to repel each other and you just have to, you have to ram them together really hard to get them to stick. And so that leads to things like endothermic reactions and exothermic reactions, Endothermic reactions, ones where they kind of take energy to make the reaction happen. Exothermic, once the reaction happens, it's going to release a bunch of energy. And that's kind of the next story of sort of how the next sort of level of thinking about chemistry is being able to figure out, okay, what is the sort of energy budget of what's going to happen. Now, another piece that's kind of complicated has to do with what has to do with, okay, it's sort of a counting thing. And it ultimately has to do with this idea of entropy which we can talk about at great length. And it's to do with, well, if this reaction is going to happen and happens at some rate, how many different ways are there for it to happen, how many different molecules are there available to make it happen, are lots of trade offs. And in the end you get these mathematical formulas that tell you things about the rate of chemical reactions and so on, and whether certain chemical reactions can happen or not, whether there's enough atoms, enough molecules there to make this reaction happen, whether that overcomes the. Okay, so a typical issue is this typical issue is when you have molecules bouncing around in a material, in a gas and a liquid, something like this. And by the way, I should say that in chemistry, liquids are the place where it's easiest to get chemical reactions to happen. In a gas, the molecules are all bouncing around, but there just aren't so many molecules. So the chance of two molecules hitting is considerably smaller. In a solid, the molecules are locked in place and so they don't get a chance to go visit other molecules. In liquid, the molecules are also bouncing around me, around. But there's a high density of molecules. And so it's possible for chemical reactions to happen. And that's why, if you're going through, I don't know, airport security or something, they're always concerned about what volume of liquids do you have? Because liquids are the things that can be used to make chemical reactions that can produce explosives or do other bad things or whatever. And so liquids are sort of the sweet spot for chemical reactions to happen. So, okay, in a liquid, there's the question of these molecules are all bouncing around. The liquid is at some temperature. The temperature characterizes the average energy of the molecules. But what's the actual distribution of speeds of molecules in the liquid? It's given by a thing called the Maxwell Boltzmann distribution. And it is of the form. Well, mathematically, it's V squared E to the minus V squared. But it basically is a curve that at zero speed, it's zero, and at very high speeds, it's zero. And it kind of has a hump in the middle, and the tail of the hump falls off exponentially. And so. Okay, so why is this relevant? It's relevant because if you have a chemical reaction that requires a certain energy of the molecules in order for it to happen, that you have to have molecules with that energy. And if that energy is sort of high compared to the hump in this distribution, only a small number of molecules will have that high energy. And it's sort of this trade off between the exponentially decay of the number of molecules with a certain energy and the total number of molecules, or the total different arrangements of molecules that you can have, and that trade off, sort of a trade off between that involves temperature, which determines the position of the hump, the average energy where the exponential lies, and the number of molecules and the number of configurations of molecules, that sort of trade off is a big determinant of what chemical reactions can happen and not. So, yeah, that's a very quick and rough discussion of chemistry. So just to say a little bit more about it, I mean, so, you know, a big piece of chemistry is. Okay, the goal of some piece of chemistry will be make a particular kind of molecule because it's useful for something or another. And the question is, you've got raw material, you've got molecules you can just get out of seawater, or molecules that you can get from a rock or something like this. How do you rearrange those molecules to turn them into the thing you want? Well, what you have to do is figure out a series of chemical reactions that will take you from the original ingredients you have to the thing you want. And there's a huge art of synthetic chemistry that involves, oh, you do this reaction, then that reaction, then that reaction. And the biggest syntheses these days are maybe 30 steps long. So you're doing 30 steps of do this, then that, then that, then that, then that. To make this particular molecule. That is the thing you're eventually going to want. Actually. Interesting question is in biology where these things work a bit differently, using bigger molecules, protein molecules, things like that. I actually don't know what the longest synthesis pathways are, but in sort of chemistry that is done on an industrial scale, for example, it's usually maybe 10 steps. And the, the sort of, the state of the art might be 30 steps. And what are those steps? Well, there's sort of an inventory of reactions. You know, if you learn organic chemistry, which I have to admit I have not. So you learn all these particular named reactions and so on. This name that name the other reaction. In fact, these reactions are often called name reactions because they're named reactions. And you say, I'm going to do a this, then a that, then a that, then a that. And how do you actually get those reactions to happen? Well, you put in some reagent, some particular chemical. That is the thing you need to make this reaction happen. You heat things up to a certain temperature, you do this, you do that. That's really. You don't have a lot of control, actually. You just get to put reagents in, you have a certain temperature. Those are the main controls you have. And then that particular reaction will happen. You let it run for a while and then all the molecules that are going to attach in this way or that way have attached. Then you go on, you do the next thing and so on. And there's a big art to being able to sort of put these steps together to get to the thing you want. And sometimes there are things like you'll put on a protecting group that will sort of arrange that the particular place you were going to that one reaction, one molecule that comes in, oh, it can't get to this place where it would otherwise attach. There's a protecting group there and you keep going. And then you do another reaction that makes the protecting group fall off later and so on. And that's a big piece to the story of what goes on there in synthetic chemistry and kind of analytical chemistry. It's all sort of, well, I've got this thing. What is it? How do I tell what molecule I Have here. What can I do with it? For example, you might put in a mass spectrometer which will sort of crush, will sort of make the molecule disintegrate into its constituent atoms and it can count how many hydrogen atoms, how many sulfur atoms, how many that were in that original molecule. Or you might do something where you will look at the interaction of light or radio energy, radio waves with a molecule. And so, for example, if you're dealing with microwaves, radio, short wavelength radio waves, what ends up happening is the radio energy comes in and it makes the atoms in the molecule wiggle around. And depending on the exact shape of the molecule, the wiggling will be different. And you can detect that because when the molecule wiggles, it absorbs some exactly which frequencies of radio energy it absorbs, determined by kind of what modes of wiggling it can have. So for example, if you were to have sort of a molecule which just consisted of two atoms on a spring, there will be some characteristic frequency where that spring goes back and forth. And at that characteristic frequency, radio energy you put in will be absorbed by the molecule because it'll just go into the wiggling of the molecule. And at other frequencies the molecule will be like, oh, that doesn't really help me. It isn't the frequency that I wiggle at, so to speak. And so that's another type of analysis one can do and many things like that. Let's see. All right, some other questions related to this. How are chemical reactions balanced? And why is it important to balance chemical reactions? Well, chemical reactions, the balance of chemical reactions. Just saying there's a certain, you know, the molecules come in, that there are certain collection of atoms in those molecules and those atoms will be the atoms that come out in the molecules that are produced by the reaction. Now what gets tricky is that sometimes in order to balance the conchal reaction, you have to say, well, we've got to have two waters plus one copper sulfate or something plus one something else. And that matches sort of three nitrogen molecules plus whatever, plus whatever. So there's this kind of idea that in the end it's some number of, in the end the number of atoms has to match of each type has to match on the left hand side and the right hand side. But to achieve that you may have to have different numbers of molecules because those are collections of atoms. And what you end up with is an equation that is a so called dipantine equation, an equation involving integers that says, okay, for every water molecule you've got two hydrogens, one oxygen, for every carbon Dioxide molecule. You've got one carbon and two oxygens. Okay, if we're going to match up a methane or something with carbon, four hydrogens, with the carbon dioxide and the water and so on, how many methane and oxygen, for example, with the carbon dioxide in the water, how many. How many waters plus how many methanes do we need to match this and that? And that becomes an equation, a set of equations that you can write out just in terms of how do we match up. We've got to have an integer number of water molecules, an integer number of methane molecules. How many do we need so that we can match up the atoms that are in them? And it's not really for Wolfram language that is a trivial sort of mathematical problem. It's for a human doing it. It can be quite tricky for the algorithms that we have for solving integer equations like that are big industrial creatures that can grind through and do that. I mean, in the footnote, there are equations involving integers that are arbitrarily difficult to solve, but they don't show up in chemistry. The ones in chemistry are comparatively modest and are completely ground up by the industrial methods of solving these kinds of equations that one has. Now, just because the equation balances, the reaction balances, so that the sort of number of atoms matches up doesn't mean the reaction will actually happen. That's a question of whether the molecules, the energies of the molecules are such that you can get the molecule, you can ram them together hard enough that they'll actually interact, or whatever else. M. Rudo asks, is it still right to use the periodic table, or is it a feature of the past? I think the periodic table is still sort of as valid as it ever was in its main elements, so to speak, its main pieces. This idea of sort of valence, which is what determines what column the atoms are in, that's still a fine thing. I'm not sure one can really do much better than the periodic table as a way to characterize sort of what reacts with what. Now, there are many, many, many details that are not covered by the periodic table. It's just a very first cut of what can react with what. And certainly in modern times, you can imagine a much more detailed sort of fingerprint for every atom that can determine, you know, can it really interact with this and can it really interact with that? And certainly the rules of thumb that say, oh, you know, like xenon, a noble gas, just doesn't interact with anything. Well, except it does, because there's a molecule called xenon hexafluoride fluorine is such an aggressive atom at interacting with things that it can even interact with xenon to make that kind of molecule. And so these kinds of rules of thumb don't go all the way through. But as a first cut, the periodic table I think remains a pretty good kind of way to know roughly what's going on. Now you know what happens in the periodic table. Okay, so it's really a weirdly set up thing because I talked about these electron shells and each successive electron shell it has, well, the number of electrons that will go in it goes up. Like if the shell is shell numbered L, then it's 2L + 1/2 is the number of electrons that will go into it. And that means that as you get to higher shells, you get more and more electrons per shell and you can kind of fill in more and more elements, but more and more types of atoms until you get ones that have those sort of, until you get to the stage where you have sort of all of them filled up and you've got this non reactive atom again. And so that's why in the periodic table at the top there's just hydrogen, helium sort of hanging out on their own. And then there start to be rows that have more atoms in them and then more and more and more. And then you get down to the later parts of the table and you've got these pieces that don't quite fit in, the lanthanides and actinides and so on that have to be sort of fitted in as a footnote. And those are bigger shells where there are lots of different kinds of atoms that all correspond to things filling in the parts of those shells. That's kind of a messy thing. And I think if one were to go on further down with periodic table, the shells would get even bigger and one would have sort of an even messier situation in terms of laying them out in two dimensions. But those, you know, those atoms aren't stable. So that's not something of relevance to chemistry. Chemistry is really dealing with the properties of molecules where what matters is the sort of configuration of electrons in the molecules. Nuclear physics is what deals with. What matters is the configuration of neutrons and protons inside the nuclei. Let's see. ERI asks, is there research on computing outside classical quantum state of electrons example biology, chemical light based data storage and processing? Well, yes, there's. Okay, so in a standard computer, one is storing information by the presence or absence of electrons and little sort of essentially traps that have been created for them in the structure of the silicon semiconductor that makes up our memory chip. So it's either there are electrons hanging out there, a thousand of them, 10,000 of them, whatever it is for each bit, or there aren't. And in a first approximation, it's a little bit more complicated in detail, but that's roughly what's happening. And so you could ask the question, well, are there other ways you could store the information? The answer is absolutely yes. Are they practical yet? Well, no, not really. I mean, you could, for example, say, well, I'm going to have this. This molecule that has a cage in it, and that cage will either have an iron atom in it or it won't. You say, well, can you really make a molecule that has a cage for an iron atom that will fit only one iron atom and nothing else? Well, absolutely, yes. That's how hemoglobin works. That's how the iron that gets used in our red blood cells to bind the oxygen that gets transported around our body. That's the way that works. So you can do these things where you make molecules that have. That can have, for example, multiple states of the molecule. Either there's an iron there or there isn't, or the molecule is in this configuration or that configuration. You can do that. That's not yet become a practical way to actually store information. Except. Well, biology uses that. But in a sense. Well, not quite. I mean, biology uses the fact that in proteins, for example, or in DNA, you have these big sort of big units of pieces of molecule that can be fitted together one after the other after the other in kind of a polymer. Something like plastic is a polymer where you have a molecule that is effectively a long chain of identical units with hydrogens and carbons and things in them. In the case of biology, this long chain of units, something like DNA, is a long chain of units, but the units aren't necessarily identical. It's a heteropolymer in the sense that it can have these four different kinds of units and each one of those units can be added in. So you can have a DNA molecule that has atg, C, D, tag, whatever, with different sequences of units. All possible sequences of units are allowed. They are all. It's possible for the molecule to stick together with all those different possible sequences of units. And that's a way to store information because the particular configuration of units determines whether you're storing a one or a zero or whatever else. And that's another thing people have experimented with is DNA storage of information. It's still more of a toy at this point, when it comes to sort of digital information that we store in things like computers, than it is something practical. But it's, of course, the storage mechanism that's used by biology. In the case of a protein, again, we've got these identical units, amino acids, in that case, about 20 of them, that are the possible units that get strung together one after the other to make a protein. And we might have 10,000 of these in a big protein. And the. It's in that case, a little bit trickier because while the sort of backbone of the protein allows any possible sequence, the protein then folds up, and not all sequences will allow the protein to consistently fold, et cetera, et cetera, et cetera. Jimmy comments. Molecules are graphs. System is balancing molecules and equations is just a new variation of things. Like, are two graphs equivalent? Yeah, that's absolutely true. I mean, you can think of chemical reactions as being examples of graph rewriting, and we've even done some experiments with that, because graph rewriting is the underlying stuff that shows up in our physics project. And there's sort of what's the analogy between what happens there and what happens in chemistry? And one can make some of those analogies, and it's quite, quite fun to do that. Okay, so Wingley asks what strategies and techniques can be employed to effectively control and optimize chemical reactions for practical applications, including maximized yield, maximizing yield, minimizing waste, achieving desired products. So in a first approximation, you've got a liquid, you've got a gas. The molecule is just sort of randomly bouncing around. One molecule hits another, et cetera, et cetera, et cetera. Big idea is the idea of catalysts. So a catalyst is something which, often in the case of industrial chemistry, there'll be some solid surface, some metal, and the surface of that metal has all kinds of shapes on it. And what happens is that the molecules and the gas or the liquid, they'll get stuck in one of those shapes. And when they stick in that shape, the molecule will be stuck, so that one end of the molecule is sticking up or whatever else, and that will cause that to be much easier for the other molecules. It kind of locks the molecule in place so that the molecules that might be going to interact with it will always be able to hit it in the right way. They won't kind of bounce off some other part of the molecule that was irrelevant to the reaction. So catalysts are a way where you can basically organize the molecules and geometrically organize the molecules so that they are optimized to interact with Each other. And that's something people discovered, Catalysts, well, in famous industrial processes 130 years ago or more, it's like, oh, you can use a silver catalyst or something for this. You can use a platinum catalyst for this. You can use this thing as a catalyst. That thing is a catalyst. That's a. And typically those are solid surfaces that can geometrically organize molecules. Now, in biology, there are enzymes, which are types of proteins, which have the feature that they will hold other proteins or other molecules in just the right configuration to be able to have a reaction, be more likely to happen. And the effect is a big effect, like it is in biology. It's not uncommon for a reaction to be a billion times more likely when it is mediated by an enzyme, effectively a catalyst that can kind of hold things in the right configuration than not. Now, I mean, in terms of other ways to control reactions, there are other. Some other things you can do. I mean, roughly, you heat things up, you cool things down, you squirt chemicals in. You don't squirt chemicals in. That's the first approximation. Then there are catalysts. Then there are things like light. So, for example, there are reactions where if you shine ultraviolet light on the thing, then a reaction will happen and it won't otherwise. So, for example, modern dentistry, there are plenty of things where there's some particular kind of glue, let's say, where the thing will sort of form into a polymer if there's ultraviolet light and won't otherwise, and other places where the ultraviolet light is enough to kind of kick the atoms to the molecules so that they can arrange themselves in a particular way and they wouldn't otherwise. So that's another type of control one has over chemical reactions. It'd be really great if there was more microscopic control, if it was possible. I mean, in biological systems there is this very elaborate control mechanism with all these different shapes of molecules all arranging themselves and. And geometrically configuring themselves in the right way. We don't have any way to do that in sort of industrial chemistry other than with things like catalysts and so on. It would be very interesting if there was sort of a more sort of, you know, nanoscale way of doing that. If there was some kind of sort of a way of getting molecules to sort of organize themselves in, you know, if you could get molecules that were sort of special little machine like molecules. And this is kind of the idea of molecular scale manufacturing. You've got a molecule that acts like a machine. Most molecules, they just sit there. Maybe they twist Around a little bit. But they really, other than having chemical reactions, they can't sort of do much. They're just, they. But imagine you could have a molecule that had a whole. Was a whole machine where if you just shine the right light on it or the right kind of radio energy on it, the molecule will say, oh yeah, that's a piece of programming. I'm going to now take that piece of programming and I'm going to rearrange myself and I'm going to make myself have this particular opening that will have particular. Where the particular other molecule will stick in. That's been a kind of a dream since the. Since the 1980s actually, to do molecular scale manufacturing to make a nanotechnology that can be operated where you can kind of make these nanomachines. Chemistry is a very coarse version of that chemistry. It's really heated up. You put the reagents in, maybe you have a catalyst, but that's as far as you go. The idea that you could actually have a programmable nanomachine that would be down at the molecular scale actually sort of determining by configuring itself what to do. That will be a wonderful thing. People tried to do this in the 1980s for a variety of reasons. They sort of gave up. I think they gave up too early. And I'm hoping that that will be a thing that comes back and that it won't be the case that biological life is the only place where it's been discovered how to do that. Biological life has this huge stack of different mechanisms and all these complicated molecules and pathways and all this kind of thing. The essence of what's needed for nanomachines is surely much simpler than that. We just don't know how to make one. But once we have made one nanomachine, we're in pretty good shape for making other ones. Because our one nanomachine, we put it to work to make other nanomachines and it will do a good job of that. People had worried in the 1980s that maybe we make these nanomachines and they just work too well and everything in the world gets turned into gray goo because everything gets turned into just a copy of the nanomachine. I think that's probably an extreme concern. But the first step is can we make a nanomachine at all? And that's something which. That's the future of chemistry is sort of truly programmable chemistry, where it's programmable at the molecular scale. And in a sense there's something sort of in between there. Of Material science, where you're making materials, let's say, particularly solids, that have not just a crystal lattice where the crystal just has pieces of, you know, atoms arranged in a particular very regular array, but let's say some more complicated arrangement of, of, of atoms. That's sort of an intermediate step there. Well, let's see. Wingley is asking about molecular level mechanisms governing the magnetic properties of materials. So the big fact about magnetism is every electron is like a tiny magnet. It's like a tiny bar magnet with a north pole and a south pole. Every single electron and electrons can be arranged in different configurations in atoms. And what happens in something like iron is it has a couple of electrons, I guess. Is that right? Is it one, is it two? I'm not sure. Anyway, it has electrons that. The real question is when electrons are like bar magnets. If you take a bunch of bar magnets, they will like to arrange themselves to be parallel. And so if these little electrons they, you know, which can be, have be like bar magnets, were oriented in different ways, if you get them close enough to each other, they'll have a habit of all the line lining themselves up. And some materials, iron, cobalt, nickel, are three common ones, have the property that in the crystals that are made from putting together atoms of those of those elements, the electrons are sort of close enough together that, that their magnetic effects kind of add up. And so what tends to happen is you get this phenomenon of ferromagnetism where you get where all the electrons can be lined up, all have their spins lined up, all have their bar magnets lined up. And that means that even though each individual electron is like a very, very, very tiny bar magnet, all those electrons together are like a big bar magnet. And so you can actually get, for example, a bar magnet made of iron that is this whole configuration, this whole, that has all these electrons where they're all lined up. If you heat it up, the electrons will lose their. They'll be sort of kicked around enough that they won't. That the forces that cause them to line up will be overwhelmed by the sort of energy of them just bouncing around. That's the so called Curie temperature at which iron loses its magnetism. But the other really what these different kinds of paramagnetism, diamagnetism and so on, they're all different effects that when you have a magnetic field, it will tend to. The magnetic field goes in a certain direction. All little magnets will tend to line up along the magnetic field lines along the direction of the magnetic field. And in the case of ferromagnetism, they'll line up and they'll stay lined up because there's just all these molecules are all together. In the case of diamagnetism, they'll tend to kind of sort of kick back against the magnetic field. Paramagnetism is, they'll sort of be locally aligned, but they won't sort of globally align. And so different materials have these different characteristics. The things that are sort of the most common magnetic materials, cobalt, iron, nickel. But then there are ones which actually are stronger magnets. Gadolinium is one of them. It's a so called rare earth magnet. That's a different part of the periodic table. It has a different arrangement of electrons. I actually don't remember exactly what it is, but. But its crystals are such that when you make it into a metal in which all the atoms are arranged in this very regular way, you end up with something that has much stronger magnetism even than iron. All right, I think I should probably wrap up there else. Let's see. Other questions about chemistry. I'm just looking for here a question here from Wingley about what about radioactive substance reactions? Yeah. Well, usually radioactivity is associated with things that happen in the nucleus. And for example, the nucleus falling apart, the neutrons in a nucleus emitting high energy electrons turning into protons, things like this. The energies associated with nuclear processes are vastly higher, 10,000 times higher than the energies associated with chemical processes. So chemistry is all about the electrons being exchanged and all this kind of thing. Nuclear physics is all about kind of much bigger, much higher energy things happening around the nucleus. So it's actually pretty rare even when. So in one form of nuclear decay, you get, well, you, for example, get electrons emitted, or you can get alpha particles, which are helium nuclei, two protons, two neutrons emitted, Those things which rarely interact chemically because they usually, they're like zap, you know, they're zipping out of there with very high energy. They never get to sort of interact with the electrons and get sort of pulled back by that. So usually the kind of. The story of the story of radioactivity is sort of a separate story from the story of chemistry. Now there's a whole field of nuclear chemistry that has to do with chemical processes that relate to things that are radioactive and so on. And that for example, I mean, usually another thing to say is that usually in chemistry it doesn't really matter. The nucleus has a certain number of protons that determines the number of electrons that are typically in that kind of Atom, the nucleus also can have different numbers of neutrons. Those are the different isotopes of different elements. Usually in chemistry, it doesn't matter what isotope you have. It matters very little. Even in the case of water, case of hydrogen, where normally hydrogen is just a proton in the nucleus, sometimes it's a proton and a neutron. That's deuterium, proton or two neutrons, that's tritium. The rates chemical reactions happening with deuterium and happening with ordinary water, heavy water, which has a deuterium and deuterium instead of ordinary hydrogen. The rates of chemical reaction is not that different even in that case. And for heavier elements, the effect is even smaller. So it tends not to. On geological timescales, there can be effects from these things, but in typical kind of lab settings, it doesn't really make any difference. All right, well, that was a short term. I'm sure I forgot a lot of. What, Of what there is to say about chemistry. I think the original question was how would I begin an introductory chemistry course? And I think the thing that I really didn't understand when I was learning chemistry is people would just tell me, oh, there's this particular chemical and you have to learn what it does and this and that and the other. And as I said, I didn't do a good job, didn't, you know, learn that stuff. And I just found it really boring because it was just like. Well, a famous quote by a physicist named Ernest Rutherford used to say, you know, science is divided into two parts, physics and stamp collecting. By which he meant that chemistry just seemed like this collection of just random facts. Oh, there's this particular molecule and it does this, oh, business molecule that does that. Whereas physics seemed more systematic. Personally, I think that that is actually a reflection of, in a sense, the greater computational sophistication of chemistry. In a sense, it's like chemistry is lots of little computational problems of can this molecule fit with that molecule, can this graph be written this, rewritten this way, and so on. And the fact that those are sort of different computational problems. There is this phenomenon of computational irreducibility that I talk about a lot that kind of forces one that there isn't just a global answer to all those little computation problems. In general, with computational problems, it's kind of like you have to do the problem, each problem in turn, to see what the answer is. And so in chemistry, it's like, because it's much more in a sense, computational, the. It's, it's kind of tying into this idea that you have to just do the computations. And that's why the results kind of seem random, because there isn't like, the big fact that kind of brings them all together. It's like you have to do each. Each computation separately. So I think the thing that would have helped me a lot in understanding chemistry is just the big picture of kind of molecules are these possible arrangements of atoms. I'm sure that's said, but it's not emphasized of, you know, really just think about it as you take these things and you put sticks together and you have these balls and sticks, and you're sort of arranging them, and what possible arrangements can you make? And usually people will say, well, we're going to just study these particular 10 molecules. But I think it's more interesting to think, well, we got this construction kit. You can get these chemical construction kits. It's like, well, what could you make? And then what characteristics does this have? Well, that molecule is probably not in the textbook. The molecule you make by just sticking things together, probably not in the textbook. Maybe nobody ever cared about that molecule. Maybe that molecule is somewhere in the databases of molecules. You go look it up, see what its properties are. It's like, okay, that's what that molecule is. And then you make another one. You look that one up. I kind of feel that that's a more. At least for. Maybe it's just somebody with my turn of mind. That's a more interesting kind of way of seeing what's the global picture of what's happening in chemistry, rather than just there's this random molecule with this fact about it, this one with this fact about it, and it all seems kind of random and really just an exercise in kind of memorizing things rather than something where there's a bigger picture involved. I think it doesn't help that in chemistry, even the specification of molecules can be a very complicated thing. Because, for example, if you've got this graph that's just all these carbon atoms and they're arranged in all these different ways, whatever else, it's like, what is the name of that graph? Well, you know, you can, You know, you could sort of at a computational level, it's pretty easy to specify the graph. But if you want to make a word for that graph, it's like, well, how do you describe the fact that there are these two molecules at the end here, then a branch and then this other one that's connected there, and you end up with these, you know, di. Butohexo, whatever it is, these long, long, long kind of constructions of Words that represent graphs. The graphs are very easy to draw, very easy to see what they are. But turning that into a word is a big sort of conventional pain. And it doesn't make the subject look good that you end up with these incredibly complicated looking words. Okay, as a graph, the molecule is something pretty straightforward. As a word, it's this long thing that goes on for half a line that you have to kind of decode. It's a little bit in modern times, although I don't think they teach this a lot. In elementary chemistry. There are these things called smile strings, which are much more systematic ways to sort of specify the graph structure of a molecule. I'm not sure why they don't teach those, why they insist on. I think they insist on still teaching these conventional kind of names, molecules. I mean, sure, if you want to look up. I'm sure you can look things up by smile strings nowadays. And it's just one of those things where it's a piece of the history of the field, but it's not terribly interesting. It's something which makes the whole thing seem very arbitrary. And I think the other thing to understand about chemistry is that certain things are known and a lot is not known. You know, if you say in detail, how does this chemical reaction happen? It's like nobody knows. And I think the fact that one then has certain things one does know that one can kind of identify, yep, we know this, we know this, we know this. For me, at least, learning chemistry, if somebody had said, look, we just don't know how, you know, you can imagine how these molecules can crash into each other and maybe sometimes they stick and sometimes they don't. And you can see that's a complicated problem. But just saying, oh, we can work this out in terms of this rate constant and this and that and this free energy thing and so on. It's not. To me, it just all seems, it seems very hard. It seems like you're kind of floating in this world of things that you don't understand. And the issue is, do you not understand them because you just didn't get far enough in the chemistry textbook, or you don't understand them because nobody understands them. And the fact is, in a lot of chemistry, the underlying principles come from physics and are quite well understood. But exactly how they're put together in chemistry is something where there just isn't an easy way to say it and to sort of just keep on poking at these things where, well, yes, we happen to be able to say something about this. We happen to be able to say something about that. I think it's a useful thing to just say, you know, there's a lot we don't know. There's a lot that's that really can't be figured out, hasn't been figured out, and is, in fact, computationally fundamentally difficult to figure out. And so we have to just poke at these individual things where we can be excited that we do know this particular fact about chemistry, even though the general story we can't tell. So, anyway, that's what I would do in my very idiosyncratic approach to trying to explain chemistry. All right. Well, thanks for joining me. Thanks for our last live stream of 2023. And I look forward to talking with you again in the New Year. Happy New Year to everybody. See you then. Bye.