Business, Innovation, and Managing Life (February 1, 2023)

Hello there and welcome to another episode of Q A about business, innovation and managing life. So let's see. It looks like I have a bunch of questions that have come in here. Jal says congratulations on the recent blog post. Can you talk about the process of writing a post like this? Okay, first of all, I, I posted something last night long thing like a hundred and maybe 150 page document about the history of thermodynamics. And let me talk a little bit about a project like that. This is a funky project because it is a piece of science that I got interested in when I was 12 years old, which is now 50 something years ago. And I'd been gradually trying to understand this one question in science about the origin of the law of entropy increase, the second law of thermodynamics. It's a question that was first really raised 150 years ago. And about 100 years ago people are like oh, it's done. We understand this. But they didn't. And the more sophisticated people who thought about it always said this isn't really understood. And the more sophisticated people who wrote textbooks said things like this isn't really understood, but it's a good, you know, it's a reasonable working hypothesis that blank, blank, blank. The other people who were not as sophisticated who wrote textbooks just said oh, it's all understood. It wasn't. As a result of things I've done in rather different areas about computation and so on, I've slowly managed to understand this. I made a lot of Progress in the 1980s, more in the 1990s, and then finally think I kind of nailed it in the last couple of years as a result of our big physics project. Okay, so I decided, and this is both good and bad, but I decided in August. I said okay, I'm finally this whole thing about the second law which I've been thinking about for 50 years. I finally, I think I understand how this works. I'm going to write a little post that explains how it works. Well, little didn't work out. I started writing it. I realized that the things that are kind of obvious to me because I've been thinking about them for 50 years are not as obvious as I had thought they were if I'm actually going to explain them honestly to people. And so that, let me just explain what's going on turned into probably 100 page document which hopefully will get posted later this week. Let me explain that. The first was the science, which is this big long description that kind of summarizes what I figured out in the last 50 years, but particularly the more recent stuff that I think kind of solves this problem that's been hanging out there for 100 years or so. So that's part one is the science. Then I realized it's actually kind of an interesting story how I've ended up working on this thing for 50 years and making incremental progress and kind of the personal trajectory of what's involved there. So then I thought, I'll write something about that. And then I was thinking about, well, you know, to most people you say the second law of thermodynamics. They say, oh, yeah, I read about that in textbooks. I heard about it in my class. Physics class, whatever. It's a solved problem. Well, it's not a solved problem. But to clarify why it's not a solved problem, you have to kind of go back and look at what people actually said in the past and try to understand one of these cases where to really understand a subject, you have to understand its history. And this is something I found over and over again, that you'll get the current state of some field. I've been looking at this a lot with large language models and machine learning around large language models. There are things where it's like, oh, yeah, everybody knows that. Well, wait a minute, where did that come from? Dig, dig, dig. Eventually you're like, well, that came from some random empirical observation that somebody made. And there isn't really, you know, it's not really that, you know, it isn't on some solid footing and so on. And you only learn that by looking at the history. And in a sense, to me, a lot of times, a lot of fields, it doesn't really quite make sense. It's like, there's this piece, there's this piece, and so on. They don't fit together unless you can see where they came from. Sort of common origin in the history. And with thermodynamics, that's really true. I mean, the history is complicated and messy. I'll give you an example. Okay, so a person called Sadiq hanaud in the 1830s had. 1820s, had figured out, basically said, oh, we know that when heat is generated, it is sort of. You can't get. You can't continually get mechanical work out of heat. You can't make a perpetual motion machine that just takes heat and continuously gets mechanical work out of it. Said, that's kind of obvious. Okay, so he takes it as kind of an axiom. Okay, so then. And then later on, people like Kelvin says, oh, you know, we know that once heat has been dissipated once, once you've taken mechanical work and you're like grinding out a. You know, you're grinding something out and you're generating heat through friction, that that heat doesn't go back and turn into mechanical work again in a systematic way. You'll say, oh, it's kind of obvious. This is how it works. I say, let's capture that in something that we call a principle. Call it the second law of thermodynamics. The first law is that energy is conserved. The second law is that energy tends to degrade into heat that cannot be reconstituted again in a systematic way into mechanical work. Okay? So let's take that as a principle and work things out from it. Okay? Then within a year, people are talking about, well, we have this principle now. So therefore, it must be the case that eventually the whole universe will run down. We'll end up with a heat death of the universe, where all the things that are happening, all the mechanical work that's happening, it's all going to turn into heat. And that's the end of the kind of interesting universe. But if you think about this, they just assumed a year or two earlier that this was something they were just taking as axiomatically that taking it as just an observation about the world. They didn't say, it's a proved thing from which we can deduce everything about the whole future of the universe. It's just, well, this is a thing that seems to be true. Why is it always true? Well, nobody ever established that. It was just an assumption that got made. It got very confused. It became very cosmic very quickly. And the confusion goes on. It gets entangled with a lot of things about whether there's a life force and so on, and what the kind of religious connotations of a life force or the lack of a life force are very confused in the kind of mid to late 1800s. And then by the time it's textbookifying in the early 1900s, everybody's forgotten that there's a controversy. Didn't help that. One of the key parts of the controversy was whether atoms and molecules exist. And this had been kind of the correctness of the second law had been sort of tied up with ideas about molecules and so on. And it hadn't been clear that molecules existed as sort of actual mechanical things in the 1800s. That wasn't clear until the first decade of the 20th century. And so when that became established, people said, oh, that part is right. Therefore, oh, the second law Must all be correct as well. Not true. So any case, the history, you know, being able to analyze that history is important. It was important to me in knowing that I really know what I'm talking about. Pretty sure I really know what I'm talking about because I really went back and, you know, when people say, oh, it wasn't that proved? Well, actually, you can go back and read what people actually wrote and know it wasn't proved. And you can see how people went from it not being proved to, oh, let's write a textbook and assume it type thing. Now, the actual process. So you asked about the process of writing these things. I decided to factor what I was writing into these three pieces because I think they're sort of cognitively separate and they have slightly different audiences. There's the piece about science, which you can read completely independent of the pieces about history, or the Personal Journey type piece. There's the Personal Journey piece, which I think might be of interest to some people who are just interested in. You know, there are not that many projects that anybody gets to do where you formulate the project and you finally kind of think you've nailed it 50 years later. You know, human lives just aren't that long and it isn't. It's rare that one gets to see that kind of arc. And I think it's sort of interesting in terms of sort of history of science and kind of the history of ideas. It's sort of interesting in this particular micro example, so to speak, to see how that works. And I have the slightly peculiar feature that I have a huge amount of data because I've kept sort of all these records, I have to say, the records going back into the 1970s, when I was an early teenager and so on. I have some, but I don't have as many as I have more recently. And certainly when things jump to electronic form by the end of the 1970s, beginning of the 1980s, I have much more data there. But so the division into these three different pieces I found worthwhile because I really think they have different audiences. Now, in terms of how you do a history project, I have to say that the one absolutely constant thing is read the original sources. Don't rely on some intermediate interpretation. The original sources are sometimes not so easy to understand because the ways people think about things have changed since those sources were written. The sources are. I make two practical comments. One is that for things from the 1800s, archive.org, brewster Kael's Internet Archive book Scanning project is fantastic because the things of that age are out of copyright. They're all fair game to scan and put on the web. And the coverage is really quite good of even very obscure things. And it is something where, you know, the ability to do history from the 1800s ish, early 1900s, late 1700s is really, really wonderful at this point. And I think that the other thing that is important is quite a lot of the material is not in English. In the particular case of thermodynamics, it's in either French or German, probably more often German. I have been discovering to my. I'm pleased to discover that the years that I spent learning French when I was a kid, even though I am way too insecure to actually speak it at all, I can more or less understand it in written form. And, and I found that pretty useful for this project. German, I don't know. And the thing that's really good today is that the automated translation systems, both the, you know, there are really three generations of automated translation systems. The ones that came before statistical machine learning, the ones that were part of statistical machine learning, and the modern large language model based capabilities from the chat systems and so on. At this point, the machine learning statistical language translation is really quite good. And the ones that come from the latest generation of last month or so of large language models seem to be even better, although they do occasionally make things up, which is kind of, kind of shocking for doing translation. But you really can take a lump of German and immediately translate it. And that's really useful in doing this kind of history. But the other thing about doing history is what I found is when you dig deep enough, everything always makes sense. Whenever there's a. And you go from here to here and there's sort of a jump and you can't see how they connect, then there's a piece you haven't found. And you know, in this particular case, one of the key figures in this particular history is a chap called Ludwig Boltzmann. And one feature of Boltzmann, which is a little bit annoying, is that Boltzmann writes a paper, then he'll write another paper five, ten years later, and it will be inconsistent with his first paper. And he won't mention that. He'll just be like, oh, you know, now I've got a new idea. And so, you know, when you try and connect those two things, you have to. You realize in the end he realized that wasn't quite right. He wrote a new paper that wrote it, said it differently, and he never went back and said, oh, this other thing wasn't right. So I think that the. So in any case, this thing about sort of read the original sources and, you know, and try and figure out, you know, try and make the thread that connects everything, you know, the history of thermodynamics is really complicated. I was sort of. I thought, oh, I don't need to write this history. Surely there's a book somewhere where somebody's already done this. Not at all. It's just, it's. It's a bit. Little bit. It's too tangled a story. There are plenty of history of science, not to say that there hasn't been work done on histories and some of it is quite good. But in terms of the big picture, that's something. It's. It's difficult to see that big picture. It's even more difficult if you don't actually know how the pieces are going to fit together in the end. Which is something which I think I've recently figured out in terms of the science, but one didn't know that before. So that's that story. This project on the second law, which is probably about 400 pages of material, has taken me much longer than I had hoped. I started it in August and I just kind of finished it. Well, I finished it around in December and then got. It's had a. I have people who work with me on these things and the sort of production process of, for example, even in these historical documents, taking the raw scans and making them so anybody can actually read them with, you know, image processing and so on. That's a, you know, that's a long process and it's just a, you know, we can do it pretty nicely with our technology stack and things, but it's still. There's hundreds and hundreds of pieces here. And there's also, you know, getting the links to all of the original sources, et cetera, et cetera, et cetera. There's a lot of. Kind of a tale of production work that ends up getting done. And then in the end there's, you know, we have. I like to, you know, be. Make things as perfect as possible. So I always get our DQA document quality assurance group to read over these things. And then it's always, there's always like just yesterday on this post, there was what do we do with the capitalization of books, book titles, where the thing is in Old English and it had a different capitalization, its original form, it's like, okay, that's a case we've never run across. It's not in our corporate style guide. What do we do. We have to decide what to do. And there are lots of these kind of micro details which, you know, I like to get right. And we have a great team that helps for all of our corporate material try and get those things right. And I use that. And there's always this tale and usually when I. Another thing that takes a long time in these posts is adding links, which I like to do. I. I hope people follow them. I don't know, we don't never really looked at the statistics of how much they're followed. I put them in there partly because I myself, when I come back to these posts five years from now, it's like, where did I get that information from? I want to see a link. And so that's useful to me, even if it's not useful to anybody else. So that's a little bit on that, on that project. Let's see. Golly. Gaz is commenting about thermodynamics and generative AI models. Well, you know, the thing I'm right now working on is a kind of a somewhat expository piece about how ChatGPT and other large language models work and what kind of the fact that they work means for the way that we think about how human thinking works. Because in a sense the fact these models work kind of tells us that if we want to know how does language get produced by our brains, there's a lot we don't need to worry about anymore because we can see that language is produced comparably in these models to the way it's produced in our brains in terms of the functionality, in terms of the output. And so it's just sort of a computational process. And now the question is, can we understand enough about sort of the big picture of that computational process to make conclusions about language and to be able to conclude things about what it is going to be possible to do with language models, what it's not, and so on. And I'm about two thirds of the way through writing something about that which hopefully will be ready to post fairly soon. It did. As these things sometimes do. It collided in time with the work that I was doing in thermodynamics. And there are some connections for sure. I was just seeing something. Yeah, there's a way in which people talk about temperature as a way of describing sort of the randomness of picking different ranked words as the next word to generate in a generative AI language model system and the sort of the relationship between that and temperature in thermodynamics. And is it really is There any connection that can be made scientifically or is that just, oh, here's a formalism and let's just wheel it in. That's a cliffhanger. I don't completely know the answer to that yet, but expect to. Let's see. Okay, there's a question from David here. What are your thoughts on salaries and compensation, especially for virtual and remote companies that employ people from different locations? You know, it's first point is we, for example, have people all over the world and we tend to pay sort of at prevailing rates for whatever the location is, but with a ceiling which is defined by, in other words, there are locations where the prevailing rates are much lower than they would be at some location in the U.S. there are also places in the U.S. where the rates are much higher than they would be at locations like our, our nominal headquarters location is in Champaign, Illinois, which is about median cost of living for the U.S. if you say, how does that compare to New York City or San Francisco? Well, it's two and a half times cheaper. And so for us, we take it as a constraint on what we do that we're just going to, you know, we're going to pay at the level that corresponds to things like our sort of headquarters location in the US and we're not going to say if somebody says, well, but I live in New York City and I need two and a half times more, we're just going to have to say, well, that's not what we pay. And that has the effect that we don't have people typically in New York City or San Francisco unless they happen to be there because have a spouse there or some such other thing, but they're not supporting themselves there from us because we're not paying at that level. Some exceptions occasionally, or when there are people where we say we really want you to live in place X because that has corporate value to us for you to be in that place. Then we take a different point of view about that. But the, you know, for us in particular, that's meant there are people where we say, you know, resume comes in from somebody who says I'm living in place X. It's like, well, you know, that's not going to work. In our particular case, there's a, there's a very good sort of ecosystem of people who use our technology stack who are not us, which might be companies based in New York City, for example. And we like to point people who know our technology and are enthusiastic to work with it say, look, you have to live in New York City. Here are these folks who really want to make more use of our technology within their company. They're a New York City company. They pay New York City rates. That's going to be a good match. I think the thing that has happened in the past sort of pre pandemic and so on, was that certainly we sort of pegged our US Rates to the sort of median cost of living and so on. And that meant that people would, you know, you could do a certain amount of arbitrage if you can sort of live remotely. And some people picked these, I think, probably quite lovely spots around the US where sort of what we would pay went further than it would do in, in the place where, you know, where it was pegged from, so to speak. And from my point of view, that's sort of a, that's, that's fair game because once somebody is remote within the US it's pretty much an equivalent story. It's, it's a little different in other places because there will be time zone issues and, and, you know, sometimes connectivity issues, other kinds of issues. And you know, our principle has been use the prevailing rates of whatever the area is with, with that, with that comment about the US the. And I think in terms of, you know, there's this kind of idea that, oh, there's going to be this, this mega salary and it's going to get paid to people who can go. I mean, you know, the salary distribution in the US has, there are some places like New York City and San Francisco that are really high. And then there's a big, broad middle area where some of the other. Plenty of big cities, you know, whether it's, you know, Phoenix or, you know, Houston or whatever, where, where it's kind of not that far away from the median. So there's a lot that's sort of close to the median. There's not a lot that's very low compared to, you know, it's, the distribution has this big blob in the center. It has this outlier at the top. There's not a lot much below that. I don't think you get. You see much that's less than like 0.8 times the median in the U.S. and so I, I kind of think that the idea that you're going to sort of, you know, there'll be the occasional sort of Silicon Valley mega salary that gets planted somewhere else. My guess is that's not a stable situation that will not persist partly because, well, for all sorts of reasons. And I think that's, it's Kind of a, A. It's sort of a mistake. And I think it's an unstable thing where, where you see that with people where they said, well, my company let me be anywhere. And then they said, no, you can't. You have to be in the office by Monday. And that's a big disaster. And everybody gets upset. And, you know, I think it's probably not supportable. So I kind of think it's sort of the prevailing, you know, person is in place X. It's the prevailing rate. There. There are tricky things that happen when people move from one place to another. From a country that has very high, you know, from, from the U.S. for example, to some. Some country where the prevailing rate is much lower. I would say that in some cases in, in our company, you know, some people have done very well from that. It's okay so long as the productivity remains good. It's, you know, everybody gets upset when the productivity drops. Um, it's one of these things where I would say it's. It's a general principle I've noticed about compensation is, you know, when somebody comes and they say, I promise I can do amazingly well. Just pay me more and I'll show you. Okay. That's usually. Does not end well. It's usually it's one of these things where when people are first coming to the company and it's like, oh, I've got all these qualifications. You got to pay me so much more. It's an unstable situation because you're paying more than you think you should be paying, and you're expecting a lot. And occasionally it'll be like, oh, wow, that really worked out. I can think of examples where that happened. But most of the time it's kind of like, well, you promised all this stuff, but you didn't quite deliver what you promised, and now everybody's upset because you got paid more because you promised so much, so to speak. And I have to say it's been my experience that, that, you know, it's also something where we're interested in having people at our company who want to be at our company rather than that they're at a company because we pay a little bit more than the people down the street type thing. And so it's better to initially push hard and say, look, you want to come here? This is what we're prepared to pay. You don't like it, don't come. And people will say, look, I really want to come. So they'll say, fine, I'll accept that starting salary. That might be lower than they might have hoped or thought that they deserve for one reason or another. They come in, they do fantastically. You can always give them a raise. They come in, you've given them a high initial salary, they don't do so well. What are you going to do? You're either letting them go or it's not a good conversation. It doesn't really happen to. To say, well, you know, you came in 20% above what you should have been and you didn't really perform in the way that you promised you'd perform. You know, will you take a 20% cut? That doesn't. I don't think that conversation is, you know, that. That is not a. That's not a useful conversation typically. So, you know, I think it's much better to sort of not, you know, to. To. To sort of, you know, to. To not pay beyond what you think you should. And then, you know, if it turns out, and, you know, this happens with considerable regularity, that actually the person is, you know, the person does spectacularly and maybe they didn't even know they would do spectacularly. Maybe they came in and it turns out one has a fertile environment and they do really well, better than they even expected to do great. You know, then one can recognize that, you know, I think it becomes quite easy that way around. It becomes really hard the other way around. Let's see, there's a question here from Annie asking. I like the way I define different writing styles for different projects. What led me to do that? How do you define the limits of an article or book and go through the writing process? Right. So first thing about the limits of a project, always a challenge. You know, I would say sometimes the best projects, the most readable things are the things where the objective was quite modest and where, you know, you could wrap your arms around the whole thing and really are not. And then, you know, it fills out what it signed up for and it doesn't have tentacles that reach elsewhere. And it doesn't have things where you have to sort of, you know, forcibly lop off a tentacle because you don't want to go and talk about all that other stuff. I would say that sort of defining the scope of these projects is, you know, I tend to start, I will write, you know, I'll try to come up with a title for the things I'm writing. If I can't come up with a title, it's bad sign. Sometimes I change the title later, but I try to come up with a title. Then I try to write the introduction Sometimes I rewrite the introduction at the end, but usually again, I like to get some scope of, you know, what is it? What is the main thing I'm trying to talk about? What really is this? And sometimes I discover when I can't write a title, it's that really it should be two separate pieces or this piece is just too big and blobulous and floppy. And you know, I don't really. Can't really write it anyway. So, you know, having when, when there's a really crisp, clear title, it really helps me at least to get scope for what it is that I'm trying to do. I think that's one thing. Now, in terms of writing styles, I think that I've gone through several different writing styles in my life. The style that I use now for my general writings, you could say blog. I don't know whether I think blog is a little bit of an under promise by the time the things are 100 pages at a time and so on. But I really like the kind of somewhat informal style that I've tended to adopt for that because it really lets one say anything. I can talk very technically, I can talk very informally. It's a style that kind of covers those different ends. I think that in the past when I started kind of writing things for publication, scientific papers, and I wrote them in a, A very, I like to have a very kind of direct but slightly more formal style. I mean, there were no didn'ts, it was, did not, you know, type thing. There were no. In early scientific things that I wrote, there were no I's, it was all, you know, we and so on. I, I realized that it was a bit constraining. And there was a tremendous habit that I had at least, okay, so there's a general academic habit of don't explain why you're doing what you're doing, just explain what you're doing. And I think that's really hostile for the reader because it's kind of like, you know, my sort of a pet example is you read a mathematics paper and it just begins, let F be a field and G be a group. We will prove this and this and this. It's like, why were you studying this to begin with? What's the point? And it's like that's nowhere in the paper. It's just like we have this thing, it does this, it does that. It's like, but why? Why do we care? And I think it's important for people to understand things when they read them to explain why you care you know, it's, it's. People have to be primed in a certain way if they're going to have a chance to understand. Another feature of that is that there are things one writes which are details. There are things one writes which are important in a particular document. It's really important to signal those things because if you have something where, oh, this incredibly critical point, it's at the end of the fifth paragraph of the section, it's like people are going to just walk straight through it and they're not going to stop and say, wait a minute, this is the big point. So I think it's important to signal those things. And that's something that in sort of traditional academic writing tends to be not done. It tends to be very much more boom, boom, boom. Is this, this, this thing. You know, I've done several different kinds of writing. I mean, I've written a bunch of software documentation, you know, that. Well, it used to be the Mathematica book, which unfortunately expanded 2,500 pages and then went online and now will be the equivalent of like 100,000 pages. But the thing that I really developed for that was just this very direct style of just say it as one would say it to a person. You know, in other words, rather than this is a formal style, that is the written thing we're saying that's different from if we ran into somebody and they said, what's the point? And you responded to that. Well, just write down what's the point? So to speak, in the writing that you do. I think, yeah, so that's a few thoughts about that. You know, I am a. I am a shockingly one pass writer. I never revise stuff. It might be better if I revised it. It might be worse if I revised it. When I wrote my big book, A New Kind of Science, I wrote it very slowly. I wrote like at most a page a day and it took nearly 10 years to write. It was a very painful process. I think in the end it's quite good and very clean. It's very minimalist. I mean, there are very few sort of words that didn't need to be there type thing. I think that I could have written it much faster and my life would have been better as a result, so to speak. It would have probably been a little bit less minimalist in terms of the words. I don't think it would have affected readability terribly much. I would say most of the time that was spent though was probably spent doing the research. So maybe that wouldn't have reduced it so much. And in a sense, by being very careful about the writing, one is forcing oneself to be careful about the research, too, and to not cut corners and say, well, I can gloss over this point by just writing this very nice rhetorical thing there. You've got to actually do the research and figure out what's true and just directly write it. But I would say that the thing that I found is that I tend to write when I know what I'm talking about. I can write quite quickly, very quickly. I can write at output speed when I don't know what I'm talking about and have to figure out what I'm talking about. It can be arbitrarily slow. What I found is that at the point where I'm really geared up and I'm writing, it usually comes out fairly coherently when I'm doing it in stop start, you know, very, you know, kind of slow. It can come out quite wooden and quite hard to understand. In other words, I do better when I'm writing quickly than when I'm writing slowly. And I'm not sure. I don't know how general that phenomenon is, but what I've also found is that when I come back to revise things and I kind of do surgery on the writing, it usually gets worse. And there's a terrible thing that happens. You know, I was just making the third edition of my little book about elementary Introduction to Wolfram Language, and I was the team that's. That's working on that. You know, they were accumulated all these things which are, you know, updates that one should consider, etc. Etc. Etc. And I. I was making this terrible fuss because it's like. Like the, you know, somebody says, here's a change you could make. It's like, have you really read the whole chapter around this? Because sometimes you get a situation where it's like, here's the thing you should also say. And then you realize, well, actually, two paragraphs later, I already said that. So it would make a total mess to just make that point. Sort of surgical, you know, insertion in the text. And, you know, I. It's. It's very difficult. I force myself when I'm making those kind of point changes. I just got to read the whole page, two pages, three pages, whatever. Because otherwise you find that you put it in, and it's like, that was, you know, you look at it later. It's like, that was completely goofy because, you know, I already said that a page later. And at the time when I'm writing it, I know What I'm saying, I can remember what the flow was. And so that's why it's better to do it in sort of one pass like that. And going back, it tends to make it worse. Now you could say, well, why don't you go back and revise the whole thing and rewrite the whole thing? And sometimes I end up doing that. I mean, I was working on. Well, actually, I always make. In my file system, I always have draft 01, draft 02, et cetera, et cetera, et cetera. I will admit that in the piece about thermodynamics, I think it's draft 24 is the one that is sort of the finishing one. And the reason that happens, well, it's partly because other people sometimes edit some of these drafts, and I always insist that they increment the number when they're making kind of production changes, of changing, you know, cleaning up pictures and things like this. But. But the other thing is that. That sometimes I'll make notes further down in the draft or there'll be pieces where I just do a complete rewrite of some. Some section. I mean, in other words, I think it's better. It kind of reminds one of sort of fixing things that got dents in them or something like that. It's better to replace the whole panel sometimes is to, you know, to just try and fix that, that individual little, little scrape or whatever it was. And so it is with writing, for me at least, that it's like you've got to take out the whole section and just redo it sometimes. Then I. I can be paralyzed by looking at what I wrote before because it's like, well, I already wrote this sentence and I end up rewriting the same sentence again. And that's bad. My own personal calculation is that I've got lots of things I could write and to go back and rewrite and revise something is not a good use of time because it's not obviously going to get much better. And you know, insofar as I've got things to write, it's better for me to get more things out, out and written than it is to make the things that I am writing perhaps 5% better, perhaps 5%, 10% worse. So that. That's at least my calculation there. Prototype comments. I find when I write something, I have to back up my assertions and. And see what I should have been investigating in the first place. Absolutely. This is a very. For me, you know, I tend to figure out the big. If I'm doing some research, type thing, figure out what I think the big sort of conclusions are, and then start writing as early as possible. Because it's when you write that you find out sort of what the. You know, if you write honestly, so to speak, and you really explain what's going on, that's when you get, when you say, well, wait a minute, why did I think this? Why did I think that? And you go back and you figure out what's going on. One thing that I noticed years ago and I pass on to people regularly, so I'm going to pass on it on again, is here's a thing not to do, which is you say, well, I'm doing all these calculations and I'm making all these visualizations and tables and this and that and the other. I'm just going to do it research grade at the beginning because, you know, when I finished, then I'll clean it all up. I'll make beautiful visualizations. And that'll be for my final write up. Okay, here's what happens. Those beautiful visualizations, they're beautiful for a reason. That is, they are better expositions of the material than the things that were just sort of the crummy research grade things at the beginning. And so what ends up happening is you get to the end and you're like, I'm just going to put the icing on the cake. And then you realize you make these nice visualizations. You look at them, you say, oh my gosh, I never noticed this or that feature. Wait a minute, that changes the whole story. So, you know, I make an effort and it, you know, Wolfram language makes it rather easy to do this, to make pretty final visualizations pretty early. I mean, the only things that might not be there are things like the best choices of colors and things like that. But even that I try and get early because sometimes the good choice of colors will pick out some feature you wouldn't otherwise have been able to see there. So it's really to front load. And again, I guess the Wolfram language makes that rather easy because we put so much effort into sort of automating the process of doing visualization and so on that, you know, it's, it's like front load that stuff because it's really part of the story of doing the research and so on. Let's see, Let's see. There's a question here from Nicole about how should one go about learning how to split up equity when founding a company? How do you know if you're giving too much or too little? Okay, so I have Seen this so many times. People say, we're going to start a company, it's going to be amazing. Then they start arguing about how to split up the pie, and they spend months arguing about how to split up the pie and coming up with these elaborate agreements about, you know, the pie will shrink in this way and that way if this happens and that happens. And then turns out they never start their company or their company, you know, doesn't really, doesn't really make it. And there was no pie. So, you know, point 1, point point two. Usually when companies get started, there's an energy source. There's somebody who has a vision, there's somebody who has. It's like, I'm going to do this, I really want to do this. I really care about this. If there isn't something like that, it's probably not going to work. So whoever's doing that is going to be the one sort of AT T equals zero, who kind of has the pie? And then the question is, how much of the pie do you give to other people who come in and say, I can do this piece, I can do that piece, I can do the other piece. You know, it's a little bit like what I was saying about compensation. The best case is that the pie is, you know, that you kind of get to figure out the pie. When you figure out what's actually delivered. When you have to say up front, you say, you know, the person's going to do amazing things, they want a big piece of pie and, you know, for that, and then they're going to do amazing things. So I will tell you, in my life over the last 45 years, the Times when I've done pie splitting, even though I've done it, and I have to say, there's been a while since I've been doing this, at least been making, I think, these kinds of mistakes with this. The, you know, I have incorrectly pie split a bunch of times and it's always the same thing. Somebody who isn't the energy source is there saying, I'm going to do this amazing stuff. And you say, oh, I should give you this piece of the pie. And then they don't deliver. And then everybody's upset because they'll say, but I would have delivered if only you'd done whatever. Or they would just say, you know, by the time money starts arriving, then they get greedy and then it's all a big mess. So I think in, you know, I think my main comment would be, start off, you know, there is an energy source, there's a visionary, there's a person who's trying to make it happen. Maybe it's two people, it's not five people usually. And you know, that's where most of the pie should start. Now in terms of other people, it's like, okay, great. You say you're going to be able to do this and this and this, you know, define, you know, and you say you're going to spend the next 10 years of your life doing this great. Set up some, you know, you get this amount, you have some vesting schedule where you get this amount per six months or whatever it is when this happens and so on. You know, I would say that that's, that is the more likely to lead to happiness than the other way around. The other thing to say is that when you have multiple founders in a company, the, you know, the thing you have to realize is people may be super aligned at the beginning and maybe they even stay aligned for a couple of years. But after enough years go by, people will tend to drift apart with the exception of if the company is successful enough and the, and the whole sort of, the whole thing is, is big enough that there's room for, for both people. I mean, some, sometimes, you know, one person will be the very business oriented, you know, I'm going to make a bunch of stuff happen. The other person will be the more of the guru, technologist or something who, as the company grows to, you know, hundreds, thousands of people, is more the person who's still sitting by themselves, coming up with good ideas but, but still is, is useful and is not kind of, you know, hasn't, hasn't obsoleted themselves. But it's, you know, the thing that will tend, that often happens is, you know, everybody's like, we're very aligned. And then things happen. Maybe it isn't as successful as you expect. Maybe people's personal situations change, etc. And they're like, hey, I want to, you know, I'm, I'm, I'm, I'm drifting, drifting apart. And then, you know, the company is just going to be one company typically, but the founders are going off in their different directions. What happens at that point, it's difficult. And if you have anticipated that that might happen and you've set things up so that nobody is super upset if that happens. Oh, the people who spent a bunch of time at the beginning, they maintained some equity, but the people who then spend the next 10 years working on the company get a lot more equity. But the people at the beginning, well, they spent their year, they did some very useful things at the beginning. They, they've got that nice piece and you know, 10 years later when the company finally has a liquidity event, they get a great big check and they're very happy and they say thank you very much to everybody else, you know, and everybody, everybody's happy. Nobody feels like they were, were taken advantage of or whatever else. In situations where you have kind of split the pie in a more, in a way where that isn't what happens, where, you know, knowing that that is not unlikely to happen, that the original founding group may not be the group that is still sort of in power three, five years later, whatever, you know, a year, two years. Yeah, people stay aligned. Five years, not so much. You know, by the time you're at, as I say, unless the whole thing is big enough that there's room for everybody and where there's sometimes, you know, places for people to move within the organization and not have to sort of break away from it. So anyway, that, that's some, that's a little bit about now in terms of, you know, you try and hire somebody, they say, oh, you know, we'll only come if you give us X. You know, you have to kind of figure out is that reasonable or not if you don't feel comfortable with it, you know, is one thing about, well, you know, can I get away with less? Don't do that. You know, in other words, for me at least, my theory of these things is there's typically a fair and reasonable number. You know, yes, you might be able to get away with less, but it's probably not going to end well. It's better to just go with the, what you think is the sort of fair and reasonable number. Now, if the person says, no, no, no, I want twice that much, etc. And you don't think that's the fair and reasonable number. Again, that's not going to end well. You might say, oh, okay, I'll give you twice as much because I really, really want you. And you know, as I say, my experience is that doesn't tend to end well. You know, there's always exceptions to these things. I'm, you know, there are some cases, actually. No, I, I pretty much, you know, when I think it's really outside the bounds, it's like, of what I think is reasonable. It's like, no, I'm not going to do it, even if it might be the expedient thing to do, because it's like, this is a really good person. We really want them for this, et cetera, et cetera, et cetera. Now how do you get a sense of what percentages and so on people should get? There's always looking at other people's companies and seeing how those have worked is a reasonable place to start, I think. Yeah, I mean, that's probably the best place to start. I mean, I think by now, I have no idea. I mean, I haven't been in this business so much in recent years, but I, I wouldn't be surprised if there aren't, you know, books that tell you, you know, this is the way I'm surprised. Actually, I haven't seen these. I mean, I, I remember when Y Combinators are sort of, What is the generic term? My gosh, not incubator, The thing that techstars and all these other things have become. And for some reason I'm, I'm blanking on the, on the generic term for these things, but a sort of a company launching entity. It's kind of the, the modern version of business school, I suppose. But I remember when that, when Y Combinator was, was just starting, I knew the chap, Paul Graham, who started it and I went to a bunch of its events and so on. I remember they had a kind of a day. In Boston where they had kind of the Y Combinator University where people were talking about sort of how to start companies and so on. And I remember these kind of. That was a long time ago now, but was sort of the early period when people were starting to say, and there's this thing, the, this thing, this thing. And it certainly, I found it very amusing that all these things that had sort of emerged as lingo in sort of almost slang lingo in the startup companies around Y Combinator and things like that. Somebody's pointing out accelerator is the, is the term. Yes, sorry, I blanked on that. The, the, the, I think it, you know, these, these things that have been like the demo day, you know, you know, I went to the first Y Combinator demo day, which I'm sure Paul Graham just named that because it was kind of like, well, we got to name it something, let's call it that. And now that's, you know, that becomes a, A, a standard term and so on. It's kind of always kind of fun to see, see how these things originate and then become standardized. But so I'm sure there are written down rules of thumb for, oh, you give this amount to this person, this, to this person and so on. And you know, that I suppose helps set expectations. Let's see. Okay, off, off. Lamb is asking, how do you research a company you're interested in working for or purchasing? I haven't bought very many companies. I bought a few, but not many. I think that's a different thing from a company that you are thinking of working for. I think that's a, that requires a. Companies, a company you're buying. It depends what you're buying it for. Are you buying it for the people? Are you buying it for technology? Are you buying it for its customer list? Those are all very different things and they require different kinds of investigation of what's, what's happening. I mean, the thing to understand about companies and the acquisition of companies, it's a difficult thing. You know, there are certainly companies that simply aggregate many, many companies together with a small amount of, kind of shared resource, sort of economy of scale. And that's probably a more straightforward case, not something I've done. When you are acquiring a company and really want to integrate the stuff it has into your company, that's a lot of work. It's complicated and it's, it's some. And sometimes if the culture of the, of the company you're acquiring doesn't merge, doesn't match, well, your culture as a company, it really is never going to work. You know, maybe you can maintain it more in the sort of aggregate of companies model where it's its own separate thing and you've never really, you know, you've never really integrated it. But as something to integrate, it can be very challenging in terms of research and companies to work at. Well, let's see. I mean, it's like understand their products, understand, you know, I don't think the, you know, watch videos of, you know, it depends on the size of the company whether you, Is it a company where you're going to be interacting with the CEO? Is it a company where you're eight levels down from the CEO? What scale of company? The goal is to understand something about the culture of the company. And you can often get that if you meet people who work at the company and things, you can get some sense of it, although it isn't completely uniform across, you know, for example, different parts of a company, different kinds of work that are done at the company. I'm not sure. I think you can probably get some, some knowledge from, from sort of talking to people. You know, I kind of, you know, watch videos of, of relevant people at the company giving, giving presentations. I suppose for a company like ours in particular, it's particularly easy because we do things like live streaming, internal Design review meetings and things. So you want to know what happens at the company, what it's like. It's like watch a live stream of what, what actually happens. It's, it's simple. I believe we're kind of the only company that does that, but that if you can get some proxy for that, that's a good way, you know, of seeing sort of what, what is it like inside the company. And different companies are very different. I mean different companies range from, you know, the company is, is very much of a think for yourself, people will be pleased if you think for yourself to very regimented to very kind of, you know, manager Pleasing is the most important thing to. Productivity is the most important thing to, you know, very sort of having, you know, for example, a lot of imposed sort of real world culture as well as corporate culture of, you know, there are like our company tends to take the point of view that, that sort of the, you know, people have their own personal views, whether they're, you know, about political, social, whatever issues and that's their business and it's not the company's business. Not all companies take that point of view. Some companies are very much more kind of involved with kind of sort of external causes and things that, you know, independent in a way that, you know, I, I tend to think that it's a, it's a healthier situation that people, you know, have whatever views and activities and so on they have as individuals. And what we do as a company is just the things we do in making our products and things like that and that those things should be separated. But that's not always the case. And some people like to have a company where the internal culture has more kind of involvement with sort of external issues and so on and you know, different from our company, for example. And I think so there are all these different parameters of kind of what a company is like. You know, you can go look on, you know, what is it? Glass Door and things like that. You know, I, to the horror of our HR department, I've taken the point of view that I want to be the worst rated CEO on Glassdoor. So whatever I'm doing that I don't, in other words, I think it's all nonsense and I don't care and I object very much to all these pieces of mail that you get from companies like that that say, don't you want to improve your ratings on one of these sites? Just work with us and we'll improve your ratings. And it's like, wait a minute, this was supposed to Be an independent, you know, just people being, you know, getting, getting independent opinions now. And who knows what's going to happen in the, in the post chat GPT world of all kinds of eloquent pieces written by supposed people at companies. I have no idea whether that stuff is accurate at all. I've made a point of, of not really looking at it. And I think it's, it's. I, you know, I, I think, I don't know. I don't know whether that gives you a reasonable insight into the culture of a company or not. I would say that perhaps if I were to guess deep inside a giant essay, you might be able to deduce two things. Number one, what was the orientation of the person who wrote the essay and were they making sense or would they have some bizarre ax to grind? And number two, you know, what is really actually going on at this company? Because by the time you've written a giant essay, you're either, you know, mostly venting about some personal issue of yours or somewhere in the middle of that is actual content. My guess. But yeah, those are a few things to say about, you know, sometimes with companies there are things where, oh, I don't know the, the, you know, you can, I'm trying to think what, you know, if there's a company with a physical location going to visit, the physical location is really useful to get some sense of the company. You know, it's funny because I've been an advisor to many companies and I usually only meet the CEO and I sometimes I'll visit the companies, though that's comparatively rare and usually, and it's very interesting because what you know about the employees of the company is only through the CEO. Typically if you're in that kind of role. And it's always interesting to me, you know, sometimes later perhaps I'll, I'll meet some person who was an employee, even a fairly senior employee at such a company. And it's always interesting to kind of make the, the kind of the, the I don't know what it is that the kind of the link together one's view of what was going on from the CEO with one's view from the individual data from, from individual people at the company. And I have to say my, my general experience is you actually get a much more accurate view sort of secondhand through the CEO than you do by talking to individual people at the company. And just my observation about these things that usually the CEO, there's a certain sort of projection of personality that happens from at least stronger CEOs founding CEOs, particularly in companies. And it's then the kind of the, the, you know, the view of sort of what's happening within the company, of all the different pieces it usually is, is better organized talking to the CEO than you learn from the individual sort of point samples, which is, I suppose to say that if you, that it's, it's probably, you know, you want to know about a company, you know, watch videos of the CEO. Although, you know, I will say that sometimes that's not accurate because there are certainly people who have a, you know, who have a particular kind of public, public Persona that's, that's different. Although, I don't know. I, I'm, I'm, I'm thinking of examples here, and it's not as different as one might think. I mean, it's. Somehow the personality does come through and maybe you have to, you have to think a little bit to see it, but it is still there. Let's see, maybe one more thing and then I need to. See. Okay, this is a question from Kelly here. Said you understand French. Are there other languages I'm familiar with? What other languages would you like to learn or wish you'd learned? I, I learned Latin and Greek when I was a kid. Those have turned out to be useful to me. I never thought they would be. When I was a kid, I made a huge fuss about learning them and said, these are never going to be useful to me. But actually they've been useful so many times. I mean, my gosh, you know, if you deal with an old field like medicine, for example, where there's all this terminology where somebody says, oh, it's a whatever, whatever, whatever, and it's like, I can tell what that means. I know those Greek words, although I know those Latin words. And you immediately know what it means. And that's helpful, I think, also in the particular things I've been interested in, some history of science, it's sort of useful to be able to pick my way through Latin, particularly. Although, unfortunately Latin evolved quite a bit between the classical period, which is what one learns in school, and more modern times. Latin is also an interesting language because it's a simple language. Its grammar is quite simple compared to, for example, English. And, you know, it is the case for me and probably for many other people. You know, I learned Latin grammar. I couldn't tell you English grammar. I couldn't tell you the names of all the tenses in English, for example, for verbs, whereas I could in Latin. There are a lot fewer in Latin. It's a lot simpler. The. I think I always thought when I was a kid that I was pretty crummy at learning languages. It's. I don't know if that's really true. I think that it was a feature that, you know, some people who are, oh, we're going to learn French, let's go hang out in France for a little while. And then you'd learn French. Well, I never did the hang out in France part, so. So it didn't. That made it proportionately much more difficult to. To know French. I wasn't that motivated, otherwise I probably would have done that. But. But I think I learned many computer languages back in the day. Haven't been learning them so much recently. When I first started designing languages, I kind of knew late 1970s, early 1980s. I kind of knew at some level all the languages, but I typically knew them rather theoretically. I didn't actually program in them. I mostly knew them by. These are the design principles that they have, I would say, in, in more recent times, you know, I don't know what the value of knowing languages is going to be because, you know, these translation mechanisms are getting better and better. And, you know, I haven't yet had the experience of having a conversation through, you know, video conferencing or something where I'm speaking in English and somebody else is speaking some completely different language. But that's certainly coming. I mean, there certainly are test systems that do that. And, you know, when that's happened, I'm not sure what the value of knowing these other languages is going to be. I mean, I'm fortunate that English happens to be my first language. And so, you know, and that happens to be the sort of the, the current de facto international language. I think that in terms of other languages, it is interesting to see how different the thinking is in other languages. But that's a thing that is more than just learning the language. That's kind of embedding in the culture that goes around that language. And that's something that is a big investment to do and I've certainly not done that and not been highly motivated to do that. In terms of. I have been curious actually. Okay, so I was learning a language just recently. I'm interested in constructed languages. And in particular there's a language called Toki Pona, which is a kind of a pidgin language. So, you know, pidgin language is kind of a language. Pidgins are usually languages P I D G I N not the other kind of flapping 1. The languages that typically sort of emerge when there are two different languages, maybe an official language and a language of the people type situation. And they develop these kind of simplified languages that maybe borrow words from both of them and just allow you to express kind of basic kinds of things. It's kind of the basic, you know, go into a coffee shop and make basic small talk type language. Well, the Toki pona is a constructed one of these with only 130 words in it. And it's interesting that you can get away with only 130 words and be able to express anything reasonable. And it is, I would say, somewhat amusing that the words are not based on English roots. They're based on roots from all kinds of languages, including languages like Finnish that have totally different word, sort of word origins, which makes it much harder to understand. You know, why is it, you know, sowelli is a land animal and lilies little and poner is good, I think. And so, you know, what is it so welli, lili pona or something means, you know, little land animals are little, little creatures are good or something like that. Those words sound really weird because they have roots that are so very unfamiliar from English and it would be, you know, but, but the very fact that it's possible to make a language that expresses sort of everyday thoughts in so few words is interesting and happens to be interesting to me right now because I'm thinking about kind of what is it that things like ChatGPT have really learnt? What is this thing that we put together that is language and is something that makes sense linguistically and how many components, how many puzzle pieces really are there in doing that? That's a kind of coming attraction thing that I've been been thinking about. But so it was, you know, a language with 130 words. It doesn't take very long to learn it. I admit that I'm only about halfway through learning it. So I know about half the vocabulary, which is kind of pathetic. But. And there, you know, there are things you can say and there are things you can't say with half the vocabulary. But. And I'm just going to be interested and curious in my own, You know, I don't know how, you know, I don't know whether I learn this quickly or not. I just haven't really learned languages in a long time. I would say that the thing I've long wanted to have a spoken version of Wolfram language and I've never figured out how to do it. And it's kind of, you know, when you end up Dictating code. It's like, you know, map F over the list, blah, blah, blah, blah, blah. And you do have ways to say it, but somehow it doesn't flow that well. And I really wanted to find a way to be able to add little particles and particles of language, particles into sequences that, you know, represent a comma with some kind of particle type thing and be able to have something where there is a spoken version of the language, which maybe is not directly the sort of character for character dictation of what you would see in the written form, just as it isn't in many, many human languages, but it's something where it's pretty easy for somebody if you hear the thing spoken to be able to understand it. See, one thing about most computer languages and our computational language is they have tree structured grammars, so things nest. But that's the same as what happens in human language. But somehow we have a much easier time decoding, you know, the cat which sat on the mat, which was this, which was this, which was this, pop up to the top again, you know, chase the mouse. We have an easy time dealing with those subclauses and decoding them. The spoken form of orphan language that I've ever been able to figure out hasn't had an easy time understanding those subclauses. But I think it's going to be possible to have a spoken version. And I think that will be interesting as a way to, I mean, I think that will create another kind of way to relate to, to engage with kind of this computational language anyway, just a thing like. So Callie asks, do you recommend encouraging exposing children to a second language when they're young? Is it harder to learn other languages? You get older? I mean, I don't know. I know with my kids who are now kind of grown up, I did have this theory at the beginning that, oh, you should, you know, play them these, these things that have all the different phonemes of the world because that way they'll kind of maybe learn, you know, all these different, these different phonemes that, that, you know, if you speak English. I don't know, you know, I don't know in most, maybe 30 different phonemes perhaps, if I remember correctly. And you know, there's a lot you don't know. There's a lot of sounds that we don't, you know, the, the typical English speaker depends on your accent. Typical English speaker doesn't make. And you know, it's always been said it's hard to learn those things later in life. I don't think that's true anymore. I think it was hard to learn when you couldn't like just look at the waveform of your. Of what you speak. And I think it became a lot easier to learn. I think it became. That was something which was kind of a long ago. People said if you don't learn those sounds when you're less than five years old or something, you're never going to learn them. I don't think that's true anymore. I haven't tried myself, but I don't think it's true. I think that being able to have this feedback that is a detailed kind of feedback that comes from just looking at the actual audio waveform and so on gives you that capability. So that's not a if you didn't learn it when you were very young, it's too late type story. I think in. I mean, it's my impression that, you know, it's one of these typical things. You know, you try and teach a kid three languages from, from day zero and the time for them to learn any language is going to be longer, is my impression. Anecdotally, I don't know. I'm sure there are. In fact, I even think I've seen studies of sort of multilingual acquisition. I suppose it's also interesting for kids when you get this sort of languages which are embedded in very different cultures. That's again, its own interesting thing. I don't think I have really a good intuition for, you know, is it great to learn those things early? Is it better to learn one solidly and then go on and learn another one? I don't really know. I think, you know, it's an interesting question about education in general. You know, one of the things that I suppose is a, is a sort of reminds one of the following thing that, you know, when you eat food, you could say, how come you can eat just a few foods and you somehow get all of the nourishment you need? Well, it's because foods are made of, you know, proteins and amino acids and so on. And you know, you can, you can have a hamburger or you can have a, you know, a finely presented, you know, whatever it is, fish thingy, dinghy or something, and you know, you'll ultimately get the same amino acids in you. And so the question for education is, as you're learning different kinds of things, as you're learning different kinds of content, are there sort of blocks of cognitive sort of learning that you do that are sort of the same across these different domains? One thing that isn't the same, is just outright facts. And the world is full of facts that are worth knowing. And that's obviously something that you have to separately learn in different areas. But I think there are some sort of meta learning kinds of things. Like for example, one thing is learning how to do a project. Okay, you do a project and it's a history project. You do a project and it's a technology project of some kind of. I think there's a certain amount that you learn just at the meta level of doing a project or doing a project deeply. You know, you write somebody does a PhD thesis about something and it's about one thing or it's about another thing. There's a certain amount of meta learning of how to explore a subject to great depth that hopefully that is, you know, transcends the details of what the actual subject was. And I think that in, you know, so that, that kind of makes it, you know, is it, is it better to, to learn, you know, the one language really deeply and then add on the others and. Because, you know, because you're always going to get the same sort of cognitive blocks whatever you do. And there's extra that you get by, by learning the thing more deeply that you wouldn't get if you, if you just learned three things more in a more shallow fashion. I'm not sure. I mean, it is my impression that, you know, for example, people learn the idea of starting from an idea and building it into something. Some people don't learn that ever. But if you can learn that, that's an important sort of meta learning kind of thing. Another thing is, well, learning to think about stuff. Learning, you know, what it takes to, you know, there's one thing is to remember what it said in a book and, you know, be able to sort of reproduce some pattern of thought that was fed from a book, so to speak. It's another thing if, if there is no book, it's like we don't know what to do. You know, can we figure it out? And that's a completely different, It's a different kind of meta. Different activity is figure out stuff where it hasn't been figured out before and where, you know, sometimes you get into situations where people are like, you're saying, in fact, I was just in one of these this very morning of, of. Of something which we're doing, where I was saying to the people, you know, look, nobody has done something like this before. We have no, there's no roadmap. We don't know what to do. We have to figure it out from scratch. There's. And that's something that the, you know, the kind of the concept of doing that and the ability to do that and the kind of pacing of doing something like that is a meta thing to learn that is probably independent of, you know, once you've done that even once actually and seen it work out, it's a. It's a great experience. And. But it's. It's something which is kind of like, really, you can actually go from nothing and make something and just figure stuff out? Well, yes, you can, but you kind of have to learn how to think about how to do that. I think. And I suppose that. So, I mean, there are these, There are the, you know, in the subject of how to learn how to think, you know, I was trying to figure out, and maybe I should think harder about this problem about how to teach how to think. But it's kind of like, what exercises can you give that kind of help the process of learning how to think about things? And, you know, there are a few obvious ones like, okay, somebody tells you a fact, claim fact. It's like, why is that true? You know, let's figure out why is that true? Do you actually know it's true? You know, what, what, what? How do you drill down? Where does it go? As you try and get down to the bedrock of is this actually true? And how would you find out if it's true? And what was the evidence that it was true? And kind of the experience of seeing that and sometimes realizing, well, actually, gosh, you can't really actually tell if this is true. People claim it's true, but you don't really know in the end. And that's one type of thing. Another type of thing would be, here's a topic. What's a question you could ask about this topic that is, you know, that interests you or that that is kind of, you know, where do you. What's the thing about this? You've been told a certain set of things. What's the stuff you haven't been told? What's the stuff that you could have been told? But, gosh, nobody knows that, so they didn't tell you that, you know, where are the. Where are the holes, so to speak? That's another type of thing. I mean, another. I suppose in. I mean, there are plenty of situations where I would say perhaps some of the things that involve explaining stuff is also a pretty good way to learn to think about things. It's like, okay, you've got this thing. Maybe it's something you understand quite well or you think you understand it quite well. How would you actually explain that? What's the main point? Try and drill down to the point where you can actually explain the thing without. In the minimal way, so to speak. I think that that has a certain, you know, in thinking about things that's often something you have to do. You have to say, well, I've got this big fuzzy thing and if I, if I, if it's only the big fuzzy thing that I have, I can't think about that thing because it's kind of like I can't fit this thing together with this other thing over here because they're big fuzzy things. But if you drill it down and you find the essence of the thing, then well, yes, you can understand how it, how it connects with these other things over here and so on. I mean, I suppose one of the things that I certainly. I'm wondering if there's a. Some of the things that, that end up being really useful in thinking about things and figuring things out are these kind of analogies where you have learnt one field quite well and you can see in that one field the kind of, you know, the, the features that exist there that you can kind of map into other things. So for example, in, in physics, you know, there are. Well, particularly this is true from things that have come from our physics project about sort of things about the way that physics works with gravity and space time and all that kind of thing. And then you can kind of see, once you understand that deeply, you can start seeing analogies in all these other places. And that's kind of an interesting sort of. Can you think what is the analogy between this and that? Another thing, another example of that's pretty good is the history analogy kind of exercise, I suppose, which is history has this terrible habit of repeating itself, but not precisely the same. It's like where have we seen before? Let me give you an example. From right now people are saying, take ChatGPT, people have kind of made this very big, large language model and it cost a lot of money to make and maybe there'll be billion dollar large language models that people make. I think there probably already are and somebody's going to spend a billion dollars to make this thing that is then something that can have a lot of uses made of it. And the question is kind of know, okay, so figure out the analogy. Where have we seen something like that before? Where, where people kind of, you know, where you, where you had to invest a lot to get this thing that you could then sort of make use of. And, you know, you start thinking about, I don't know, mining companies and things like that, where you're, you know, you're going to. You're going to ex. You're going to find an excavate that, you know, set up gold mine, and then you can, like, you know, get gold out of it for a while. Or actually, more directly, you think about cryptocurrencies and you think about the early days of things like bitcoin and bitcoin mining, where it really was, rather amusingly, it really was an exercise in let's burn those GPUs. And it's the very same kind of GPUs that people are now using for machine learning training, although there's some even more specialized hardware there, as there was eventually specialized hardware for bitcoin mining. And so it's kind of a. Maybe that's not the best example, but it's kind of interesting and I find it a good sort of thing. You see something that's happening now and it's kind of like, what was the historical analog of this? Can you, you know, it's a. It's a. And that's often a very useful way, in my experience, to think about things because, yeah, it may not be a precise repeat, but at least it tells you what questions to ask. You know, oh, we've seen this before. You know, this is how it usually ends, or this is how it ended in the past. And this is the thing that happened which was, gosh, we didn't think that was what was going to happen. You know, somebody will say, oh, well, you know, at some point, you know, I don't know, the price of silver or something has gone. Gone unbelievably high. And then, then you realize, well, people are starting to take their, you know, silver spoons and melt them down and turn them into ingots or something like that. And that, that's a sort of a thing that happens when the price of something gets high enough as you start finding these other, you know, sources of the thing or whatever. And that's something that you can see repeat in other places. And it's. Anyway, I think that's sort of a useful thing to think about anyway. Okay, that was talking about thinking about thinking and training and learning how to think about things. So I suppose that we got about as meta as one's going to get. Maybe I get even more meta than that because I've been thinking about the process of thinking and what we learn about the process of thinking from watching sort of the AIs think, so to speak. But maybe that's a topic for another day. All right, should wrap up for now and thank you for some interesting questions and comments here and look forward to chatting with you all again another time. All right, bye for now.