History of Science and Technology Q&A (April 17, 2024)

Welcome to another episode of Q and A about history of science and technology. And I see a bunch of questions here saved up. There's one from Johnny. Are there languages or logic systems we haven't yet discovered from the past? I think the answer to that is surely yes, certainly on the languages side, let's talk about languages for a second. There are about 7,000 kind of known languages that are sort of in use today, of which a decent fraction are endangered in the sense that not many new people are learning them. And there is a risk that the languages will just get to the point where they can't be used for communication because at best one person knows them, or maybe nobody knows them and they're only in historical documents. And those languages, we can kind of trace them backwards and see to some extent the kind of tree of evolution of those languages. And we know that there are groups of languages like Indo European, which many languages like English are part. And there are other languages that are isolates in the sense that they don't seem to have any known obvious connection to other languages like Korean, I think Basque, for example, a bunch of other such languages. So there's been a complicated sort of history of evolution of languages. I mean, in the couple of hundred thousand years that there probably been languages for our species, so to speak, it's unclear how many languages there have been that went extinct. And of those languages that have been and went extinct, which ones have any trace left of them? I mean, some of them, the only trace may be sort of the presence of words in current languages. I mean, it's kind of reminiscent of what's happened in biological evolution, where there are genes that maybe we have now that were very ancient origin, but the critters that sort of where those genes were first invented are long gone. But we get to see some traces of those things in our genome today. And I think the same is potentially true of human languages, where that language that was spoken at some time 100,000 years ago among early humans or something, it's long gone. But some surviving pieces of that language exist, perhaps even in English today or something like this. I mean, it's very. One could sort of trace back, try and trace back the sort of Indo European at least, roots of lots of language as it is today. And there are lots of ur&ug&og& so on, sort of little pieces of language today that people certainly claim were sort of the Indo European roots of words across many different languages. But so I think it's undeniably the case that there are Languages that existed in the past that have gone extinct today. How would we even know about them? Well, the primary way that we know about sort of languages of old is through written records. But writing wasn't something that was invented for all kinds of languages. The languages that there are probably what, four or five different inventions of writing that we're aware of and that have different schemes like alphabetic versus ideographic and so on. And perhaps there were other inventions of writing. It's not clear. Perhaps there were sort of pre inventions of writing. You know, they're things like the. What are they called? Kippus in Peru, These things made of string with knots on them, where presumably they were some kind of accounting data collection thing. But maybe they were a representation of language. Maybe there isn't such a distinction between sort of the accounting data and language. I think it's sort of unclear how that worked. And there certainly are a decent number of written languages where we have records that were inscriptions carved in stone, where we still don't really understand what that language. We don't have a way to translate that language. And generally the main way that we know translations of languages is when there's sort of a chain of this was connected to that which was connected to that or whatever. Or we happen to find these parallel texts like the Rosetta stone from Egypt and so on. That. That which listed in that case three different languages, including hieroglyphic, on the same text in the three languages. It's kind of interesting that in modern times when we're trying to train machine translation systems, some of the best sources of that are parallel texts. And that happens. For example, the European Union has this sort of requirement to translate all its regulatory material into all the languages of the European Union. So there are many texts there that are sort of in parallel between those different languages. And there are other places like for example, documentation for computer systems, other kinds of systems where there's kind of parallel versions of that text and things like the Bible that have been translated into many languages and so on, also provide sort of parallel text that you can train a machine translation system on. And it's the same kind of idea that has been very useful in the translation of ancient languages too. But I think in sort of one question is, will we ever be able to find records of languages that were not written down? Is it conceivable? Certainly the phonograph wasn't invented until, well, the 1900s, I guess, maybe the very late 1800s. Yes, there were very late 1800s. There were some of those things but could it be the case that some strange situation, there was some piece of wax or something where somebody was at some critical moment, this thing got sort of frozen, but it had just had these various sound vibrations that were kind of had a trace on this thing. And now, few thousand years later, we get to find the thing. I mean, that attempt to sort of reproduce the sounds of ancient times is a complicated one. For example, when one finds musical instruments or pictures of musical instruments, that's another kind of source of what were the sounds of ancient times like. But it would be cool if it turned out that there was some sort of piece of archaeological, reconstructable archaeology that would keep the sounds of ancient times. I mean, I think one of the things that is really notable in sort of the history of archaeology is more and more things where you thought that's just gone, there'll be no trace of that. It turned out that with more sensitive techniques for detecting things, whether it was kind of detecting something that was sort of decayed in the ground and you could see the difference between the piece of ground where it was and where it wasn't, or whether it's kind of molecular scale analysis of residues on things, what was the last meal that so and so had ate before all the stuff was put away in some burial chamber or something like this. These kinds of things where solids particularly and molecules in general tell many tales that last a very, very long time. So I don't consider it impossible that we could know something about even spoken languages, although I don't yet see how that would really work. But in terms of kind of ways of thinking about things and kind of logic of things and so on, that is sometimes more challenging because it can be the case that people say, oh, that's my way of thinking about it, but I never wrote it down. It's one of the things of modern times. For example, things like computer documentation, it's reconstructing even the history of early computers. It's sometimes not so easy because was there really documentation? Well, what was it? It was a bunch of sort of photocopied or pre photocopying, kind of copied typewritten notes. But it wasn't a book, so it wasn't kept in a library. And it was kind of all a bit vague how it was preserved. And that's typical of things that sort of emerge for the first time in some place. And I wouldn't be surprised if there were things that were, for example, methods of calculation that people knew where somebody would pass down. Oh, yeah, you can use an abacus and do it really fast, this way, that way, the other way. Most of the time that wasn't written down. There were a few people who were essentially professional arithmetic tutors or consultants or something who did write books as kind of self promotional kinds of things. I mean, Fibonacci wrote this book called Liber Abaci which was sort of of that type around 1200 or so and many people since then, but that's probably a very small part of the general practice of things like how to do arithmetic and so on. I think there's this sort of question about if you are asking about the structure of how you think about things in a formal way. One of the things I've long been curious about is when did people start thinking about using rules to define things and then seeing what the consequences of those rules are. Now obviously there are cases like people write down systems of laws, the code of Hammurabi or something, written down as a system of laws that could define things. There were. But when it came to kind of mathematical descriptions of things, that wasn't something that got written down for a really long time. My own efforts studying simple computational systems, simple programs, things like cellular automata where you might have an array of black and white cells, for example, and you just go down a page or a tablet or whatever, saying each successive row is determined from the one above it according to a rule that looks at the cell right there and the cells to its left and right. It's a form of description that doesn't seem like it should have been beyond folks in Paleolithic times, but so I've always wondered, you know, will it be the case that one day there'll be a 5,000 year old tablet that will be unearthed that will be a picture of one of these cellular automata that I started studying with computers in the, the beginning of the 1980s. And I don't think it's impossible that such a thing might exist, but we haven't found any such thing. Now of course there's then the further challenge that when we do find things that are just sort of this arrangement of, I don't know, black and red squares, for example, do we know what it was? Do we know what it means? Famous example, I think it's from what was it? Maybe even as much as 11,000 years ago. I think it's a piece of archaeological findings in Syria that's a wall that's kind of painted with red and black rectangles and some kind of arrangement. We don't know what the arrangement Means it looks. The fact that they're rectangles kind of makes it a bit of a giveaway that somebody sort of did that on purpose, presumably. But we don't know what that arrangement means. And perhaps it is some system of rules. We could think of it as a logic of some kind that is just something that was there then and isn't determinable today. I mean, another kind of question like that is things about the origin of numbers and counting and when did people understand various kinds of levels of abstraction about the concept of numbers? The disembodied number five independent of five rocks or five sheep or whatever else? Just the disembodied five. When did people understand things about the disembodied edition of numbers? When did people presumably much later Understand about number 0 or negative numbers, whatever else? And there's this whole general question, it's sort of a recently quite active area, I think, in archaeology of what can you reconstruct from the artifacts that we have about the concepts that people had about those artifacts? And numbers are an obvious case, but it's very unclear. When you see marks on a bone or something, and they might be tally marks, they might just be marks, what does it mean? What was people's internal conception of those things? Were they abstract numbers or were they not, or were they merely. I put a mark every time I sort of kill a woolly mammoth or something like this. So complicated set of issues. Comments. There was an attempt to do this with ceramics, to play them a modified needle to see if local sound had been imprinted on them. Oh, yes, that. That's referring to my comment about whether sounds of ancient times could have been preserved. Interesting. Loan asks, can smart keyboards help with this process of language discovery? I don't know. I think that in modern times, I mean, by the time we've had keyboards, we've had recording, we've had all sorts of mechanisms for knowing about languages. I think there are various initiatives which unfortunately have not been as energetically pursued as I think they perhaps could have been to do with preserving endangered languages. I mean, it's kind of like the endangered species story, except that it's a lot easier to deal with than endangered species. Well, it's somewhat easier to deal with in the sense that you can go record the language. And part of the reason that's a potential interest is insofar as we're interested in kind of the way we can think about things. Different languages do encode different patterns of thought about things, at least to some extent. And there are languages where there are presumably quite different kinds of ways of presenting things than we normally know. And by all means, if there are sort of languages that exist among humans, we should be able to capture these things and learn about different ways to think about things. We've never been able to capture the language of the whales or whatever else which might have a yet still very different way of thinking about things. And even beyond that, the kind of putative, the extraterrestrial, the aliens language, which I tend to think is, is sort of too far away in rulial space for us to really have an human interpretation of these processes out in the natural world. But be that as it may, in terms of sort of broadening our way of thinking about things, capturing endangered languages that are being spoken by humans and where we can actually make a reasonable level of translation, because you can be talking to somebody who speaks the language and they're pointing at things and saying this is the word for cat in this language, and so on, when, or you can sort of see the expression on their face and you can get some idea of what the emotional import of some particular comment is or something like that. So I think it's something that deserves to be more pursued than it has been. I think it's an interesting question whether in the world of LLMs, there are new opportunities for endangered language work, because one of the issues is it's sort of fun at some people I know at one time were doing this, I don't know if they still are, where they have sort of study groups just for the sake of learning some obscure endangered language. And it's kind of fun, you know, if you're a little group of people and you learn this bizarre language that was that, I don't know, spoken in the Canary Islands, full of whistles and things like this, and you want to communicate with your friends, you don't want anybody to understand what you're saying, know, speak in, whistle talk. And you'll probably be able to do that. I mean, that was something done in World War II with the indigenous languages in, in, in North America as a kind of a way to have a code that would be hard to break. I have to say I'm not, I don't really know the history of that, but Germany was sort of a, a center of philology, study of languages. So I, I, I'm surprised that there were languages that were really so undocumented that they were useful for codes. But I don't really know that history. But any case, this idea. So one can imagine the Possibility of if one could get an LLM to actually successfully engage with one of these obscure endangered languages, one could imagine kind of the opportunity to start learning that language by conversing with an LLM. It is, however, a challenge to get the LLM to understand an endangered language, because the LLM is really based on having a large corpus of a particular language. And all it can do if it doesn't have a large corpus is essentially fine tune itself from existing languages. So insofar as one's interested in endangered language, because it's far away from existing languages, the LLM is not going to be successful with it. It's only if it's rather close to existing languages that one can immediately expect a success. Let's see, there's a question here from Malcolm. Do you view mathematics as a subset of language or the other way around? Mathematics is its own kind of formalized way of talking about the world. I mean, language, human natural language, is one formalized, somewhat formalized way of talking about the world. My own efforts in building our computational language are another kind of formalization of the world. Mathematics is a particular formalization that, among other things, kind of relies on the inventions of mathematical notation, which mostly was a 1600s type of story. The plus sign, the equal sign, the division sign, all those kinds of things. That was a really 1600s kind of development. I think one of the things that's interesting about mathematics as the notation of mathematics is it's pretty universal worldwide, and it kind of makes people have the thought, oh, if we run into the extraterrestrials, they'll be speaking mathematics, too. I don't think that's the correct inference. I think that the thing that happened on our planet, in our civilization, so to speak, is that the development of mathematicalization was quite a late stage thing. And so by that time, there was sort of enough connection between different places that it got invented once and the diffusion time for those ideas was short enough that it kind of spread everywhere. Now, obviously, numbers got invented separately a bunch of times, which led to different number systems, Roman numerals, the Greek number system based on letters, all kinds of different number systems. And it's been sort of a gradual process that mostly the Hindu Arabic number system that we generally use has become the dominant number system that kind of started really spreading out to the west, so to speak, around 1200, particularly Fibonacci was involved in sort of bringing that notation to the West. And I think. But this idea that mathematics was introduced as a notational language mostly in the 1600s, with further tweaking since then, a little bit different from the way that human language works. I think computational language is yet a different story because in computational language, like for Wolfram language, for example, in the end, I'm the one trying to invent that. And we have 7,000 built in functions, essentially words in the language, they do a lot more work actually than typical words in a natural language. But one of the things that's really useful, important to us in building that computational language is that we're able to leverage natural language. We're able to have names for functions, names for constructs in the language that are based on English. Which means that people have an immediate kind of, oh, I roughly know what that means. Even though the actual meaning in the computational language is, is something precise and specific, that may not be everything that those words could mean in the natural language. But it's sort of a different process for creating language. In human natural language, most of the time the language just sort of evolves. And yes, you know, folks like Shakespeare add lots of words to the language that then get used. People, you know, lots of companies, for example, have effectively added words to the language by either naming what their products do, or naming their products or their company or whatever. And those become effectively words in the language after a while. But it's something where on a large scale, sort of human natural language tends to evolve without a lot of kind of specific sources of words. Computational language is a quite different story. It's the designer of the language and the only sort of by far the largest sort of real computational language that's been built as our Wolfram language system. In that case, what's happening is somebody has to invent all that stuff. That's been my job for the last, I don't know, 40 years or so. And I don't think people really recognize that inventing a language that is a way of formalizing things, that's a language to think in terms of. It is something that quite pivotal in the story of how people think about things. It's something where it's just like, oh yeah, there's this language design thing. We don't really talk about that particularly. It's just a thing that gets done. And so long as the designer did it right, everybody just sort of thinks it's obvious type thing. But actually it's something that really affects kind of how one could think about things, how one ends up choosing to think about things and so on. But it's a new case. The computational language story is a new case, not Seen before where that's something you just invent. I mean, in the constructed languages, from Esperanto on, those are also cases where you're just inventing the words. Although it's a little bit different because it's something where. Well, it has been. None of those languages have ended up being that widely used. Esperanto had some moments in the mid 20th century where it seemed to be getting some degree of popularity, but it never really made it, and it certainly has not had. I'm sure there's been much more Wolfram language written and used than Esperanto ever was. And I think it's an interesting question for constructed languages whether the extent to which, as you have, for example, more elaborate constructed languages, whether that sort of leads people to think in different ways. That's certainly a belief of some folk who were learning this language, Ithquil, which is the most sophisticated of the constructed languages. Let's see, There's a question here. How do different languages come to develop? Will we slowly move towards a universal language? This question of how languages speciated, how one ended up with distinctly different languages. Interesting question. I think it's a bit like speciation in biology. There's a reproductive isolation type thing that happens in biology. And for groups of people who have kind of. If they don't interact with each other, there's no reason for them to have a common language. You know, if they were living in different valleys in some, you know, mountainous area where they couldn't get from one valley to another easily, the languages will tend to be different. I think there are places like Papua New guinea that have huge diversity of languages in a small area. And that's probably because people aren't particularly mobile there. I don't, you know, it's a mountainous jungle area, and I think that. So when groups of people separate, their languages that they speak will evolve separately and can evolve quite differently. So to speak. How many times did language get invented by a species? We don't know. We just don't know it. I don't think we even know from the fact that the sort of divergence of languages. I don't think we can deduce whether there was one originator or more. I think the old biblical story of the Tower of Babel, that originally there was universal language and then sort of the people did bad things and so everything was fragmented into this, you know, all the different languages that people then couldn't understand each other in is, you know, that. That's a. That's a curious story. Even imagining that there Was at one time a universal language is an interesting feature of that story. I think the. Okay, so if we think about language and what language really is, language is a packaging of human thoughts that make it make those thoughts transportable to other humans. But the other humans have to kind of know the code. They have to know how to unpack those thoughts as represented in that language. Now one might imagine that the underlying thoughts are in some sense universal. I don't know how true that really is because certainly the details of an individual thought by one human brain are very different from the details of the individual thoughts by another human brain. We can see that very clearly by, with neural nets and LLMs and things like this, that two LLMs that sort of talk the same way. If you looked at the details of the weights that are used in the neural net, they're completely different. And the details of what's going on inside the LLM very different. Perhaps we may start to learn some natural science that lets us see sort of the commonality in what's happening as a sort of matter of scientific narrative. But there's definitely going to be detailed differences. So in the sense, oh, we all sort of think the same way and therefore there must be an underlying universal language. I don't think that depends what you mean by think the same way. We all have to some extent the same biology. That's true. And that will, I mean the details of the layout of brains is different, but the overall architecture, the overall construction is the same. And maybe that leads to some, and this is a long time debate in linguistics, the extent to which there are universals in human language, the extent to which sort of all languages operate in a particular way. I think the history of that is sort of a big step in 1956 with the invention of generative grammar. Although some people say that that kind of idea goes back to folks like Panini 2000 years earlier. But the kind of the notion that we're sort of, we're constructing sentences in particular ways and in particular we're constructing them using essentially these tree like essentially context free grammars. You know, a sentence is made of a noun phrase, a verb phrase, a noun phrase, let's say a noun phrase is made of a noun or an adjective and a noun, or I don't know, an adjective and an adjective and a noun and so on. There's a sort of recursive construction and that is very characteristic of human languages and seems to be fairly universal, that level of, of thing. The idea that every language has nouns and verbs and adjectives and adverbs and prepositions. Actually, in more generality, they're usually called adpositions because sometimes they come before the word, sometimes they're post positions, they come after the word, and so on. Some languages have case endings, some languages have kind of marker words and so on. But for example, the question of whether there are always nouns, verbs, adjectives and so on, even that is not completely clear because you can certainly have constructed languages in which sort of everything is a noun. And you kind of get to say verby things by just sort of stating noun like things. I don't know how well that works, but it's something which one can at least imagine could be set up that way. But anyway, there's this sort of long running question of how universal, to what extent can you translate from one human language to another? To what extent can the thoughts represented in one language be represented in another language? And so on. I think these are very. There are a lot of slippery issues here and quite a lot that I think is somewhat informed by some recent science that we've been able to do. And it's somewhat grounded in things one knows from actually operating with computational language, which is sort of a different story that really has this kind of anchor in not only do you have to be able to sort of say the words, but you also have to be able to execute computationally something based on that, on that language that you've given. But I think in this question about sort of what's universal in human language, there are things that are presumably limitations of our hardware. Like for example, if you try and say a sentence that has a huge number of subclauses. You know, the cat which sat on the mat, which was orange, which was sitting on the floor, which was this, which was this, which, which, which, which, which, which, which. Eventually, after, I don't know, five levels or something, you pretty much lose it. A computer, a parser can deal with sort of many nested parentheses type thing. It has no problem with that. But we humans first, for whatever reasons of our short term memory or whatever else, after you stack it too deep, we lose it. And you could say that sort of a universal language. People are always trotting out these obscure universal things. Whenever there's a functional head with a this and a that and the other, there's always a this and that and the other. I always think that's one of these kinds of things where people are saying, you know, every animal that you know is warm blooded. You know, no animals that are warm blooded. Lay eggs or something. Well, that's obviously not true for birds. The, you know, some, some statement, there is no animal that does XYZ and it's. And then you go to some obscure island somewhere and gosh, by gosh, there's an animal that does this. And I kind of think these kind of more esoteric universals of languages are subject to that issue. By the way, I see this kind of thing a lot in studying the computational universe of simple programs. In fact, I was just experiencing this last few days with a particular set of programs that I was investigating where I certainly had the intuition it's never going to do this. But I've learned from decades of doing this that one has to recognize that the computational animals are always smarter than you are, is my usual statement. And even though I'm absolutely certain that I just can't see how this could possibly do this, when you run it, you do the big search and so on, by golly, there's one of these things that does that weird thing you didn't think it could do. You look at it and you say, oh, that's interesting. I didn't think of that. I kind of think a lot of these more esoteric language universals will fall prey to that kind of issue when you, you know, if you really start exploring other languages and so on in, in. In a complete way. But let's see, the question here was about the origin of languages and kind of one can plainly see in different languages sort of a cultural imprint on that language of features of the local culture. I think in, oh, I don't know, in the Indian subcontinent, for example, there are these many layers of sort of formality and informality and pronouns and things like this, which is characteristic of much of the culture there now imprinted in the language. And similarly the oft quoted, but I'm not sure I've ever really investigated this for myself, statement that the Eskimo languages have many words for snow, because snow is a big issue if you're living in those parts. And it's something which we don't make so much of the distinction of in other places in the world. And so there's sort of these imprints of local cultural, local environment on the language. I think there are also features of languages that are often surprising that at first that are sort of inevitable progressions of language. So there's one that I often quote which, you know, when you do written language and you have words like website or freeform, that was one that came up just today, actually. Are those Words, separate words Web site, are they hyphenated or are they smooshed? And my statement is the uniform tendency of languages to smoosh. You know, if web site was a separate word, you know, with separated words at some point, then maybe they were hyphenated, then they got smooshed as a single word. That seems to be a feature of the development of language. There are also other features. There's Grimm's Law, for example, which is about the pronunciation of vowels, I guess, and the development of that over time in languages. I'm not sure why that one is the way it is, but that seems to be at least a widespread trend. And maybe some of those things are of physiological origin. Maybe if you have a way of saying things that involves some weird construction of your tongue and throat and so on, that people will tend to get lazy and just by the construction of our physiology that they'll be sort of, they'll leave out that extra syllable and then that will become some progression in the development of that language. I mean, having said that, it's worth remembering that, for example, English has, I don't know what, 30 phonemes or something like that, but there are hundreds that exist across all the languages of the world. And there are ones that a person who grew up as an English speaker has a hard time making that phoneme or even recognizing that there is a distinction between one phoneme and another. So it's sometimes a little hard to tell kind of what's possible because you're very much based on what you've learned, so to speak. Let's see, people are quoting various languages that are spoken only by one person and so on. To me that's sort of a sad situation. I mean, it's kind of. I remember in my youth visiting the London Zoo and seeing this giant tortoise which was the last of its species. And you could, when I was like five years old, they were giving rides on the back of this tortoise at the zoo. So not a thing probably done today. I'm sure the tortoise didn't notice the 5 year old me in terms of weight on top of a multi ton tortoise, so to speak. But in any case, let's see, RBS is commenting on unique role of mathematics in expressing and formalizing ideas in ways that transcend linguistic and cultural boundaries. Well, that's true sort of as a matter of the facts of history in the world, it was not obvious that there wouldn't be kind of an Eastern mathematics and a Western mathematics that they wouldn't just have completely separated or been constructed differently. I mean, there were certainly ideas like binary, for example, which presumably existed for a long time in the east and took a long time to get to the West. But as I say, the mixing time is short enough relative to sort of intellectual history by the time mathematics was being seriously practiced that I think it kind of uniformized throughout the world. I mean, I think that, so it's a matter of the facts of how it's developed that yes, it's universal today, but I don't think it needed to be that way. I think it just is that way now. There have certainly been moments in scientific history where different cultures, and it's even true to some extent today where different cultures have profoundly different views of what are essentially scientific things. For example, that happens in medicine, it happens in traditional medicine of various places versus Western medicine. And one might say, well, we've got Western medicine is on the side of science and so on. I think that's not a totally convincing argument. I think that a lot of the kind of practices of traditional medicine that are kind of holistic in various ways probably have elements of good sense in them. Just as some of the practice of Western medicine has elements of lunacy in it as you kind of drive down to some very specific symptom of some very specific thing. And it's like treat that symptom. Oh, we forgot about the fact that that makes the person as a whole totally non functional or whatever else. So I think that's one of these cases where kind of even in the world as it is today, there are sort of multiple systems that are operating even in kind of an area. I mean, one of them is sort of feels that it's very much based on statistics and so on. I think the other one is much less based on that. But I think that's a thing that it's not obvious that it's kind of these things can coexist. And I think as I say, the reason in mathematics that it's so sort of universal across the world is just because the diffusion time of knowledge is short compared to the timescales of intellectual development there. I think, I think that if you look, for instance, I'm trying to think of examples during the Cold War, for instance, there were definitely not huge differences, but there were definitely distinct differences in, let's say the Soviet approach to various kinds of mathematical physics problems and the American approach. And like, for example, some, I don't know, mathematical functions and so on had different names. It wasn't really that universal. I mean, I have to say that particular thing was made to be mixed by the fact that each side was translating each other's journals into their language and so on. And that sort of forced a certain degree of mixing. So it didn't separate as much as it might have done. But I think the. I don't think it's self evident that it wouldn't separate in that kind of way. Maybe it's too late now in the sense that there's so much, you know, spreading of knowledge that one couldn't sort of develop the. The different area. You know what even that is not really right, because in. In any area of technical development, there are these sort of schools of work that develop that. You know, somebody has all these students and they have grand students and so on and so on and so on. And the. They have a particular way of talking about things. And sometimes it's quite disjoint from other ways. For example, reinforcement learning has a whole language of how to talk about things. Feedback control has a whole other language of how to talk about the same things, basically. But they're different languages and they're actually quite separated and the communities are quite separate and the communication is perhaps not as good as it should be. So I think these things happen. Sort of there's speciation in technical language as there is speciation in human languages and so on. Let's see. Comments. Language came before humans. We just scaled it up and complexified it, as in dolphins and whales. You know, I think the thing we don't know is in human language, it's very modular, it's very compositional. You can take one piece of language and you can kind of use it in lots of different places. It's not obvious whether that was a human only invention, whether that also exists for other critters. I think that the kind of just the nouns is a somewhat more primitive form of language that doesn't have this full sort of compositional aspect. I mean, obviously the thing one's curious about is, okay, we went from the nouns to this whole compositional type of language, modular language. What's the next stage? Is there a next stage? Do you go up? And I think to some extent in computational language, we start seeing higher order constructs that are sort of functional type things, functions that operate on functions, things like this, which I think, as I think about it, I think that's a little bit of a different level than what we have reached in human language. And that perhaps defines something that we have to go to some effort to get to that next level, it's worth remembering that human language has this fundamentally one dimensional character to it. It's like words follow words follow words follow words. And it's just in that sequence. When we look at pictures, for example, they have a fundamentally two dimensional character to them. And there are things we can readily express and diagr that pictures being worth a thousand words or something. There are things we can express in diagrams in this kind of two dimensional form that it's not very easy to express by just saying the words in this one dimensional way. And when we think about that, when we think about graphs of arbitrary connections of this and that, we just don't know what the analog of language is for a graph. We don't know. Humans are not very good. Most humans, at least some humans are a lot better than others actually at recognizing, you know, you've got this graph, it's got all these tangled pieces and so on. What really is going on here. That's the thing that we. And one could imagine a version of something like human language that sort of lives on a graph rather than living in this one dimensional form that traditional human language lives in. It's very hard for us with our current sort of background in education to wrap our brains around this. It's the kind of thing, if one's sort of imagining what's the future of these kinds of things. It's a thing to sort of think about. Let's see, there's a question here. Was Shakespeare's style unique to him? Would there have been a possibility for people to speak in a more poetic language? You know, I have to say it's very commonly the case that if you read sort of works of old, they seem ponderous and poetic. And I kind of wonder, sort of, there's a. Even in my own life I've seen sort of the simplification of language in typical presentations of things. I mean, if you look at, I don't know, there's a period of time when the typical scientific paper was very flowery and very ponderous in its prose. And it became, I think, less so. I mean, sometimes I think the style of writing of academic papers leaves a lot to be desired, but it is more direct and straightforward. I mean, in my own life I've gone through several different iterations of my style of writing. For example, whether I use don't or do not, I kind of made that transition about 20 years ago of going more informal about those kinds of things and a lot of different things that sort of deformalize what's going on. And I think you see in. Well, there are also languages where there's a level of formality that is conventional in certain kinds of communication. I tell a story when book I wrote about mathematica, this is 30 something years ago, was translated into Japanese. There was an initial translation done and I don't know a single word of Japanese, I'm sorry to say. Actually, maybe I know about two words, but that's it. But the first translation that was done was in one style. And people came along and said that translation is just terrible, there's a different style. So it turned out that there were, I think, two styles. One was kind of the style of a textbook, which was professor tells student authoritatively, this is the way it is. And another is the style of computer documentation where it's more may it please the customer to learn that this or that thing. So one of them is much more of a sort of a top down, let me just tell you what the story is. And another one is I am trying to please the customer type thing. And these were sort of disjoint styles of Japanese, apparently. I think we finally managed to get some kind of compromise between these in some way. But that's sort of a, a case where even within 1, 1 period of time there are different sort of forms of presentation of things. And I kind of think the. Well, I'm reminded of many, many different stories here, but one that just comes to mind is a sometime friend of mine, Marvin Minsky, who was a sort of AI artificial intelligence pioneer, mostly around mit. He wrote a book called Society of Mind, which he gave me some early drafts of and so on. This is in the early 1980s, maybe 1984, 85 type time frame. And Marvin was a person with a large number of sort of modular ideas. Like he would have an idea, you talk to him, he would generate an idea every few minutes. They didn't necessarily match with each other at all and they were often not very implementable. But there were many disparate ideas. But he had the notion that he would write his book Society of Mind in verse. And in the end the book ended up being sort of one page per idea. It's just a sort of a collection, it's an idea gallery. But the original idea was to make those ideas be presented each as a little piece of verse, which I don't know, I don't know that would have been better or worse for the presentation of that book. But I think, I mean, it's kind of. Yeah, I think even Some parts of the world, even speaking English, people have a more formal way of speaking it than they do in other places. I mean, I know, well, yeah, even my own life growing up in the uk, moving to the us there's definitely a more ponderous. Maybe it's partly the times, but I think it's also the sort of the cultural environment that more ponderous ways of saying things than the very direct US way of saying things. I mean, it's always used to amuse me that I don't know if it's still true that the ads you'd see on television or something in the UK would sometimes be really hard to understand. What are they advertising? What is the point? But nevertheless, it was a successful ad in the uk. In the us people just say, I don't understand what you're talking about. It's hopeless. I think the us, by being a rather heterogeneous country, had sort of no choice but to have more directness in communication than some of these places that have a little bit less sort of mixing of different kinds of cultures and so on. At least that's my sort of proto theory of that. Let's see, There's a comment here, slightly different topic. Well, okay, there's a few, few comments here about language and then we'll go back to some other other topics. So Jas comments. They think language is closer to 1.5 dimensional, considering we have relative pronouns and other constructions that link up with previous statements. So sort of a two dimensional diagram can be made. Yeah, I mean, it's kind of like a transformer in the modern LLM sense, in the sense that, you know, a transformer is going along and it is kind of referring back to things earlier in the sentence. And that is like the way we use pronouns and so on. I mean, one of the things that is sort of an issue of modern times is that pronouns are a hack. I mean, you know, when you say, oh, I don't know, something like, you know, Jane chased the cat and it ran fast. Okay, that sentence we can decode because we don't think we would use the pronoun it to refer to Jane. We assume it refers to the cat. But if we said, you know, Jane chased the cat and she ran fast, well, we kind of probably think that's Jane. But maybe it was the cat, who knows? Because maybe the cat was known to be a female cat. Who knows? But so in it is an interesting phenomenon that as so the gendering of pronouns becomes such an issue. The possibility of disambiguating sentences is dramatically reduced. But it's kind of a reflection of the fact that we have this sort of hack of oh, there isn't just one pronoun that refers back to something else. There's a bunch that are specified by different genders. And some languages have, you know, in English we have roughly 3 genders. In other languages there are 5, 6 genders that you know, in English things like ships are typically, you know, female gendered things. In, you know, in Latin, for example, there are, in French, for that matter, there are genders for, you know, you kind of have to know a chair, a house, whatever else, what gender is it? And that's, you know, part of the sort of hack of when how can you, you use one? You know, if you have six genders, then you have a higher probability that you can just refer back to that thing in the previous sentence by a pronoun rather than having to refer to it by saying the thing again, so to speak. But I think in this, you know, it is interesting to see what kind of ideas there are for making language easier to express things in. And language has a certain. Human language has a certain inventory of ideas like pronouns, like case endings in some languages, like tenses, things like this. And it is, it would be, I don't really know. I mean there's pretty good inventories of sort of atlases of language construction of types of constructs that exist in languages. I don't really know how much is known about the evolution of those constructs. And when, you know, who first invented pronouns, so to speak, like it's commonly said, things like, you know, Latin has no word for yes. And I could say, how could you possibly have a language with no word for yes? Well, presumably what was done was that people would just say, you know, you know, do you have a cat? Well, in English you might say yes. In Latin you would just respond, I have a cat. And presumably the yes we can think of as more efficient in some sense. I mean, I suppose this is another claim that's sometimes made that in the evolution of languages, do we or do we not end up with sort of more efficient languages, Maybe all of the sort of honorifics, and if it may, all the sort of boilerplate complexity might be thought of as something that would gradually be. Be removed by the evolution of language. I'm not sure Am Rudo comments. If I want to write a short statement, I prefer English, but for a detailed style, I prefer German, which is usually longer. Not so nice to read as short English texts. That's interesting. I mean, I think the language in a place, I don't know how this works, but in a place where everybody knows multiple languages. It is an interesting thing when one is making a stylistic statement by saying something in one language rather than another. And I suppose that happens in different places, sometimes for good reasons, sometimes for other unfortunate reasons. But the interesting kind of, you know, it's kind of like when you typeset something and some things are in italics and some things are not, you're kind of expressing them in a. You're having a meta expression that's a bit different. Let's see. Probably wrap up soon, but let's see a few other things here. Comment here. Bulgarian is pronounced exactly as it is written. One of its quirks. Yeah. Some languages are phonetically spelled and so on, and some are not. I mean, I think in languages like, I would assume there aren't spelling bee competitions in Bulgarian if it is a phonetically expressed language, because it's kind of like, well, it's obvious how to spell that word. English has this weird, perhaps mistakes in its history that have caused it to be hard to spell. I mean, a famous one is the word det, which I think originally was D E T T often, although spelling wasn't really standardized until coming on for the 1700s and so on. But somebody had the bright idea, let's make sure we can really express this word. Well, it comes from the Latin debitur, but let's put a B in there. Well, we're not going to say the B, but we'll put it in there when it's spelled to give more of a clue about the Latin origin of the word. Arguably not a good design idea because it's led to the fact that English, when you hear the word, you don't know how it's spelled. Now, of course, there's also things that can happen with sort of convergent evolution of words like PI versus PI, PI versus pieces. That's something where I'm sure those words didn't. They had no common. There wasn't a common evolution of those words. It just they happen to converge. They're simple sound, simple words and they wound up meaning completely different things. Certainly when we've in the early days of Wolfram Alpha being the backend for voice assistant systems, intelligent assistants, that was one of the amusing kind of you have to clean it up because the thing would say, somebody would say what's the value of PI squared? And the voice to text system would bring that back as pie squared. And that had to be Post processed. Later on the system started to give homophone stacks where they have sort of, it could be PI, it could be pie, and then it's a matter for our natural language understanding system to disentangle that. But it's, it's a, let's see, it's always kind of, you might say, well, it's obvious that a language should be written as it is said. But there were sort of historical reasons why that didn't happen. Maybe the way the language was said changed over time and it would have been obvious that it would be written in this way at one point and then later it, you know, the way it was said changed, but yet you didn't want to, you know, you had sort of standardized the way it was written. There's another issue about those things, which is always the crossword puzzle question of are languages such that you can make a crossword puzzle meaningfully? Because if every sequence of letters is a valid word, then you can just put a random collection of letters on a two dimensional grid and it will make a valid crossword puzzle, so to speak. Or if a language is very redundant in the way that it arranges letters, it could be the case that you can't make a properly filled in crossword, that only a very sparse set of possible sequences of letters make words. I think English is right around being marginal for three dimensional crossword puzzles that whether you can make a decently dense one in English, it has about the redundancy that is just sort of marginal for the 3D case. Let's see, maybe one or two more. And then I need to run along here. WW asks if LLMs are hallucinating all the time and good ones are just hallucinating correctly and accurately. Does that explain how Ramanujan might have arrived at his formulae without proofs? I don't think that's the Ramanujan path. I think Ramanujan was very non LLM like in that sense. I think there's pretty good evidence that Ramanujan's main skill was precisely something that LLMs are quite bad at, which is calculating. And what I think Ramanujan did was he just tried out a bunch of experimental mathematics, maybe on paper, maybe even sometimes in his head, and noticed, oh, e to the PI squared of 100, what is it? 73, is that right? I forget is very close to an integer. But then he realized, oh, that's significant, you can use that, that's something related to elliptic functions, et cetera, et cetera, et cetera. But the origin of a Lot of his ideas was experimental mathematics, just noticing patterns in numbers in formulas and so on. And I think one of the things that reveals that that's really what was going on was he believed he had a proof of the prime number theorem, a statement about the density of primes, and his proof was wrong. Well, didn't have a proof, he had a statement about it, he had something to say about it. And what he had to say about it works until you get to the 10 to the 10 to the 10 to THE 10th or whatever prime, until you get to a very, very big primes, it works. So any experimental mathematics that Ramanujan might have done on that question, it would have been, yup, I'm right, I'm right. But in fact, the full sort of proof from the axioms of mathematics doesn't pan out. And one could even find, in principle, counter examples, but just outside of the domain that was sort of experimentally accessible to him. So I think it was sort of a, you know, reading some of what he wrote and so on and hearing about some of those kinds of things. I think to The British mathematicians, G. H. Hardy and people like that, the only thing they knew was mathematics is all about making proofs. So when Ramanujan shows up with all these elaborate formulae more complicated than they ever seen, it's like, he must have proofs, because that's the only way you do mathematics. But it wasn't true. He was doing those things as a matter of experimentation and intuition. Very impressive, but a different track than the kind of British sort of we must have proofs type mathematicians. And I think, I think there's some quotes where Raunujan says, you know, it comes to me in dreams and so on. I'm pretty sure that was a joke. I'm pretty sure that he just got fed up with answering the question, so where is the proof? And it's like, you know, he doesn't even. That. That wasn't a thing, that was part of his methodology. I think perhaps when he came to England in what, 1913 or so, the. It was. It may have been kind of a. One of the things he said actually was, gosh, I'm so happy these theorems of mine are correct. And I think that's another indication that he didn't know he didn't have the formal proof. He thought it was true based on intuition and calculation. And when he was told, yes, yes, sir, we filled in the whole proof, it's like, great, how nice. Although not everything he did ended up having that foolproof so to speak. So I think the, you know, the oft quoted kind of it came to him in a dream from some Indian goddess or something like this. I think that was him being funny. And I think if you see other places where he was kind of making kind of slightly not quite snarky, but sort of comments that were sort of humorous comments, I think that's in line with those. And I think GH Hardy was probably a singularly humorless character. I think he was a very austere mathematician with a lot of funny characteristics and very. I don't know, I shouldn't say this for my. As a criticism, but he was a very habitual person about, you know, he folded his newspaper one way and he went to the cricket game in a particular way. I shouldn't say this because I discover from doing personal analytics on myself that even though I believe I'm not a deeply habitual person, when I actually go and look up, you know, the time when I wake up, eat breakfast, whatever else, whatever else it's really. Or when I do this and that, it's. It's surprisingly precise kinds of things. Even though I think I'm exercising free will and doing what I want to do with that, I probably should. Should get going here, thinking of doing what one's supposed to do. So thanks for lots of interesting questions here and I see so many more that I'd love to chat about, so I'll look forward to doing that another time. Thanks for joining me. See you another time. Bye.