Stephen Wolfram presents the 2023 Innovator Awards, honoring researchers who used Wolfram Language and related tools in robotics, healthcare modeling, quantum simulation, and education. The ceremony includes a Q&A on GPU support, LLM integration with Wolfram Language, computational thinking pedagogy, and formalized mathematics.
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All right, well, let's get started. So today I was going to say this evening, but I don't think that's right for many people who are here today. What we're going to do, two things. First, we have our innovator awards of 2023. And after that, I'm signed up to do general Q and A about whatever people want to talk about. So our Innovator Awards, we started quite a number of years ago now, are intended to recognize people who've been doing interesting, innovative things with our technology. And it's always exciting for me because we spend all this effort building tools, building technology at a selfish level. I'm always interested in building tools that I can use myself. But we put an awful lot of effort into making tools that are as broadly useful as possible. And it's frankly really exciting to me to see all the interesting things that people end up doing with our technology and our internal process. We have nominations from people around our company, and it's always a very interesting group of nominations and award winners of people who've been doing interesting things without technology. And I had the opportunity, usually when we're in person it's a lunch, but in this case it's a virtual lunch to chat with some of the folks, with the folks who are our Innovator award winners for 2023. So I'm going to start off here. The. I will say I'd like to tell people a little bit about some of our award winners and some of what they've been doing. I'm going to keep my remarks fairly short with the hopes that I can well represent what people have been doing. And then after this, we'll turn it over into Q and A. So. So the theory of things, I will say, is we've got these fine awards which hopefully have been finding their physical way to people in the last week or so, or will do so in the next week or so. And this is what we are. This is the physical instantiation of what we're presenting this evening, this today. All right, I think we should get started here. And we have people listed by alphabetical order of the first word that appears in the awardee name. So our first Innovator Award of the evening goes to Alejandre Leiter, engineering director and mechatronics at Austral Dynamics, which is a company in Brazil that is involved in making controller systems for electrical, electrical vehicles and machinery. And they've been using system modeler. And as I understand it, what they've been able to do is to build Kind of a new generation of pipeline for going from the structure of the machine to the control system that will be used in the machine. And they've been building that pipeline using System modeler and using it to eventually produce the systems that will be used in these various machines, whether they're for agriculture, heavy duty equipment and so on. That all has to be retooled because it's all going electric now and that means they've got to be new machines. And Austral Dynamics is leading a charge in using System Modeler to do all of that engineering work. So our first award is going to Alejandra Leite and you've got the award. Great. We can swap it here. This is our mechanical process. Thank you very much. So our next award goes to the Australian Christian College. The awards being accepted by Jeremy Kwok, Director of Technology. Australian Christian College, I gather, is the largest non governmental provider of distance education in the K12 sector in Australia. And they have been retooling their math and other education systems using Wolfram language and both in terms of and integrating that with their existing learning management system to deliver what I think everyone hopes is an increasingly compelling experience for K12 learners in Australia, keeping them. I was told that math has become a non compulsory subject in the last couple Of Years of K12 education in Australia and I think now there's hopefully with our technology in place it will be possible to get all these kids to be so enthusiastic about math and other STEM subjects that they insist on continuing them through their K through 12 trajectory. So our second award here goes to Australian Christian College and thank you very much. Let me see our next award here goes. Oh, I should have put up that screen of all these actual deployed questions being assessed using our technology stack. The next award goes to Bill Helton, Emeritus professor of Math at UC San Diego. And I've had the pleasure of meeting Bill in the very distant past, I think when Mathematica was new. Bill has been a longtime developer of non commutative algebra and particularly a package called NC Algebra which is a long running kind of leading edge system for computing things like polynomials where the variables are matrices and figuring out things about those kinds of mathematical structures, as used in control theory, as used in studying things about chemical reaction networks, as used in recent times in quantum information. And so we're very pleased that Bill has been pursuing this as we've been sort of single mindedly pursuing the development of mathematical wolf and language all these years. Bill has been pursuing the development of NC Algebra and using our technology for all these years and we're very happy to see that. So next award goes to Bill Helton. And let's see next. Our next award goes to Esmer Gel, who is professor of supply chain management analytics at University of Nebraska. And Esma had an adventure, I gather, during the pandemic. She's an operations researcher who got pulled in, she was then at Arizona State University, got pulled in early in the pandemic to be a modeler because lots of modeling was needed for particular utilization of medical facilities and other kinds of things. And Esma produced with Wolfram language, produced models and visualizations and everybody wanted to know what was going to happen. And I gather that Esma's visualizations made it onto the evening news and so on as scientific study of what was going to happen. And apparently the predictions that she made turned out to be better or worse, turned out to be accurate. I gather Esma has been, is now involved in optimization and operations research for particularly healthcare, providing healthcare and making use of our technology and spreading the word about our technology, which we, which we greatly appreciate. And so thank you very much. And our next award goes to Esmeralda. Thank you. Our next award goes to Marcio Rosa, professor of mathematics in Brazil. And the. Oops, that was out of order. Ah, what am I doing? What am I doing? There we go. Here we go. Marcio has been teaching with Wolfram Language and Mathematica for many years and is teaching both math and physics and in particular has really been energetically pushing for the use of kind of geometrical visual ways to understand mathematics, mathematical physics and has written a book that even with my extremely limited knowledge of Portuguese, I can guess that that means virtual labs. Hope it means virtual labs. Of exploring concepts and mathematical concepts geometrically. So our next award goes to Marcio Rosa. Thank you. Our next award goes to Mark Rawlins, executive chair and chief engineer of Energy and Combustion services company in South Africa that is concerned with helping mining companies make their big decisions of technology, the stacks to use and, and how to deploy them. And I was hearing about all sorts of machines that carry millions of, that carry hundreds of tons of ore and so on and where decisions have to be made about just what kind of machine should you get with what kind of power source and how should it actually operate and when should it only make left turns and so on. It sounds like one of those great applications for our technology stack where sort of many different domains of expertise have to be pulled together to make what end up being in the end, perhaps even billion dollar decisions about how to set up mining operations and so on. So our next award goes to. Mark Rollins. Thank you. Next award goes to Martin Froling, Assistant professor, University Medical center in Utrecht in the Netherlands. And Martin is involved with quantitative magnetic resonance imaging. And in fact, I know recently gave a very successful webinar about QMRI for us. And I gather that I didn't know that in MRI that you get to actually see water molecules moving by a nanometer and you get to. I gather the main thing that Martin has been involved in is quantitative studies of muscle tissue using MRI and figuring out is the water really going just in the direction of the muscle fiber or is it leaking out in the orthogonal direction, which is a bad thing. And how does that all work? And I must say again, as all of the things we've been talking about here, it's just what a lovely application of our technology, Stack, to kind of go from what I gather are complicated sort of analog signals within the MRI machine to this ultimate analysis of what's actually going on at a medical level in muscles and so on. So our next award goes to Martin Frohling. Thank you. Our next award goes to Oliver Nell of Harvard University. Oliver has the distinction of having seen our technology before it even was a thing. As a student at ETH, where Roman Meder was teaching, Oliver got exposed to. I'm guessing it was version 0.9 of Mathematica. And Oliver has been teaching and doing research with our technology all those years and has exposed a huge number of Harvard students, particularly in the last many years, to our technology and done so in a. In a very lively way, as we can perhaps guess from the interesting creatures shown there on, on the screen. And I think that's, I'm kind of, it's. It's tremendous too. I'm. I'm sure that the, the people who've come through Oliver's courses have, have been going on to do a whole range of different kinds of things. And in fact, I think I, from time to time, who know about our technology because they went through Oliver's class. So that's always a very nice thing. Meanwhile, Oliver has also been an enthusiast of discrete space, discrete geometry and so on, an interest which I share. So our next award here goes to Oliver Nil. Our next award goes to Patrick Scheibe, whose day job is involved with MRI also, and as it happens, at the Max Planck Institute. But the thing that perhaps the Wolfram language community is most familiar with Patrick for is his extremely extensive contributions to Mathematica Stack Exchange and his Willingness to answer all sorts of questions and provide all sorts of useful information to our users. Patrick has also developed a Wolfram language plugin for IntelliJ and IDE. And, well, we thank Patrick for, particularly for his contributions to the Wolfram language community. So, next. Oh, I should put up a display. We've got lots of pictures. Hold on. There we go. Those are. Oh, yes. And that's an optical. I even recognize that's an OCT image. Optical computer tomography image, which I know Patrick has worked on. Very interesting. Okay, well, anyway, our next award goes to Patrick Scheibe. Next. Our next award goes to Peter. To Borak, professor of Physics and Astronomy and UC Irvine. I've actually known Peter off and on for, what is it now, 43 years from the time when we were at Caltech together. And I actually realize that I've sort of been aware of some of Peter's contributions to physics in fluid dynamics and low temperature physics and so on over the years. I realized that it's the same Peter Daborak who's showing up in different places. And I'm very pleased that Peter has been using our technology for many years in, in teaching and has developed teaching materials and a Mathematica handbook that's been used. It's used with many, many students at UC Irvine, I gather now getting into automated assessment and the further computerization of the education process. I'm also interested to hear about Peter's work on superfluid drops and drops of fluid. And they're breaking apart, which I feel like I have to study more because it seems an awful lot like the kinds of singularities that happen in general relativity in space time. And so I'm really curious about that. But in any case, our next award for today goes to Peter Taborak. Thank you. Next we have an award for Pickett Pharmaceuticals, represented by. The CEO joshua krieger, as well as lauren williams, who I think is the head of data science. Yes, Pickett has been using our technology for a little while now. Their mission is to, I guess I could describe it as optimize the supply chain for drugs and generic drugs and to be able to predict when there will be shortages of generic drugs and then by one means or another, make sure that there is supply of those generic drugs available that they can sell into the distribution channel. And so I find it an interesting kind of. It's one of these things where you're kind of taking diverse data about the world and trying to deduce something about what's going to happen. And again, a Lovely example of a place where our technology can be used and making use of machine learning and data analysis and so on to predict something which people have not been able to predict before. And that's kind of a great use of our technology. So our next award here goes to Picket Pharmaceuticals. Thank you. Our next award goes to Sandor Heusmann. And I feel like I get to interact with Sander practically every week because Sander has been a great contributor to our design live streams, our making all sorts of suggestions which make it into versions of Wolfram language, as well as contributing function repository entries for all sorts of useful and interesting things. And Sanders day job is professor of Physics of Fluids at University of Twente in Netherlands. And he studies turbulence in fluids and particularly does that by using imaging technologies. To take for example, as he was explaining to me earlier today, strangely shaped objects whose orientation can be determined by that are strangely enough shaped that you can determine their orientation by just looking at a projection of them and using that to map out the velocity fields and so on of fluids. I think Sander doesn't just do ordinary fluids. He does fluids that are being generated by melting fluids that have bubbles in them. Fluids in all sorts of extreme situations, making use of our technology. And as I say, I also know him from his participation in our live streams and his many contributions to the function repository, which I quite often find myself using. So thank you very much. And our next award goes to Sandor Heisman. My next award goes to Sandipan Band. Yeah, and I'm going to say that wrong. And I'm sorry, I'm just not. Sandipan is a associate professor at IIT Madras specializing in robotics. And he's been very instrumental in bringing our technology to IIT Madras, Indian Institute of Technology in Madras, and teaching with IT. And having courses where people where students deliver their results as Wolfram notebooks, which is great. His own research involves robotics. Robotics is a long time application of symbolic computation. And I can see even on the screen here some kind of classic problems in how do you get that robot arm to the place where you want it to go based on the angles of joints and so on. So our next award here goes to Sandipan. Thank you very much. Thank you. Our next award goes to Thomas Tibbles, head of International equities at Madison Investments. And I gather that we have our technology gets used to a lot by the world's leading quant hedge funds and so on. I gather that Madison Investments is an investment firm that actually knows what they're Investing in where the tickers are not just tickers, they're actual companies with, with lots of detailed characteristics. And they've been using our technology to do something that again is, is just a great use of our technology integrating lots of different kinds of information about international companies to provide kind of the information that's needed to make investment decisions. And I gather initially that was done primarily by making the right kinds of visual presentations of information and now increasingly also by using technology like machine learning. So our next award here goes to Thomas Tibbles. And I think it's our last award for the day goes to Tyson Jones and Simon Benjamin. Tyson is a postdoc and Simon Benjamin is a professor in quantum technologies at Oxford University. The the they built with Wolfram language. So Tyson has, I know, been using Wolfram language for quite a while because he was a student at our summer school back six years ago now. And not only has been using Wolfram language, he's also been doing quantum stuff for at least six years because was already doing that back in 2017. One of the big contributions here is making a link questlink which is a link between Wolfram language and a simulator for quantum computers. And quantum computers are always an interesting subject where there is a fascinating formalism and interesting physics and a lot to be done in simulating them. Not always sure about the actual running of the quantum computer itself, but the simulation is definitely interesting. But not only are Tyson and Simon involved in simulating, Simon is also co founder of a company that is taking an innovative approach to quantum computing, leveraging the traditional semiconductor silicon technology to get I think in a typical CMOS circuit that we use in computers there are like a hundred thousand electrons per bit. But I think in, in, in the quantum machines that Simon is is building, the idea there's just one electron, well at least its spin defines one bit sort of trapped in this thing constructed using standard semiconductor manufacturing technology. So I think that would be. I look forward to being able to just type into orphan language something some specification of a circuit and having it run all the way down on the. Now we can say raw silicon in this case of the quantum computer rather than we usually say raw silicon when we're referring just to standard microprocessors. But this would be a still raw silicon, but doing something truly quantum. And I think I gather that the simulator is able to particularly do things like study all sorts of different kinds of noise profiles. Again sort of a critical thing in the world of quantum computing. So our last award here goes to Tyson Jones and Simon Benjamin, thank you. All right, well, let me see. What a lovely collection of examples of using our technology and of computational thinking in general. It's, it's always great to see the kind of range of different uses and different kinds of innovative ideas that get enabled by the tools that we've spent so much effort building. And it's kind of, as I think about kind of presenting the idea of computational thinking as a general concept, I'm steadily trying to build up for myself kind of this inventory of all the different ways that computational thinking can really be used. And our Innovator Awards are always provide me with yet more kind of raw material to think about in terms of the different applications of computational thinking. So in any case, I thank you all very much and congratulations to, to all of you and thanks for being part of our 2023 Innovator Award Group. And I wonder if we're going to try and take a zoom picture here. Is that a theory or not? Maybe we can do that a bit later. All right. I think that in the assume we were all eating dinner at this point we would have kind of had, you know, this would have been the dessert stage and then I would have been gulping down my dessert and then we would have been having a a, Q and A period. So I'm happy to, to do that now. And I'm only just wondering how are we going to get the, How are we going to get these questions from people? Somebody who's organizing, please help. Can folks use the chat? I have just enabled attendee chat. Yep. So they can reach out to panelists and hosts now, which would be us. Great. So I'm happy to talk about anything about our strategy. And okay, let's see, we have Dave here asking about now that single processor socket WorkStation processors have 96 physical CPU cores from AMD and 56 physical cores from Intel. Have you considered increasing the number of computation kernels that are included with professional versions of Mathematica to more than eight? Yes, we keep on talking about that and yes, we are on top of that issue and yes, we will do things about that. And one of the things that a little bit tricky. We have a dollar processor count variable, but it's a little bit unclear what that value should be because there are all of this kind of hyper threading technologies and so on. And it's like we don't really want to say let's break things up in parallel to 50 different processes to find out that actually 30 of those processes are very weak pseudo cores that can't really support that. And then when you try and do your computation where you're feeding things out to these 50 different sub processors, that it actually takes longer to finish than it would have done if you'd kept it concentrated to 20 cores. So there's some trickiness in figuring out just how seriously to take each core. And we've certainly been talking about ideas about sort of capability information for these different types of cores on different machines and in terms of kind of licensing technologies. Yeah, there are a couple of things going on there. One is just pure policy, things which are easy to change. And the other is technology issues about the way that license management works. And we are in the process of greatly modernizing that. It's something where we were very ahead of the market 35 years ago and we better do some more modernization now on it. Let's see, from Nigel do you have suggestions for a quotes gateway drug to bring in new converts to computational thinking without scaring them off? Well, I think my main comment is meet them where they are already. If it's students, if it's professionals, they're doing something now. The question is, can you have the sort of Socratic dialogue with them that leads them to realize that what they're doing now is. Can be done in a computational kind of way? So I would say it really is almost a Socratic dialogue process. I've certainly seen that myself. When people say we're doing this thing and it's like, well, wait a minute, why aren't you doing that in a more computational way? And they're like, well, I didn't think about that. And you have to kind of lead them to what is the one way to think about it is you got this whole thing you're doing. If you were to break it into a collection of functions where the function takes some arguments, it grinds away, it produces some output, how would you break down the process that you have into a collection of functions? How would you take the things you're thinking about and represent them as some kind of symbolic structure, represent that state of the world or that set of things that are going on as a computable construction that you can then apply these functions to? And I think this sort of process of how do you take kind of a thing you're thinking about in the world and make it computational? This is a process that is critical to teach to people, and people mostly aren't teaching it. It's not what computer science is teaching. Computer science is teaching much more well on the sort of more practical Side, it's teaching much more how to write a program with this specification type thing rather than how to take just something that's out there in the world and kind of turn it into something that can be thought about computationally. This is a critical skill. And you know, I haven't, you know, I'm, I, as I've mentioned, I've. I'm kind of planning to write this book and course and so on to kind of describe how to think about things computationally. And it isn't a thing which I necessarily understand is how to, how to lead people. I know in the kind of Socratic dialogue mechanism I know how to do this. I think of taking things people are talking about and kind of with the knowledge that I have about sort of how you can make things computational, how to make that happen. But doing that kind of in a self service way is still something which I'm trying to work out what the best way to do it is. Let me tell you a few things that I think I do know so far. I mean, first of all, our computational language is simply the only real game in town in terms of making this work. I mean, if this can be made to work, and it can be, Wolfram language is the thing that's going to make it work. Because what we have in Wolfram language is this very broad way of thinking about the world computationally. And when one starts getting into that Socratic dialogue, so to speak with people about how to take what they're doing and make it computational, you find out that, well, there's this piece over here that requires processing natural language. There's a piece over here that involves geography. There's this piece over here that involves this kind of combinatorial optimization algorithm. There are all these pieces and they have to be fit together and that's what's really going to make the thing successfully computational. Just sort of dealing with one of those things isn't going to be enough. So that's sort of the base level is we get to leverage our computational language. But then what do you actually teach? And I'm not sure. I think there's a style of teaching that's kind of a case study style of teaching and I think that will be a great thing to do. It's probably not what I'm going to do. I think it's the kind of thing where people should be writing up cases. And pretty much every one of our innovator award winners today, we could write a case study of computational thinking based on the kinds of things that they're doing, and it will be a great case study. But that's. So that's. One approach is kind of the case study approach of this is what the problem was. This is how it got solved in this case. How would you think through solving that? Another thing I think is that there's just a knowledge of what computation can do in the world. It's kind of a sort of, you know, what are the facts of computational thinking? It's kind of like, well, if you are going to study, I don't know, history, for example, you can talk about kind of the arc of history at some. Some generalized way, but you kind of have to know some facts of history to get started. And I think that with computational thinking, knowing facts like how does one represent an image computationally? What things might one pick out of an audio signal? What. How does one kind of label things in the world computationally? How does one kind of present information in a way that people can understand? What is the core idea of all these different things? And so part of what I'm planning to do is to write something which is sort of a computational introduction to all those places where people have managed to formalize the world computationally, whether that's information visualization, user experience, computer security, areas of mathematics, data science, these kinds of things. And part of my concept, which we'll see how it works out, is that when you have this overall computational framework, when you have this kind of formalized way of thinking, it becomes surprising, surprisingly easy. I claim to kind of explain some things which people in the past have found very difficult to explain. I mean, we're certainly well aware of a lot of progress that's been made in, for example, math education using our technology stack by, in a sense, concretifying what math is like. You know, being able to show those visualizations, those geometric pictures, being able to actually manipulate those algebraic expressions and sort of see. See how they flow, so to speak, rather than just kind of talking about them, being able to sort of have a concrete representation of what's going on. And it is my belief that even at the conceptual level, when you kind of understand things conceptually, computationally, the concepts of algebra, the concepts of calculus, the concepts of statistics, and so on will become a lot easier to explain. My claim. We'll see what happens. But that's. So, you know, what I'm. What I'm hoping is that we'll be able to have this base. It's kind of, let's say it's computation underneath, and then it's all These different fields built on all these different current areas, built on top of that understanding how they work computationally. I think people sometimes have the view, you know, you should learn math first and then later on maybe you learn programming and computer science and so on. My concept here is computation is the base layer. And because I think, and my experience even in teaching, you know, middle school age kids at least this stuff, is that they can understand this. It's very concrete, they can kind of see this is a thing, you're transforming it in this way. This seems to be something that us humans understand very easily, much more easily. Some fraction of humans also understand these very abstract mathematical ideas easily, but a lot don't. But I think this kind of very concrete notion of you've got this thing, you can see it on the screen, you transform it in this way. It's something people can understand and it can be used as sort of the base for sort of creating this, for learning about all these different areas where it's impossible to kind of formalize the world. And my concept is that once you kind of know all those ways to formalize the world and you understand these sort of principles of formalizing the world, then you have the opportunity to apply those to things that you're interested in for yourself and to sort of create the computational X, the CX for all these different fields. So that's my long answer to this suggestion for bringing people into computational thinking. My first suggestion is start with a Socratic dialogue, so to speak. Bruce is saying our tech support is still the best part of our company. I'm sure they'll be pleased to hear that their efforts to help us make our lives productive. Thank you and thank you on their behalf. Technical support has been a. We've been fortunate to attract a lot of very talented and educated folklore. It's kind of full of PhDs and things and some. Some who stay in technical support and can continue getting interesting problems at the rate of, you know, many per hour or something to solve. And others who move from our technical support team to other parts of the company. Some of our longtime developers started in technical support, so that's a one of the pathways in our company. Let's see. George Woodrow is asking any progress in making full use of Apple's GPUs for neural nets and machine learning? The answer is yes, we're working on that. I don't think it was in some design review recently. I don't think it's making it into 14.0, but it will make it into the version Right after that we have been, we've been refactoring our, some of the kind of base level of our machine learning stack. You know, one of the things with machine learning is it's like, okay, back in the day you had to pick which language you're going to write your system in. Back in the very ancient past, when I was building SMP, kind of forerunner of Mathematica, back in 1979, one of the big decisions was what language are we going to use? And we picked C. C was a good language to use. The people, it was a new language at the time and the people who were into Lisp and so on, it's. Lisp is going to be everything for artificial intelligence were all like, how could you have used C? Well, because we couldn't really use Lisp because it wasn't really practical then or even subsequently for doing this. Actually, the person who was then kind of a student working with me who really said C is the language of the future was a chap called Rob pike, who was then a physics graduate student. Later I kind of convinced him he should go and work at Bell Labs, where he had a very successful career. But one of the things that. And then he moved to Google. But Rob is perhaps best known for having developed the GO programming language. So even though back in 1979, C was the language of the future, Rob went on and did another language, go, which is. Rob is a very minimalist language designer. And GO has that kind of minimalism to it. But in any case, the thing that is a decision you make is like, well, what are we going to build our machine learning framework on? Because in the end you have to compile it down to the lowest level, most GPU ified and so on kind of technology. And we are now on our fourth sort of base for machine learning. No, we're on our third and we're about to be on our. But we're about to move to a fourth kind of base for our machine learning system. And the goal now is to really have it be as transportable as possible. You know, back when we, when we, when we started building Wolfram language back in 1986, for example, we use C. We couldn't use C. C wasn't developed to the point where we could use it. We built our own extension to C. We've subsequent. A lot of things are done in C, although now when it comes to new code written for Wolfram language, it's all written in Wolfram language. And we've been able to make an important Transition in the last couple of years to the sort of low level code that we would be writing in, cuz it wants to be really close to the metal. We're writing that in Wolfram language, but with the annotations needed for the compiler. So with type declarations and all these kinds of things which kind of are pandering to the low level structure of the machine. But the result of doing that is we can just write a Wolfram language code which is much more efficient for the programmer. And in the end the code that's produced in LLVM is certainly as efficient, if not more efficient than the code that we would get from custom writing in C and then compiling. So that's been an important development for us and that's part of what will enable a bunch of this movement to better kind of GPU support and so on for machine learning. But yes, this is definitely coming. We're fully on top of this issue. George is commenting plans to retire the name Mathematica. It no longer describes what Wolfram Language can do. Well, that's why we introduced the name Wolfram Language. And I would say that, you know, it's always a challenge to sort of modernize a name. I will say that Mathematica is a great name for the mathematical and mathematical science kinds of things that Wolfram Language does. It's a great name and we're going to keep that name for that. But Wolfram language is a better representation. I mean, it could be called anything language. It just needs a name that doesn't mean mathematics. For example, I will say that when we first introduced Mathematica, it wasn't clear what the future of mathematics itself would be. And it wasn't clear the extent to which the sort of separation of the computational from the mathematical, how complete that would be. And it was something where, you know, when Steve Jobs originally encouraged us to use the name Mathematica, it was something where we knew mathematics was a big use case. I didn't know that mathematics would sort of as a, as a field, stay as comparatively insular as it has and not kind of. I think perhaps with my greater understanding of the history of ideas nowadays, I might have been more able to predict that, that it's kind of, it stays within its domain, it's good domain, but it stays within its domain. And that which is new, whether it's what would now be called machine learning, whether it would now be called theoretical computer science, whatever those are things that are outside that domain and really constitute the only word we've been able to use to describe all of this stuff is computation. And that word is, one could argue, it's not the perfect word because it suggests pure calculation. And really this idea of computation is an idea of finding this sort of formalization of the world in terms of structure, in terms of systematic structure, systematic rules, systematic symbolic representations. That's the essence of this idea of computation. And that's kind of the idea that our whole system is based on and that we're hoping to move forward. Satiris Mitchos says LLMs and machine learning representations in general allow for ambiguity or ill definedness to enter into our communication with the machine. Something that up to now is difficult to handle formally. How do you see ambiguity from the perspective of computational thinking? Interesting question. You know, I think the great achievement of kind of the big intellectual towers that have been built have been built in some kind of formal way. When you see a field that is really progressing sort of systematically over the centuries, it does so on kind of a base of formalism. And that's happened with mathematics, it's happened with physics, it has less so happened with something like philosophy, where one's still sort of discussing the same things one was discussing 2,000 years ago. There isn't really that stacked formalism that exists in some of these fields like mathematics and so on. I think the great opportunity that we have with computation is to make this kind of tower of capability. And that's I think, the really valuable thing we have with sort of the formalization from computation and so on. We humans are not, you know, we don't run these formalizations. We can sort of connect to them, we can create them, we can understand them, but that we don't run with them. The computers run with them. And that's the great value of computers in sort of augmenting our thinking processes. So I kind of see the structure as being we humans are doing those things which are sort of quotes, ill defined and ambiguous. We're formalizing them and then we're building these big towers. And I fully expect that the computational X in all these different areas, the big thing that's going to happen is that these fields that have been rather flat, just a bunch of facts to know and so on, will start building towers. They'll start being able to build capabilities that are far beyond what were just a person's unaided capability, so to speak. Now having said that, I would say that one of the things that we're working towards is this thing I call symbolic discourse language, which is an attempt to take sort of everyday Discourse and extract from it as formal a structure as we can. We have with Wilkin language to date been able to formalize a lot of kinds of things. This is an effort to formalize more of sort of everyday discourse. And I think it is not clear the extent to which sort of formalized everyday discourse people be like, wow, that's a much better way to communicate. And to what extent people will say, that's very non human, that's going off into this sort of formal computational direction and not. And not something that we humans can as much relate to. So I think that's still a bit unclear. The theory of human ambiguity is an interesting question. I mean, when we look at. We're starting to be able to much more computationally think about questions like meaning. What is the space of meanings? I've studied, I had this thing I wrote about, well, cats in party hats really, but it was kind of studying the space of images generated across sort of concept space. And this kind of notion of, well, what is the meaning? What is the word cat? What is that concept of cattiness, so to speak? Where does it sit in the space of all possible concepts and the space of all possible meanings? And this is kind of giving us some characterization of, in a sense, ambiguity. It's how big is cat island? Is the cat concept just this delta function concept at this one point in concept space? Or is it this extended blob of kind of cattiness, so to speak, in concept space? And in fact, it's an extended blob. Characterizing the shape of that blob is an interesting thing to do. I mean, in a sense, any machine learning classifier is defining some. Some sort of shape in the space of possible inputs. It says, this is an image of a cat. This is an image of a dog. There's some kind of fuzzy region of what counts as cat, what counts as dog. I think the characterization of that is, in a sense, a lot of what's happening in machine learning and classification and so on is to go from the fuzzy to the symbolic. And I suppose that the general understanding of the fuzzy is an interesting thing. It's an interesting direction in science that I've been curious about actually since the beginning of the 1980s, when I first started looking at neural nets and first started to try to understand the attractor basins of neural nets, and first tried to find a characterization of just what does characterize the things that will eventually evolve to that one symbolic output. And I think even all these years later, we have almost no knowledge of that it's kind of a field of science that sort of doesn't really exist, the science of the structure of meaning space and so on. And I think it's really an interesting thing to think about. And the question of whether we will be able to take that meaning space shape and have a symbolic representation of the fuzziness, so to speak. Interesting question, I don't know the answer. Not a lot of progress in 40 years. And things like dynamical system theory, one could study attractor basins. It's complicated to characterize attractive basins. In this case of something like Newton's method. Let's say we do know something about the attractive basins. They make these complicated fractals that correspond to, let's say they're nice pictures. Even in new kind of science. There's a nice picture of the attractor basins for finding the solution to some polynomial equation. And it's this whole fractal sort of space. And even that right there is telling you this is a complicated story of how do you characterize the space of attractor basins. Does it really look like what kinds of geometry, what kinds of mathematics are relevant for that characterization? Let's see, from Marnie Landon, Jeff Hinton and others have been speaking about their concerns about the dark side of AI and potential unintended consequences. Have you thought written about ways to mitigate some of their concerns which could prevent myopic ill informed policy reacting out of the fear of and stopping massive discovery? Well, yes, I have thought quite a bit about kind of the governance of AI. And you know, I had this moment when we were connecting our LLM technology to Wolfram language back in the spring here at this moment where I'm like, as soon as I press this button, the LLM can run any piece of orphan language code on my computer. Is this a good idea? Well, maybe not. It's like let me constrain it, let me make it do only the things I wanted to do. You know, I don't necessarily not want it to touch my file system because I might want it to find a file, organize, reorganize my files. But I don't want it to do things I don't want it to do, like delete all my files. How do I characterize what I want and what I don't want. And that was sort of a very microscopic example of the bigger picture of how do we get the AIs to do what we want and or we don't want. And of course that we need a definition of what we want and what we don't want. And that's a very hard thing to give because in a sense that's exactly where kind of symbolic language, computational kinds of things, then we can say precisely what we want. It's kind of like you can give a verbal description of something that you want to do, then you can get the computational language version, which is now precise, and you can then go and see what's really going to happen and do it. But the verbal version is not. Is the. Is not. Is not something like that that you can build on. So this question of, of sort of how do we characterize what we want out of our AIs. And so I've been involved for quite a number of years now in sort of AI ethics discussions and so on. And I have to say that I'm always a little bit sort of traumatized, I suppose, by the fact that it seems like quite a lot of the level of thinking is very naive. And, you know, I've done a certain amount of sort of philosophical type thinking in my life, applied to science and applied to other kinds of things. And I think some of the things that one sort of here's an AI ethics are typical kind of thing is people will say, well, we're just going to write code that will make our system only do the right things. Okay, what do you mean by the right things? Well, the things that are provably right. What do you mean provably right? The notion of right is a human concept. It's something that there's no right answer to what's right. It's what we humans feel should be done. One of the things I found confusing about ethics is this. When you do science, it's possible to control your experiments. It's possible to say, I'm going to look at this little corner of the world and I'm going to have it in a sealed box and I'm going to do my physics experiment. It's a little bit more difficult in biology and areas like that. But fundamentally you say, this is the precise strain of mouse I want to use. It's controlled ethics. I think one can make kind of fake ethics situations like trolley problems and things like that, where you're trying to carve out an ethics situation kind of separated from the rest of the world. But in reality that's just not doable. Ethics is not separable in the way that we're used to in science. It's kind of like one decision kind of entrains sort of everything in the world type thing. And that makes it confusing from a Sort of science point of view to think about, at least for me. And so then you end up with these questions about well, what do people want out of their AIs. And you'll say, well, one thing would be get the AIs to do what people do. And people say, well that's not a good idea because people do all sorts of terrible things. We don't want to be done, we don't want to be amplified. So then what it really turns into is let's have the AIs do what people aspire to do. Well then you're in a total morass of the question of well, what do people aspire to do? We can look at different cultures, we can look at different books and so on. We get all sorts of different views of what people should aspire to doing. And I've certainly thought about the idea of let's make up 200 provisions for a possible kind of AI constitution. And some of them people will say, yeah, we like that one, we don't like that one. Different people, different cultures, different parts of the world, different situations will pick different clauses in this potential constitution. That's one thing. I don't think that's quite strong enough. But that's at least good thought experiment. Even making up those provisions is not easy. And I've been quite unsuccessful at that. I mean there are all sorts of questions like, you know, should every AI have an owner? Maybe, maybe not, probably not. Should AIs do what humans tell them to do? You know, it turns out the sort of old Asimov's Laws of robotics people haven't actually come up with those are very simple minded. And you know, Asimov himself kind of demonstrated in all his stories all the ways that sort of those three basic laws of robotics could sort of tangle on themselves. But people haven't really come up with better kind of general principles like that. And I think that's a challenge. But I have this hope that there is a way of thinking about political philosophy that applies to AIs and that is somehow sort of self answering. I mean, I think what's happened in political philosophy is two, 300 years ago was a big kind of period of the development of political philosophy that led to ideas of modern democracy, for example, and other ideas. But that was one of the outgrowths of that. And it's sort of a structuring idea that in the abstract you would describe how a democracy might work. And it's like, how could that possibly work? But in fact, up to a point, at least it Seems to work quite well. So how do economic markets work in the abstract? It's hard to know if that will work. In actuality, they seem to work quite well. But the question is, when you put AI into the mix, how do these things fundamentally change? What are the equilibrium points when there are lots of AIs in the world? So one of the things I recently is that the case of n equals 1 for 1 AI is very different from the case N goes to infinity, where the world is full of AIs and where you have kind of a society of AIs and where there is a whole dynamic and potential equilibrium in the society of the AIs, it's kind of like imagine the AIs are very powerful compared to humans. It's the bulldozer versus the human type thing. Well, if that's the competition, the bulldozer is going to run over the human and that's going to be the end of it. But if it's a whole collection of bulldozers, they're going to be in some kind of dynamic equilibrium with each other, using their sort of comparable strength, so to speak. And then what you have to do is figure out how do you build a sort of stable society of those things that can interact with human society. So that's kind of where I'm at thinking about that. I tend to think that as a practical matter, this whole question of, of kind of, you know, I, I, you know, okay, the cynic in me, I shouldn't say this, but the cynic in me says, you know, if you give people who are in government or in, in sort of the largest companies, if you say, here's this lever that you can use to get more control of the world, it's like, okay, we're going to pick that, we're gonna, we're gonna move that lever. So if the, if the thing is, look, the AIs are going to eat us all unless we all get together and regulate what's happening and put all these controls in place. If you're somebody who is involved with sort of the thing that would put those controls in place, how could you not choose to. It's kind of like a candy store situation. How could you not choose to pull that lever? And there's been some perhaps, I think, unfortunate sort of experience of governments seeing the kinds of levers that can be pulled in the pandemic and other kinds of things that kind of gives a sort of casts this funny shadow on what it means to have sort of this levers that can be pulled. Now, the problem is, it'd be one thing if one could say, okay, we know exactly which lever to pull, and if you pull this lever, and if the government can pull this lever, the world's going to be a better place. But we don't know which lever to pull. We really have no idea. You know the thing when we say, let's have AIs, like, here's a typical mistake. We can say, let's say all AIs must do only predictable things. We say, no AI can ever do something that we don't understand, that we can't predict. Okay, well, we just wrote out essentially the great advantage of AI, the great advantage of computation, this whole idea of mine of computational irreducibility, that even though you know the rules, you can't know what the computational system is going to do. That's kind of the thing that if you say we got to know what it does, then you can't have computational irreducibility, and you can't really have the computation do meaningful things. So you really have this choice. Society has this choice. Do we say, let's let computation really do things that are of value to us, even though sometimes it'll do something unexpected? Or do we say, let's prevent that from happening? Let's say you're not allowed to kind of drive a car or something. You have to walk. Because we know what happens when we walk. And if you drive a car, all sorts of things that we don't know how they'll turn out might happen. So, you know, do we all have to walk? Or can we drive our cars and use our AIs and so on? And I think this is sort of a societal decision to what extent we can live with the fact that there is uncertainty, just as there is uncertainty from nature. We don't know when the tornado is going to come, but that's something we've managed to find a way to live with. We kind of feel like because we've created the AIs, we feel like we have to have them under our thumb. But if we do that, they can't do the things that they can add value to our world by doing so. I think that's an example of a kind of a dichotomy, which I think is a little hard to understand because people will say, look, it's the software. It's this machine. We built it. Surely you can understand everything it's doing. Well, no, you can't. And if you try to, you prevent it from doing the things you really Want it to do. So one of the things that is sort of on the ground challenge is yes, I've thought a bunch about this. I've written a little bit about it. I've written about sort of the future of jobs in the world of AI where I think the main thing that one can see happen is as an area gets automated, more new possibilities open up and the end result is that the world of jobs gets more fragmented. Not smaller, just more fragmented and more diversity of opportunity actually for people. But any case, I think that one of the things that is a challenge for me, for us, is how to engage with these discussions. Because for me, for example, the swirl of political discussion is very complicated. I don't know much about it. It's. And it has many forces that can kind of rip things apart very easily and it's, it's sort of it. So it's difficult to, to really engage in that way. I think, you know, I, I get, for example these days lots and lots of invitations to lots of, you know, things from different governments and organizations and so on of let's talk about what should be done with AI. And you know, I have, I have two reasons for hesitation. One, I don't know. I don't know the answer. I think the answer, I think there is an answer. I think there's going to be an answer which is perhaps as non obvious as democracy and market economy these days. Of course those don't seem at all non obvious, but there are constructs in the world that I think can be built in a society of AIs, but we don't really know quite what they are yet. So that's one thing that holds me back. Another is just the dynamics of engagement with these kinds of forces and frankly the fact that, well, for somebody like me and for a company like ours, we're really interested in like just do stuff, just do stuff, just make things happen. Whereas the dynamics of the kind of political sphere and regulatory sphere is much more ponderous and frankly not a very good fit for the kinds of things we do. So I think it's an important sort of opportunity to kind of bridge that gap and to sort of bring some of the ideas that we're starting to be able to sort of have and kind of be able to present those and connect those to folks who are trying to make these decisions at a governmental level and so on. And I've done a tiny bit of that kind of thing and I suppose the most, I did some testimony for US Congress in, in 2019, for example. And I think the main thing that was sort of a little bit terrifying about that was that was about kind of AI selected content on the Internet was how much of a vacuum there was outside of things. The little things that I was able to figure out in terms of other things people have figured out. So I think it's a tremendously important area and one that, as I said, I'm trying to think about, but I don't think I've got great solutions for it right now. Satyris asks, is there any update on using Apple's Vision Pro to create VR renderings of Wolfram language visualization and interacting with them? What about Unity Link and so on? Well, we had the misfortune of working on virtual reality in the early 1990s, and I'm having a hard time with our team living down my enthusiasm from the early 1990s for virtual reality because it was a bust at that time. And, you know, we're still, it's still sort of in rehab, sort of in. It's a probationary period for VR. We are doing some things, working towards things like spherical image and working on various kinds of image, image representations that are relevant for virtual reality. And I hope we'll have some really cool things that will be able to run on the next generation of VR and AR technology. I would say that for me personally, I've jury's still out for me on whether that's going to be useful for things I do. You know, I have to say, in the early 1990s, when VR was. Was a thing, before I was first thinking about these kind of network models for space time and so on, and I had this kind of vision, I was like, I'm imagining that I'm there and we've got this whole giant cobweb and it's updating, all these pieces are updating. And I'm able to use my fingers in virtual reality to move a little piece of that cobweb, to render the graph a little differently and see what happens and open a little piece out, see what's behind there and so on. I have to say that I think the video we just made about sort of the beginning of the universe in our models based on graphs and so on, is kind of one of the first examples of even just the video version of this, let alone the VR version. But we did a few experiments back three years ago now on VR renderings of the hypergraphs for our physics project. And I have to say I didn't find them terribly compelling. And I also Got motion sick using the VR headset of the time, which hopefully is something that is now getting fixed as the hardware gets faster and better. But so I think it's still. I don't yet understand the use cases. I think I understand more of the use cases for AR in sort of the practical world of going around and using AR to kind of do material identification with using some other kinds of sensors. One of the interesting questions there is if, you know, if you have a camera on your AR system and the camera is seeing in the ultraviolet, for example, we don't have have sensors in our eyes for ultraviolet. We don't know what it should look like to have, you know, to superimpose the ultraviolet sort of color band on top of our RGB color bands. And that's sort of a UX problem is figuring out how to do that. And I think using Wolfram language to prototype things like that, things like captioning in ar, things like being able to get sort of enhanced information about objects or people or whatever you're looking at, those are things that I think we can do rather a lot with Wolfm language to prototype type those kinds of things. Bill Helton is asking Lean is a community effort towards automatic theorem proving and formulation. How do you see it in relation to Wolfram language? Good question. We've had lots of interaction with the Lean community. I would say the jury is still out. Let me tell you what I think I know. So Lean is more than anything a proof assistant system. It is not really an automated theorem proving system as such. It is a system for sort of doing mathematics like you would do Tetris, in the sense that you are sort of trying to build things up by saying this piece fits, this piece fits, this piece fits. It's up to you to decide what piece to put in. It can sometimes give you some suggestions, but you are basically building your mathematical tower in the direction you want to build it in. And I think that's rather different from automated theorem proving where you say here's a collection of axioms. Let's see whether we can get from this theorem to this other theorem by using these laws of inference or axioms or whatever. One of the things that I view as being sort of a downer for automated theorem proving is that I ask the question what's been discovered with automated theorem proving? Not what's been rediscovered and re presented with automated theorem proving, but what's been surprising and discovered with automated theorem proving knowledge. The only example, literally the only example of a surprising unexpected result discovered by Automated theorem proving was something I discovered in year 2000, which is the simplest axiom system for Boolean algebra, which I found by doing automated theorem proving and just trying 50,000 axioms until I found one that worked, basically, and knowing that that was the simplest one that could represent Boolean algebra. So that was a case where we really were able to use automated theorem proving for exploration, for discovery. Much of what it's been used for is for validation, and it's been used to some extent in mathematics. I would say more so in system design, validating protocols, validating hardware. The big prize there has been can you validate a crypto system? And that really hasn't been, sorry, cryptocurrency. A blockchain system that really hasn't been done successfully. Complicated. And there's sort of a kind of concept, maybe if we could, you know, can we validate our blockchain based on set theory? That's a meaningless idea because in the end, the blockchain should do what the blockchain users want it to do. And that isn't defined by set theory. That's defined by what you say the kind of constitution of the blockchain is. Now, there's sort of been a big push. I mean, I've made use of, of the kind of formalized mathematics that exists in Lean and another system called Metamath. There are about 200,000 theorems that have been formalized. Maybe that number has gone up a little bit in the last six months or so. I've been interested in doing empirical metamathematics, looking at what is this space of possible theorems that humans have decided are interesting enough to put in the corpus of a few million theorems that exist in the literature of mathematics. And I've been interested in kind of what the ultimate limit of mathematics is from theorems, you prove theorems, and from that, you build this big network of all theorems of mathematics. You can construct sort of all theorems. And that thing you construct is kind of a metamathematical space. And it turns out that it's deeply analogous to the space that we see in physical space. And that's something that comes out of our physics project and out of this idea of the ruliad, this entangled limit of all possible computations that's sort of at the foundation of both physics and mathematics. And so I've been interested in this kind of space of all possible theorems, and then this question of where do humans pick to sort of colonize in the space of possible theorems? And that's very well captured in these formalized mathematics systems. And it's quite interesting to see what the kind of, what the network of kind of human populated areas of mathematics actually is. And you can kind of get some notion of what the progress of mathematics looks like. And it's a whole topic we can talk about. I even wrote this book, let's see, I might even have one copy of it here. Look at that. I even have a copy so I can wave it around. It's a book about the physicalization of metamathematics, which is all about these kinds of questions, but practicalities of this. You know. Let me explain two things. Well, first thing is, in today's world, people are saying let's use machine learning and let's sort of make it precise with Lean or some proof assistant system. I'm not very convinced about that. I think it's going to make nice demos. I'm not sure how well it's going to do. I will say that when you ask what is mathematics really? Is mathematics really this thing like Hilbert thought that could be built from anything. He thought about tables and chairs. But you can build it from any kind of axiomatic structure. And it's just something you build based on that axiomatic structure or is it something different from that? And I think the analogy that I've found useful in recent times is fluid mechanics. There's a molecular level of describing a fluid and there's the fluid dynamics level of describing a fluid. And the molecular level is like the axiomatic level of describing mathematics. You've got all these little pieces and you're fitting them together and it's all kind of molecule by molecule. The fluid dynamics level is more the level that typical actual pure mathematicians work at. It's more the kind of conceptual level. And so a good example is, let's say the Pythagorean theorem. You can take that, you can grind it down to the molecular level. You have to pick which axioms you're going to use for real numbers, et cetera, et cetera, et cetera. You can grind it down. You have this thing. You can then build up from those axioms back up to the Pythagorean theorem. It's 7,000 steps. You have a giant network of 7,000 lemmas that eventually build up on that order, at least to the Pythagorean theorem. But yet in doing mathematics, we can operate just at the level of Pythagorean theorem. We don't have to grind down to say which axioms for real numbers are we going to use? We can just do mathematics at the Pythagorean theorem level. And I think that's analogous to the idea that you can just do fluid mechanics at the fluid mechanics level. You don't have to grind it down to the molecular level. And I think we organized a conference, what was it, six, seven years ago, about the formalization of pure mathematics. And we invited a lot of pure mathematicians and a lot of people involved in the mechanics of formalizing mathematics. And I think it was a kind of vote with your feet type situation because basically all the people involved with the formalization of mathematics showed up and very few of the pure mathematicians showed up. They just didn't care. They said this isn't mathematics the way we think of doing mathematics. And I think what we understand now is that that's sort of they think of mathematics at this fluid dynamics level. So I think the thing that is formalized mathematics is a bit different from the thing that is mathematics as done by mathematicians. I also think that that formalized area is the real thing that is of great value. There is more kind of thinking about things in terms of what I call these days ruliology, studying the science of simple rules and what they do that aren't necessarily mathematical rules, they're computational rules. And I think that's a very rich area. And that's kind of the future of this much more ground down axiomatic approach to mathematics. It's a much richer version of that, much more closely related to things that happen in the natural world. But I mean, we've been in these discussions for years now about just what connections should there be? And there is a connection from Lean to Wolfram language. You can use Wolfram language as a kind of superpower for Lean to say, what do they call a hammer, I think they call it to get to the next stage in the theorem rather than going through all the steps. But in the end, what one's doing with these proof assistance systems in a sense is can you build mathematics from the axioms as Hilbert wanted to do? Well, yes, maybe you can. I don't know how far you can get, but it's not what mathematicians typically want to do. I am very interested in how can we better formalize what pure mathematicians want to do. We were very interested a number of years ago now in kind of extending Wolfram language to really have all the constructs of pure mathematics. And we're slowly getting there. I mean, we're slowly getting more kinds of topological constructs, geometric constructs abstract algebra constructs and so on into the language. It's a gradual process where at every stage we're really making sure we can compute as much as possible with those things. We're not for the most part just saying let's go introduce type model spaces or something, even though we can't compute anything with them, but we're sort of slowly getting there. It might be worth our while to come from the top as well and introduce, as we do with entities, those things as entities. And we indeed started doing that and we've had a whole entity store about function spaces, for example, that, that was a beginning for that long answer. Thank you for that question. Let's see. From George Suppos. Do you, do you think that as neural network based AI grows in abilities it will more closely resemble biological intelligence instead of traditional computing? Is it a mistake to expect that these networks to function like traditional expert systems? Yeah, I mean, I think the thing we've learned from ChatGPT and the LLMs and so on is that the thing that seems to matter about the structure of the brain in generating things like human language is the stuff that's captured in artificial neural nets. It wasn't obvious a year ago. I think somebody could have said to generate language there has to be quantum mechanics in the brain. And I don't think anybody could really have given good evidence that that was not true. I think now you can give really good evidence that that's not true. So that's a, that's a major sort of scientific discovery from the technological observation of, of ChatGPT is, is we know that what matters in brains at least the level of generating language is pretty much just this kind of artificial neural net architecture. Now the question of whether what we can get from that kind of architecture is going to be just brain like, or whether it's going to do things that are more like our kind of computational systems. My guess is it's pretty much brain like that. We've got the essence of what brains do. We've built our world and our way of thinking around what brains successfully are able to do. And so a lot of, you know, we could imagine a technology of aliens, let's say, that is not built around what brains find easy. You know, the fact that we have, oh, let me give you an example. We have language, computational language, human language, which is essentially one dimensional. It's like, and it's essentially tree structured. We could imagine a version of language which is graphical, has, is, is networks, graphs that represent things and so on. 1 But people don't find it easy to untangle what that means. They, they find there are certain sets of things they find easier, there are other things they find difficult. I think that we tend to build our world to work with things that we find easy to work with. And so that's, and, and, and so that, that will be, you know, as we extend this kind of neural net idea and so on, we'll get to these things that, yeah, we've typically built our world around those things. They'll be easy for us to look at, to understand. The natural world, for example, might work differently. There are plenty of things in nature that are really hard for us to understand. There are things in, for example, I've been thinking recently about molecular biology and kind of the sort of core ideas there and the extent to which there are things that we really don't understand there and ways of thinking about things that we really don't have and that are very non human. There's no reason to think that there's kind of a human narrative that we can extract that is simple enough for us to understand. Lauren Williams asks, what do you see as the most promising ways for businesses to adopt AI in the workplace? And what specific applications of use cases do envision AI having most significant impact on in coming years to enhance productivity and information? The okay, so you know, thing to understand. Okay, what do we mean by AI? Well, the, what we mean by AI has shifted over time. Let's for these practical purposes mean kind of neural netish but based machine learning, LLMs, things like that. The thing to understand about those technologies is they're great for the 80% level, maybe even the 90% level. Sometimes anything where you have a use case where getting it right 80% of the time is a big win, they're going to be interesting. So for example, let's say you're ranking search results and you put good results most of the time in the top five. But occasionally you have some totally goofball thing that's there. It doesn't matter. You have a totally goofball thing because the purpose is to be able to expose to a human things they might think are interesting. They'll say that one's great, I'm happy, it's a win. Now if on the other hand, you're doing something where you have to have 100% success, you're launching the rocket or whatever and you've got to hit the moon and you can't be, oh, whoops, well, we missed the moon. Most applications it wouldn't Be bad news if you missed the moon 10% of the time. Time. So, you know these cases where you have the harness around the AI such that the use case you build is a big success. If the AI is like 80, 90% accurate, successful, that's going to be a win. Now, you know, we can back up the AI by connecting it to Wolfram language and so on. And again, that connection won't be perfect. We can set it up so that. And this is again an example where the. If you say, okay, AI go and write Wolfram language code, okay, you as a human look at it, you run it, you see some test cases, you say, yep, that's what I wanted. That's a good use case. Because again, if the AI produces what you want, it's a win. If it does something goofy, you just say, well, it did something goofy. I'm going to ignore that. It's not a lose, so to speak. So I think that's a thing. I think the other thing to say is that, you know, I see neural nets and AI machine learning as a component, and I think it's a very interesting component, but it's a component. And when you build out use cases, there's going to be a lot of just the thinking, the engineering and so on that goes into the harness around the AI system. And that's where a lot of the value is going to be. I think that the raw we see, and this is such a typical thing in sort of the technology hype cycle, we see kind of people say it's an LLM, it can do this, it can do that, it can do everything. We're just going to plug it in and immediately it's going to be an AI tutor. It's going to be a thing that does stock picking. It's going to be a thing that does, you know, this and that and the other. And guess what? It sort of works some of the time, but it's a great demo. But it doesn't really work in the production setting. To make it really work in the production setting, you have to build all this, harness all this structure around, kind of around the core AI system. And I think that's where a lot of the value comes, is understanding what you can do with AI, then building a harness that is sort of, that really provides a use case that is enabled by AI. And I think the things we built in W from language now integrating kind of LLM technology into the language, are really a terrific place to do this. I mean, a terrific way to combine kind of the Strengths of the sort of the computational approach, the ability to do that kind of precise engineering and so on, together with, oh, you need some machine learning, you need some AI. It's very integrated and you can immediately make use of it and put it into your workflow and so on. So that's a few thoughts on that. Let's see. George is commenting. A lot of discussion about AI misses the point. AI is just a tool. The discussion seems to amplify the problems with social economic systems. To me, it seems at that one main concern is that AI will just amplify greed and make problems like inequality worse. Well, yeah, I mean, whenever there is tools and technology, it gets, you know, technology and tools, as you say, amplify what people can do. That's what the story of technology and automation throughout history has been. What originally was just a person doing it with their own hands ends up being something where they get various kinds of superpowers, so to speak. Whether it's the earth digging machine or whether it's the computational language or the AI that is giving them the ability to just touch that one button. And then all this stuff happens. And of course at the beginning it's like, well, which button are you going to push? It's the human who's going to push the button. But actually it gets more complicated than that because increasingly the world will be run by AIs, increasingly the timescales, the complexity of what's going on, the number of different kinds of data inputs and so on. We're going to cede control of many, many things. We've already done that for many purposes to AIs that operate in milliseconds, microseconds, do things where they're taking in gobs of data in very short amounts of time beyond what we humans can do. So we're going to give AIs lots of control of our world. And it isn't really a question so much of will the human pressed the wrong button. It's really the intrinsic Dynamics of these AIs and what will happen. And one thing to realize is a lot of science fiction scenarios kind of say, well, the AIs are going to do these things and when the AIs are in control, they're going to crush the humans or whatever. And they're going to want to crush the humans for some reason. And I think the thing to understand about computation and AIs in general is the computational universe is very big. There are a lot of computations you can do. The question is which computations are kind of which you can do all these computations, you can have machines running all these kind of ruleological experiments and so on, generating all these different kinds of systems. The question is, which ones even relate to what we humans care about? Many of those computations, we look at them and it's just like that's just a piece of noise, that's random. We don't care about that. There's no structure in that. Now to the aliens or Even to the AIs, they might say that's not random. That's got all this amazing structure, that's, that's the great poetry of our civilization or whatever, but looks random to us humans. So there's this question of what things do we care about that are going on in this potential computational world? And then how do we kind of align ourselves? Where do we choose to live in that kind of environment? And you know, I think there's. So I think that the core problem of AI is more now, given that we cede control of many things to AIs and many AIs interacting with other AIs, what does that society look like? What are the dynamics of that society? What are its equilibria? What can we do to kind of make it be a society? I mean, to what extent is human society. It's a question, sort of a science question. To what extent is it inexorable that human society is somewhat stable? Not completely, as we can plainly see, but in general terms it's somewhat stable. Now maybe that's a self fulfilling prophecy because it wasn't. If it wasn't, it would all have gone extinct. Maybe that's something more like statistical mechanics and thermodynamics, where you put all the gas molecules or people in the box and eventually they'll come to some kind of equilibrium. I don't think we really know. And I think that those understanding those kinds of questions informs how we should think about AIs. Esmeralda, what are your thoughts on how publishing and the traditional mode of reporting research outcomes will change with AI? Well, I think the really big change which I've been pushing for, for 40 years, it's both kind of inspiring, I suppose, to always have the artifacts from the future, but it's also a little frustrating. I mean, the thing that is is this idea of computational publishing, this idea of publishing computational essays, this idea of using computational language to precisely describe sort of thoughts in a formal way. This to me is the most important part of the future of publishing. I know that in the things I've written I've tried to have it so you can click every picture and reproduce the results. Unfortunately, yesterday when I was demoing that, we had a couple that didn't work, which hopefully will work again today. The but it's really valuable. I mean, I know from our summer schools that people, they come to the summer school, they want to go on from some piece of research that I did, for example, they just click that, that picture, they get the code, they keep going from there. They can build on it immediately. It's not like, oh, I got to read the paper and I got to reimplement this and I've got to understand what the person was talking about. It's like it's right there, you can do something with it. And this is a place where Wolfram language is really unique in its ability to have this well encapsulated, easy to build on, easy to manipulate kinds of representations of formal ideas. It's also a language where if it's well written, it's good for people to read as well as to write. So I see that as being the most important long term thing is computational publishing. Get these papers not just to be readable by humans, but by their computers in the sense that you can take the ideas they're talking about and actually run them computationally. Now, in terms of the AIs writing the text and so on, I think there are places where that's pretty useful. Like for example, we get internal to our company right now, a digest every day of papers about LLMs. And for a while it was like, oh, all the abstracts are coming in and it's like I'm trying to read these things and it's like it's really a lot of work to read all these abstracts, but we just told an LLM, make a two sentence summary of each paper. Paper. The text is quite bland and maybe the summaries aren't perfect, but they're very easy to read. And I can just grind through and I can read 10 of these very, very quickly and I don't have to kind of adjust to the style of one author or another. So I think that's a good use case. Now, no doubt I missed some things, but it's a statistical process anyway, so that's a good use case. So I think that's the type of thing, I think that the ability to, for example, extract. So here's another, another type of use case. So company Emerald Cloud Lab, maybe there's some people from there at this conference, longtime partner of ours building automated biology and chemistry lab They've automated most of the experiments that people normally do in biology and chemistry, a couple hundred of them. And, you know, it's all programmed with Wolfram language. And one of the things that comes up there is. Well, you know, there are method sections in life sciences papers, for example, which describe how an experiment was done. Can you get an LLM to read that method section and write candidate Wolfram language code that can turn this paper into a fully reproducible paper where we just got this description of do this, this, this and this, have the liquid handling robot, put this thing in there. Eventually they'll have a mouse colony, pick out a mouse of this strain and go and run it through this maze or whatever else you're going to do. And that becomes a very interesting kind of way in which science is much more buildable. I mean, science right now you read most papers and it's just like you're reading it in an armchair type thing and then you've got to sort of get up and do something different to make use of what's in that paper. Paper, as opposed to that paper, is a component, and that's what we get with a function repository, data repository and so on. That paper is a component that you can immediately build on. I think that's the really important future as I see it. Mark Rollins asks, how does simulations from our physics project tie up with simulations people have done from Flamingo? I'm not sure I know that particular one. Do these projects have different objectives? So, I mean, the story of our physics project is a kind of dramatic story because for the last hundred years, there have been basically three core theories of physics. Statistical mechanics, general relativity, and quantum mechanics. And these are the things which all were introduced in the early part of the 20th century. And they've had a lot of mileage. But the question of what's the universe ultimately made of? They don't answer. They're kind of wheel in theories that say, these are particular ways we found the universe works. The thing that's really exciting is that three years ago now we kind of found that there's this kind of underlying structure which by the way, gives you all three of those theories of physics as emerged in the early 20th century. It's kind of a new paradigm for thinking about how to build physical theories. And the thing that's been really cool about it is as we take that paradigm and kind of try and see how it connects with all the different areas of mathematical physics and so on, we are still at a no clue jizz situation. It's been hard work, but it's like everything just fits together. All these features of how black holes work and how this works and that works it all. It's hard work to get from this very low level description of hypergraphy writing and so on up to talking about black holes. But it all seems to work and that's pretty exciting. And the things that we're doing. So we're operating at the level of the atoms of space. Basically, we don't know what the scale of the elementary length is. Hopefully in the next few years there'll be experiments which can at least give us more constraints on that. If we find the elementary length, then it's really cool because we've really validated this idea that space, like matter and like light, is discrete, which is something that has been for the last hundred years. 100 years ago, people thought space was going to be discrete, but then nobody could make it work. And so people said, well, let's assume space is continuous. We finally now have a way of understanding the discreteness of space. And you know, back in the early part of the 20th century, Brownian motion was the thing that really clinched that idea of that matter is discrete. What we will. Will we find an analog of Brownian motion for space? I'm not sure. We have some ideas about actually related to dark matter. Just like Brownian motion was actually originally discovered as a phenomenon 100 years before it was explained in terms of molecules, it may be that dark matter which was discovered 100 years ago might actually be the thing that shows us the discreetness of space. We shall see. That's still a coming attraction. But no, what we're doing. So one thing that's happened is a practical thing. We're starting from this very discrete model of the structure of space and we're building up to the sort of continuum structure of space time. You can. As a matter of fact, the system gravitas system that Jonathan Gorard's been developing, based on Wolfram language, based on our physics project, is something that you can think of as being a numerical scheme for solving Einstein's equations. Except really what it is is it's working from hypergraphs up, as opposed to taking the Einstein equations and breaking them into discrete with finite element methods or something, breaking them into something discrete. And the thing that's really cool and seems to be starting to get used a bunch by groups that are studying numerical relativity and so on, is you can really use our methods to make what people can think of as a scheme for the Einstein equations and a Good scheme. And there's this wonderful situation where people are starting to use it for that. And they say this is a good numerical scheme for the Einstein equations. We don't really care what the underlying kind of epistemology of it is. It's just a scheme for solving the Einstein equations. But as soon as they find a deviation, oops, your scheme differs from the predictions of Einstein's equations. For us, that's a huge win because that's a place where you can look for the discreteness of space. So that's kind of a little bit, but bit of that story. Let's see. So a couple more questions here and then I think we should wrap for the day. George is commenting. Just like the 1970s when some counterculture types wanted their own computer so they can be independent of faceless corporations. One reason I want Wolfram Language to use all my. All to use all the resources I have is so that in some sense I can have my own personal AI, which could theoretically be able to push back against the faceless corporation. Boy, we, we definitely have a, an ideology going here. You know, I have to say there is a, there is an interesting tension in the world between centralized AI and distributed AI, and I think it's. It's also a tension in the world between centralized government and distributed and centralized control and sort of the decentralized, individualized way of thinking about things. And I do think it's a dynamic right now that I think is going to come down, as it did with computers for a long time, on the sort of it can be personalized, so to speak. Now there are economies of scale and collecting it together as a big cloud service or something. But I think that kind of the I've got my own pet architect is going to be a thing. There certainly are both corporate and governmental forces that might prefer it to be centralized. But I think that the technology forces will push in the other direction, independent of ideology. Just the pure practical technology of the thing will make it so that indeed, as you say that with your orphan language in a box, plus, maybe we'll have an LLM, we'll see. Plus other kinds of things that are just right there in the box on your desk that becomes something over which you kind of have control. And it's like a personal AI as opposed to just there's the central AI in the cloud type thing. And I tend to think that's what the technology will come down as for all kinds of reasons. I think that although there may be sort of a push from both certain kinds of economic and governmental forces to go in the other direction. Action. Let's see. Satyris comments. The search for equilibrium though in game theory is a ppad. Not quite sure what that means. I'm not educated enough suggesting it's probably hard to reach even for a society of AIs. If the system gets too big in a non equilibrium, away from equilibrium dynamics approach, isn't that more suitable for giving insight about what a community might do? It's a good question whether have we in a statistical mechanics sense, has modern society come to equilibrium or not? I would say that enough things are time independent that I would consider that there's some degree of equilibrium. I mean it's kind of like. And there's some degree of large scale predictability. Of course there are pieces that are not predictable and there are things that happen that aren't predictable. But I think that the. I mean my guess would be that there's some sense of equilibrium. Although I really, you know, there's a lot of aspects of this that I certainly don't understand. And it's always been very striking to me that when you look at statistical mechanics, particles in a box, particle physics, whatever, you see certain statistical predictions and you can, particularly in particle physics, you might have lots of probabilities involved and you do, you know, particle experiments and different things happen. You have probability curves and so on. On. Well then you do web analytics and you look at all those humans coming through a website and you say what do they do? And they have statistics of what they do. And one of the things that was really striking to me in earlier years was you look at those statistics, the distributions are very smooth of what the people do. They're as smooth, if not smoother than the ones from what the particles do in particle physics. It's as if all these people with all our individual choices, all our kind of free will about what we do, at least in the aggregate, we have a surprising degree of predictability. I mean I know that even for, I have to say I find that even for myself because I collect a lot of kind of personal analytics data on myself and I always think I'm choosing what I do every day. I'm doing all these different things and I am at some level. But if I look at like, you know, this particular time of day, I know I'm going to get hungry. And it happens every day at the same time, at this particular time of day, I'm going to do this at this particular time of day, whatever. And so. That's something which even for myself, as an n of 1, I'm surprisingly predictable and I think society may be something like that too. All right, I think we have to wrap up for now. And actually I see one question here from Marnie Landon asking, is there anything you wish you could ask or show to my former friend and mentor of a sort, Richard Feynman? You know, it's funny because I was just doing an interview, hadn't talked about Feynman much for ages, but I was doing some interview, I think, for NPR a few days ago, which hasn't aired yet, but probably will, in which I was talking about that. And one of the things the person asked was what would Dick Feynman make of the kind of anti science views associated with people saying, look, science, we don't believe in science related to things like the pandemic and so on. I have to say my immediate response to that was he would say about some things, some calculations, he'd say, yeah, that makes sense. And some things he would say, wait a minute, you can't show that from the sort of scientific evidence that we have. I think it was a case where some parts of that story were really oversold and that made science look bad. And I think that's the thing which Dick Feynman would have been very sensitive to and would have been very outspoken about those kinds of things. In terms of what we're doing now, I think the most dramatic thing I always use used to talk to Dick Feynman about quantum mechanics and he would always say he studied quantum mechanics all his life, but the one thing he can say is nobody understands quantum mechanics. And I think I'm getting pretty close to being able to say I actually really understand quantum mechanics and sort of how it works from the ground up, so to speak, and where it comes from and why it's there. And that would be an interesting thing to be able to chat about. And I think I need to go go. But. Well, I'd like to just say congratulations to all our Innovator award winners today and thank you for all the, all the great things that you guys have done. And it's really just such a pleasure for me to see these ways that the things we put so much effort and so many years into building end up getting used and the extent to which that's been able to lead to some great careers and so on. So thank you very much and bye for now.
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