So… What Happened?

Today is my birthday—for the 65th time. Five years ago, on my 60th birthday, I did a livestream where I talked about some of my plans. So… what happened? Well, what happened was great. And in fact I’ve just had the most productive five years of my life. Nine books. 3939 pages of writings (1,283,267 words). 499 hours of podcasts and 1369 hours of livestreams. 14 software product releases (with our great team). Oh, and a bunch of big—and beautiful—ideas and results.

It’s been wonderful. And unexpected. I’ve spent my life alternating between technology and basic science, progressively building a taller and taller tower of practical capabilities and intellectual concepts (and sharing what I’ve done with the world). Five years ago everything was going well, and making steady progress. But then there were the questions I never got to. Over the years I’d come up with a certain number of big questions. And some of them, within a few years, I’d answered. But others I never managed to get around to.

And five years ago, as I explained in my birthday livestream, I began to think “it’s now or never”. I had no idea how hard the questions were. Yes, I’d spent a lifetime building up tools and knowledge. But would they be enough? Or were the questions just not for our time, but only perhaps for some future century?

At several points before in my life I’d faced such issues—and things had worked out well (A New Kind of Science, Wolfram|Alpha, etc.). And from this, I had gotten a certain confidence about what might be possible. In addition, as a serious student of intellectual history, I had a sense of what kind of boldness was needed. Five years ago there wasn’t really anything that made me need to do something big and new. But I thought: “What the heck. I might as well try. I’ll never know what’s possible unless I try.”

A major theme of my work since the early 1980s had been exploring the consequences of simple computational rules. And I had found the surprising result that even extremely simple rules could lead to immensely complex behavior. So what about the universe? Could it be that at a fundamental level our whole universe is just following some simple computational rule?

I had begun my career in the 1970s as a teenager studying the frontiers of existing physics. And at first I couldn’t see how computational rules could connect to what is known in physics. But in the early 1990s I had an idea, and by the late 1990s I had developed it and gotten some very suggestive results. But when I published these in A New Kind of Science in 2002, even my friends in the physics community didn’t seem to care—and I decided to concentrate my efforts elsewhere (e.g. building Wolfram|Alpha, Wolfram Language, etc.).

But I didn’t stop thinking “one day I need to get back to my physics project”. And in 2019 I decided: “What the heck. Let’s try it now.” It helped that I’d made a piece of technical progress the year before, and that now two young physicists were enthusiastic to work with me on the project.

And so it was, soon after my birthday in 2019, that we embarked on our Physics Project. It was a mixture of computer experiments and big concepts. But before the end of 2019 it was clear: it was going to work! It was an amazing experience. Thing after thing in physics that had always been mysterious I suddenly understood. And it was beautiful—a theory of such strength built on a structure of such incredible simplicity and elegance.

We announced what we’d figured out in April 2020, right when the pandemic was in full swing. There was still much to do (and there still is today). But the overall picture was clear. I later learned that a century earlier many well-known physicists were beginning to think in a similar direction (matter is discrete, light is discrete; space must be too) but back then they hadn’t had the computational paradigm or the other tools needed to move this forward. And now the responsibility had fallen on us to do this. (Pleasantly enough, given our framework, many modern areas of mathematical physics seemed to fit right in.)

And, yes, figuring out the basic “machine code” for our universe was of course pretty exciting. But seeing an old idea of mine blossom like this had another very big effect on me. It made me think: “OK, what about all those other projects I’ve been meaning to do? Maybe it’s time to do those too.”

And something else had happened as well. In doing the Physics Project we’d developed a new way of thinking about things—not just computational, but “multicomputational”. And actually, the core ideas behind this were in A New Kind of Science too. But somehow I’d never taken them seriously enough before, and never extended my intuition to encompass them. But now with the Physics Project I was doing this. And I could see that the ideas could also go much further.

So, yes, I had a new and powerful conceptual framework for doing science. And I had all the technology of the modern Wolfram Language. But in 2020 I had another thing too—in effect, a new distribution channel for my ideas and efforts. Early in my career I had used academic papers as my “channel” (at one point in 1979 even averaging a paper every few weeks). But in the late 1980s I had a very different kind of channel: embodying my ideas in the design and implementation of Mathematica and what’s now the Wolfram Language. Then in the 1990s I had another channel: putting everything together into what became my book A New Kind of Science.

After that was published in 2002 I would occasionally write small posts—for the community site around the science in my book, for our corporate blog, etc. And in 2010 I started my own blog. At first I mostly just wrote small, fun pieces. But by 2015—partly driven by telling historical stories (200th anniversary of George Boole, 200th anniversary of Ada Lovelace, …)—the things I was writing were getting ever meatier. (There’d actually already been some meaty ones about personal analytics in 2012.)

And by 2020 my pattern was set and I would routinely write 50+ -page pieces, full of pictures (all with immediately runnable “click-to-copy” code) and intended for anyone who cared to read them. Finally I had a good channel again. And I started using it. As I’d found over the years—whether with language documentation or with A New Kind of Science—the very act of exposition was a critical part of organizing and developing my ideas.

And now I started producing pieces. Some were directly about specific topics around the Physics Project. But within two months I was already writing about a “spinoff”: “Exploring Rulial Space: The Case of Turing Machines”. I had realized that one of the places the ideas of the Physics Project should apply was to the foundations of mathematics, and to metamathematics. In a footnote to A New Kind of Science I had introduced the idea of “empirical metamathematics”. And in the summer of 2020, fuelled by my newfound “finish those old projects” mindset, I ended up writing an 80-page piece on “The Empirical Metamathematics of Euclid and Beyond”.

December 7, 1920 was the date a certain Moses Schönfinkel introduced what we now call combinators: the very first clear foundations for universal computation. I had always found combinators interesting (if hard to understand). I had used ideas from them back around 1980 in the predecessor of what’s now the Wolfram Language. And I had talked about them a bit in A New Kind of Science. But as the centenary approached, I decided to make a more definitive study, in particular using methods from the Physics Project. And, for good measure, even in the middle of the pandemic I tracked down the mysterious history of Moses Schönfinkel.

In March 2021, there was another centenary, this time of Emil Post’s tag system, and again I decided to finish what I’d started in A New Kind of Science, and write a definitive piece, this time running to about 75 pages.

One might have thought that the excursions into empirical metamathematics, combinators, tag systems, rulial and multiway Turing machines would be distractions. But they were not. Instead, they just deepened my understanding and intuition for the new ideas and methods that had come out of the Physics Project. As well as finishing projects that I’d wondered about for decades (and the world had had open for a century).

Perhaps not surprisingly given its fundamental nature, the Physics Project also engaged with some deep philosophical issues. People would ask me about them with some regularity. And in March 2021 I started writing a bit about them, beginning with a piece on consciousness. The next month I wrote “Why Does the Universe Exist? Some Perspectives from Our Physics Project”. (This piece of writing happened to coincide with the few days in my life when I’ve needed to do active cryptocurrency trading—so I was in the amusing position of thinking about a philosophical question about as deep as they come, interspersed with making cryptocurrency trades.)

Everything kept weaving together. These philosophical questions made me internalize just how important the nature of the observer is in our Physics Project. Meanwhile I started thinking about the relationship of methods from the Physics Project to distributed computing, and to economics. And in May 2021 that intersected with practical blockchain questions, which caused me to write about “The Problem of Distributed Consensus”—which would soon show up again in the science and philosophy of observers.

The fall of 2021 involved really leaning into the new multicomputational paradigm, among other things giving a long list of where it might apply: metamathematics, chemistry, molecular biology, evolutionary biology, neuroscience, immunology, linguistics, economics, machine learning, distributed computing. And, yes, in a sense this was my “to do” list. In many ways, half the battle was just defining this. And I’m happy to say that just three years later, we’ve already made a big dent in it.

While all of this was going on, I was also energetically pursuing my “day job” as CEO of Wolfram Research. Version 12.1 of the Wolfram Language had come out less than a month before the Physics Project was announced. Version 12.2 right after the combinator centenary. And in 2021 there were two new versions. In all 635 new functions, all of which I had carefully reviewed, and many of which I’d been deeply involved in designing.

It’s a pattern in the history of science (as well as technology): some new methodology or some new paradigm is introduced. And suddenly vast new areas are opened up. And there’s lots of juicy “low-hanging fruit” to be picked. Well, that’s what had happened with the ideas from our Physics Project, and the concept of multicomputation. There were many directions to go, and many people wanting to get involved. And in 2021 it was becoming clear that something organizational had to be done: this wasn’t a job for a company (even for one as terrific and innovative as ours is), it was a job for something like an institute. (And, yes, in 2022, we indeed launched what’s now the Wolfram Institute for Computational Foundations of Science.)

But back in 1986, I had started the very first institute concentrating on complexity and how it could arise from simple rules. Running it hadn’t been a good fit for me back then, and very quickly I started our company. In 2002, when A New Kind of Science was published, I’d thought again about starting an institute. But it didn’t happen. But now there really seemed to be no choice. I started reflecting on what had happened to “complexity”, and whether there was something to leverage from the institutional structure that had grown up around it. Nearly 20 years after the publication of A New Kind of Science, what should “complexity” be now?

I wrote “Charting a Course for ‘Complexity’: Metamodeling, Ruliology and More”—and in doing so, finally invented a word for the “pure basic science of what simple rules do”: ruliology.

My original framing of what became our Physics Project had been to try to “find a computational rule that gives our universe”. But I’d always found this unsatisfying. Because even if we had the rule, we’d still be left asking “why this one, and not another?” But in 2020 there’d been a dawning awareness of a possible answer.

Our Physics Project is based on the idea of applying rules to abstract hypergraphs that represent space and everything in it. But given a particular rule, there are in general many ways it can be applied. And a key idea in our Physics Project is that somehow it’s always applied in all these ways—leading to many separate threads of history, that branch and merge—and, importantly, giving us a way to understand quantum mechanics.

We talked about these different threads of history corresponding to different places in branchial space—and about how the laws of quantum mechanics are the direct analogs in branchial space (or branchtime) of the laws of classical mechanics (and gravity) in physical space (or spacetime). But what if instead of just applying a given rule in all possible ways, we applied all possible rules in all possible ways?

What would one get? In November 2021 I came up with a name for it: the ruliad. A year and a half earlier I’d already been starting to talk about rulial space—and the idea of us as observers perceiving the universe in terms of our particular sampling of rulial space. But naming the ruliad really helped to crystallize the concept. And I began to realize that I had come upon a breathtakingly broad intellectual arc.

The ruliad is the biggest computational thing there can be: it’s the entangled limit of all possible computations. It’s abstract and it’s unique—and it’s as inevitable in its structure as 2 + 2 = 4. It encompasses everything computational—including us. So what then is physics? Well, it’s a description of how observers like us embedded in the ruliad perceive the ruliad.

Back in 1984 I’d introduced what I saw as being the very central concept of computational irreducibility: the idea that there are many computational processes whose outcomes can be found only by following them step by step—with no possibility of doing what mathematical science was used to, and being able to “jump ahead” and make predictions without going through each step. At the beginning of the 1990s, when I began to work on A New Kind of Science, I’d invented the Principle of Computational Equivalence—the idea that systems whose behavior isn’t obviously simple will always tend to be equivalent in the sophistication of the computations they do.

Given the Principle of Computational Equivalence, computational irreducibility was inevitable. It followed from the fact that the observer could only be as computationally sophisticated as the system they were observing, and so would never be able to “jump ahead” and shortcut the computation. There’d come to be a belief that eventually science would always let one predict (and control) things. But here—from inside science—was a fundamental limitation on the power of science. All these things I’d known in some form since the 1980s, and with clarity since the 1990s.

But the ruliad took things to another level. For now I could see that the very laws of physics we know were determined by the way we are as observers. I’d always imagined that the laws of physics just are the way they are. But now I realized that we could potentially derive them from the inevitable structure of the ruliad, and very basic features of what we’re like as observers.

I hadn’t seen this philosophical twist coming. But somehow it immediately made sense. We weren’t getting our laws of physics from nothing; we were getting them from being the way we are. Two things seemed to be critical: that as observers we are computationally bounded, and that (somewhat relatedly) we believe we are persistent in time (i.e. we have a continuing thread of experience through time).

But even as I was homing in on the idea of the ruliad as it applied to physics, I was also thinking about another application: the foundations of mathematics. I’d been interested in the foundations of mathematics for a very long time; in fact, in the design of Mathematica (and what’s now the Wolfram Language) and its predecessor SMP, I’d made central use of ideas that I’d developed from thinking about the foundations of mathematics. And in A New Kind of Science, I’d included a long section on the foundations of mathematics, discussing things like the network of all possible theorems, and the space of all possible axiom systems.

But now I was developing a clearer picture. The ruliad represented not only all possible physics, but also all possible mathematics. And the actual mathematics that we perceive—like the actual physics—would be determined by our nature as observers, in this case mathematical observers. There were lots of technical details, and it wasn’t until March 2022 that I published “The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics”.

In some ways this finished what I’d started in the mid-1990s. But it went much further than I expected, in particular in providing a sweeping unification of the foundations of physics and mathematics. It talked about what the ultimate limit of mathematics would be like. And it talked about how “human-level mathematics”—where we can discuss things like the Pythagorean theorem rather than just the microdetails of underlying axioms—emerges for observers like us just like our human-level impression of physical space emerges from the underlying network of atoms of space.

One of the things I’d discovered in computational systems is how common computational irreducibility is, along with undecidability. And I had always wondered why undecidability wasn’t more common in typical mathematics. But now I had an answer: it just isn’t what mathematical observers like us “see” in the ruliad. At some level, this was a very philosophical result. But for me it also had practical implications, notably greatly validating the idea of using higher-level computational language to represent useful human-level mathematics, rather than trying to drill down to “axiomatic machine code”.

October 22, 2021 had marked a third of a century of Mathematica. And May 14, 2022 was the 20th anniversary of A New Kind of Science. And in contextualizing my activities, and planning for the future, I’ve increasingly found it useful to reflect on what I’ve done before, and how it’s worked out. And in both these cases I could see that seeds I’d planted many years earlier had blossomed, sometimes in ways I’d suspected they might, and sometimes in ways that far exceeded what I’d imagined.

What had I done right? The key, it seemed, was drilling down to find the essence of things, and then developing that. Even if I hadn’t been able to imagine quite what could be built on them, I’d been able to construct solid foundations, that successfully encapsulated things in the cleanest and simplest ways.

In talking about observers and the ruliad—and in fact our Physics Project in general—I kept on making analogies to the way that the gas laws and fluid dynamics emerge from the complicated underlying dynamics of molecules. And at the core of this is the Second Law of thermodynamics.

Well, as it happens, the very first foundational question in physics that I ever seriously studied was the origin of the Second Law. But that was when I was 12 years old, in 1972. For more than a century the Second Law had been quite mysterious. But when I discovered computational irreducibility in 1984 I soon realized that it might be the key to the Second Law. And in the summer of 2022—armed with a new perspective on the importance of observers—I decided I’d better once and for all write down how the Second Law works.

Once again, there were lots of technical details. And as a way to check my ideas I decided to go back and try to untangle the rather confused 150-year history of the Second Law. It was an interesting exercise, satisfying for seeing how my new ways of thinking clarified things, but cautionary in seeing how wrong turns had been taken—and solidified—in the past. But in the end, there it was: the Second Law was a consequence of the interplay between underlying computational irreducibility, and our limitations as observers.

It had taken half a century, but finally I had finished the project I’d started when I was 12 years old. I was on a roll finishing things. But I was also realizing that a bigger structure than I’d ever imagined was emerging. The Second Law project completed what I think is the most beautiful thing I’ve ever discovered. That all three of the core theories of twentieth century physics—general relativity, quantum mechanics and the Second Law (statistical mechanics)—have the same origin: the interplay between the underlying computational structure of the ruliad, and our characteristics and limitations as observers.

And I knew it didn’t stop there. I’d already applied the same kind of thinking to the foundations of mathematics. And I was ready to start applying it to all sorts of deep questions in science, in philosophy, and beyond. But at the end of 2022, just as I was finishing my pieces about the Second Law, there was a surprise: ChatGPT.

I’d been following AI and neural nets for decades. I first simulated a neural net in 1981. My first company, started in 1981, had, to my chagrin, been labeled an “AI company”. And from the early 2010s we’d integrated neural nets into the Wolfram Language. But—like the creators of ChatGPT—I didn’t expect the capabilities that emerged in ChatGPT. And as soon as I saw ChatGPT I started trying to understand it. What was it really doing? What would its capabilities be?

In the world at large, there was a sense of shock: if AI can do this now, soon it’ll be able to do everything. But I immediately thought about computational irreducibility. And it gave us limitations. But those limitations would inevitably apply to AIs as well. There would be things that couldn’t be “quickly figured out by pure thought”—by humans and AIs alike. And, by the way, I’d just spent four decades building a way to represent things computationally, and actually do systematic computations on them—because that was the point of the Wolfram Language.

So immediately I could see we were in a very interesting position. The Wolfram Language had the completely unique mission of creating a full-scale computational language. And now this was a crucial tool for AIs. The AIs could provide a very interesting and useful broad linguistic interface. But when it came to solid computation, they were—like humans—going to need a tool. Conveniently, Wolfram|Alpha already communicated in natural language. And it took only a few weeks to hook up Wolfram|Alpha—and Wolfram Language—to ChatGPT. We’d given “computational superpowers” to the AI.

ChatGPT was everywhere. And people kept asking me about it. And over and over again I ended up explaining things about it. So at the beginning of February 2023 I decided it’d be better for me just to write down once and for all what I knew. It took a little over a week (yes, I’m a fast writer)—and then I had an “explainer” (that ran altogether to 76 pages) of ChatGPT.

Partly it talked in general about how machine learning and neural nets work, and how ChatGPT in particular works. But what a lot of people wanted to know was not “how” but “why” ChatGPT works. Why was something like that possible? Well, in effect ChatGPT was showing us a new science discovery—about language. Everyone knows that there’s a certain syntactic grammar of language—like that, in English, sentences typically have the form noun-verb-noun. But what ChatGPT was showing us is that there’s also a semantic grammar—some pattern of rules for what words can be put together and make sense.

I’ve thought about the foundations of language for a long time (which isn’t too surprising, given the four decades I’ve spent as a computational language designer). So in effect I was well primed to think about its interaction with ChatGPT. And it also helped that—as I’ll talk about below—one of my long-unfinished projects is precisely on a formal framework for capturing meaning that I call “symbolic discourse language”.

In technology and other things I always like best situations where basically nothing is known, and one has to invent everything from scratch. And that’s what was happening for functionality based on LLMs in the middle of 2023. How would LLM-based Wolfram Language functions work? How would a prompt repository work? How would LLMs interact with notebooks?

Meanwhile, there was still lots of foment in the world about the “AI shock”. Before the arrival of the Physics Project in 2019—I’d been quite involved in AI philosophy, AI ethics, etc. And in March 2023 I wrote a piece on “Will AIs Take All Our Jobs and End Human History—or Not?” In the end—after all sorts of philosophical arguments, and an analysis of actual historical data—the answer was: “It’s Complicated”. But along the way computational irreducibility and the ruliad were central elements: limiting the controllability of AIs, allowing for an infinite frontier of invention, and highlighting the inevitable meaninglessness of everything in the absence of human choice.

By this point (and actually, with remarkable speed) my explainer on ChatGPT had turned into a book—that proved extremely popular (and now, for example, exists in over 10 languages). It was nice that people found the book useful—and perhaps it helped remove some of the alarming mystique of AI. But I couldn’t help noticing that of all the many things I’d written, this had been one of the fastest to write, yet it was garnering one of the largest readerships.

One might have imagined that AI was pretty far from our Physics Project, the ruliad, etc. But actually it soon became clear that there were close connections, and that there were things to learn in both directions. In particular, I’d come to think of minds that work in different ways as occupying different positions in the ruliad. But how could one get intuition about what such minds would experience—or observe? Well, I realized, one could just look at generative AI. In July I wrote “Generative AI Space and the Mental Imagery of Alien Minds”. I called this the “cats in hats piece”, because, yes, it has lots of pictures of (often bizarrely distorted) cats (in hats)—used as examples of what happens if one moves a mind around in rulial space. But despite the whimsy of the cats, this piece provided a surprisingly useful window into what for me has been a very longstanding question of how other minds might perceive things.

And this fed quite directly into my piece on “Observer Theory” in December 2023. Ever since things like Turing machines we’ve had a formal model for the process of computation. My goal was to do the same kind of thing for the process of observation. In a sense, computation constructs sequences of new things, say with time. Observation, on the other hand, equivalences things together, so they fit in finite minds. And just what equivalencing is done—by our senses, our measuring devices, our thinking—determines what our ultimate perceptions will be. Or, put another way, if we can characterize well enough what we’re like as observers, it’ll show us how we sample the ruliad, and what we’ll perceive the laws of physics to be.

When I started the Physics Project I wasn’t counting on it having any applications for hundreds of years. But quite soon it became clear that actually there were going to be all sorts of near-term applications, particularly of the formalism of multicomputation. And every time one used that formalism one could get more intuition about features of the Physics Project, particularly related to quantum mechanics. I ended up writing a variety of “ruliological” pieces, all, as it happens, expanding on footnotes in A New Kind of Science. There was “Multicomputation with Numbers” (October 2021), “Games and Puzzles as Multicomputational Systems” (June 2022) and “Aggregation and Tiling as Multicomputational Processes” (November 2023). And in September 2023 there was also “Expression Evaluation and Fundamental Physics”.

Back around 1980—when I was working on SMP—I’d become interested in the theory of expression evaluation. And finally, now, with the Physics Project—and my work on combinators and metamathematics—four decades later I had a principled way to study it (potentially with immediate application in distributed computing and computational language design around that). And I could check off progress on another long-pending project.

I give many talks, and do many podcasts and livestreams—essentially all unprepared. But in October 2023 I agreed to give a TED talk. And I just didn’t see any way to fit a reasonable snapshot of my activities into 18 minutes without preparation. How was I to coherently explain the Physics Project, the ruliad and computational language in such a short time? I called the talk “How to Think Computationally about AI, the Universe and Everything”. And I began with what for me was a new condensation: “Human language. Mathematics. Logic. These are all ways to formalize the world. And in our century there’s a new and yet more powerful one: computation.”

Over the years I’d done all sorts of seemingly very different projects in science and in technology. But somehow it seemed like they were now all converging. Back in 1979, for example, I’d invented the idea of transformations for symbolic expressions as a foundation for computational language. But now—more than four decades later—our Physics Project was saying that those kinds of transformations (specifically on hypergraphs) were just what the “machine code of the universe” was made of.

Since the 1980s I’d thought that computation was a useful paradigm with which to think about the world. But now our Physics Project and the ruliad were saying that it wasn’t just useful; it was the underlying paradigm of the world. For some time I’d been viewing our whole Wolfram Language effort as a way to provide a way to formalize computation for the purposes of both humans and machines. Four hundred years ago mathematical notation had streamlined mathematical thinking, allowing what became the mathematical sciences to develop. I saw what we were doing with our computational language as a way to streamline computational thinking, and allow “computational X” for all fields “X” to develop.

I began to see computational thinking as a way to “humanize” the ruliad; to pick out those parts that are meaningful to humans. And I began to see computational language as the bridge between the power of raw computation, and the kinds of things we humans think about.

But how did AI fit in? At the beginning of 2024, lots of people were still asking in effect “Can AI Solve Science?” So I decided to analyze that. I certainly didn’t expect AI to be able to “break computational irreducibility”. And it didn’t. Yes, it could automate much of what humans could do in a quick look. But formalized, irreducible computation: that was going to need computational language, not AI.

It’s easy to be original in the computational universe: if you pick a rule at random, it’s overwhelmingly likely nobody’s ever looked at it before. But will anyone care? They’ll care if in effect that part of the ruliad has been “colonized”; if there’s already a human connection to it. But what if you define some attribute that you want, then just “search out there” for a rule that exhibits it? That’s basically what biological evolution—or machine learning training—seems to do.

And as a kind of off-hand note I decided to just see if I could make a minimal model for that. I’d tried before—in the mid-1980s. And in the 1990s when I was writing A New Kind of Science I’d become convinced that computational irreducibility was in a sense a stronger force than adaptive evolution, and that when complex behavior was seen in biology, it was computational irreducibility that should take most of the credit.

But I decided to just do the experiment and see. And although computational irreducibility in a sense tells one to always “expect the unexpected”, in all these years I’ve never fully come to terms with that—and I’m still regularly surprised by what simple systems somehow “cleverly” manage to do. And so it was with my minimal model of biological evolution.

I’d always wondered why biological evolution managed to work at all, why it didn’t “get stuck”, and how it managed to come up with the ornate “solutions” it did. Well, now I knew: and it turned out it was, once again, a story of computational irreducibility. And I’d managed to finish another project that I started in the 1980s.

But then there was machine learning. And despite all the energy around it—as well as practical experience with it—it didn’t seem like there was a good foundational understanding of what it was doing or why it worked. For a couple of years I’d been asking all the machine learning experts I ran into what they knew. But mostly they confirmed that, yes, it wasn’t well understood. And in fact several of them suggested that I’d be the best person to figure it out.

So just a few weeks ago, starting with ideas from the biological evolution project, and mixing in some things I tried back in 1985, I decided to embark on exploring minimal models of machine learning. I just posted the results last week. And, yes, one seems to be able to see the essence of machine learning in systems vastly simpler than neural nets. In these systems one can visualize what’s going on—and it’s basically a story of finding ways to put together lumps of irreducible computation to do the tasks we want. Like stones one might pick up off the ground to put together into a stone wall, one gets something that works, but there’s no reason for there to be any understandable structure to it.

Like so many of the projects I’ve done in the past five years, I could in principle have done this project much earlier—even in the 1980s. But back then I didn’t have the intuition, the tools or the intellectual confidence to actually dive in and get the project done. And what’s been particularly exciting over the past five years is that I can feel—and even very tangibly see—how what I can do has grown. With every project I’ve done I’ve further honed my intuition, developed more tools (both conceptual and practical), and built my intellectual confidence. Could I have gotten here earlier in my life? I don’t think so. I think to get to where I am now required the kind of journey I’ve taken through science, technology and the other things I’ve done. A living example of the phenomenon of computational irreducibility.

The Process of Getting Things Done

I started my career young—and usually found myself the “youngest person in the room”. But shockingly fast all those years whizzed by, and now I’m usually the “oldest person in the room”. But somehow I always still seem to feel like a young whippersnapper—not settled into some expected pattern, and “pushing for the future”.

I’ve always done projects that are hard. Projects that many people thought were impossible. Projects that stretched my capabilities to the limit. And to do this has required a certain mixture of confidence and humility. Confidence that it’s worth me trying the project. Humility in not assuming that it’ll be easy for me.

I’ve learned a lot of fields by now, and with them a lot of different ways of thinking. But somehow it’s never enough to make the projects I do easy. Somehow the projects are always far enough out on the frontier that I have to learn new things and new ways of thinking to succeed at them. And so there I am, often the only person in the room whose project isn’t somehow easy for them. And who still has to be pushing, whippersnapper style.

At this point, a fair fraction of the projects I do are ones that I’ve thought about for a long time; a smaller fraction are opportunistic—coming into scope just now as a result of something I’ve done, or something that’s happened in the world at large. Before the past five years I had a lot of projects that had languished, often for decades. Yes, I thought they would be interesting, and I gradually collected information about them. But somehow I wasn’t quite in a place to tackle them.

But now I feel quite differently. In the past five years, I’ve gone back and finished a fair fraction of all those languishing projects. And it’s been great. Without exception, the projects turned out to be richer and more interesting than I expected. Often I realized I really couldn’t have done them without the tools and ideas (and infrastructure) I now have. And—often to my great surprise—the projects turned out to have very direct connections to big themes around the ruliad, the Physics Project and, for that matter, computational language.

Why was this happening? Partly it’s a tribute to the breadth of the computational (and now multicomputational) paradigm. But partly it has to do with the specific character of projects I was choosing—always seeking what seemed like the simplest, most foundational versions of things.

I’ve done quite a few big projects in my life, many seemingly very different. But as I look back, I realize that all my projects have a certain overall pattern to them. They’re all about taking something that seems complicated, then drilling down to find the foundations of what’s going on, and then building up from these—often with considerable engineering-style effort. And the methods and tools I’ve developed have in a sense implicitly been optimized for this pattern of work.

I suppose one gets used to the rhythm of it all. The time when one’s drilling down, slowly trying to understand things. The time when one’s doing all the work to build the big structure up. And yes, it’s all hard. But by now I know the signs of progress, and they’re always energizing to see.

At any given time, I’ll have many projects gestating—often for years or decades. But once a project becomes active, it’s usually the only one I’m working on. And I’ll work on it with great intensity, pushing hard to keep going until it’s done. Often I’ll be working with other people, usually much younger than me. And I think it’s always a surprise that I’ll routinely be the one who works with the greatest intensity—every day, at all hours.

I think I’m pretty efficient too. Of course, it helps that I have a tool—Wolfram Language—that I’ve been building for decades to support me. And it helps that I’ve developed all kinds of practices around how I organize code and notebooks I create, and how I set up my process of writing about things. Of course, it also helps that I have very capable people around me to make suggestions, explore additional directions, fill in details, check things, and get my write-ups produced and published.

As I have written about elsewhere, my life is in many ways set up to be quite simple and routine. I get up at the same time every day, eat the same thing for breakfast, and so on. But in a sense this frees me to concentrate on the intellectual things I’m doing—which are different every day, often in unexpected ways.

But how is it that I even get the time to do all these intellectual things? After all, I am—as I have been for the past 38 years—the CEO of a very active tech company. Two things I think help (in addition, of course, to the fact that I have such a great long-term team at the company). First, organization. And second, resolve. Every day I’ll have tightly scheduled meetings over the course of the working day. (And there are lots of details to this. I get up in the late morning, then do my first two meetings while walking, and so on.) But somehow—mostly on evenings and weekends—I find time to work intensely on my intellectual projects.

It’s not as if I ignore everything else in the world. But I do have a certain drive—and resolve—that fills any time available with my projects, and somehow seems to succeed in getting them done. (And, yes, there are many optimizations in the details of my life, saving me all sorts of time. And it probably helps that I’ve been a work-from-home CEO now for 33 years.)

One might have thought that CEOing would greatly detract from being able to do intellectual work. But I find the exact opposite. Because in my experience the discipline of strategy and decision making (as well as communicating thoughts and ideas to other people) that comes with CEOing is critical to being able to do incisive intellectual work. And, by the way, the kind of thinking that goes with intellectual work is also incredibly valuable in being an effective CEO.

There’s another critical part to my “formula”. And that has to do with exposition. For me, the exposition of a project is an integral part of the project. Part of it is that the very definition of the question is often one of the most important parts of a project. But more than that, it’s through exposition that I find I really understand things. It takes a certain discipline. It can be easy enough to make some highfalutin technical statement. But can one grind it down into truly simple pieces that one can immediately understand? Yes, that means other people will be able to understand it too. But for me, what’s critical is that that’s the way I can tell if I’m getting things right. And for me the exposition is what in the end defines the backbone of a project.

Normally I write quickly, and basically without revision. But whenever there’s a piece I’m finding unduly hard to write I know that’s where I’m muddled, and need to go back and understand what’s going on. Some of my projects (like creating this piece, for example) end up being essentially “pure writing”. But most are deeply computational—and full of computer experiments. And just as I put a lot of effort into making written exposition clear, I do the same for computational language, and for pictures. Indeed, many of my projects are in large measure driven by pictures. Usually these are what one can think of as “algorithmic diagrams”—created automatically with a structure optimized for exposition.

And the pictures aren’t just useful for presenting what I’ve done; they’re also critical to my own efforts to figure things out. And I’ve learned that it’s important to get the presentational details of pictures right as early as possible in a project—to give myself the best chance to notice things.

Often the projects I do require exploring large numbers of possible systems. And somehow with great regularity this leads to me ending up looking at large arrays of little pictures. Yes, there’s a lot of “looking” that can be automated. But in the end computational irreducibility means there’ll always be the unexpected, that I basically have to see for myself.

A great thing about the Wolfram Language is that it’s been very stable ever since it was first released. And that means that I can take notebooks even from the 1980s and immediately run them today. And, yes, given all the “old” projects I’ve worked on in the past five years, that’s been very important.

But in addition to being very stable, the Wolfram Language is also very self contained—and very much intended to be readable by humans. And the result is something that I’ve found increasingly important: every computational picture in everything I write has Wolfram Language code “behind it”, that you can get by clicking. All the time I find myself going back to previous things I’ve written, and picking up click-to-copy code to run for some new case, or use as the basis for something new I’m doing.

And of course that click-to-copy code is open for anyone to use. Not only for its “computational content”, but also for the often-elaborate visuals it implements.

Most of my writings over the past five years have been about new basic science. But interspersed with this—along with pieces about technology and about philosophy—are pieces about history. And in fact many of my scientific pieces have had extensive historical sections as well.

Why do I put such effort into history? Partly I just find it fun to figure out. But mostly it’s to contextualize my understanding of things. Particularly in the past five years I’ve ended up working on a whole sequence of projects that are in a sense about changing longstanding directions in science. And to feel confident about making such changes, one has to know why people went in those directions in the first place. And that requires studying history.

Make no mistake: history—or at least good history—is hard. Often there’ll be a standard simple story about how some discovery was suddenly made, or how some direction was immediately defined. But the real story is usually much more complicated—and much more revealing of the true intellectual foundations of what was figured out. Almost never did someone discover something “one day”; almost always it took many years to build up the conceptual framework so that “one day” the key thing could even be noticed.

When I do history I always make a big effort to look at the original documents. And often I realize that’s critical—because it’s only with whatever new understanding I’ve developed that one would stand a chance of correctly interpreting what’s in the documents. And even if one’s mainly interested in the history of ideas, I’ve always found it’s crucial to also understand the people who were involved with them. What was their motivation? What was their practical situation? What kinds of things did they know about? What was their intellectual style in thinking about things?

It has helped me greatly that I’ve had my own experiences in making discoveries—that gives me an intuition for how the process of discovery works. And it also helps that I’ve had my fair share of “worldly” experiences. Still, often it’s at first a mystery how some idea developed or some discovery got made. But my consistent experience is that with enough effort one can almost always solve it.

Particularly for the projects I’ve done in recent years, it often leaves me with a strange feeling of connection. For in many cases I find out that the things I’ve now done can be viewed as direct follow-ons to ideas that were thought about a century or more ago, and for one reason or another ignored or abandoned since.

And I’m then usually left with a strong sense of responsibility. An idea that was someone’s great achievement had been buried and lost to the world. But now I have found it again, and it rests on me to bring it into the future.

In addition to writing about “other people’s history”, I’ve also been writing quite a bit about my own history. And in the last few years I’ve made a point of explaining my personal history around the science—and technology—I describe. In doing this, it helps a lot that I have excellent personal archives—that routinely let me track to within minutes discoveries I made even four decades ago.

My goal in describing my own history is to help other people contextualize things I write about. But I have to say that time and time again I’ve found the effort to piece together my own history extremely valuable just for me. As I go through life, I try to build up a repertoire of patterns for how things I do fit together. But often those patterns aren’t visible at the time. And it takes going back—often years later—to see them.

I do the projects I do first and foremost for myself. But I’ve always liked the idea that other people can get their own pleasure and benefit from my projects. And—basically starting with the Physics Project—I’ve tried to open to the world not just the results of my projects, but the process by which they’re done.

I post my working notebooks. Whenever practical I livestream my working meetings. And, perhaps taking things to an extreme, I record even my own solitary work, posting it in “video work logs”. (Except I just realized I forgot to record the writing I’m doing right now!)

A couple of years before the Physics Project I actually also opened up my technology development activities—livestreaming our software design reviews, in the past five years 692 hours of them. (And, yes, I put a lot of work and effort into designing the Wolfram Language!)

At the beginning of the pandemic I thought: “There are all these kids out of school. Let me try to do a little bit of public service and livestream something about science and technology for them.” And that’s how I started my “Science & Technology Q&A for Kids & Others” livestreams, that I’ve now been doing for four and a half years. Along the way, I’ve added “History of Science & Technology Q&A”, “Future of Science & Technology Q&A”, and “Business, Innovation & Managing Life Q&A”. Altogether I’ve done 272 hours of these, that have generated 376 podcast episodes.

Twice a week I sit down in front of a camera, watch the feed of questions, and try to answer them. It’s always off the cuff, completely unprepared. And I find it a great experience. I can tell that over the time I’ve been doing this, I’ve become a better and more fluent explainer, which no doubt helps my written exposition too. Often in answering questions I’ll come up with a new way to explain something, that I’ve never thought of before. And often there’ll be questions that make me think about things I’ve never thought about at all before. Indeed, several of my recent projects actually got started as a result of questions people asked.

When I was younger I always just wanted to get on with research, create things, and so on; I wasn’t interested in education. But as I’ve gotten older I’ve come to really like education. Partly it’s because I feel I learn a lot myself from it, but mostly it’s because I find it fulfilling to use what I know and try to help people develop.

I’ve always been interested in people—a useful attribute in running a talent-rich company for four decades. (I’m particularly interested in how people develop through their lives—leading me recently, for example, to organize a 50-year reunion for my elementary school class.) I’ve had a long-time “hobby” of mentoring CEOs and kids (both being categories of people who tend to believe that anything is possible).

But my main educational efforts are concentrated in a few weeks of the year when we do our Wolfram Summer School (started in 2003) and our Wolfram High School Summer Research Program (started in 2012). All the students in these programs (775 of them over the past five years) do an original project, and one of my jobs is to come up with what all these projects should be. Over the course of the year I’ll accumulate ideas—though rather often when I actually meet a student I’ll invent something new.

I obviously do plenty of projects myself. But it’s always an interesting—and invigorating—experience to see so many projects get done with such intensity at our summer programs. Plus, I get lots of extra practice in framing projects that helps when I come to frame my own projects.

At this point, I’ve spent years trying to organize my life to optimize it for what I want to get out of it. I need long stretches of time when I can concentrate coherently. But I like having a diversity of activities, and I’m pretty sure I wouldn’t have the energy and effectiveness I do without that. Over the years, I’ve added in little pieces. Like my weekly virtual sessions where I “do my homework” with a group of kids, working on something that I need to get done, but that doesn’t quite fit elsewhere. Or my weekly sessions with local kids, talking about things that make me and them think. Or, for that matter, my “call while driving” list of calls it’s good to make, but wouldn’t usually quite get the priority to happen.

Doing all the things I do is hard work. But it’s what I want to do. Yes, things can drag from time to time. But at this point I’m so used to the rhythm of projects that I don’t think I notice much. And, yes, I work basically every hour of every day I can. Do I have hobbies? Well, back when I was an academic, business was my main “hobby”. When I started CEOing, science became a “hobby”. Writing. Education. Livestreaming. These were all “hobbies” too. But somehow one of the patterns of my life is that nothing really stays quite as a “true hobby”.

What’s Next?

The past five years have not only been my most productive ever, but they’ve also built more “productivity momentum” than I’ve had before. So, what’s next? I have a lot of projects currently “in motion”, or ready to “get into motion”. Then I have many more that are in gestation, for which the time may finally have come. But I know there’ll also be surprises: projects that suddenly occur to me, or that I suddenly realize are possible. And one of the great challenges is to be in a position to actually jump into such things.

It has to be said that there’s always a potentially complicated tradeoff. To what extent should one “tend” the things one’s already done, and to what extent should one do new things? Of course, there are some things that are never “done”—like the Wolfram Language, which I started building 38 years ago, and still (energetically) work on every day. Or the Physics Project, where there’s just so much to figure out. But one of the things that’s worked well in most of the basic science projects I’ve done in the past five years or is that once I’ve written my piece about the project, I can usually consider the project “done for now”. It always takes a lot of effort to get a project to the point where I can write about it. But I work hard to make sure I only have to do it once; that I’ve “picked the low-hanging fruit”, so I don’t feel I have to come back “to add a little more”.

I put a lot of effort into the pieces I write about my projects. And I also give talks, do interviews, etc. (about 500 altogether in the past five years). But I certainly don’t “market” my efforts as much as I could. It’s a decision I’ve made: that at this point in my life—particularly with the burst of productivity I’m experiencing—I want to spend as much of my time as possible doing new things. And so I need to count on others to follow up and spread knowledge about what I’ve done, whether in the academic world, on Wikipedia, the web, etc. (And, yes, pieces I write and the pictures they contain are set up to be immediately reproducible wherever appropriate.)

OK, so what specific new things are currently in my pipeline? Well, there’s lots of science (and related intellectual things). And there’s also lots of technology. But let’s talk about science first.

A big story is the Physics Project—where there’s a lot to be done, in many different directions. There’s foundational theory to be developed. And there are experimental implications to be found.

It’d be great if we could find experimental evidence of the discreteness of space, or maximum entanglement speed, or a host of other unexpected phenomena in our models. A century or so ago it was something of a stroke of luck that atoms were big enough that they could be detected. And we don’t know if the discreteness of space is something we’ll be able to detect now—or only centuries from now.

There are phenomena—particularly associated with black holes—that might effectively serve as powerful “spacetime microscopes”. And there are phenomena like dimension fluctuations that could potentially show up in a variety of astrophysical settings. But one direction I’m particularly interested in exploring is what one might call “spacetime heat”—the effect of detailed microscopic dynamics in the hypergraph that makes up spacetime. Could “dark matter”, for example, not be “matter” at all, but instead be associated with spacetime heat?

Part of investigating this involves building practical simulation software to investigate our models on as large a scale as possible. And part of it involves “good, old-fashioned physics”, figuring out how to go from underlying foundational effects to observable phenomena.

And there’s a foundational piece to this too. How does one set up mathematics—and mathematical physics—when one’s starting from a hypergraph? A traditional manifold is ultimately built up from Euclidean space. But what kind of object is the limit of a hypergraph? To understand this, we need to construct what I’m calling infrageometry—and infracalculus alongside it. Infrageometry—as its name suggests—starts from something lower level than traditional geometry. And the challenge is in effect to build a “21st century Euclid”, then Newton, etc.—eventually finding generalizations of things like differential geometry and algebraic topology that answer questions like what 3-dimensional curvature tensors are like, or how we might distinguish local gauge degrees of freedom from spatial ones in a limiting hypergraph.

Another direction has to do with particles—like electrons. The fact is that existing quantum field theory in a sense only really deals with particles indirectly, by thinking of them as perturbations in a field—which in turn is full of (usually unobservable) zero-point fluctuations. In our models, the structure of everything—from spacetime up—is determined by the “fluctuating” structure of the underlying hypergraph (or, more accurately, by the whole multiway graph of “possible fluctuations”). And what this suggests is that there’s in a sense a much lower level version of the Feynman diagrams we use in quantum field theory and where we can discuss the “effect of particles” without ever having to say exactly what a particle “is”.

I must say that I expected we’d have to know what particles were even to talk about energy. But it turned out there was a “bulk” way to do that. And maybe similarly there’s an indirect way to talk about interactions between particles. My guess is that in our model particles are structures a bit like black holes—but we may be able to go a very long way without having to know the details.

One of the important features of our models is that quantum mechanics is “inevitable” in them. And one of the projects I’m hoping to do is to finally “really understand quantum mechanics”. In general terms, it’s connected to the way branching observers (like us) perceive branching universes. But how do we get intuition for this, and what effects can we expect? Several projects over the past years (like multiway Turing machines, multiway games, multiway aggregation, etc.) I’ve done in large part to bolster my intuition about branchial space and quantum mechanics.

I first worked on quantum computers back in 1980. And at the time, I thought that the measurement process (whose mechanism isn’t described in the standard formalism of quantum mechanics) would be a big problem for them. Years have gone by, and enthusiasm for quantum computers has skyrocketed. In our models there’s a rather clear picture that inside a quantum computer there are “many threads of history” that can in effect do computations in parallel. But for an observer like us to “know what the answer is” we have to knit those threads together. And in our models (particularly with my observer theory efforts) we start to be able to see how that might happen, and what the limitations might be.

Meanwhile, in the world at large there are all sorts of experimental quantum computers being built. But what are their limitations? I have a suspicion that there’s some as-yet-unknown fundamental physics associated with these limitations. It’s like building telescopes: you polish the mirror, and keep on making engineering tweaks. But unless you know about diffraction, you won’t understand why your resolution is limited. And I have a slight hope that even existing results on quantum computers may be enough to see limitations perhaps associated with maximum entanglement speed in our models. And the way our models work, knowing this speed, you can for example immediately deduce the discreteness scale of space.

Back in 1982, I and another physicist wrote two papers on “Properties of the Vacuum”. Part 1 was mechanical properties. Part 2 was electrodynamic. We announced a part 3, on gravitational properties. But we never wrote it. Well, finally, it looks as if our Physics Project shows us how to think about such properties. So perhaps it’s time to finally write “Part 3”, and respond to all those people who sent preprint request cards for it four decades ago.

One of the great conclusions of our Physics Project—and the concept of the ruliad—is that we have the laws of physics we do because we are observers of the kind we are. And just knowing very coarsely about us as observers seems to already imply the major laws of twentieth century physics. And to be able to say more, I think we need more characterization of us as observers. And my guess is, for example, that some feature of us that we probably consider completely obvious is what leads us to perceive space as (roughly) three dimensional. And indeed I increasingly suspect that the whole structure of our Physics Project can be derived—a bit like early derivations of special relativity—from certain axiomatic assumptions about our nature as observers, and fundamental features of computation.

There’s plenty to do on our Physics Project, and I’m looking forward to making progress with all of it. But the ideas of the Physics Project—and multicomputation in general—apply to lots of other fields too. And I have many projects planned on these.

Let’s talk first about chemistry. I never found chemistry interesting as a kid. But as we’ve added chemistry functionality in the Wolfram Language, I’ve understood more about it, and why it’s interesting. And I’ve also followed molecular computing since the 1980s. And now, largely inspired by thinking about multicomputation, I’ve become very interested in what one might call the foundations of chemistry. Actually, what I’m most interested in is what I’m calling “subchemistry”. I suppose one can think of it as having a similar kind of relation to chemistry as infrageometry has to geometry.

In ordinary chemistry, one thinks about reactions between different species of molecules. And to calculate rates of reactions, one multiplies concentrations of different species, implicitly assuming that there’s perfect randomness in which specific molecules interact. But what if one goes to a lower level, and starts talking about the interactions not of species of molecules, but individual molecules? From our Physics Project we get the idea of making causal graphs that represent the causal relations between different specific interaction events.

In a gas the assumption of molecular-level randomness will probably be pretty good. But even in a liquid it’ll be more questionable. And in more exotic materials it’ll be a completely different story. And I suspect that there are “subchemical” processes that can potentially be important, perhaps in a sense finding a new “slice of computational reducibility” within the general computational irreducibility associated with the Second Law.

But the most important potential application of subchemistry is in biology. If we look at biological tissue, a basic question might be: “What phase of matter is it?” One of the major takeaways from molecular biology in the last few decades has been that in biological systems, molecules (or at least large ones) are basically never just “bouncing around randomly”. Instead, their motion is typically carefully orchestrated.

So when we look at biological tissue—or a biological system—we’re basically seeing the result of “bulk orchestration”. But what are the laws of bulk orchestration? We don’t know. But I want to find out. I think the “mechanoidal phase” that I identified in studying the Second Law is potentially a good test case.

If we look at a microprocessor, it’s not very useful to describe it as “containing a gas of electrons”. And similarly, it’s not useful to describe a biological cell as “being liquid inside”. But just what kind of theory is needed to have a more useful description we don’t know. And my guess is that there’ll be some new level of abstraction that’s needed to think about this (perhaps a bit like the new abstraction that was needed to formulate information theory).

Biology is not big on theory. Yes, there’s natural selection. And there’s the digital nature of biomolecules. But mostly biology has ended up just accumulating vast amounts of data (using ever better instrumentation) without any overarching theory. But I suspect that in fact there’s another foundational theory to be found in biology. And if we find it, a lot of the data that’s been collected will suddenly fall into place.

There’s the “frankly molecular” level of biology. And there’s the more “functional” level. And I was surprised recently to be able to find a very minimal model that seems to capture “functional” aspects of biological evolution. It’s a surprisingly rich model, and there’s much more to explore with it, notably about how different “ideas” get propagated and developed in the process of adaptive evolution—and what kinds of tree-of-life-style branchings occur.

And then there’s the question of self replication—a core feature of biology. Just how simple a system can exhibit it in a “biologically relevant way”? I had thought that self replication was “just relevant for biology”. But in thinking about the problem of observers in the ruliad, I’ve come to realize that it’s also relevant at a foundational level there. It’s no good to just have one observer; you have to have a whole “rulial flock” of similar ones. And to get similar ones you need something like self replication.

Talking of “societies of observers” brings me to another area I want to study: economics. How does a coherent economic system emerge from all the microscopic transactions and other events in a society? I suspect it’s a story that’s in the end similar to the theories we’ve studied in physics—from the emergence of bulk properties in fluids, to the emergence of continuum spacetime, and so on. But now in economics we’re dealing not with fluid density or metric, but instead with things like price. I don’t yet know how it will work out. Maybe computational reducibility will be associated with value. Maybe computational irreducibility will be what determines robustness of value. But I suspect that there’s a way of thinking about “economic observers” in the ruliad—and figuring out what “natural laws” they’ll “inevitably observe”. And maybe some of those natural laws will be relevant in thinking about the kind of questions we humans care about in economics.

It’s rather amazing in how many different areas one seems to be able to apply the kind of approach that’s emerged from the Physics Project, the ruliad, etc. One that I’ve very recently tackled is machine learning. And in my effort to understand its foundations, I’ve ended up coming up with some very minimal models. My purpose was to understand the essence of machine learning. But—somewhat to my surprise—it looks as if these minimal models can actually be practical ways to do machine learning. Their hardware-level tradeoffs are somewhat different. But—given my interest in practical technology—I want to see if one can build out a practical machine-learning framework that’s based on these (fundamentally discrete) models.

And while I’m not currently planning to investigate this myself, I suspect that the approach I’ve used to study machine learning can also be applied to neuroscience, and perhaps to linguistics. And, yes, there’ll probably be a lot of computational irreducibility in evidence. And once again one has to hope that the pockets of computational reducibility that exist will give rise to “natural laws” that are useful for what we care about in these fields.

In addition to these “big” projects, I’m also hoping to do a variety of “smaller” projects. Many I started decades ago, and in fact mentioned in A New Kind of Science. But now I feel I have the tools, intuition and intellectual momentum to finally finish them. Nestedly recursive functions. Deterministic random tilings. Undecidability in the three-body problem. “Meta-engineering” in the Game of Life. These might on their own seem esoteric. But my repeated experience—particularly in the past five years—is that by solving problems like these one builds examples and intuition that have surprisingly broad application.

And then there are history projects. Just what did happen to theories of discrete space in the early twentieth century (and how close did people like Einstein get to the ideas of our Physics Project)? What was “ancient history” of neural nets, and why did people come to assume they should be based on continuous real numbers? I fully expect that as I investigate these things, I’ll encounter all sorts of “if only” situations—where for example some unpublished note languishing in an archive (or attic) would have changed the course of science if it had seen the light of day long ago. And when I find something like this, it’s yet more motivation to actually finish those projects of mine that have been languishing so long in the filesystem of my computer.

There’s a lot I want to do “down in the computational trenches”, in physics, chemistry, biology, economics, etc. But there are also things at a more abstract level in the ruliad. There’s more to study about metamathematics, and about how mathematics that we humans care about can emerge from the ruliad. And there are also foundational questions in computer science. P vs. NP, for example, can be formulated as an essentially geometric problem in the ruliad—and conceivably there are mathematical methods (say from higher category theory) that might give insight into it.

Then there are questions about hyperruliads and hyporuliads. In a hyperruliad that’s based on hypercomputation, there will be hyperobservers. But is there a kind of “rulial relativity” that makes their perception of things just the same as “ordinary observers” in the ordinary ruliad? A way to get some insight into this may be to study hyporuliads—versions of the ruliad in which there are only limited levels of computation possible. A bit like the way a spacelike singularity associated with a black hole supports only limited time histories, or a decidable axiomatic theory supports only proofs of limited length, there will be limitations in the hyporuliad. And by studying them, there’s a possibility that we’ll be able to see more about issues like what kinds of mathematical axioms can be compatible with observers like us.

It’s worth commenting that our Physics Project—and the ruliad—have all sorts of connections and resonances with long-studied ideas in philosophy. “Didn’t Kant talk about that? Isn’t that similar to Leibniz?”, etc. I’ve wanted to try to understand these historical connections. But while I’ve done a lot of work on the historical development of ideas, the ideas in question have tended to be more focused, and more tied to concrete formalism than they usually are in philosophy. “Did Kant actually mean that, or something completely different?” You might have to understand all his works to know. And that’s more than I think I can do.

I invented the concept of the ruliad as a matter of science. But it’s now clear that the ruliad has all sorts of connections and resonances not only with philosophy but also with theology. Indeed, in a great many belief systems there’s always been the idea that somehow in the end “everything is one”. In cases where this gets slightly more formalized, there’s often some kind of combinatorial enumeration involved (think: I Ching, or various versions of “counting the names of God”).

There are all sorts of examples where long-surviving “ancient beliefs” end up having something to them, even if the specific methods of post-1600s science don’t have much to say about them. One example is the notion of a soul, which we might now see as an ancient premonition of the modern notion of abstract computation. And whenever there’s a belief that’s ancient, there’s likely to have been lots of thinking done around it over the millennia. So if we can, for example, see a connection to the ruliad, we can expect to leverage that thinking. And perhaps also be able to provide new input that can refine the belief system in interesting and valuable ways.

I’m always interested in different viewpoints about things—whether from science, philosophy, theology, wherever. And an extreme version of this is to think about how other “alien” minds might view things. Nowadays I think of different minds as effectively being at different places in the ruliad. Humans with similar backgrounds have minds that are close in rulial space. Cats and dogs have minds that are further away. And the weather (with its “mind of its own”) is still further.

Now that we have AIs we potentially have a way to study the correspondence—and communication—between “different minds”. I looked at one aspect of this in my “cats” piece. But my recent work on the foundations of machine learning suggests a broader approach, that can also potentially tell us things about the fundamental character of language, and about how it serves as a medium that can “transport thoughts” from one mind to another.

Many non-human animals seem to have at least some form of language—though mostly in effect just a few standalone words. But pretty unquestionably the greatest single invention of our species is language—and particularly compositional language where words and phrases can fit together in an infinite number of ways. But is there something beyond compositional language? And, for example, where might we get if our brains were bigger?

With the 100 billion neurons in our brains, we seem to be able to handle about 50,000 words. If we had a trillion neurons we’d probably be able to handle more words (though perhaps more slowly), in effect letting us describe more things more easily. But what about something fundamentally beyond compositional language? Something perhaps “higher order”?

With a word we are in effect conflating all instances of a certain concept into a single object that we can then work with. But typically with ordinary words we’re dealing with what we might call “static concepts”. So what about “ways of thinking”, or paradigms? They’re more like active, functional concepts. And it’s a bit like dogs versus us: dogs deal with a few standalone words; we “package” those together into whole sentences and beyond. And at the next level, we could imagine in effect packaging things like generators of meaningful sentences.

Interestingly enough, we have something of a preview of ideas like this—in computational language. And this is one of those places where my efforts in science—and philosophy—start to directly intersect with my efforts in technology.

The foundation of the Wolfram Language is the idea of representing everything in computational terms, and in particular in symbolic computational terms. And one feature of such a representation is that it can encompass both “data” and “code”—i.e. both things one might think about, and ways one might think about them.

I first started building Wolfram Language as a practical tool—though one very much informed by my foundational ideas. And now, four decades later, the Wolfram Language has emerged as the largest single project of my life, and something that, yes, I expect to always put immense effort into. It wasn’t long ago that we finally finished my 1991 to-do list for Wolfram Language—and we have many projects running now that will take years to complete. But the mission has always remained the same: to take the concept of computation and apply it as broadly as possible, through the medium of computational language.

Now, however, I have some additional context for that—viewing computational language as a bridge from what we humans think about to what’s possible in the computational universe. And this helps in framing some of the ways to expand the foundations of our computational language, for example to multicomputation, or to hypergraph-based representations. It also helps in understanding the character of current AI, and how it needs to interact with computational language.

In the Wolfram Language we’ve been steadily trying to create a representation for everything. And when it comes to definitive, objective things we’ve gotten a long way. But there’s more than that in everyday discourse. For example, I might say “I’m going to drink a glass of orange juice.” Well, we do just fine at representing “a glass of orange juice” in the Wolfram Language, and we can compute lots of things—like nutrition content—about it. But what about “I’m going to drink…”? For that we need something different.

And, actually, I’ve been thinking for a shockingly long time about what one might need. I first considered the question in the early 1980s, in connection with “extending SMP to AI”. I learned about the attempts to make “philosophical languages” in the 1600s, and about some of the thinking around modern conlangs (constructed languages). Something that always held me back, though, was use cases. Yes, I could see how one could use things like this for tasks like customer service. But I wasn’t too excited about that.

But finally there was blockchain, and with it, smart contracts. And around 2015 I started thinking about how one might represent contracts in general not in legalese but in some precise computational way. And the result was that I began to crispen my ideas about what I called “symbolic discourse language”. I thought about how this might relate to questions like a “constitution for AIs” and so on. But I never quite got around to actually starting to design the specifics of the symbolic discourse language.

But then along came LLMs, together with my theory that their success had to do with a “semantic grammar” of language. And finally now we’ve launched a serious project to build a symbolic discourse language. And, yes, it’s a difficult language design problem, deeply entangled with a whole range of foundational issues in philosophy. But as, by now at least, the world’s most experienced language designer (for better or worse), I feel a responsibility to try to do it.

In addition to language design, there’s also the question of making all the various “symbolic calculi” that describe in appropriately coarse terms the operation of the world. Calculi of motion. Calculi of life (eating, dying, etc.). Calculi of human desires. Etc. As well as calculi that are directly supported by the computation and knowledge in the Wolfram Language.

And just as LLMs can provide a kind of conversational linguistic interface to the Wolfram Language, one can expect them also to do this to our symbolic discourse language. So the pattern will be similar to what it is for Wolfram Language: the symbolic discourse language will provide a formal and (at least within its purview) correct underpinning for the LLM. It may lose the poetry of language that the LLM handles. But from the outset it’ll get its reasoning straight.

The symbolic discourse language is a broad project. But in some sense breadth is what I have specialized in. Because that’s what’s needed to build out the Wolfram Language, and that’s what’s needed in my efforts to pull together the foundations of so many fields.

And in maintaining a broad range of interests there are some where I imagine that someday there’ll be a project I can do, but there may for example be many years of “ambient technology” that are needed before that project will be feasible. Usually, though, I have some “conceptual idea” of what the project might be. For example, I’ve followed robotics, imagining that one day there’ll be a way to do “general-purpose robotics”, perhaps constructing everything out of modular elements. I’ve followed biomedicine, partly out of personal self interest, and partly because I think it’ll relate to some of the foundational questions I’m asking in biology.

But in addition to all the projects where the goal is basic research, or technology development, I’m also hoping to pursue my interests in education. Much of what I hope to do relates to content, but some of it relates to access and motivation. I don’t have perfect evidence, but I strongly believe there’s a lot of young talent out there in the world that never manages to connect for example with things like the educational programs we put on. We–and I—have tried quite hard over the years to “bridge the gap”. But with the world as it is, it’s proved remarkably difficult. But it’s still a problem I’d like to solve, and I’ll keep picking away at it, hoping to change for the better some kids’ “trajectories”.

But about content I believe my path is clearer. With the modern Wolfram Language I think we’ve gone a long way towards being able to take computational thinking about almost anything, and being able to represent it in a formalized way, and compute from it. But how do people manage to do the computational thinking in the first place? Well, like mathematical thinking and other formalized kinds of thinking, they have to learn how to do it.

For years people have been telling me I should “write the book” to teach this. And finally in January of this year I started. I’m not sure how long it will take, but I’ll soon be starting to post sections I’ve written so far.

My goal is to create a general book—and course—that’s an introduction to computational thinking at a level suitable for typical first-year college students. Lots of college students these days say they want to study “computer science”. But really it’s computational X for some field X that they’re ultimately interested in. And neither the theoretical nor the engineering aspects of typical “computer science” are what’s most relevant to them. What they need to know is computational thinking as it might be applied to computational X—not “CS” but what one might call “CX”.

So what will CX101 be like? In some ways more like a philosophy course than a CS one. Because in the end it’s about generally learning to think, albeit in the new paradigm of computation. And the point is that once someone has a clear computational conceptualization of something, then it’s our job in the Wolfram Language to make sure that it’s easy for them to concretely implement it.

But how does one teach computational conceptualization? What I’ve concluded is that one needs to anchor it in actual things in the world. Geography. Video. Genomics. Yes, there are principles to explain. But they need practical context to make them useful, or even understandable. And what I’m finding is that framing everything computationally makes things incredibly much easier to explain than before. (A test example coming soon is whether I can easily explain math ideas like algebra and calculus this way.)

OK, so that’s a lot of projects. But I’m excited about all of them, and can’t wait to make them happen. At an age when many of my contemporaries are retiring, I feel like I’m just getting started. And somehow the way my projects keep on connecting back to things I did decades ago makes me feel—in a computational irreducibility kind of way—that there’s something necessary about all the steps I’ve taken. I feel like the things I’ve done have let me climb some hills. But now there are many more hills that have come into view. And I look forward to being able to climb those too. For myself and for the world.