Stephen Wolfram tackles the big questions—from God and free will to whether AI will destroy us all.

The main tool Wolfram built is a programming language called Wolfram Language, designed to have a notation for thinking about the world computationally, similar to how mathematical notation streamlined talking about mathematical things 500 years ago.

“the main tool I built is from language and the main idea there is to have a way to kind of have a notation for thinking about the world computationally. Just like, you know, mathematical notation from 500 years ago kind of made it sort of streamlined to talk about mathematical kinds of things, our goal is to sort of have it be streamlined to talk about computational kinds of things.”

The foundational question of why machine learning works—why optimizing a simple loss function leads to intelligent behavior—has not been studied nearly enough and deserves much deeper investigation.

“there's I have to say I think this these foundational questions about why machine learning works are really interesting deserve to be studied a bunch more and I don't think have been studied nearly nearly enough.”

In certain fields (unnamed), some practitioners express pride in being opaque to outsiders, framing complexity and inaccessibility as markers of sophistication; this is intellectual hubris.

“I find that in certain fields, not mentioning any maths, um where there is from certain practitioners a certain pride in being opaque to appeal to their community and I find that to be a sort of hubris that is actually not useful.”

Primes are an example of a reducible pocket within the computationally irreducible system of integers. There's no efficient way to generate primes, but you can say meaningful things about them.

“You mean so we we the the primes there's no like efficient way to get the primes, but we might be able to say something about the primes. And that's an irreducible pocket, right? That's a reducible pocket.”

The view that mathematics is purely formal (mechanical derivation from axioms) came about in the late 19th century with Hilbert, but Gödel's incompleteness theorems undermined this view, and the fact that working mathematicians ignore Gödel shows mathematics isn't actually practiced at the axiomatic level.

“the view that came about you know end of the 19th century right was math is this formal thing that is derivable mechanically Hilbert had this idea we just write down the axioms of mathematics and we grind out with this machine we work out all the true theorems of mathematics. Girdle's theorem kind of blew that up. But the the fact is the fact that Girdle's theorem blew that up and the fact that most working mathematicians don't care about Girdle's theorem tells one something.”

The heat death of the universe is only true for computationally bounded observers like us; a sufficiently sophisticated future observer could recognize that molecules in the far future are the result of computations from our present conversation, making apparent randomness actually traceable order.

“it looks like you know things will randomize and and but but yet that future of all the molecules that are us today that will be some you know will be something different in the future. If we were more sophisticated observers of that future we would know oh those molecules you know uh a trillion years in the future are the result of this conversation that happened in 2025 or whatever else.”

Within computationally irreducible systems, there must inevitably be infinite pockets of computational reducibility—regions where one can make predictive or explanatory statements—which is why science and mathematics never run out of problems to solve.

“whenever you have one of these computationally irreducible processes...it's actually inevitable that there have to be pockets of computational reducibility places where you can actually say something. In fact, there have to be an infinite number of these...And the the fact that there are an infinite number of reducible pockets is why we'll never run out of inventions.”

The strategy of which questions to ask is the most important factor in scientific discovery, more important than the mechanics of how to do discovery. At universities, lack of strategic direction leads to researchers spending decades redoing their thesis work.

“in terms of discovery, for me the absolutely dominant effect in how much discovery happens is strategy. what is it you're trying to discover? What are the questions you're asking much more than the mechanics of how to do it... the fact is people you know spend decades you know they kind of redoing what they did in their thesis but it doesn't really work out very well”

A black-box AI answer based on training data is not science in the traditional sense. Science is about understanding a narrative about how the world works. A black-box answer is technologically useful but is not science.

“we use the scientific model where we can see how the inodes of the model work and we can answer the question branch number two we use a blackbox AI and we just sort of say based on your training data what's going to happen you know that second thing can be technologically very useful it is not going to give us you know science in the same sense that we've thought about science in the past to to have a a this is what's going to happen blackbox answer is not what we have traditionally thought of as science. It's something that can be useful in technology, but science tends to be the thing where we are understanding a narrative about some aspect of how the world works.”

Consciousness involves a belief in a single thread of experience and persistent identity, which is not obvious—atoms are replaced and different parts of the brain might be doing different things, yet we experience continuity.

“a lot of the importance you know a lot of I think our notion of consciousness is a lot related to the fact that we believe in the single thread of experience that we have. It's not obvious that we should have a persistent thread of experience. You know in our models of physics we're made of different atoms of space at every successive moment of time. So the fact that we have this belief that we are somehow persistent, we have this thread of experience that extends through time is is not obvious.”

The term 'artificial general intelligence' (AGI) is a meaningless concept because it's defined as something intelligent like a human, and the definition keeps changing. As AI advances, each new capability is dismissed as 'just engineering' rather than true intelligence.

“I think it's sort of a meaningless thing because you say, well, what does it really mean? Well, it means something that's intelligent like a human. And you say, well, you know, over the course of the time that I've been doing things in computation and sort of AI like areas, there have been lots of times where people have said, when the AIs can do XYZ, like do symbolic integrals, let's say, then we'll know they're intelligent. Pretty soon they can do symbolic integrals and everybody says it's just engineering, which it is.”

Science has become too big and too institutionalized, which makes it difficult for innovative things to happen. The solution involves creating 'puffs of newness' from new methodologies.

“What's wrong with science today? It's too big. There's too many people doing it which causes it to be too institutionalized and too make it too difficult for for innovative things to really happen.”

Wolfram has been working on understanding life as bulk orchestration—the idea that living systems are organized collections of molecules engaged in active orchestration, in contrast to statistical physics models where molecules bounce randomly.

“So really what we are is some kind of bulk orchestrated collection of molecules. Can we have a theory of bulk orchestration? That's the question”

Wolfram had a breakthrough a few weeks ago (relative to the interview date) on the theory of bulk orchestration after working on it for years, using the insight from machine learning that if you 'bash a neural net hard enough, it will learn,' which surprised everyone around 2011 or so.

“I've been thinking about this for a few years I finally made a little bit of a breakthrough a few weeks ago”

LLMs performing well has put a nail in the coffin of the idea that consciousness requires something magical beyond physics. Tasks that seemed to require consciousness are performed by simple artificial neural nets.

“the idea that there's sort of something magic that goes beyond physics that leads to sort of conscious behavior I kind of think that LLM's kind of put the final nail in that in that coffin because I kind of think that you know the there were all these things where it's like oh it could maybe it can't do this but actually it does and it's just an artificial neural net.”

A questioner (Juven Wong, research scientist at London Institute) asks what single message about scientific knowledge Wolfram would preserve if civilization had to rebuild from zero, invoking Feynman's answer about the atomic hypothesis.

“if if there's any single message that we want to preserve as a scientific knowledge for the next future generation if the all the civilization are destroyed and we need to rebuild from ground zero. So what will be the message that you would like to convey and just recall fman gave the answer say that uh it's more like atomic hypothesis that all things are made by atoms.”

If civilization had to rebuild from zero, the most valuable message to preserve is that universal computation is possible—computation at the level of full Turing completeness—which Leibniz would have understood and built upon, had he had the idea.

“I would say if there was one thing that it's like this is an idea that's possible that would be a thing worth communicating so to speak because then you can build a lot from that...if you'd gone back and told linenets universal computation is possible he would have understood tood that I think and he would have built a whole bunch on that basis.”

Human mathematics is more of an artistic endeavor than a mechanistic process. What you choose to do and at what level is a human choice, not something forced by the structure of the mathematical universe.

“I think the human ma mathematics is more of an artistic endeavor”

Von Neumann's formulation of quantum mechanics (with measurement as an instantaneous operator) has led people in quantum computing down a problematic path. Measurement is actually a process, not an instantaneous event, and quantum computers actually involve threads of computation that must be 'knitted together' to get the answer.

“his formulation of quantum mechanics I think is is uh you know that has led people down very much down the wrong path in for example quantum computing because people you know in the Bonoya formulation of quantum mechanics it's like and then you do a measurement boom it just happens there's that isn't really how things work in the physical world measurement is actually a process and you know the fact that when you imagine in a quantum computer there are all these threads of computation that happen but to know what the answer is you have to knit those threads of computation together but vonoman told us it's just a measurement operator so nobody's taken you know people have not tended to take that apart”

Wolfram tries to write things so that anyone willing to put effort in could understand them, but this doesn't always work; readability depends on reader background, field paradigms, and what counts as 'clear.'

“I try really hard to write things that I think anybody who puts enough effort in could understand obviously, but a lot of people find it impossibly technical, right?”

In cellular automaton evolution experiments, when Wolfram applied a simple fitness function (patterns that live as long as possible but not infinitely), the system discovered elaborate forms that build on prior discoveries layer by layer, resembling the fossil record—showing how computation can generate complexity adapted to fitness functions.

“what you find out is it discovers these very elaborate forms. It'll make some discovery about, you know, oh, if you have this runner that goes this way and then that way, then you can live a bit longer and then it will build on that discovery. You know, roll the dice for the mutations of the genome again, it'll make a different discovery and it'll build on things in a different way. And it's rather wonderfully like the fossil record.”

The ruliad is the entangled limit of all possible computations, which is abstractly defined and contains everything that can be. Observers like us inevitably perceive the ruliad in the ways that we see physics to be.

“So what I realized is this is this idea of the rulad, the the entangled limit of all possible computations. And it turns out that it seems that sort of the rouad which is sort of all possible computation this abstractly defined thing is in some sense sort of everything that can be and observers like us inevitably perceive the rouad in the ways that we see physics to be.”

The laws of physics come from the interplay between computational irreducibility underneath and the computational weakness of observers like us. Both general relativity and quantum mechanics are consequences of this interaction.

“It turns out this interplay between computational irreducibility underneath and the computational weakness of observers like us. It turns out one of the big exciting things that I think I figured out in the last few years is that's where the laws of physics come from. That's that's both general relativity and quantum mechanics and the second order of thermodynamics are all consequences of that interplay.”

The 'rule ensemble' is the set of all rules that could be successfully evolved to satisfy any computationally simple fitness function. By knowing just one thing—that they are computationally simple—you can say something about what underlying rules would be the successes.

“the notion in in traditional statistical mechanics these ideas of ensembles the set of all possible configurations of a system and you say well you know the behavior we see is typical of all possible configurations of a system. So I have this thing I'm calling the rule ensemble which is the the set of rules which are consistent with having been evolved for a computationally simple purpose. And so the claim is that biology is kind of you can think of a theory of biology not by knowing all the details of what all the particular mechanisms of the splicesome or whatever else are but just by knowing this one fact that they were evolved for a computationally simple purpose.”

Whenever an entity has a monopoly on how basic science gets used, it has a reason to support that science. Bell Labs supported innovation because the US government and Bell would benefit. In Wolfram's areas of mathematical computation, they invest in basic research because they control the distribution channel.

“I've noticed that whenever some entity has a monopoly on on how basic science gets used then it justifies supporting it so for example you know Bell Labs in its day you know lots of kinds of innovations Bell Labs is going to the main you know main beneficiary the US government as the economy... in our small corner of the world in various kinds of mathematical computation we do basic research because we pretty much know we have the distribution channel for making use of that it makes it's rational thing to to invest in pure basic research”

Scientific discovery happens largely through universities, and one opportunity for acceleration is to study how athletes improved over 75 years from amateur to professional standards, and apply similar methodologies to scientific discovery.

“if you look at you know athletes over the last 75 years basically gone from amateur to professional I sort of pushing the boundaries of human achievement you have uh seen multiple or I I feel you've investigated multiple ways of thinking about how to do discovery”

The ruliad makes the existence of the universe necessary—it is not contingent. However, the existence of observers like us within the universe is less necessary.

“This whole idea of the rulad gives you makes the existence of the universe something necessary. What it doesn't make necessary is our existence. And that's actually quite related to all these questions about biology.”

Scientific fields follow a pattern: a methodological advance is followed by 5-20 years of rapidly picking low-hanging fruit and rapid growth, then a century-long period of slow growth, institutionalization, and institutional resistance to new ideas.

“when you get a field of science, there's typically, you know, some methodological advance, then there's five or 10 years, maybe 20, where there's low hanging fruit to be picked. Lots of, you know, lots of things get discovered. there's a very rapid growth period and then things slow down and for a hundred years you know it's it's sort of slow growth the thing is very institutionalized there's sort of a force against new ideas”

The laws of physics are shaped by the way that humans perceive the world, given our observation bandwidth and brain processing speeds. If our brains processed a million times faster, we would not perceive space as having definite states at successive moments of time.

“a very basic example the idea of space which seems pretty obvious to us but you know I look around this room you know I can see maybe 10 meters away light comes to me in you know fraction of a microscond from 10 meters away it takes my brain many milliseconds to process that signal so for me as I look around the room it's like it's it's very reasonable to think of the room as having a certain state across all of space at successive moments of time. If my brain thought a million times faster than it does, that picture wouldn't make a lot of sense.”

Wolfram hopes one day to write a proper history of discrete space theories because while extensive letters and private notes exist, there are few published papers (since the work was abandoned), making the historical record incomplete.

“I'm hoping one day to write a history of this. It's it's a little bit hard to dig out because these things are there are letters but there aren't published papers because they just didn't make progress”

The platonic view of mathematics (mathematics as discovered) and the conventionalist view (mathematics as created) can be reconciled: the ruliad containing all possible mathematicses is a platonic object, but how we parse and express that object is human and creative.

“the ruliad as this entangled limit of all possible computations is something that is both our physical universe and mathematics... So whether we perceive it as physics or as mathematics depends on how we are observing it. There is a single object that is sort of one slice of it is physics and another slice of it is mathematics. And I think in so far as we believe that the physical universe exists, we have to believe that there's some in some sense the mathematical universe also exists. So it's kind of a a definitively platonic thing to say. On the other hand, the way that we choose to parse that rouad that all possible mathematicses is something that is very human and very kind of we can construct it in a variety of different ways.”

In so far as the physical universe is believed to exist, the mathematical universe must also exist by the same logic, making mathematics Platonically real and not constructed.

“in so far as we believe that the physical universe exists, we have to believe that there's some in some sense the mathematical universe also exists. So it's kind of a a definitively platonic thing to say.”

Computational irreducibility is a fundamental phenomenon where simple rules produce complex behavior, and the only way to know what a computationally irreducible system will do is to run it and see what happens—you cannot jump ahead with a formula.

“you might think if you have the rules for something then you're done. You you know everything about how the system will behave. In some sense you do because you can just run the rules and see what happens. But the question is you know you might have to run the rules for a billion steps. The question is can you jump ahead and say I know what's going to happen. I've just got a formula for the answer. Right? The claim is that in general you can't do that with computational systems. In general they are computationally irreducible. The only way you can know what's going to happen is to run them and see what happens.”

Science is a bridge between what actually happens in the natural world and the narrative that fits in the human mind. We extract from the natural world the small thread of narrative that we can understand with our minds.

“what is science? I view it as being this kind of bridge between what actually happens in the world and the narrative that we can understand with our minds. So science is this way of of extracting from the natural world just that small thread of narrative that actually fits in the human mind.”

In so far as mathematics captures pieces of reducibility, the mathematics we do captures the parts of the world that we are capable of understanding, not the whole of what happens in the world.

“mathematics captures a certain you know piece of reducibility the mathematics that we do captures a certain sort of piece of reducibility that's something we can use to understand slices of what happens in the world. It's not the whole of what happens in the world. It's the part of what happens in the world that we're capable of understanding”

The term 'artificial intelligence' is a poor name for the field because it labels a long-term ambition rather than describing what the field actually does; fields are not named after aspirations (e.g., 'economics' is not called 'universal prosperity').

“artificial intelligence, it's a ridiculous name for a field. It's because it's a it's a long-term ambition. You don't name fields after long-term ambition. It'd be like calling economics universal prosperity and and and you know, universal health.”

The origin of consciousness likely comes from a simple need in animal evolution: when animals first needed to move around, they needed to make single definitive decisions about direction (left or right), which required concentrating sensory input into a single decision. This bottleneck created the unified consciousness experience.

“when animals first existed in sort of the history of life on Earth, that's when we started needing brains. If you're a thing that doesn't have to move around, the different parts of you can be doing different kinds of things. If you're an animal, then one thing you have to do is decide, are you going to go left or are you going to go right there sort of, you know, there's there's a there's a single decision you have to make. And I I kind of think it's a little disappointing to feel that this whole wanted thing that ends up being what we think of as consciousness might have originated in just that very simple need to decide if you are an animal that can move.”

AI is obviously in the midst of a bubble. However, bubbles often enable valuable developments—like during the dot-com bubble, the infrastructure built became valuable even though the original investments were not.

“The answer is obviously yes. Okay. I mean it, you know, it's uh uh AI is certainly a useful thing... it's often opens up possibilities to backfill with things that are then quite valuable you know even if the thing itself that was originally invested in wasn't you know was just the the the flag that caused people to come there and put lots of money in”

In cellular automata evolution, if every organism when born had to be able to do calculus, none would survive because it's too fine-grained a requirement. But because all organisms have to do is survive and reproduce—a coarse objective—the underlying computational irreducibility is sufficiently powerful to achieve it.

“let's say that every organism when born had to be able to do calculus... you wouldn't get any organisms to survive because it's too difficult a thing. it's too fine grained a thing. But because all it has to do is, you know, hang out and make more organisms and so on, that's a coarse enough thing that it's possible that the the underlying computational irreducibility of the development of organisms is sufficiently powerful that that kind of weak objective is is is achievable.”

The proof of the Boolean algebra axiom discovered by automated theorem proving is about 120 lemmas long and incomprehensible—Wolfram tried with AI tools to understand it and failed, as have others. The steps are easy to verify but there is no conceptual understanding of why it works.

“The proof is about 120 lmas long and it's incomprehensible. Right... I mean, I tried, you know, I made quite a serious effort with sort of the finest AI tools and maybe a little bit of cleverness to decode what on earth is going on in this proof. And it's just like it's it's just, you know, you can you can verify the steps. It's easy to verify the steps, but it's incomprehensible what this is.”

Machine learning works because complex computational substrates (neural networks) allow simple objective functions (minimize loss) to find effective solutions; the success of ML depends on the fact that objectives are computationally weak compared to the system capacity.

“if you think about what is machine learning really doing and you know the way I see it is let's say your objective is to build a wall well you could build a wall by making bricks that are very precise precise. You arrange the bricks in a very engineering kind of way. Or you could say, I'm going to find these rocks that are lying around on the ground and they're all these weird different shapes and I can more or less fit them together to build this wall. I think that second thing is what machine learning is doing.”

Progress on the foundations of established fields has high leverage because nobody has looked at foundations for a long time and current methods are very different from past methods, so new progress is possible.

“the fact is if you can make progress on the foundations of a field is incredibly high leverage. I mean that's the um and often you can make progress not least because nobody looked at it for so long and the methods that exist now are really different from the methods that existed before.”

A journalist (Hannah Develin, Guardian) asks about science becoming AI-mediated and whether humans will be disempowered in science if results are increasingly produced by and for AIs rather than humans.

“I'm interested in what you think of the idea that the world is kind of maybe going to be increasingly things being done by AIS for AIs rather than for humans and whether you think that that's a problem in science...are we going to be less able to kind of contribute to science as humans.”

Wolfram has been live-streaming a Q&A a couple times weekly since the pandemic began, initially for kids during school closures; he continues because he finds it both fun and educational, and questions he thought he understood since age 12 often trip him up.

“I've had this weird hobby that I started at the beginning of the pandemic of doing a live stream Q&A a couple of times a week typically. I started it as a science and technology Q&A for kids...I found it sufficiently fun and sufficiently educational for me that I've kept on doing it. Um, I do find that the the one thing that happens is whenever there's a question, which I think I known the answer to that question since I was 12 years old, those are the ones that always trip me up.”

A Ukrainian mathematician in his youth won competitions using intuition—predicting answers then working backward to understand them—and asks whether this mirrors Wolfram's approach and how intuition works in scientific thinking.

“back days a lot of uh my success in the competition was triggered by the what I can describe as intuition So most of time I predict something and I then took like another hour to explain to myself why then.”

Wolfram's principle: 'Computational animals are always smarter than we are'—experiments repeatedly yield unexpected results, violating predictions, which is not a past experience but a current and ongoing phenomenon.

“One of the things that I've learned I say to people who work with me, I my my line is usually the computational animals are always smarter than we are. So, you know, we think we know what's going to happen and we do the experiment and it never quite works the way we expect and that, you know, that's happened to me within the last week.”

Language design is a form of exposition that forces you to understand with great clarity how things work, and Wolfram steadily understands more about how different things fit together, making language design the primary intellectual challenge of his work.

“language design is like this way of forcing you it's like a form of exposition. It's a it forces you to understand with great clarity how things work and I'm steadily understanding more and more about kind of how different things get put together”

Human direction and strategic choice of what to do remain the binding constraint on achievement; automation removes friction but cannot choose direction, which remains a human responsibility and privilege.

“the definition of which direction you go is something that you know we humans uh you know it's our choice what what to do...there's sort of an infinite set of possibilities it's you know you have to you have to pick some of those possibilities and that's something for the time being that we get to do.”

Just as humans have coexisted with natural systems of vast computational complexity (weather, ecosystems) that we do not understand, we must learn to coexist with AI systems that are computationally opaque to us.

“we're very familiar with that because the natural world is another example of something where you can think of it as doing lots of computation. The weather or lots of other kinds of things are in effect doing lots of computation that we don't understand but we have found ways to coexist with that.”

A fiction writer (David Ambrose) asks whether Wolfram believes in the hard problem of consciousness, given that he hasn't mentioned consciousness or mind and seems to reduce them to computation.

“Does this mean you you actually don't believe there is such a thing as the hard question of consciousness? Um I mean as you know um um Penrose has long argued that it is not simply a matter of computation.”

Humans should try to see many things and build intuition; Dick Feynman was a good calculator but incomprehensible to Wolfram, while Wolfram's computational approach is incomprehensible to Feynman; the best approach combines both.

“the best way to get intuition is to just see a lot of things...Dick Feman...was um you know a really good calculator really good human calculator...I found that absolutely incomprehensible...he would say I don't understand how you could possibly know whether this is right um...it's it's what what um...you need intuition as a And the the best way to get intuition is to just see a lot of things.”

Whether an entity has free will operationally is whether you can look from outside and predict what it will do more efficiently than just watching it. From a computationally arbitrarily sophisticated observer's perspective, the answer is yes (you could predict everything), but for us it's no.

“Free will in some sense operationally is you can't predict what the thing is going to do. It is its will is not obviously determined by this these underlying rules. And that's the story of computational irreducibilities, I think.”

Niels Bohr also had a discrete theory of space, and Chandrasekhar carried around a card that Bohr had written at a dinner containing commutation relations for the quantization of space, which Chandrasekhar said he kept as a reminder that even the most brilliant scientists could be completely wrong, like thinking space was discrete.

“that's another one was bore also I learned recently also had a discrete theory of of space and actually here's a funny story. So Chandra Seckar apparently had in his um this is a a multi-level story that that um but Chandra Seckar carried around with him a little card that Bore had written for him at some dinner or something that contained essentially commutation relations for the structure of space. So a quantization of space and the person who told me this said that Chandra Sakar had told him that he carried this card around as a reminder that even the most brilliant scientists could do things that were completely wrong like think that space was discreet so to speak.”

Most theorems in mathematics are perfectly valid but humans don't care about them. The question of which theorems humans care about is something current LLMs have not managed to solve, though in principle this is where LLMs could be useful—to identify which abstract theorems might matter to humans.

“when you start just sort of you know enumerating possible theorems most of the theorems you enumerate are ones which are perfectly valid theorems they're just ones where a typical human will just shrug their shoulder you know it's like why do we care you know what what matters is which of those theorems are ones that humans care about and that's a thing which I think the the current generation of LLMs and so on I haven't managed to make this work but In principle, one can imagine that that's a place where that can be useful”

Mathematics is not like axiom-grinding but like fluid dynamics—you can operate at a high level without analyzing every individual molecule. Just as high-level fluid mechanics is possible, high-level mathematics is possible without dropping down to axioms.

“In other words, this level of mathematics of just at the level of the axioms grinding one step in front of the next is not what mathematicians typically do. There's an analogy actually with something we just talked about which is thermodynamics... in order to know how a gas is going to behave we have to go look at how every molecule behaves that is one possibility but the fact is we know we don't have to do that we know we can do fluid mechanics at the level of just talking about you know velocity fields and things like this not what does every individual molecule do the question is what what is mathematics really doing is mathematics something that is operating at this aimatic level or is mathemat mathematics as humans do it something that is operating at this more fluid dynamics type level”

Physics is shaped by physical intuition and what we can perceive. Newton was lucky to study rigid body mechanics rather than fluid mechanics; if he had studied turbulent fluids, he would not have been able to derive simple laws because turbulence is too complex.

“Newton was really lucky that he studied rigid body mechanics that he studied you know we have that he wasn't doing for example fluid mechanics if instead of trying to make laws of mechanics with you know solid objects moving around he tried to make laws of fluid mechanics that have included fluid turbulence and things like that he would not have come up with any simple kind of reducible statements about how the world works”

We use mathematics to build technology because technology operates within the reducible slices of the world. Before the Industrial Revolution, people didn't expect to understand technology (you used a donkey without understanding how it works). We are now returning to that situation with modern AI.

“a fun fact that you know post-industrial revolution people expected to understand technology they expected they could see the cogs see how it worked and so on before that time you got a donkey the donkey did what you wanted it to do you didn't really ask how the donkey worked side. We're now back to more of that situation, so to speak”

It is shocking that computationally reproducible journals do not exist yet. The journal model predates Faraday's time, but late 1600s journals were more like blog posts and read more like what Wolfram writes than modern academic journals.

“the fact that there still aren't sort of forced computationally reproducible journals is kind of shocking to me. I mean it's it's you know the the model of journals predates long predates you know Faraday's time and so on. It's a late 1600 except the late 1600s journals were much more like blog posts and if you read those things they read a lot more like the kind of stuff I write than what you find in typical academic journals.”

You must have some prejudice about how things are going to work to explore anything in science, but you must also be careful not to become so invested in that prejudice that you fail to notice when results fall elsewhere.

“you have to realize in doing science you have to have some prejudice about how things are going to come turn out otherwise you never even explore that thing but the trick is to not be so invested in that prejudice that you don't realize the chips are falling somewhere else and they weren't you know agreeing with that prejudice”

Philosophical language would formalize another level of what happens in the world (everyday discourse) beyond what has been formalized through science, capturing something from human culture rather than nature.

“it's sort of interesting because it is another it's a way of formalizing another level of of of what happens in the world and you know we've been able to formalize a lot of things that have come out of things like science. This is a way of formalizing something that comes out of kind of everyday discourse.”

An infinite meta-mathematical space exists with infinite directions you can go in. Mathematicians populate certain parts of this space just as humans invent certain words because those are useful for the things we think about, while millions of other possible words/concepts exist that we don't use.

“there is a infinite meta mathematical space is is very infinite and there are many different directions you can go in mathematical space many different kinds of theorems you could prove many many fields of mathematics you could invent the question of which ones you choose to invent is a very human thing right it's like asking for human language we have 50,000 words in typical languages We've invented certain words because we find those useful for the kinds of things that we tend to think about. You could imagine inventing millions of other words”

Wolfram is not afraid of AGI because he believes it's not a meaningful concept. However, he notes that the weather has a mind of its own—the natural world is full of different forms of intelligence, not aligned with human thinking.

“No, because I don't think it's a concept that makes a lot of sense... My guess is people will get come to terms with the fact that sort of the natural world is full of intelligence about the same time as they sort of come to terms with the fact that sort of there's there's you know there's these different forms of intelligence in different places they are more or less aligned with with the way we humans operate.”

There is a society of AIs that exists in the world right now, with possibly more AIs than humans by some count, doing things like buying and selling ads. This AI society is largely incomprehensible to humans.

“there's sort of a society of AIs that exists. There are probably more AIs in the world in some definition of, you know, counting AIs than there are humans in the world. And those AIs are interacting with each other and they're, you know, doing all kinds of things. They're buying and selling ads and all kinds of all kinds of other things that AIs like to do, so to speak, or end up doing.”

Wolfram's methodology involves searching through the computational universe—trillions of possible programs—to discover what is actually out there, revealing phenomena that are very surprising, non-human, and counter-intuitive.

“the most powerful methodology is just using that stack of tools and kind of looking out into the computational universe and just sort of searching through trillions of programs, let's say, and seeing, you know, what what's out there. And it's very surprising what's out there. Now, it's very different. You know, what's out there revealed by the raw computational universe is very surprising, very non-human, very kind of uh against our intuition.”

Exposition is an integral part of doing good science. If you really want to understand something, you have to be able to explain it.

“exposition is an integral part of doing good science in other words if you really want to do science that you know if you really want to understand it you have to you know you have to be able to explain in it”

About half of Wolfram's work is on things he's been thinking about for decades, and half is things that are opportunistically made possible by world events.

“in general in in a lot of things I do about half of what I do is stuff that I've been thinking about for decades and half of it is things that are sort of opportunistically made possible by things that happen in the world.”

Wolfram does not do science for a living, which psychologically helps him avoid over-investing in initial prejudices; he has developed a discipline of letting findings guide him rather than defending preconceived ideas.

“I don't do it for a living, which helps the psychology of doing it because for me, you know, it's like I discover something about meta mathematics. That's great. I didn't need to discover something about metamatics and it's much easier to you know you have to realize in doing science you have to have some prejudice about how things are going to come turn out otherwise you never even explore that thing but the trick is to not be so invested in that prejudice that you don't realize the chips are falling somewhere else.”

Wolfram has been living the 'AI dream' for the last 40 years, which is to have a thing he wants to do and get it done as automatically as possible, using tools and company structures to go from idea to implementation as efficiently as possible.

“Well, I mean I I think of myself as having lived the AI dream for the last 40 years. Okay. What is the AI dream? The AI dream as I see it is, you know, I have a thing that I want to do. Let me get it done as automatically as possible.”

A brain with 100 billion neurons (human) can do things like invent compositional language, which creatures with fewer neurons (cats, dogs) cannot. A hypothetical brain with 100 trillion neurons would likely be able to think about qualitatively different things.

“our brains have maybe 100 billion neurons in them... all those 100 billion neurons could be doing different things, but yet we concentrate things down to have a single thread of experience... if we had 100 trillion neurons, what qualitatively different things would we think about the world? You know, at 100 billion neurons, we can do things like invent compositional language. You know, cats and dogs don't do that, so far as we know.”

The 'interconcept space' exists as the vast majority of the space in a generative AI system's embedding space—pictures of things that are not cats, not things we have named or concepts we have filled in. The fraction of space that contains things with names is something like one part in 10^600.

“You're out in what I call interconcept space in the space where there are pictures and you can look at them, but they're not things for which we have words. They're not things where we have filled in a human concept. And it's actually a bit humbling that even with a very simple generative AI system, the fraction of the space that is interconcept space is absolutely overwhelming. It's like, you know, there's only one part in 10 the 600 or something that is things that we've given names to.”

Live-streaming scientific work is valuable. During the pandemic, Wolfram live-streamed internal physics project discussions, and was surprised to find 5,000 people watching highly technical discussion about mathematical physics.

“One thing is live streaming a lot of stuff. You know, most science you never get to see it done... we were live streaming a lot of our internal discussions and it was right in the middle of the pandemic. So, I have to say it surprised me that we would get like 5,000 people watching some incredibly technical, you know, discussion about mathematical physics”

Papers on cellular automata are so technical that Wolfram found he could not understand one of the papers describing his own work when he looked it up in a library. This suggests physicists and mathematicians are making things unnecessarily obscure.

“I was amused literally yesterday. I was in some math library. I looking at some book about cellular automter actually and I look up some stuff that that I invented and I couldn't understand it in this book. So you know that that maybe tells one something.”

Writing 'A New Kind of Science' took a decade partly because of the effort required to grind ideas down to the point where they were clean enough to explain without heavy technical apparatus. Technical apparatus usually doesn't help and is often a smokescreen.

“it is a lot more effort to say things in a way that people can understand. I mean like with my new kind of science book took me a decade to write that book and part of that time was grinding these ideas down to the point where they were actually clean enough that you could explain them without a lot of technical sort of you know apparatus. The technical apparatus usually doesn't really help. It's usually it's in I think it's often just sort of a smoke screen”

Among Alexander Grothendieck and John von Neumann, Wolfram would choose von Neumann as an influence. Von Neumann asked many interesting questions but sometimes didn't go deep enough. Grothendieck dove deep but wasn't always clear why those questions mattered.

“I would say that um you know I always have thought of vonoyman as somebody who asked a lot of very interesting questions sometimes did not choose to go as deep as he might have done um and uh you know asked the right questions didn't dive deep and really find the foundational thing growth sort of perhaps the opposite of diving deep and uh you know asking the deepest questions but not always clear why those questions were being asked”

Exposition clarity may depend on whether what is being explained is fundamentally new; new paradigms require new forms of exposition, and judging them by old standards misses the point.

“to me you know if it's a piece of code that I can run then it feels like something that I can understand. Um whereas if it's a piece of you know elaborate higher category theory or something maybe it doesn't feel like a thing that one I more or less understand these days but but um you know it's it's more difficult to understand.”

Questions about basic science that Wolfram has known since childhood often trip him up the most when asked in Q&A format. This suggests that early knowledge may become invisible or hard to articulate.

“I do find that the the one thing that happens is whenever there's a question, which I think I known the answer to that question since I was 12 years old, those are the ones that always trip me up.”