This essay is a response to the debate between the computer scientist and physicist Stephen Wolfram and the cognitive psychologist and popular science author Donald Hoffman. The debate was hosted by Curt Jaimungal, and it can be found on YouTube here. On the surface at least, the theories of these two men have much in common. However, on analysis, these similarities are only superficial and surface-level. Indeed, Hoffman’s idealism often clashes with Wolfram’s more practical ideas. Hoffman wants consciousness to be “outside” the rules (Wolfram’s or anyone’s), while Wolfram wants the rules to be the “source” of everything, including consciousness.
It’s worth noting that Stephen Wolfram seems to have had little knowledge of Donald Hoffman before this YouTube debate. Rather, he noted that people had told him that his own work and that of Hoffman were “related”. In addition, there is no mention of Hoffman on Wolfram’s website. However, there is a bare link to this debate on YouTube. As for the debate itself, that was initiated and hosted by Curt Jaimungal, who hosts Theories of Everything (TOE) on YouTube. The two met for the first time during this recorded session in June 2024.
Let Curt Jaimungal pick up on one of the similarities between Wolfram’s work and Hoffman’s work. In the YouTube debate, he says:
“Don [Hoffman], I don’t think you’re disagreeing with what Stephen [Wolfram] just said. Stephen, what you had said is that, look, we can start with something that’s simple, mechanically simple, and then get to something that is extremely mechanically complex, such that we would never think, looking at the complex case, that it could be made of these elementary elements. And Don is saying that’s correct.”
None of this is original to either Wolfram or Hoffman. Weak and strong emergence (if that’s what they’re talking about) are commonplace subjects in both physics and the philosophy of physics.
On the surface at least, some readers may wonder why Wolfram was at all interested in seeing if Hoffman’s “conscious agents” could be mapped (or “projected”) onto his own Ruliad framework. After all, Hoffman’s position is philosophical and idealist.
Wolfram Defends Large Language Models
One of the most relevant ways in which Wolfram states that rules can generate, well, anything and everything is when he mentions Large Language Models. He says:
“You [Hoffman] have rather dismissively said that my friends the LLMs are all merely regurgitating the things that went into them. But you claim that we are not.”
In very simple terms, Hoffman’s conscious agents do the work of Wolfram’s rules. Thus, to Wolfram, consciousness is generated by rules. To Hoffman, consciousness is fundamental.
What Wolfram says about not being able to use Hoffman’s theory probably applies to all physicists too. This is how Wolfram puts it:
“Is that definition of success transportable enough that I can really apply it to an LLM? And perhaps the answer will be, the LLM is not conscious. But right now you haven’t given me anything that is concrete enough that I can take it and fit it onto the LLM and say, ‘Do you win or do you lose?’”
During this debate, Wolfram kept trying to read through Hoffman’s jargon in order to see if there is a program he can run. He couldn’t find one. Alternatively, Wolfram wanted to know how Hoffman’s conscious agents could be “translated” into code.
Readers may wonder why Wolfram would ever have thought that Hoffman’s theory would be transportable to his own work. (Perhaps he never thought that.) Similarly, readers may wonder why Hoffman would ever have thought that Wolfram’s Ruliad would be transportable to his work. More strongly, one wouldn’t think that Hoffman would have any (relevant) interest in LLMs at all, save to say that they are “icons”.
All this raises the possibility that the similarities between Wolfram’s work and Hoffman’s work are merely superficial or surface-level. Sure, both men use graph theory, and both believe that (to use Hoffman’s words) “spacetime is doomed”.
So despite all the mathematics in Hoffman’s papers, Wolfram, and I suspect most physicists, can’t use his theory. Oddly, Hoffman kind of admits this himself when he responded in the following way:
“So I owe you a mathematically precise theory of consciousness, a scientific theory of consciousness that could try to do that kind of thing. [ ] It uses Markovian dynamics in the model. And what we’re doing right now is to try to answer your question.”
Actually, Hoffman doesn’t “owe” Wolfram anything more. Doesn’t he claim to already have a “mathematically precise theory of consciousness”? Unless, that is, Hoffman simply means that Wolfram needs to actually read his papers before commenting in detail.
Hoffman’s Leibnizian Idealism
Hoffman puts his idealist (or consciousness-first) philosophy in the following:
“What I do know is that consciousness is what I know firsthand. What I call inanimate matter is an extrapolation. What’s directly available to me are experiences, conscious experiences, and what I call an unconscious physical world is an extrapolation that I’m making. What I only have are my conscious experiences. I have nothing else.”
In turn, Wolfram picks up on Hoffman’s idealism in the following passage:
“Do you believe that if I could accurately measure the electrochemistry of the nematode that I would capture the whole story? Or do you believe that there’s something that is beyond the physical that’s not capturable by any physical measurement that is something about what the nematode feels?”
Now let Wolfram put Hoffman’s position on consciousness. He states: “So the claim is that there’s a spark of consciousness that can simply not be reached mechanically.”
Hoffman explains his idealism and offers us his either/or logic:
“If we don’t assume that consciousness is fundamental in the foundations of our theories, then we either have to dismiss consciousness and say it’s not there, or we have to give a theory in terms of unconscious entities about how consciousness emerges.”
Many scientists and philosophers have indeed dismissed consciousness. (Similarly, we do have to give a theory (at least partly) in terms of unconscious entities. (Readers could embrace panpsychism!)
Hoffman claims that “it’s not logically possible to start with unconscious ingredients and to have consciousness emerge”. Why “logically impossible”? It’s here that Leibniz enters the picture.
Hoffman doesn’t only substitute Leibniz’s monads with his own conscious agents, he’s motivated by Leibniz’s claim that consciousness cannot come from “unconscious ingredients” too. In this debate, Hoffman admits that his conscious agents basically do the work of Leibniz’s monads. (This is the first time that I’ve come across Hoffman actually saying that.)
Why bring up Leibniz at all?
Well, for one, Wolfram brings Leibniz up in direct response to Hoffman’s claim of logical impossibility. (Wolfram’s own unconscious ingredients are his “simple rules”.) Wolfram says:
“If you’d asked me in 1980, do I disagree with Leibniz’s intuition? I would have said, I don’t know. I don’t know how you would get a mind-like thing to arise from a non-mind-like sort of origin. But then, by 1981, I was starting to do all kinds of computer experiments about what simple rules can actually do. And it really surprised me. In other words, what could emerge from something that seemed like it was too sterile to generate anything interesting, I was completely wrong.”
One basic point to extract from all the above is that Wolfram believes that Hoffman relies on intuition when he makes his claim about the logical impossibility of consciousness arising from non-conscious ingredients.
Hoffman Believes Modern Physics Fails. Long Live Postmodern Physics
To Hoffman, physics is incomplete. It’s incomplete because it doesn’t include consciousness. However, this isn’t only about physics failing to explain consciousness: it’s also about physics failing to incorporate consciousness. Thus, consciousness is primary to Hoffman, yet he states “that is not what has been the observation of the last few hundred years of science”.
Hoffman also asks: “In the case of conscious experience, is it enough to merely talk about kind of the laws of physics that we know?” He adds: “There is no meaningful science that can be done without entraining consciousness in it.”
So does Hoffman actually offer us an alternative physics? Yes.
Hear out Hoffman using a lot of technical terms in a short space of time:
“The high-energy theoretical physicists in the last 10 years have discovered these positive geometries beyond spacetime and quantum theory. And behind those positive geometries, they found these combinatorial objects that classify them. They’re called decorative permutations.”
What is the relevance of Hoffman’s talk of “positive geometries” and “decorative permutations” to his idealism? He explains:
“So we’ve taken off the headset, the space-time headset, and we’ve gone outside for the first time, and we’re finding these obelisks, these positive geometries outside of spacetime and these combinatorial objects.”
The important word here is “headset”. Spacetime is a headset. It’s not, well, reality.
In terms of “empirical tests”, if not predictions, Hoffman does explain himself. His claim is that his theories can be tested, and they do (or can) include predictions. Yet that’s simply because his metaphysical speculations are “projected” onto already-existing physics. Relatedly, Wolfram himself seems to suspect that if Hoffman’s maths were to ever actually work to, say, predict a particle, it would only be because it had recreated the computational graphs that he is already studying.
In Hoffman’s own words:
“What we’re trying to do is to show that we could get all of physics, plus more, from a theory of conscious agents being assumed to be fundamental outside of spacetime and projecting through decorative permutations positive geometries into space-time where we can make our empirical test.”
Again, Hoffman’s metaphysics is projected onto spacetime and the real world of physics. Therefore, the tests and predictions Hoffman cites will fall within the domain of physics, not his own metaphysics.
Idealism as a Use of Occam’s Razor
Wolfram picks up on Hoffman’s use of the words “Occam’s razor”, which is interesting because panpsychists use this term too — or at least they discuss the parsimonious nature of panpsychism. (Other philosophers who advance other isms do so too.) In Hoffman’s case, starting the whole show with conscious agents may well seem to be a particular use of Occam’s razor. In other words, boiling the whole of physics, spacetime, trees, biological persons, brains, etc. down to conscious agents and their interactions — in an ultimate example of reductionism! — does seem ontologically parsimonious. Let’s see how Wolfram puts it:
“Let me see if I understand you [Hoffman] correctly. In the same way that we observe general relativity because of the kinds of observers we are in the Wolfram model, and in the same way that we see quantum mechanics because of the kinds of observers we are in the Wolfram model, we also, many people, many philosophers, many cognitive scientists, for instance [ ].”
Hoffman uses the term “Occam’s razor” and says (in Wolfram’s words) “look, we can move beyond spacetime and we can find something that can give rise to the physics that we have”. But then Wolfram believes he’s found a self-referential trap. He concludes by saying “Occam’s razor itself may be something that we find appealing because of the kinds of observers we are”. If consciousness is literally everything, then any use of Occam’s razor is solely down to consciousness too. Thus, Hoffman isn’t using Occam’s razor to get to the fundamentals of physical theory and reality, but to analyse the consciousnesses which have given birth to the notion Occam’s razor.
Much more broadly, Wolfram argues that if mathematics is part of the what Hoffman calls the “headset”, then using it to build a fundamental theory is self-referentially problematic.
Hoffman’s Conscious Agents
Hoffman says that it’s more correct to say that “observers that have conscious experiences” are the fundamentals or building blocks of his theory. But, surely, an observer is over and above (mere) consciousness. Perhaps because of that, Hoffman himself says, “If you imagine an observer that has no conscious experiences, it’s not really clear what we’re talking about.”
What do these conscious agents do? Hoffman explains:
“So it’s like a network of interacting conscious agents. So it’s a social network, and it’s governed by Markovian dynamics.”
Hoffman says that “it’s like” a network of interacting social agents. Some people who’ve read Hoffman will have thought that it literally is a network of conscious agents. Isn’t that the whole point of the graphs and schematics in Hoffman’s work — that we literally have a network of interacting conscious agents?
Two other words are odd too: “governed by” (as in “governed by Markovian dynamics”). Don’t Markovian dynamics describe or map the network, not govern them? Hoffman makes it seem as if the (Markovian) map is more important than the territory (i.e., a network of conscious agents). Thus, is Hoffman’s map calling the shots?
Yet Hoffman himself does use the word “describing” elsewhere in this YouTube debate when he claims that the
“Markovian kernel is basically describing, given that my current experience is red, what’s the probability the next one will be green and so forth, and you can write down a matrix of it”.
This passage is astonishing. Even though Hoffman says that the Markovian kernel is describing (rather than governing) stuff, it’s still hard to make sense of his claim. The very sentence “given that my current experience is red, what’s the probability the next one will be green” strikes me as being bizarre, almost surreal. (Sure, there may have been a lot of work elsewhere to explain this move from an experience of red to an experience of green, but I haven’t seen it.) And what work is mathematical probability doing here?
What follows this is radical, and hard to understand. Hoffman links his talk about Markovian dynamics and conscious agents to things beyond spacetime. In Hoffman’s own words:
“What we’re doing then is saying, can we take this Markovian dynamics and first show that we can project onto the decorative permutations that the physicists have found, and then from there project onto the positive geometries?”
Here the reader will need to know what “decorative permutations’” and “positive geometries” are. The reader will then need to know how Hoffman is using the word “project” (as in “we can project onto the decorative permutations” and “project onto the positive geometries”). More importantly, what philosophical work are these projections doing? (Hoffman does say that a “projection” is a “dramatic simplification of the more complex, yet more unified, dynamics of [conscious agents]”.)
Hoffman then brings all the above back to consciousness and how it impacts on his view of spacetime when he concludes:
“We can project all the way into spacetime, and then we would actually be able to make testable predictions inside space-time from a theory that says consciousness is fundamental, and we start there.”
Some readers may have absolutely no idea how “predictions” fit into all this. What kind of predictions is Hoffman talking about? However, as already stated, Hoffman’s metaphysics is projected onto spacetime and the real world of physics. Therefore, any predictions he or others make will fall within the domain of physics, not Hoffman’s own metaphysics.
Conclusion: Hoffman’s Pythagoreanism
Wolfram sums up one of the main problems he has with Hoffman’s theory of consciousness in a single clause. He states that he’s
“hoping that there’s more to consciousness than Markovian matrices, because that’s a shockingly minimal kind of view”.
Considering that Wolfram is a mathematician and Hoffman isn’t (though Hoffman may well have used Markovian kernels, probability theory, etc. in his previous work in cognitive psychology), it’s ironic that Wolfram spots a kind of Pythagoreanism (without actually using that term) in the words of Hoffman. Wolfram also makes the point that he’s “never [been] a believer in theories that have [mathematical] probability as a fundamental component”.
Wolfram wants to use Hoffman’s maths as a way to describe how an observer processes the universe. However, it’s easy to conclude that Hoffman himself tacitly believes that the maths somehow creates the universe… Yet that belief isn’t idealism! This means that Hoffman balances on the line between Pythagoreanism and idealism, and that’s largely because, as a scientist, he became intent on using mathematical models to justify his metaphysical idealism.
The bottom line here is that there’s a certain triviality in Hoffman’s use of mathematics to describe (or justify) his idealism. That’s because, in a strong sense, almost anything can be mathematicised.
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