“When a cognitive psychologist is talking a lot about fundamental physics to make his argument, it makes me very skeptical. Hoffman repeatedly says ‘the physicists,’ but he admits that most experts disagree with him. [] By the same token, he shouldn’t say ‘the math tells us that ____’ [] he shouldn’t claim that ‘the math’ tells us anything, instead he should say ‘my [or Chetan Prakash’s] math’ tells us something.”
— Anon X
[This reply can be found after the YouTube video ‘What Is Reality?’, in which Donald Hoffman is interviewed by the philosophers Philip Goff and Keith Frankish.]
Donald Hoffman is a cognitive psychologist who works at the University of California, Irvine. He hasn’t written any papers on mathematics or physics. However, he has made extensive use of both mathematics and physics in work which is firmly outside both of these disciplines.
This essay concentrates on the paper ‘Fusions of Consciousness’, which includes lots and lots of maths.
In that publication we have references to “permutated decorations”, “the Parke–Taylor formula”, “positive Grassmannians”, “Plücker coordinates”, “Feynman diagrams”, “quantum field theory”, “gluons”, “scattering amplitudes”, “countable infinities”, “on-shell diagrams”, “cosmological polytopes”, “the entropic arrow of time”, “dimensional simplex”, “Planck time”, “Markovian kernels”, “𝜎-algebra 𝒳”, “qualia kernels”, “Cantor’s hierarchy”, “n-dimensional vector space”, “communicating classes”, etc.
Yet the central theme of ‘Fusions of Consciousness’ is philosophical in nature. Indeed, it’s also highly speculative.
It’s important to stress here that this essay isn’t a long argument against interdisciplinary work, or against the use of mathematics in philosophy. Rather, I’m simply a critic of Donald Hoffman’s interdisciplinary work, and the use of mathematics in his own philosophy.
It really doesn’t go beyond that.
So, for example, I’m a fan of the philosopher Owen Flanagan and his use of cognitive psychology, (general) psychology, neuroscience, etc. in his writings. [See Flanagan’s books The Science of Mind and Consciousness Reconsidered.]
Anyway, to put all the detail which follows in its broad context, it’s worth stating Hoffman’s grand vision: that of creating his very own “theory of everything”.
Donald Hoffman’s Theory of Everything
In his own words, Hoffman believes that his idealism (or what he calls conscious realism) is a
“vehicle sufficiently robust to sustain the next leg of our search for a theory of everything”.
Indeed, Hoffman compares what he’s doing to what Alan Turing did all those years ago. [See here.]
Hoffman also tells us that
“the laws of physics and the special sciences are themselves a projection of the dynamics of conscious agents”.
Not surprisingly, then, Hoffman adds that
“we sketched how spacetime and particles may arise as a projection of the dynamics of conscious agents”.
As some readers will already know (due to his popular book The Case Against Reality), Hoffman applies his idealism to evolutionary theory too. In Hoffman’s own words:
“[Could it be that the entire] evolutionary framework is an artifact of projection from the dynamics of conscious agents?”
Hoffman then adds that “[w]e would require to obtain evolution as a projection of agent dynamics”.
However, let’s now focus on Hoffman’s use of mathematics and physics.
Donald Hoffman’s Use of Mathematics and Physics
At least in terms of Donald Hoffman’s academic publications which deal with conscious realism (or idealism), it’s wrong to focus on him alone. That’s because Hoffman is actually a (as it were) fusion of two conscious agents: himself and Chetan Prakash. Indeed, Hoffman and Prakash have been working together since the 1980s. (Hoffman has also worked with Robert Prentner, Manish Singh and other academics with very similar philosophical views.)
It’s highly likely that Chetan Prakash is responsible for nearly (perhaps literally) all of the mathematics included in their cowritten published papers. (It’s even possible that Prakash introduced Hoffman to this brand of “mathematical idealism”.)
It can also be guessed nearly all of Hoffman’s followers and fans who’ve read the paper ‘Fusions of Consciousness’ (January 2023) won’t have understood much — or even any — of the mathematics in it. This is certainly true of virtually all the people who’ve interviewed Hoffman for the their YouTube channels. [See the dozens — or even more — of interviews of Hoffman here.] Of course, it would be hard to establish this claim without a survey of some kind. However, it’s far less speculative than some of Hoffman’s own philosophical and cosmological claims.
Mathematicians and physicists, on the other hand, may (or even will) understand the maths (qua maths) and the physics (qua physics) in that paper. However, most of them won’t also understand how Hoffman is tying all the maths and physics to philosophical issues, consciousness and to idealism generally. (Most mathematicians and physicists will be perplexed by the references to “qualia”, “monads”, “the One”, “conscious agents”, “free will”, etc.)
All that said, Hoffman himself doesn’t understand much of the maths he uses either.
Why do I say that?
There are a few reasons.
Firstly, he’s a cognitive psychologist with no (professional) background in either mathematics or physics. Secondly, we can accept Hoffman’s own word on his lack of maths skills.
For example, in a YouTube video called ‘Abstract Math of Conscious Agent Theory w/ Dr. Donald Hoffman’, Hoffman stated the following:
“[W]hen you have limited math talents like me [] That’s what led me to then go to a real mathematician [and fellow idealist] Chetan Prakash and pursue the theorems now in the case of the agent dynamics.”
Again, it can be assumed that nearly all the mathematics is down to Chetan Prakash, whom Hoffman has worked with on almost everything he’s published — at least when it comes to consciousness, conscious realism, doomed spacetime, etc. [See a long list of Hoffman-Prakash collaborations here.] What’s more, when you see Prakash’s independent papers and live presentations (at least on the subjects Prakash and Hoffman share), you’ll note that they’re almost identical to Hoffman’s own — even down to the deployments of exactly the same phrases, as well as using the same the images, graphs, slides, and so on. [See the presentation — on YouTube — ‘Conscious Agent Dynamics: Chetan Prakash’, which could easily have been given by Hoffman himself.]
Bearing in mind all the above, it won’t be a surprise to find out that Hoffman hasn’t discussed these issues with professional physicists, professional mathematicians or with any other professional scientists outside his own idealist (or “constructivist”) colleagues and cowriters. (At least there aren’t any publications and videos which show that there’ve been such discussions.) Indeed, in a question-and-answer session published in Science & Nonduality called ‘The Universe is a Conscious Agent’ (starting at 13.09 minutes), Chetan Prakash himself makes this clear when he tells the person who’s interviewing him that “scientists, generally, have more or less ignored [their work]”, and that “philosophers get very upset by it”.
The problem here is that this frank acknowledgement by Prakash sets both himself and Hoffman up to be what’s often called “scientific heretics”. And this designation is always a boon when it comes to many people with religious and “spiritual” inclinations.
But what of that very-extensive use of maths in Hoffman’s papers?
Essentially, Hoffman and Prakash are simply replicating the mathematics and physics which already exists, and then applying both to their idealist philosophy. Indeed, Hoffman admits he’s reliant on other people’s physics, as well as on the mathematics of Prakash.
However, it needs to be said that all the maths (qua maths) and physics (qua physics) in this paper may well be largely correct.
However, that’s not the issue here.
The issue is that virtually none of the physics and maths is original to Hoffman and Prakash. What is original to them is the way they apply that preexisting maths and physics to their philosophical idealism. More relevantly, it’s the applications of the maths and physics that’s philosophically — and otherwise — highly suspect.
So, in simple terms, Hoffman’s “theory of conscious agents” uses preexisting maths and physics, and then takes such things in an idealist direction.
Ultimately, Hoffman takes maths and physics in a “spiritual” direction too. However, that wont be tackled in this essay. [See here.]
So let’s tackle the maths and physics in Hoffman’s paper a little more.
Abstract and/or Beyond Spacetime?
Donald Hoffman relies heavily on Nima Arkani-Hamed and Jaroslav Trnka’s amplituhedron.
Let Hoffman himself state the following:
“Another new candidate is a class of geometric constructions outside of space and time, including the amplituhedron discovered by Nima Arkani-Hamed and Jaroslav Trnka. Subatomic particles collide and scatter in a multitude of ways, and physicists have for decades had formulas for computing their probabilities, formulas that assume physical processes which evolve locally in space and time. But, as it happens, these formulas are unnecessarily complex and hide deep symmetries of nature. The amplituhedron simplifies the formulas, exposes the symmetries hidden by space-time and, in the process, abandons the assumption that space and time are fundamental.”
There’s a strong sense in which “a class of geometric constructions” must be outside of spacetime by virtue of the simple fact that such geometrical constructions are abstract. [See here.] However, this is only in the sense that numbers, geometrical shapes, functions, etc. can be deemed to be outside of space and time according to a (purely) Platonic philosophy of mathematics. [See here.]
Yet this Platonic picture of maths doesn’t have much — or even anything — to do with either idealism or consciousness.
In specific terms of Nima Arkani-Hamed’s amplituhedron: it’s a geometrical tool which is used by theoretical physicists. It can also be seen as a pure abstraction. (The words “highly abstract” are often used about the amplituhedron.) In other words, amplituhedron theory provides physicists with a geometric model that’s essentially abstract in nature. Indeed, it’s abstract primarily because the geometrical space it offers theoretical physicists is not a (physical) spacetime.
In any case, how, exactly, can a geometrical tool which simplifies the calculations which account for the interactions of particles be tied to Hoffman’s philosophical idealism? (Arkani-Hamed himself has stated that the amplituhedron helps simplify scattering-amplitude calculations.) Inversely, how can Hoffman’s philosophical idealism be tied to a very particular model of particle interactions?
All that said, Hoffman actually tells us what he’s doing. He writes:
“This section and the next propose how to project the dynamics of conscious agents down to spacetime, using structures called ‘decorated permutations’. [] The theory of conscious agents starts with a dynamics of agents that is, by hypothesis, outside of spacetime. So this theory must explain how spacetime and objects arise entirely from the dynamics of agents. This is a colossal project.”
This is a “colossal project” to establish a consciousness-first “theory of everything”. However, this isn’t subjective idealism. Instead, it’s essentially a 21st-century brand of objective idealism in that Hoffman focuses on “the dynamics of conscious agents” (i.e., in the plural) and their “interactions”.
Now for those “Markov chains” and “decorated permutations”, which Hoffman keeps on mentioning (i.e., in almost every interview his gives).
Decorated Permutations, Markov Chains and Mapping
Donald Hoffman tells us that he’s attempting to
“show how decorated permutations, and other structures that physicists have found beyond spacetime, arise as a projection of a deeper theory of conscious agents”.
In Hoffman’s idealism, it’s not only that brains, neurons, trees, particles, football matches, sex acts, gluons, etc. are all the product of conscious agents, so too are the “decorated permutations, and other structures” which Hoffman uses and frequently mentions.
Hoffman tells us more about the decorated permutation:
“One key insight is this: the deepest structure beyond spacetime that distills physics is the decorated permutation.”
Is the decorated permutation “beyond spacetime”, or, instead, is it simply abstract? Alternatively, is it beyond spacetime because it is abstract?
Yet these two alternatives don’t do much work for Hoffman. That’s because his philosophy isn’t actually about anything abstract (i.e., as in the Platonic view of numbers, geometrical shapes, etc.): it’s about something entirely different.
Let’s go into a little more detail on mathematical abstractions.
Hoffman uses the term “correspondence” a few times. (As in the subsection called ‘Correspondence between Agent Dynamics and Physical Particles’.) He also refers to mapping.
Hoffman writes about his “theory of conscious agents” in the following way:
“[I]ts Markov-chain dynamics must map to decorated permutations and spins. With that map, we can propose a precise correspondence between (1) the Markov polytopes that describe all possible agent dynamics and (2) the on-shell diagrams that generate scattering amplitudes.”
In Hoffman’s philosophy, “Markov-chain dynamics” map “decorated permutations and spins”. However, the former also map the “dynamics of conscious agents”. Thus, to state the obvious, neither Markov chains nor decorated permutations actually are conscious agents, their interactions and dynamics. They’re supposed to map — or correspond to — such things.
In simple terms, Markov chains are used as tools. They’re ways of statistically modelling “real-world processes”.
Hoffman, on the other hand, uses Markov chains to model processes outside the (as it were) world — or at least outside physics and anything observable or empirical.
Just to show how odd — or simply different — Hoffman’s use of Markov chains is, it’s worth knowing that they’re used as ways to study animal population dynamics, currency exchange rates, cruise control systems in cars, queues of customers arriving at an airport, etc.
In detail.
A Markov chain (or Markov process) describes a sequence of events, and assigns probabilities to that sequence (or to each step in that sequence). What matters in this description is that, basically, each event depends on the previous event — or on the precise state of that previous event.
Hoffman, on the other hand, applies Markov chains to conscious agents and their interactions.
None of this work tells us what a conscious agent is. [See my ‘What Is a Conscious Agent? Donald Hoffman, Please Tell Me’.]
None of this work tells us how Hoffman actually (as it were) gets hold of consciousness agents and their interactions in order to map them with Markov chains and decorated permutations.
Consequently, what, exactly, is Hoffman mapping, and how has he gained access to what it is he’s mapping?
In any case, all this clearly takes Hoffman beyond physics and science generally. Specifically, conscious agents and their interactions don’t belong to physics.
What do they belong to?
The answer to that question is simple: they belong to Hoffman’s philosophical idealism.
So what has all this to do with “the death of spacetime”?
Spacetime Is Doomed
Donald Hoffman warns us about something he calls “spacetime recidivism”.
According to Hoffman, “the physicists” themselves have gone beyond spacetime. [Read the opening quote again in reference to Hoffman’s repeated phrase “the physicists”.]
An (or the) alternative to spacetime recidivism, however, can be found in Hoffman’s following words:
“Spacetime is doomed. It, and its particles, cannot be fundamental in physical theory, but must emerge from a more fundamental theory.”
Hoffman believes that this “more fundamental theory” is his very own conscious realism — aka, his (scare-quoted) “scientific idealism”.
From another angle, Hoffman also believes that he needs to get outside spacetime in order to establish his (objective) idealism.
So not only must Hoffman’s philosophy account for particles, brains, neurons, trees, cups, football games, sexual acts, etc. in idealist terms: it must also do so with spacetime itself. In Hoffman’s philosophy, this means that “spacetime and objects arise entirely from the dynamics of agents”.
Basically, in Hoffman’s idealism literally everything is down to (or a “projection of”) conscious agents — or everything is (as it were) in the Big Consciousness of what Hoffman calls “the One”.
In detail.
Hoffman tells us that
“‘[p]hysics’ here is usually taken to refer to the physics of spacetime and objects, namely quantum field theory and general relativity”.
Hoffman goes beyond spacetime in the following way:
“[W]e do not locate the network of conscious agents inside spacetime precisely because physics and evolution tell us that these structures are not fundamental, and because physics itself has found new structures beyond spacetime, such as amplituhedra and their associated decorated permutations.”
However, what’s original to Hoffman can be found in this conclusion:
“So instead of merely re-describing conventional physics with conscious agents, we aim to show how decorated permutations, and other structures that physicists have found beyond spacetime, arise as a projection of a deeper theory of conscious agents.”
This “deeper theory of conscious agents” is the ultimate form or reductionism.
Yet it needs to be stated here that Hoffman’s idealist philosophy doesn’t stop being reductionist (or an example of a reduction) simply because it’s dealing with “non-physical” conscious agents, consciousness, and the One. Indeed, it has all the hallmarks of a classic reductive philosophy. However, it just also happens to have many “spiritual” elements within it.
To repeat. In Hoffman’s philosophy, literally everything in physics and the universe itself is reduced to conscious agents — or to the consciousness of the One.
That is the central thesis of Donald Hoffman’s idealism.
Note: A Small Selection of Mathematical Extracts From ‘Fusions of Consciousness’
