How to think like a quantum monadologist

Half the responses to my last article focused on the subject of consciousness, understandably so. Back when LW was still part of OB, I stated my views in more detail (e.g. here, here, here, and here); and I also think it's just obvious, once you allow yourself to notice, that the physics we have does not even contain the everyday phenomenon of color, so something has to change. However, it also seems that people won't change their minds until a concrete alternative to physics-as-usual and de facto property dualism actually comes along. Therefore, I have set out to explain how to think like a quantum monadologist, which is what I will call myself.

Fortunately, this new outlook agrees with the existing outlook far more than it disagrees. For example, even though I'm a quantum monadologist, I'm still seeking to identify the self and its experiences with some part of the physical brain. And I'm not seeking to add big new annexes to the physical formalism that we have, just in order to house the mind; though I may feel the need to impose a certain structure on that formalism, for ontological reasons, and that may or may not have empirical consequences in the macro-quantum realm.

So what are the distinctive novelties of this other approach to the problem? There is an ontological hypothesis, that conscious states are states of a single physical entity, which we may call the self. There is a preferred version of the quantum formalism, in which the world is described by quantum jumps between spacelike tensor products of abstract quantum states (more on this below). The self is represented by one of the tensor factors appearing in these products. There is an inversion of attitude with respect to the mathematical formalism; we do not say that the self is actually a vector in a Hilbert space, we say that the nature of the self is as revealed by phenomenology, and the mathematics is just a way of describing its structure and dynamics. Finally, it is implied that significant quantum effects are functionally relevant to cognition, though so far this tells us nothing about where or how.

Quantum Jumps Between Tensor Products?

For this audience, I think it's best that I start by explaining the quantum formalism I propose, even though the formalism has been chosen solely to match the ontology. I will assume familiarity with the basics of quantum mechanics, including superposition, entanglement, and the fact that we only ever see one outcome, even though the wavefunction describes many.

Suppose we have three qubits, allegedly in a state like |011> + |101> + |110>. In a many-worlds interpretation, we suppose that all three components are equally real. In a one-world interpretation, we normally assume that reality is just one of the three, e.g. |011>, which can be expanded as |0> x |1> x |1>: the first qubit is actually in the 0 state, the second and third qubits in the 1 state.

However, we may, with just as much mathematical validity, express the original state as {|01>+|10>}|1> + |110>. If we look at that first term, how many things are present in it? If the defining property of a thing is that it has a state of its own, then we only have two things, and not three, because two of our qubits are entangled and don't have independent states. It is logically possible to have a one-world interpretation according to which there are two things actually there - one with quite a few degrees of freedom, in the state |01>+|10>, and the other in the much simpler state |1> (and with |110> being unreal, an artefact of the Schrodinger formalism, as must be all the unreal "branches" and "worlds" according to any single-world interpretation).

And there you have it. This is, in its essence, the quantum formalism or quantum interpretation I want to use, as a neo-monadologist. At any time, the universe consists of a number of entities whose formal states inhabit Hilbert spaces of various dimension (thus |01>+|10> comes from a four-dimensional Hilbert space, while |1> comes from a two-dimensional Hilbert space), and the true dynamics consists of repeatedly jumping from one such set of entity-states to another set of entity-states. Models like this exist in the physics literature (see especially Figure 1; you may think of the points as qubits, and the ovals around them as indicating potential entanglement). For those who think in terms of "collapse interpretations", this may be regarded as a "partial collapse theory" in which most things, at any given time, are completely disentangled; actually realized entanglements are relatively local and transient. However, from the monadological perspective, we want to get away from the idea of entanglement, somewhat. We don't want to think of this as a world in which there are two entangled qubits and one un-entangled qubit, but rather a world in which there is one monad with four degrees of freedom, and another monad with two degrees of freedom. (The degrees of freedom correspond to the number of complex amplitudes required to specify the quantum state.)

The Actual Ontology of the Self and Its Relationship to the Formalism

I've said that the self, the entity which you are and which is experiencing what you experience, is to be formally represented by one of these tensor factors; like |01>+|10>, though much much bigger. But I've also said that this is still just formalism; I'm not saying that the actual state of the self consists of a vector in a Hilbert space or a big set of complex numbers. So what is the actual state of the self, and how does it relate to the mathematics?

The actual nature of the self I take to be at least partly revealed by phenomenology. You are, when awake, experiencing sensations; and you are experiencing them as something - there is a conceptual element to experience. Thoughts and emotions also, I think, conform somewhat to this dual description; there is an aspect of veridical awareness, and an aspect of conceptual projection. If we adopt Husserl's quasi-Cartesian method of investigating consciousness - neither believing in that which is not definitely there, nor outright rejecting any of the stream of suppositions which make up the conceptual side of experience - we find that a specific consciousness, whatever else may be true about it, is partly characterized by this stream of double-sided states: on one side, the "data", the "raw sensations" and even "raw thoughts"; on the other side, the "interpretation", all the things which are posited to be true about the data.

Husserl says all this much better than I do, and says much more as well, and he has a precise technical vocabulary in which to say it. As phenomenology, what I just wrote is crude and elementary. But I do want to point out one thing, which is that there is a phenomenology of thought and not just a phenomenology of sensation. Because sensations are so noticeable, philosophers of consciousness generally accept that they are there, and that a description of consciousness must include sensations; but there is a tendency (not universal) to regard thought, cognition, as unconscious. I see this as just footdragging on the part of materialist philosophers who have at length been compelled to admit that colors, et cetera, are there, somewhere; if you were setting out to describe your experience without ontological prejudice, of course you would say something about what you think and not just what you sense, and you would say that you have at least partial awareness of what you're thinking.

But this poses a minor ontological challenge. So long as the ontology of consciousness is restricted to sensation, you can get away with saying that the contents of consciousness consist of a visual sensory field in a certain state, an auditory sensory field in another state, and so on through all the senses, and then all of these integrated in a unitary spatiotemporal meta-perception. A thought, however, is a rather different thing; it is something like a consciously apprehended conceptual structure. There are at least two ontological challenges here: what is a "conceptual structure", and how does it unite with raw sensory data to produce an interpreted experience, such as an experience of seeing an apple? The philosophers who limit consciousness to raw sensation alone don't face these problems; they can describe concepts and thinking in a purely computational and unconscious fashion. However, in reality there clearly is such a thing as conceptual phenomenology (or else we wouldn't talk about beliefs and thoughts and awareness of them), and the actual ontology of the self must reflect this.

A crude way to proceed here, which I introduce more as a suggestion than as the answer, is to distinguish between presence and interpretation as aspects of consciousness. It's almost just terminology; but it's terminology constructed to resemble the reality. So, we say there is a self, whatever that is; everything "raw" is "present" to that self; and everything with a conceptual element is some raw presence that is being "interpreted". And since interpretations are themselves processes occurring within the self, logically they are themselves potentially present to it; and their presence may itself be conceptually interpreted. Thus we have the possibility of iteratively more complex "higher-order thoughts", thoughts about thoughts.

Enough with the poetics for a moment. Is there a natural formalism for talking about such an entity? It would seem to require a conjunction of qualitative continua and sentential structure. For example, a standard way of talking about the raw visual field specifies hue, saturation, and intensity at every point in that field. But we also want to be able to say that a particular substructure within that field is being "seen as a square" or even "seen as an apple". We might build up these complex concepts square or apple combinatorially from a set of primitive concepts; and then we need a further notation to say that raw sensory structure X is currently being experienced as a Y. I emphasize again that I am not talking about the computation whereby input X is processed or categorized as a Y, but the conscious experience of interpreting sensation X as an object Y. It can be a slippery idea to hold onto, but I maintain that the situation is analogous to how it was with sensation. You can't say that a particular shade of red is really some colorless physical entity; you have to turn it around and say that the entity in your theory, which hitherto you only knew formally and mathematically, is actually a shade of red. And similarly, we are going to have to say that certain states and certain transitions of state, which we only knew formally and computationally, are actually conceptually interpreted perceptions, reflectively driven thought processes, and so forth.

Returning to the second part of the question with which we started - how does the actual ontology of the self relate to the quantum mathematics - I have supposed that there is a mapping (maybe not 1-to-1, we may be overlooking other aspects of the self) from states of the self to descriptions of those states in a hybrid qualitative/sentential formalism. The implication is that there is a further mapping from this intermediate formalism into the quantum formalism of Hilbert spaces. This isn't actually so amazing. One way to do it is to have a separate basis state for each state in the intermediate formalism - so the basis states are formally labelled by the qualitative/sentential structures - and to also postulate that superpositions of these basis states never actually show up (as we would be unable to interpret them as states of consciousness). But there may be more subtle ways to do it which take advantage of more of the structure of Hilbert space.

What About Unconscious Matter? 

If I continue to use this terminology of "monads" to describe the entities whose quantum states, tensored together, form the formal state of the universe from moment to moment, then my basic supposition is that conscious minds, e.g. as known from within to adult humans, correspond to monads with very many degrees of freedom, and that these are causally surrounded by (and interact with) many lesser monads in simpler, unconscious states. I'm not saying that complexity causes consciousness, but rather that conscious states, on account of having a minimum internal structure of a certain complexity, cannot be found in (say) a two-qubit monad, and that these simple monads make up the vast majority of them in nature.

In fact, this might be an apt moment to say something about the relationship between these "monads" and the elementary particles in terms of which physics is normally described. I think of this in terms of string theory; not to be dogmatic about it, but it just concretely illustrates a way of thinking. There is a formulation of string theory in which everything is made up of entangled "D0-branes". An individual D0-brane, as I understand it, has just one scalar internal degree of freedom. A particular spatial geometry can be formed by a quantum condensate of D0-branes, and particles in that geometry are themselves individual D0-branes or are lesser condensates (e.g. a string would be, I suppose, a 1-dimensional D0-brane condensate). Living matter is made up of electrons and quarks; but these are themselves just D0-brane composites. So here we have the answer. The D0-branes are the fundamental degrees of freedom - the qubits of nature, so to speak - and their entanglements and disentanglements define the boundaries of the monads.

Abrupt Conclusion

This is obviously more of a research program than a theory. About a dozen separate instances of handwaving need to be turned into concrete propositions before it has produced an actual theory. The section on how to talk about the actual nature of consciousness without implicitly falling back into the habit of treating the formalism as the reality may seem especially slippery and mystical; but in the end I think it's just another problem we have to face and solve. However, the point of this article is not to carry out the research program, but just to suggest what I'm actually on about. It will be interesting to see how much sense people are able to extract from it.

P.S. I will get around to responding to comments from the previous article soon.

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I may feel the need to impose a certain structure on that formalism, for ontological reasons, and that may or may not have empirical consequences in the macro-quantum realm.

This sentence pretty much guaranteed that the entire article would be vague, riddled with empty jargon, unfocused, and uninformative. It was right. Not saying you don't have a point; I'm saying this article is not clear enough for me to begin to determine if you have a point or not.

I very much suspect it's woo, but in any case it's written for a wrong audience. Mixing physics and thought raises red flags. Downvoted.

This site is full of people interested in implementing intelligence (and even themselves) on a new substrate .... but they're not going to be interested in the relationship between physics and thought ?

Articles should be legible to the audience. You can't just throw in a position written in terms that require special knowledge not possessed by the readers. It may be interesting, but then the goal should be exposition, showing importance and encouraging study.

It's great when thought is considered mechanistically, in terms of physics. It's also instructive to build ontology around knowability. There is a path across levels of abstraction between physics and intuition, and arguably a shorter path between intuition and logic. But mixing precision of physics with vague intuitive concepts such as "consciousness" at the same level is a no-no, an umbrella fallacy with supernatural a prominent example.

"Articles should be legible to the audience. You can't just throw in a position written in terms that require special knowledge not possessed by the readers. It may be interesting, but then the goal should be exposition, showing importance and encouraging study."

I both agree with and disagree with this statement. I agree that a post should be written for the audience. I disagree in that I think people here spend a lot of time talking about QM and if they do not have the knowledge to understand this post then they should not be talking about QM. The other issue is I think this post may be too muddled to really require special knowledge before the author clarifies the post.

General Post Question The one big thing that confuses me is the title do you actually mean Quantum Monadology? If so are you claiming some use of the formal term monad, or some definition of your own? I don't see this post as following from some real definition of monads as seen in scientific literature.

General Post Comment I think to be blunt this post is a bit muddled with ideas from all over the place put into one big pot and the result is not very enlightening. If you haven't already I suggest you lookup the precise definition of monad. I can't find it now but there was a paper a while back published on this topic of formalizing QM within the formal idea of monads.

I disagree in that I think people here spend a lot of time talking about QM and if they do not have the knowledge to understand this post then they should not be talking about QM.

Maybe they shouldn't (but not because they can't understand this post).

As I've been saying, I mean pseudo-Leibnizian monads (pseudo because unlike Leibniz's, they can interact), not computer-science monads.

We're all interested in the 'relationship' between thought and reality, but I think it's unlikely that thought exists at the simple, fundamental level of reality that is studied by physicists.

Why would you try to approach consciousness this way, as opposed to through neuroscience? Neuroscience has been making some real progress lately; what is it that you think this approach could add?

I can't help but notice that the "self-monad" looks a lot like a "soul" in a thin, crispy quantum shell. What are the differences? Are there differences? Dressing it up this way allows you to do math with the monad. Does that math tell you anything? Especially, can any testable prediction come out of this?

You describe how to think like a quantum monadologist. If you answer these questions, I'll be able to decide if thinking like a quantum monadologist is worth attempting.

This is not in opposition to neuroscience. It implicitly calls for attention to quantum effects in the brain, and not just electrical and chemical signaling; and then there's the step where you explain the formal ontology of physics (used to describe the state of the monad) in terms of the ontology revealed by phenomenology, rather than vice versa. But that is all in addition.

The root of it all is that you take phenomenology seriously, and you don't think it can be reduced to the physics we have, and you take that seriously enough to look for ways to revise the physics, both ontologically and mathematically. The majority of commenters here appear to be content with the theory of consciousness they have, or at least with the prospects for reduction of consciousness to existing physics. I am not, and we are therefore going over some of the familiar disputations in comments, but I really didn't write this to present the case against ordinary physicalism one more time. Chalmers does that, many others have done that. Some people get it and some people don't. This article is a sketch (and only a sketch) of a new alternative - a new starting point, rather than an argument against the old one. If you don't feel the need for a new starting point, you may not be interested.

Is the self-monad like a soul? Yes and no, just as the brain is like and unlike a soul according to classic mind-brain identity theory. A monad is a "single substance", but here it is not a different sort of substance. A simple monad should be able to evolve into a complex one, or vice versa, given the right boundary conditions. There is also no radical independence of it from the body; it's a condensate of entangled electrons (or whatever) that forms as the brain develops, nothing more. As a quantum state, you might be able to transfer it into a new environment by a process resembling quantum teleportation; that's about as close to the traditional detachability of the soul as I can get in this theory.

The one inescapable empirical conclusion is that quantum effects are functionally relevant for consciousness and cognition, somewhere, somehow. But if that's a fact, plain old empirical neuroscience, biophysics, and psychology should turn it up eventually anyway, whether or not a theory of monads is a recognized intellectual option.

Gotta agree with Psychohistorian and Nesov: this post is woo. Admittedly it's pretty hard to imagine how a classical computation can give rise to consciousness, but I don't see how quantum mechanics helps you. Please pinpoint the exact step in the reasoning where your monads actually require the quantum special sauce, rather than some massively complex Tinkertoys.

Actually, let me make a more general comment. This article seems to be aimed almost entirely at those who already agree that physics is going to have to change to account for qualia. I don't know if there's anyone but you here who accepts that, though. Your aim seems to be to show that a physics that could account for qualia in the way you want it to is possible, but I think the bit you needed to argue first was that it was necessary.

In particular, I'm really surprised that my Google searches haven't turned up anything by you setting out what problems you see with Dennett's account in Consciousness Explained, as I refer to in my earlier comment.

This article seems to be aimed almost entirely at those who already agree that physics is going to have to change to account for qualia.

Not quite. It is an experiment in seeing whether the people who insist that there is no problem may be moved by seeing a concrete alternative, rather than being told that their existing account of color, etc, is inadequate. (See first paragraph, last sentences.) No success so far.

What do I think of Dennett? It is a while since I read him. But while of course I disagree with him, I think he is a superior exponent of the true consequences of standard physicalism. I have accused most physicalists of being stealth dualists, who posit an association between, say, color and some computational or other physical property, but call it an identity. Dennett simply says, there is no subjective color (which he calls "figment") and no unity of consciousness ("the Cartesian theater"). These are just intersubjective figures of speech, etc. And he's quite right: subjective color and the unity of consciousness do not exist in standard physics. But they do actually exist, which is why I've posited a monadic physics. A conscious monad is a Cartesian theater, a place where the components of conscious experience are genuinely simultaneously present, and among those components are color sensations.

Responding to your other question - heterophenomenology is where you agree that other people's phenomenological reports must be explained, but you feel no commitment to the ontologies implied by taking the reports literally. In principle, I have no problem with that. People can be wrong. But I disagree with Dennett's specific eliminations, and especially want to show that they are not necessitated by physical ontology, because physical ontology can be different.

unity of consciousness... [does] actually exist,

The point of my earlier comment about touching a hot plate (ETA: link) was that once you know that your brain is capable of that kind of fiddling, you ought to be convinced of the essential unreliability of all subjective experiences up to and including unity of consciousness. Like the temporal order of events during a burn, unity of consciousness may not be what it subjectively appears to be, so you don't get to take it as a premise.

So Mitchell's perception of colors as fundamental irreducible qualia could be a similar illusion. Intriguing possibility!

It's not just an intriguing possibility, it's really the only counterargument anyone has, given that no-one has actually produced a way to make color out of noncolor.