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.