*[Edit: Scott Aaronson has posted on his blog with extensive criticism of Integrated Information Theory, which motivated Tegmark’s paper.]*

Max Tegmark’s recent paper entitled “Consciousness as a State of Matter” has been making the rounds. See especially Sabine Hossenfelder’s critique on her blog that agrees in several places with what I say below.

Tegmark’s paper didn’t convince me that there’s anything new here with regards to the big questions of consciousness. (In fairness, I haven’t read the work of neuroscientist Giulio Tononi that motivated Tegmark’s claims). However, I *was* interested in what he has to say about the proper way to define subsystems in a quantum universe (i.e. to “carve reality at its joints”) and how this relates to the quantum-classical transition. There is a sense in which the modern understanding of decoherence simplifies the vague questions “How does (the appearance of) a classical world emerge in a quantum universe? ” to the slightly-less-vague question “what are the preferred subsystems of the universe, and how do they change with time?”. Tegmark describes essentially this as the “quantum factorization problem” on page 3. (My preferred formulation is as the “set-selection problem” by Dowker and Kent. Note that this is a separate problem from the origin of probability in quantum mechanics^{ a }.)

Therefore, my comments are going to focus on the “object-level” calculations of the paper, and I won’t have much to say about the implications for consciousness except at the very end. However, Tegmark’s paper cannot be understood without looking at the list of principles in Table II on page 3. At my level of understanding, the thrust of the paper is this: “Here is a list of English words with intuitive but imprecise definitions that, at the least, seem to be necessary conditions for anything we might reasonably call consciousness. Let’s postulate that these are well measured by some very simple abstract mathematical quantities. Then, by looking at some toy models, let’s try to get a sense of the types of classical and quantum systems that extremize these quantities.”

The paper has 5 sections. Section I is the introduction, and Section V is the extensive concluding section with much discussion on the outlook for future work. The middle three sections compose the main text, and they are titled after the principles that are explored through toy models: “Integration”, “Independence”, and “Dynamics and Autonomy”.

**Main critique**

The principles that Tegmark identifies are the following: “information”, “dynamics”, “independence”, “integration”, “utility”^{ b }. He does not spend much time justifying these choices in terms of consciousness (leaving this mostly to Tononi). Instead, he jumps quickly into introducing some mathematical quantities (hereafter: “metrics”) which might measure these intuitive principles and then exploring them in toy models, looking especially for states and Hamiltonians that extremize the metrics. Unfortunately, I didn’t get much out of the toy model calculations. The importance of most of the metrics (e.g. “energy coherence”, “probability velocity”, “independence time scale”) that are postulated by Tegmark to capture the aforementioned principles remain unclear to me, even after seeing their definitions and their calculated behavior. Here is a test: if we replaced each of these motivating words with, say, their Irish Gaelic translation–a mere relabeling–would the results (now unattached from lofty language about consciousness) lose their appeal? I’m afraid they might.

Taking the principles at face value, I have a hard time being convinced that they are pointing toward consciousness in even a rough way. It looks like a Turing machine running a near *trivial* program satisfies all the criteria (save “utility”, I suppose^{ c }.) So maybe the idea is that *maximizing* the criteria bring us closer to consciousness? I don’t see how; I think you’ll just find a pathalogical quantum state that artificially maximizes whatever crude metric you’ve chosen, as happens several times in the main text every time an extremization is attempted. I found no examples where the principle of “integration”, as captured by any of the metrics used by Tegmark, ever lead to the kind of rich and robust information processing ability I’d expect to find in a conscious being.

**Aside**

I think this paragraph touches on something important:

In summary, the quantum factorization problem is both very interesting and very hard. However, as opposed to the hard problem of quantum gravity, say, where we have few if any observational clues to guide us, physics research has produced many valuable hints and clues relevant to the quantum factorization problem. The factorization of the world that we perceive and the quantum states that we find objects in have turned out to be exceptionally unusual and special in various ways, and for each such way that we can identify, quantify and understand the underlying principle responsible for, we will make another important stride towards solving the factorization problem.

Folks who look doubt that the field of “quantum foundations” has much value may look on this with alarm. In quantum gravity, we have a plausible excuse for lack of progress: no data. On the other hand, non-relativistic quantum mechanics has been studied to death, and we are awash with data. I think the claim then has to be that (a) there is some huge hole in our understanding yet (b) there will not be actual experimental departures from quantum mechanics even when it is understood. So are we even doing science, or are we just making ourselves feel better? I’ll address this in a different blog post in the future, but it’s worth highlighting for now.

**Concluding remarks**

In general, I thought this paper was simply premature. Lots of suggestions and poorly motivated toy calculations, but not many concrete results that I might personally build from. There’s nothing wrong with Tegmark putting this paper out there, but I put in some time working my way through it without feeling like I got much out of it. The paper is hard to summarize because there are many small ideas and suggestion, but no central claim or result.

The introductory and concluding sections (I and V) are lucid. My suggestion, if you’re interested in this, is to read through them. You’ll note that the Summary of Findings [section V-A] in the concluding section is rather long and has many minor claims that are hard to integrate together, and I think this accurately represents the main contents of the paper found in Section II, III, and IV. The rest of the concluding section [V-B through V-E] can thankfully be read largely independent on the main text of the paper. It can be taken on its own merits as a manifesto of sorts for Tegmark’s view of what the important questions are in understanding the “physics from scratch” problem, among them the “quantum factorization problem” so dear to my heart.

Finally, a word about consciousness versus classicality.^{ d } In short, I don’t think that consciousness is key to understanding classicality because I think that a sensible (and essentially unique) classical universe existed before life appeared. So we ought to be able to derive the classical domain without reference to consciousness, and then–conditional on new physics being unnecessary–we might then eventually understand consciousness as a purely classical phenomenon.

I suppose it’s conceivable that there are many incompatible classical domains on equal footing, but only a small number (or only just ours) is compatible with consciousness. (In that case, consciousness would crucial to deriving our classical domain.) But that seems unlikely to me.

### Footnotes

(↵ returns to text)

- The problem of probability as described by Weinberg: “The difficulty is not that quantum mechanics is probabilistic—that is something we apparently just have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.” HT Steve Hsu.↵
- Tegmark also uses “autonomy” as a combination for “dynamics” and “independence”.↵
- “Utility” is only mentioned briefly in the conclusions, especially Section V-D1, and is not discussed in the main text.↵
- Thanks to David Steglet for prompting me to address this.↵

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