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Consciousness: the trouble with Tononi's critics

In recent years, several readers have asked about my opinion about the Integrated Information Theory (IIT), a theory about "what consciousness is and where it is" started by neuroscientist Giulio Tononi in 2004. Some of them have expressed the opinion that IIT seems compatible with my understanding of the role of the ("conscious") observer in quantum mechanics etc.

My knowledge about IIT slowly grew and my opinions gradually strengthened. But it was the 2014 texts by computer scientist Scott Aaronson

Why I Am Not An Integrated Information Theorist (or, The Unconscious Expander)

Why Scott should stare at a blank wall and reconsider (or, the conscious grid)

Giulio Tononi and Me: A Phi-nal Exchange
that I only saw now (hat tip: Pig) have convinced me that despite my and our ignorance about most of the key questions, my opinions are already rather strong and my basis to be certain that e.g. Scott Aaronson's critique is a pile of šit is rather solid.

That doesn't mean that I believe that IIT is a correct let alone proven theory and it has no problems. I feel somewhat inspired by IIT but I find many of its axioms and formulae arbitrary, suffering from undesirable technical features, while others are vacuous. Also, IIT doesn't answer many questions that a "theory of consciousness" as I imagine it should also (or primarily) answer.

OK, let's begin. IIT primarily claims to be able to say which physical objects – not only humans – have consciousness and how much of it. The amount of consciousness in an object is called \(\Phi\) (capital phi) and there is a formula for \(\Phi\), although it's not always the same formula. When an object has a high \(\Phi\), it has a lot of consciousness. When it has a low \(\Phi\), it has a low consciousness.

There are lots of uncertainties about the "right form of the formula for \(\Phi\)" but roughly speaking, it's a realization of Aristotle's
The whole is greater than the sum of its parts.
Tononi's \(\Phi\) is basically the maximum of "something similar to the entanglement entropy" taken over all possible ways to divide the object to two subsystems \(A,B\). The amount of consciousness \(\Phi\) is therefore "some form of information" that can't be attributed to the individual parts of the object – information that is therefore "integrated" to the whole.

In other words, Tononi believes that some "non-local existence" of the information is a necessary condition for one to be conscious. In the most general discussions in quantum gravity, the notion therefore depends on the "emergent spacetime geometry and locality". I find this idea very interesting and possible to be correct. For some technical reasons, Tononi's consciousness \(\Phi\) doesn't arise for 1D chains and requires at least 2D grids, if I simplify a bit.

One may try Tononi's first formula and its refinements and calculate the amount of consciousness of a human. By design, one always gets a high enough value. However, one also gets high values for objects that are less charming – those are said by Tononi to be conscious. Aaronson's criticism almost entirely focuses on Aaronson's prejudices that "these and other systems just don't have the right to be conscious because I don't like it". Spoiled brat Aaronson doesn't have a glimpse of an argument for his prejudices but he tries to spread them aggressively, anyway. I will get to this point soon.

But for a while, let me discuss issues unrelated to these critiques. From a theory of consciousness, one could expect an explanation of the following things:
  1. The hard problem: the explanation why consciousness exists at all, where it comes from, why we "feel" the bitter taste of fernet, why our world differs from a structurally similar world of formulae where no one is aware of anything (or is the consciousness inseparable from the mathematical structures?)
  2. The pretty hard problem: that's a term coined by Aaronson and one means the division of objects to conscious and unconscious ones, or the quantification how much consciousness there is
  3. The qualia classification problem: this is my term and these explanations should classify different kinds of qualia – perceptions – and define rules saying which other humans or objects feel or are conscious about "exactly the same thing" as you are under which circumstances
  4. Mechanisms of the Heisenberg choice: that's my term, too: in quantum mechanics, the Heisenberg choice is the observer's choice "which observable \(\hat L\) he wants to be measured"; this is followed by Nature's "Dirac choice" which says what the outcome \(\lambda_i\) is. Quantum mechanics predicts probabilities of various \(\lambda_i\), the Dirac choice, but it can't predict the probabilities that the observer "wants" to measure one thing or another. Are these choices predictable in any way? Probabilistically? And if not – I think they can't be – are there at least constraints that say what \(\hat L\) an observer may choose and when?
As you can see, the last two items are "mine". I believe that they're ambitious but most reasonably believed to be accessible to science. But people's (and I think that even Tononi's) focus on them seems minimal. Note that the qualia classification problem requires one to talk not just about "how much" consciousness there is but also "which of the possible conscious events" took place. The last, Heisenberg choice mechanism obviously requires the neuroscientist to understand quantum mechanics well. An average neuroscientist probably doesn't even appreciate that quantum mechanics requires an observer to choose his observables of interests before the laws of physics may be applied.

OK, I have some vague opinions about the truly interesting – third and fourth – problems but IIT seems to be largely silent about them and because this blog post is supposed to be about IIT, I won't elaborate on my ideas much because the value of the blog post could quickly surpass the value of the whole IIT literature by several orders of magnitude, yet remain too provocative and incomplete, and I just don't intend to throw these pearls before swine.

Instead, let me restrict our attention to the easy-to-formulate – first and second – problems, the hard problem and the pretty hard problem. The hard problem is hard – and there are reasons to think that it could be too ambitious for any scientific theory. Science ultimately studies objects as "external objects" and may look at their inner organization and externally detectable behavior and that's it. But that's exactly what we feel to be insufficient to discuss "pure" consciousness which is a purely internal, subjective phenomenon.

OK, is there something "unobservable externally" about consciousness that may be studied by nontrivial papers? I am aware of my feelings and conscious experiences to a greater extent than anyone else can be. Can I use this extra access to my own consciousness for finding something more about myself, consciousness, or the brain that external neuroscientists can't do with their experiments? This is an interesting question and I am highly uncertain about the answer.

Most of IIT and Aaronson's discussion focuses on the second problem, the right way to quantify \(\Phi\). IIT says that you divide the object into \(A,B\) in all possible ways and quantify the amount of information between \(A\)'s outputs and \(B\)'s inputs. Then you maximize over all divisions to \(A,B\), and you basically get \(\Phi\), the measure of consciousness, except that various ad hoc denominators were sometimes added and one doesn't have any real evidence that any of the formulae is correct – and one doesn't have any way to observe this \(\Phi\) or find its implications, either. ;-) And if \(\Phi\) has no observable or perceivable (by me) implications, should I be interested in this quantity at all?

OK, almost all of Aaronson's criticism is about the particular values of \(\Phi\) that IIT calculates for various systems and Aaronson believes that the values are too high because those objects "should" be (basically) unconscious. And it's this criticism that makes me certain than Aaronson's attitude to all these issues is absolutely irrational, prejudiced, and worthless.

His final example is a "machine that multiplies a vector \(\vec v\) by a Vandermonde matrix \({\bf V}\)". Well, as Tononi points out, Aaronson doesn't quite distinguish matrices from mathematical objects (it's the latter that are assigned \(\Phi\) by Tononi while Aaronson wants to calculate \(\Phi\) for matrices) so all Aaronson's sentences always immediately show that he doesn't really know what he's talking about. Some algebra is used to argue that Tononi's IIT formulae will conclude that \(\Phi\) of this system is huge – it has lots of consciousness. Just make the matrix large enough and the "mechanical multiplier" will have more consciousness than a human. That shouldn't happen, Aaronson says. But should it?

There are some problems on both sides. We don't have any prescription to empirically measure \(\Phi\) of objects – at most ours, but even that is not quantitative – because we can't see into other objects' (internal) consciousness and there are no \(\Phi\)-meters. So it's hard to apply the scientific method and rule out (or confirm) some hypotheses about the right formulae to quantify \(\Phi\). But some quantity such as \(\Phi\) could exist and it could be important – because many of us "feel" that consciousness is important by itself. Aaaronson's attitude to claims about \(\Phi\) is purely irrational, emotional, and prejudiced and one should pay no attention to it.

Aaronson uses his "intuition" and "common sense" to refuse Tononi's theory. It's just amazing how many times Aaronson repeats the word "intuition" or "common sense" in consequential sentences of his essay:
[...] On the other hand, for the theory to work, it had better be the case that \(\Phi\) is small for “intuitively unconscious” systems, and only large for “intuitively conscious” systems. [...]

[...] The test of such a theory is whether it can produce results agreeing with “commonsense intuition”: for example, [...]

[...] The reason it’s so important that the theory uphold “common sense” on these test cases is that, given the experimental inaccessibility of consciousness, this is basically the only test available to us. [...]
And there are a dozens of others. Aaronson's attitude is spectacularly idiotic. If a "theory of consciousness" is being rated purely according to how well it agrees with Aaronson's "intuition" or "common sense", the value of the theory just can't possibly exceed the value of Aaronson's "intuition" and "common sense" themselves. Instead of constructing IIT, why don't we ask Oracle Aaronson directly? What does your infallible intuition or common sense say about the consciousness of an elephant with a supercomputer connected to its brain?

A rational person won't do it because a rational person knows that Aaronson doesn't know anything about the consciousness of the enhanced elephant. It's the very point of the search for theories such as IIT to find interesting answers that we couldn't otherwise find – or at least, that we couldn't rationally trust. If a convincing or even established theory will tell me that some particular engine has the amount of consciousness \(\Phi\) much greater than mine, I will happily learn. Such insights – and especially surprising insights – are why we wanted the theory to be found in the first place. Relativity and quantum mechanics are important exactly because they imply lots of correct insights that couldn't have been deduced previously – or that would look incredible before 1905.

Just to be sure, when I find out that a tree or a Vandermonde multiplier has a greater amount of consciousness than I do, it will be an interesting lesson but it won't imply that I will struggle to become a tree or a Vandermonde multiplier. Something's having lots of consciousness is not equivalent to our duty to want to become these objects or the rights that these objects get in our constitutions or the attention they get in our schools etc. I feel that Aaronson conflates all these totally inequivalent properties all the time.

(Tononi says that IIT predicts high \(\Phi\) for many "dull" objects but also low \(\Phi\) for many "incorrectly" organized complex biological networks. There are lots of interesting "predictions" except that it's not clear to me how these predictions could be tested, even in principle – the "in principle" part is what makes this problem more serious than e.g. the experimental inaccessibility of string theory.)

More importantly, Aaronson doesn't seem to get the totally elementary point, the point of all scientific research, that we are looking for theories exactly because we ultimately want to have something that is more trustworthy than our prejudices, intuition, and common sense. If he rejects the very thesis that his prejudices may be beaten by a theory, he shouldn't study theories at all because he clearly has no respect to them – and to this very method of studying the world that we call science (or its generalizations). For Aaronson, a "scientific" theory is just a pile of intimidating symbols designed to promote someone's (more precisely, his) prejudices. Sorry, that's not what actual science is. At every level of learning, a rational human being has some opinions or expectations about everything. But the very point of further research is to find insights that may negate, debunk, or otherwise change the current opinions. To assume that this isn't "allowed" to happen is completely equivalent to a ban on all scientific research.

OK, let's stop talking about Aaronson's fundamental misunderstanding of the scientific or rational thinking. Let's say a few words about the values of \(\Phi\). Do I believe that a quantity like that exists? And is Tononi's Ansatz right or close to the truth?

First, I am not certain but I can imagine that a quantity like that exists. The amount of consciousness \(\Phi\) could be a quantity somewhat analogous to the information, entropy, von Neumann entropy, entanglement entropy, complexity, and other things that have been given some definitions that are justified and quantitative to one extent or another.

Second, I do feel that the "integrated aspect" is close to the truth. If a formula for \(\Phi\) exists, it should probably be additive/extensive under simple enough circumstances and it should be strictly additive for composite decoupled systems. For that reason, it should count some "links" between parts of the system. So I do feel that the "integrated" adjective is on the right track. Instead of "integrated information", you could say "delocalized entropy". Try to define "consciousness" as "delocalized entropy" and I think that if you're smart enough, you will get something similar to Tononi or better.

There are other things that seem less correct to me, however.

For example, I do believe that consciousness is a process, not static stuff.

When you sleep, especially at some stages of the night, your consciousness apparently drops to zero or nearly to zero. That's despite the fact that the neurons still remember all the things you will recall tomorrow in the morning. I guess that "to be conscious" is really about "doing", not just "being".

Formally, this should mean that a correct \(\Phi\) shouldn't count the "number of bit-like things in the space" but rather "the weighted number of events of a sort in the spacetime". In other words, I think that consciousness should be extensive not only in space but also in time. If you live for 100 years instead of 50 with the same "rate of conscious experiences", you will have gone through the double amount of consciousness.

So I do think that consciousness is something like that "production of a quantity similar to entropy", or a "subset of entropy" of a certain kind. Imagine that someone's thinking is 10 times slower than yours – for example because he's freezing in the fridge. ;-) His consciousness at a given moment should be 10 times lower. The instantaneous consciousness should count the "number of certain 'ideas' per second". In particular, I believe that "completely frozen objects" have zero consciousness.

Because Tononi's \(\Phi\) doesn't seem to agree even with this basic property that I associate with consciousness, it's hard for me to take his formulae seriously or spend too much time with their detailed properties. Yes, I do think that the detailed formulae have rather serious defects. For this reason, the bulk of the papers about IIT – but also the mathematical part of Aaronson's and other criticisms of IIT – seems like useless mathematical masturbation designed to make the texts longer and more intimidating (and perhaps get some grants if the agency requires equations) but the actual value of these mathematical additions is very low at this moment.

One more stunning issue with Aaronson. He can't think rationally enough to decouple the problem with some petty irrelevant technicalities that his normal research is about. For example, Aaronson wrote:
I conjecture that approximating \(\Phi\) is an NP-hard problem, even for restricted families of f’s like \(NC^0\) circuits—which invites the amusing thought that God, or Nature, would need to solve an NP-hard problem just to decide whether or not to imbue a given physical system with consciousness!
Well, this is as stupid as a doorknob (I haven't calculated \(\Phi\) of a doorknob yet, however). Approximating some quantity may be hard work but that doesn't mean that the quantity is unscientific or ill-defined. Whether something is an NP-hard problem is just a technical detail unrelated to the basic questions. Something's being NP-hard is just about our ability – or our computers' ability – to find an answer.

But Nature isn't constrained by any of these human or technological constraints. If the laws of physics dictate something that would be "factorially factorially hard" – taking time similar to \((N!)!\), i.e. much much longer time than any normal non-polynomial time that Aaronson uses as a bogeyman – to be calculated by humans or simple von Neumann computers, Nature may (and according to Her laws, must) find the answers, anyway. The idea that the laws of Nature should be "easy to be calculated" by humans or computers is absolutely unjustified and idiotic. In fact, there are lots of examples that show that the laws of Nature indeed are hard to calculate (in the NP-like sense). That doesn't imply any inconsistency or a paradox: Nature finds it easy to solve many tasks that would be hard for us. It just implies that computers as we know them aren't promising tools to solve some problems or simulate Nature or something like that. This fact may make computer scientists and programmers feel less self-confident but there's nothing wrong about it. There is not much reason for them to be too self-confident – their field is basically just a part of engineering, not a field solving the deepest problems of the Universe. If they find something to be hard, it's just hard for "some current technology" – it's not shown to be impossible in Nature.

Equivalently, look at this part of his sentence:
[...] Nature, would need to solve an NP-hard problem just to decide whether or not to imbue a given physical system with consciousness!
That's a silly formulation, too, and not just because Nature has no trouble to solve NP-hard and even much harder problems. Also, Nature isn't "deciding" whether a physical system should have consciousness. Nature is deciding how physical systems arise, evolve, merge, and split, and their consciousness is a consequence of these things. So the quantification of \(\Phi\) is a consequence of many events that may be calculated at the end – it is not a "decision" one starts with. He just completely misunderstands the logical and causal relationships and chronology of all these things. In fact, it looks like this self-described atheist believes that God started with some teleological goal to create a human to His image, with a plan of how big \(\Phi\) the man should have etc., and all the other details have to be adjusted in order to achieve this goal.

And my problems with Aaronson's text go on and on and on. When he points out the "blasphemy" that the Vandermonde multiplication engine has a high amount of consciousness \(\Phi\), he says:
And yet this Vandermonde system doesn’t even come close to doing anything that we’d want to call intelligent, let alone conscious!
The words "intelligent, let alone conscious" are cute. You may see that Aaronson implicitly states that consciousness is a higher form of intelligence. But that's just silly. There is no strict dependence of consciousness on high intelligence. Dogs are cute, somewhat smart but not terribly smart. But I am pretty sure that the conscious feelings of a dog caused by seeing red and green are pretty much identical to the feelings experienced by the red-green color-blind people who have a similar vision. The amount of consciousness in these two pairs of eyes or brains is almost certainly "about the same" according to any reasonable formula, too.

Consciousness is about having "feelings" and knowing about them. It is something very different from intelligence. None of these two concepts depends on the other.


I don't believe that Tononi's theory is flawless or that he has solved all the important problems of consciousness correctly – instead, I think that he hasn't even started to address some problems that could and should be addressed and some details of his answers to other questions seem incorrect to me – but IIT is a respectable attempt to introduce some mathematics to the discussions of consciousness.

When I compare my problems with some issues of Tononi's theory and Tononi's reasoning with the fundamental defects manifested e.g. by Aaronson's criticism, I must conclude that all my criticisms of IIT are minor in comparison. People like Aaronson don't even get the point that some conclusions of the scientific research or predictions by theories (when they're justified by something) could be more important than his prejudices and random "intuitive" and "common sense" guesses.

Even if IIT is a combination of wrong, vacuous, and arbitrary propositions at this moment, Tononi is still throwing pearls before swine if he addresses his texts to readers such as Scott Aaronson. There is zero chance for them to ever appreciate any important insight, even if one emerges, because these mediocre and unjustifiably self-confident would-be scholars are convinced that they were given all the important answers to everything once they were born.

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