# Understandability

In my  post on panpsychism, a commenter, Matt Sigl, made a valiant defense of the ideas of Koch and Tononi about consciousness. I claimed in my post that panpsychism, where some or all the constituents of a system possess some elementary form of consciousness, is no different from dualism, which says that mind and body are separate entities. Our discussion, which can be found in the comment thread, made me think more about what it means for a theory to be monistic and understandable.  I have now revised my claim to be that panpsychism is either dualist or superfluous. Tononi’s idea of integrated information may be completely correct but panpsychism would not add anything more to it. In my view, a  monistic theory is one where all the properties of a system can be explained by the fundamental governing rules. Most importantly there can only be a finite set of rules. A system with an infinite set of rules is not understandable since every situation has its own consequence. There would be no predictability; there would  be no science. There would only be history where we could write down each rule whenever we observed it.

Consider a system of identical particles that can move around in a three dimensional space and interact with each other in a pairwise fashion. Let the motion of these particles obey Newton’s laws, where their acceleration is determined by a force that is given by an interaction rule or potential. The proportionality constant between acceleration and force is the mass, which is assigned to each particle. The particles are then given an initial position and velocity. All of these rules can be specified in absolute precise terms mathematically. Space can be discrete so the particles can only occupy a finite or countably infinite number of points or continuous where the particles can occupy an uncountable infinite number of points.

Depending on how I define the interactions, select the masses, and specify the initial conditions, various things could happen.  For example,  I could have an attractive interaction, start all the particles with no velocity at the same point, and they would stay clumped together. This clumped state is a fixed point of the system. If I can move one of the particles slightly away from the point and it falls back to the clump then the fixed point is stable.  However, even a stable fixed point doesn’t mean all initial conditions will end up clumped. For example, if I have a square law attraction like gravity, then particles can orbit one another or scatter off of each other. For many initial conditions, the particles could just bounce around indefinitely and never settle into a fixed point. For more than two particles, the fate of all initial conditions is generally  impossible to predict. However, I claim that the configuration of the system at any given time is explainable or understandable because I could in principle simulate the system from a given specific initial condition and determine its trajectory for any amount of time. For a continuous system, where positions require an infinite amount of information to specify, an understandable system would be one where one could prove that there is always an initial condition that can be specified with a finite amount of information that remains close to any arbitrary initial condition.

If I make the dynamics sufficiently complex then there could be some form of basic chemistry and even biology. This need not be fully quantum mechanical;  Bohr-like atoms may be enough. If the system can form sufficiently complex molecules then evolution could take over and generate multi-cellular life forms. At some point, animals with brains could arise.  These animals could possess memory and enough computational capability to strategize and plan for the future.  There could be an entire ecosystem of plants and animals at multiple scales interacting in highly complex ways. All of this could be understandable in the sense that all of the observed dynamics could be simulated on a big enough computer if you knew the rules and the initial conditions. You may even be lucky enough that almost all initial conditions will lead to complex life.

At this point, all the properties of the system can be completely specified by an outside observer. Understandable means that all of these properties can be shown to arise from a finite set of rules and initial conditions. Now, suppose that some of the animals are also conscious in the sense that they have a subjective experience. The  panpsychic hypothesis is that consciousness is a property of some or all the particles. However, proponents must then explain why even the biggest rock does not seem conscious or human consciousness disappears when we are in deep sleep. Tononi and Koch try to finesse this problem by saying that it is only if one has enough integrated information does one notice the effect of the accumulated consciousness. However, bringing in this secondary criterion obviates the panpsychic hypothesis because there is now a systematic way to identify consciousness that is completely consistent with an emergent theory of consciousness. This doesn’t dispel the mystery of  “the hard problem” of consciousness of what exactly happens when the threshold is crossed to give subjective experience. However, the resolution is either that consciousness can be described by the finite set of rules of the constituent particles or there is a dualistic explanation where the brain “taps” into some other system that generates consciousness.  Panpsychism does not help in resolving this dilemma. Finally, it might be that the question of whether or not a system has sufficient integrated information to exhibit noticeable consciousness may be undecidable in which case there would be  no algorithm to test for consciousness. The best that one could do is to point to specific cases. If this were true then panpsychism does not solve any problem at all. We would never have a theory of consciousness. We would only have examples.

## 14 thoughts on “Understandability”

1. I’m not sure this comment is coherent, but when i think of emergence i think of a phase transition, and symmetry breaking (which may be the same thing). With a finite set of rules and initial conditions, it seems one could generate an infinite set of phase transitions—a series of bifurcations each leading to an attractor of some symmetry.

In a sense this is what math does—-from an axiomatic system one can define sets or theorems which then have their own emergent properties (eg the primes emerge from the integers by defining multiplication). So an emergent entity of this sort has its own properties and there can be ‘nonunderstandably’ many of them—no finite list. Evolution may be another example—new forms emerge from old with their own kinds of laws. These emergent laws (symmetries) may in a asense be reducible to the primary axioms or evolutionary law, but cannot really be explained in terms of them. eg any theorem involved primes by simply explaining them as operations on a set consisting of 0 and its succesors, defined by induction, leaves out some of the ‘quality’ of the emrgent phenomnena.

One more example would be in transfinite logic or set theory where undecidable statements in one formal system can be decided by adding a new axiom. So one can have an infinite number of laws (and one can I think arbitrarily have contradictory systems depending on what axiom is added—‘not a is true’ versus ‘a is true’.) usually these new axioms aare called axioms of infinity, because they essentially require closing some infinite universe of sets specified by the original axioms, and treating that as a new object defined by a transfinite cardinal (infinity). In a way the classical limit of quantum theory makes such an assumption, as does statistical mechanics of phase transitions which uses the n->infinity limit.

in a sense a phase transition is a bit like a singularity—it does introduce a new rule. I also think of what Turing called an ‘oracle’ when he was thinking of how undecidable problems might be decided (ie by some outside source, or higher authority—which of course is what humans do when they decide to halt some non-stopping ujncomputable program). Wave function collapse might also fall into this category, though here its a random choice.

I dont know how one decides if this monistic or dualistic.

Also i am not sure if math is the same as physics except analogically. Also, i think some people dont think transfinite arithmatic really makes much sense—people do prove theorems but others think there is really only uncountable and countable infinity and no more. (continuum hypothesuis.

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2. Ishi: Thanks for your comments. You are absolutely correct that infinite things can be generated out of a finite set of rules, like the reals from integers. There may also be undecidable statements. This is all fine. What I mean by understandable is that the emergent properties arise directly out of the system without further input. You do not need to be able to understand everything in an understandable system. You just need to have the potential to generate it.

I am not trying to resolve undecidability. What I wanted to get at was that consciousness could be either monist or dualist but assigning a nonobservable property as is done in panpsychism does not automatically make a theory monist.

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3. Matt Sigl says:

Thanks for the shout-out!

I can’t say I totally follow your whole argument but I just want to clarify a few things about panpsychism and the IIT.

1. The IIT claims that the “hard problem” of consciousness -subjectivity itself, the “internal character” of reality – is a fundamental property of the world. There is no solution to WHY it exists, (or at least no solution within the normal scientific paradigm).

2. There is no threshold where suddenly consciousness exists because information becomes integrated. ALL causation generates information and so ALL causation is conscious. Even if it’s generating the maximally small amount of 1-bit of information, this is true. (This is made explicit in Tononi’s photodiode thought experiment. The photodiode experiences the absolute smallest amount of consciousness possible.) This form of panpsychism does not attach itself to “particles” or any other such ‘physcial’ entities. Rather, it attaches to (or rather is generated necessarily by) causal systems. It’s the ‘inside’ of the actual causal world of which we ‘see’ only representations…representations generated by the real causal nature of our brain/mind system.

3. A rock is not conscious because, in the IIT, a rock doesn’t really ‘exist.’ A rock exists as we know it only as a discrimination made by our consciousness (which unlike the rock does exist in and of itself). An entity exists in and of itself iff it exists as ONE thing, able to generate information “to itself” by its causal structure. It’s as if the world is carved up into causal nodes each node necessarily having a internal subjective experience. Each node is fully describable using information theory; the relation and evolution of the nodes over time is also fully describable in mathematical/computational/informational terms.

4. We can see this as kind of an identity trinity (even better than a duality!): Consciousness is information and information is causation. So here we have a identity thesis between the subjective(mind)/objective(physical reality)/and platonic or mathematical(information). According to the IIT you can’t have any one without the others. Physics was already moving in this direction (holographic principle, Wheeler’s IT from BIT), it just left the mind part out.

5. It’s clear that panpsychism troubles you. As for me, I don’t see why imagining that your three particles are super-minimally conscious should be unpalatable. Just intuitively, it makes sense to me that a rat would have a smaller, simpler mind than me and a worm even simpler still. Our solar system? Simpler still! Now certainly, if there weren’t good theoretical reasons to believe this true than it would be worth a high degree of skepticism. But, as so it happens there are good reasons to believe this so! I find it plausible. Panpsychism is simply a natural extension of the suspicion that REAL emergence–mind from total insentience–is philosophically untenable and would signal a radical discontinuity in how the world works structurally and metaphysically. Plus, it would leave open the door to epiphenominalism, and that’s a theory NO ONE likes.

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4. Matt: Panpsychism doesn’t trouble me. I’m agnostic on theories of consciousness. I just want to point out that simply claiming that particles have a property doesn’t automatically make a theory monistic. I also want to point out that you could have an integrated information theory of consciousness without relying on a panpsychic crutch. You could still have a theory where consciousness emerges when sufficient integrated information accrues.

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5. PS. Actually, I have no problems whatsoever with epiphenominalism. At least it is self-consistent.

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6. PPS I have no problems with three particles experiencing consciousness. You just need to explain why I lose consciousness when I sleep or why my stomach doesn’t seem to experience consciousness, at least none that I can access. To say that there is no threshold implies that there is always consciousness, which belies observation.

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7. Matt Sigl says:

Just a quick final thought.

The IIT has a clear answer to the riddle of why our brains lose consciousness in sleep even though our neurons remain active. Indeed, it’s one of the best empirical pieces of evidence for the theory.

In computer simulations of networks with different firing patterns the systems that generate the most information have a particular causal structure and firing pattern. When all the nodes fire synchronously phi values are low. Similarly, when all the nodes fire randomly, phi values are also low. But, when the the system fires with nodes that are functionally specialized and highly connected, phi values (aka integrated information values) are high.

According to the theory then, during sleep our neurons, for biological reasons, take on near synchronous firing patterns and that is why no (or very little) information is generated. Consciousness disappears. When they return to a more normal firing pattern subjects transition to REM sleep and experience conscious dreams, just as the theory predicts. Scientists have even done magnetic stimulation of parts of the cortex in both wakefulness and sleep and recorded how the stimulation either causes a consistent firing pattern over the whole cortex (wakefullness, REM-sleep) or simply fires locally and then makes no other difference in the brains firing pattern (sleep).

A metaphor: The awake brain is always playing a beautiful symphony and each of the neurons are an instrument in the orchestra; they all work together to create music. In sleep, all the instruments are just “tuning,” making random blats of noise but they aren’t working together and make no music.

As for your stomach, the answer is straightforward. Your neuronal system simply has no direct causal interaction with the nerves in your stomach except insofar as they feed back to your brain and cause you the sensation of fullness or hunger. If there is any integrated information generated independently by the stomach “brain” the that system will, in fact, have a stream of conscious experience of its own. The brain system would have no more access to this stomach mind than it does the mind of your pet cat. It’s a different system. However, given the complexity level of the stomach compared to the brain, it’s fair to guess that whatever consciousness the stomach does generate, it’s very shallow and small compared to the richness of the human mind.

So is the asleep non-REM mind truly totally unconscious? The theory predicts that there most likely would be some phi value to this system and therefore some consciousness (or consciousnesses depending on whether or not the systems splits into smaller systems). Of course, this wouldn’t be YOUR consciousness; your memory system would have no access to it (or them). Just because an experience happens in your brain doesn’t make it YOUR experience. Plus, these experiences are probably so uninteresting, they aren’t much worth worrying about.

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8. Matt: Exactly, different values of phi lead to different values of consciousness. This means that consciousness could be entirely an emergent phenomenon. The assignment of panpsychism is a secondary hypothesis. My post is about why this is dualistic.

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9. Matt Sigl says:

It’s a semantic point we’re stuck on I think. Yes, consciousness “emerges” (leaving aside how tricky the concept of emergence really is) from any and all causal processes but, at phi values higher than one-bit, the macroscopic conscious information “controls” the systems behavior. You can call this dualism if you like, but only of a very attenuated sort.

Bottom line: I suspect the IIT IMPLIES, but doesn’t (yet) require, that fundamental ontology be informational. In this case “consciousness” and “matter” are actually both information, hence monism. (i.e.- if we could see a person like “God” does, body and mind would be just a unified causal stream of zeroes and ones) Sure, it may be that the ontological gap is truly real and dualism is correct after all, but this is philosophically troublesome for well rehearsed reasons. Traditionally in dualism, the problem of causal relations between fundamentally different substances is a real sticking point, unless, of course, consciousness is completely epiphenominal, which the IIT claims is false.

In fact, the problem of the causal efficacy of the mind is what made many turn away from dualism in the centuries following Descartes. I suppose we differ in that I find epiphenominalism so counter-intuitive that I want to rule it out, if not a priori, than at least through reasonable conceptual schematics of body/mind relations.

Thanks for the stimulating conversation. it was very enjoyable!

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10. Matt: This is not a semantic point but a philosophical point that I am trying to untangle. I completely understand your argument. What I’m trying to do is to tease out the inherent duality in it. When you say information, you have to be specific. Is this computable information or not? If it is computable information then it must be entirely contained in a finite set of rules and initial data. But then panpsychism is unnecessary. Consciousness is an emergent property of the system.

If it is not computable then you have the situation where some of the universe is computable (at least well enough that we can simulate the weather, galaxy formation, neurons, etc) while one part is not. To me, that is dualistic. When you say that consciousness is just a property of the universe and cannot be understood in more elementary terms, then this is intrinsically different from other properties like mass, which can be completely understood self-consistently.

The major theme of my blog is that the fundamental ontology is purely informational given that I think the universe can be simulated on a computer (not all would agree). However, you cannot just include consciousness in the ontology and call it monism. If consciousness is distinctly different from the other properties, then that qualifies as dualism.

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11. Matt Sigl says:

Point taken and understood. I think any speculations further dive us into baroque metaphysics so maddening that they would make me high-tail it toward the nearest bar to drown my brain in grain alcohol.

Bottom line, (and this is my extrapolation, not Tononi’s): Consciousness IS different from mass in that it is NECESSARILY fundamental (mass and other physcial properties like gravity probably can emerge from some abstract computation) and cannot be seen to “emerge” AS A PROPERTY from anything else. Instances of it emerge, not the thing itself. Consciousness IS information. It’s Kant’s “Ding an sich.” It’s the “inside” of all causation. It’s what makes a world actual as opposed to possible. But, arguing for this would take, well, a lifetime…

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12. I think your idea is perfectly reasonable. Like I said, I have no problem with the idea itself, just the supposition that it is monistic.

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13. ishi says:

interesting discussion tho i can’t exactly understand it (i think (i think) and i ‘wonder why i wonder why i wonder…’).
thanks for the reply also. i guess i am not sure that even with a finite set of rules generating an infinite number of things if that might not be inherintly dualist in the sense that a higher level system may be irreducible and hence one could even ignore the microsystem since there may be other microsystems (finite sets of rules) which generate the same system—no isomorphism, so one doesnt know which set of rules is basic, apart from maybe ZFC.

i wonder if you ever look at john baez blog azimuth—especially the information geometry stuff—replicator equations and relation to other math—entropy increase, lyapunov functions, etc. I know some apply this to cancer research.

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14. […] some amount of integrated information, I am skeptical that it is the only relevant measure. See here and here for some of my previous thoughts on the topic. One of the reasons that Tononi has proposed […]

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