Extract from Principia Qualia (2016) by my colleague Michael E. Johnson (from Qualia Research Institute). This is intended to summarize the core ideas of chapter 2, which proposes a precise, testable, simple, and so far science-compatible theory of the fundamental nature of valence (also called *hedonic tone* or the *pleasure-pain axis*; what makes experiences *feel good or bad*).

## VII. Three principles for a mathematical derivation of valence

We’ve covered a lot of ground with the above literature reviews, and synthesizing a new framework for understanding consciousness research. But we haven’t yet fulfilled the promise about valence made in Section II- to offer a rigorous, crisp, and relatively simple hypothesis about valence. This is the goal of Part II.

Drawing from the framework in Section VI, I offer three principles to frame this problem:

**1. Qualia Formalism**: for any given conscious experience, there exists- in principle- a mathematical object isomorphic to its phenomenology. This is a formal way of saying that consciousness is in principle quantifiable- much as electromagnetism, or the square root of nine is quantifiable. I.e. IIT’s goal, to generate such a mathematical object, is a valid one.

**2. Qualia Structuralism**: this mathematical object has a rich set of formal structures. Based on the regularities & invariances in phenomenology, it seems safe to say that qualia has a non-trivial amount of structure. It likely exhibits connectedness (i.e., it’s a unified whole, not the union of multiple disjoint sets), and compactness, and so we can speak of qualia as having a topology.

More speculatively, based on the following:

(a) IIT’s output format is data in a vector space,

(b) Modern physics models reality as a wave function within Hilbert Space, which has substantial structure,

(c) Components of phenomenology such as color behave as vectors (Feynman 1965), and

(d) Spatial awareness is explicitly geometric,

…I propose that Qualia space also likely satisfies the requirements of being a metric space, and we can speak of qualia as having a *geometry*.

Mathematical structures are important, since the more formal structures a mathematical object has, the more elegantly we can speak about patterns within it, and the closer our words can get to “carving reality at the joints”.

**3. Valence Realism**: valence is a crisp phenomenon of conscious states upon which we can apply a measure.

–> I.e. some experiences do feel holistically better than others, and (in principle) we can associate a value to this. Furthermore, to combine (2) and (3), this pleasantness could be encoded into the mathematical object isomorphic to the experience in an efficient way (we should look for a concise equation, not an infinitely-large lookup table for valence). […]

I believe my three principles are all necessary for a satisfying solution to valence (and the first two are necessary for any satisfying solution to consciousness):

### Considering the inverses:

If *Qualia Formalism* is false, then consciousness is not quantifiable, and there exists no formal knowledge about consciousness to discover. But if the history of science is any guide, we don’t live in a universe where phenomena are intrinsically unquantifiable- rather, we just haven’t been able to crisply quantify consciousness yet.

If *Qualia Structuralism* is false and Qualia space has no meaningful structure to discover and generalize from, then most sorts of knowledge about qualia (such as which experiences feel better than others) will likely be forever beyond our empirical grasp. I.e., if Qualia space lacks structure, there will exist no elegant heuristics or principles for interpreting what a mathematical object isomorphic to a conscious experience *means*. But this doesn’t seem to match the story from affective neuroscience, nor from our everyday experience: we have *plenty* of evidence for patterns, regularities, and invariances in phenomenological experiences. Moreover, our informal, intuitive models for predicting our future qualia are generally very good. This implies our brains have figured out some simple rules-of-thumb for how qualia is structured, and so qualia does have substantial mathematical structure, even if our formal models lag behind.

If *Valence Realism* is false, then we really can’t say very much about ethics, normativity, or valence with any confidence, ever. But this seems to violate the revealed preferences of the vast majority of people: we sure behave as if some experiences are objectively superior to others, at arbitrarily-fine levels of distinction. It may be very difficult to put an objective valence on a given experience, but in practice we don’t behave as if this valence doesn’t exist.

[…]

### VIII. Distinctions in qualia: charting the explanation space for valence

Sections II-III made the claim that we need a bottom-up quantitative theory like IIT in order to successfully reverse-engineer valence, Section VI suggested some core problems & issues theories like IIT will need to address, and Section VII proposed three principles for interpreting IIT-style output:

- We should think of qualia as having a mathematical representation,
- This mathematical representation has a topology and probably a geometry, and perhaps more structure, and
- Valence is real; some things do feel better than others, and we should try to explain why in terms of qualia’s mathematical representation.

But what does this get us? Specifically, how does assuming these three things get us any closer to solving valence if we *don’t have an actual, validated dataset (“data structure isomorphic to the phenomenology”) from *any* system, much less a real brain?*

It actually helps a *surprising amount*, since an *isomorphism* between a structured (e.g., topological, geometric) space and qualia implies that *any clean or useful distinction we can make in one realm automatically applies in the other realm as well*. And if we can explore what kinds of distinctions in qualia we can make, we can start to chart the explanation space for valence (what ‘kind’ of answer it will be).

I propose the following four distinctions which depend on only a very small amount of mathematical structure inherent in qualia space, which should apply equally to qualia and to qualia’s mathematical representation:

- Global vs local
- Simple vs complex
- Atomic vs composite
- Intuitively important vs intuitively trivial

[…]

Takeaways: this section has suggested that we can get *surprising mileage* out of the hypothesis that there will exist a geometric data structure isomorphic to the phenomenology of a system, since if we can make a distinction in one domain (math or qualia), it will carry over into the other domain ‘for free’. Given this, I put forth the hypothesis that valence may plausibly be a *simple, global, atomic, and intuitively important property* of both qualia and its mathematical representation.

## IX. Summary of heuristics for reverse-engineering the pattern for valence

Reverse-engineering the precise mathematical property that corresponds to valence may seem like finding a needle in a haystack, but I propose that it may be easier than it appears. Broadly speaking, I see six heuristics for zeroing in on valence:

A. Structural distinctions in Qualia space (Section VIII);

B. Empirical hints from affective neuroscience (Section I);

C. A priori hints from phenomenology;

D. Empirical hints from neurocomputational syntax;

E. The Non-adaptedness Principle;

F. Common patterns across physical formalisms (lessons from physics). None of these heuristics determine the answer, but in aggregate they dramatically reduce the search space.

#### IX.A: Structural distinctions in Qualia space (Section VIII):

In the previous section, we noted that the following distinctions about qualia can be made: Global vs local; Simple vs complex; Atomic vs composite; Intuitively important vs intuitively trivial. Valence plausibly corresponds to a *global*, *simple*, *atomic*, and *intuitively important* mathematical property.

[…]

**Music is surprisingly pleasurable; auditory dissonance is surprisingly unpleasant.** Clearly, music has many adaptive signaling & social bonding aspects (Storr 1992; Mcdermott and Hauser 2005)- yet if we subtract everything that could be considered signaling or social bonding (e.g., lyrics, performative aspects, social bonding & enjoyment), we’re still left with something very emotionally powerful. However, this pleasantness can vanish abruptly- and even *reverse*– if dissonance is added.

Much more could be said here, but a few of the more interesting data points are:

- Pleasurable music tends to involve elegant structure when represented geometrically (Tymoczko 2006);
- Non-human animals don’t seem to find human music pleasant (with some exceptions), but with knowledge of what pitch range and tempo their auditory systems are optimized to pay attention to, we’ve been able to adapt human music to get animals to prefer it over silence (Snowdon and Teie 2010).
- Results suggest that consonance is a primary factor in which sounds are pleasant vs unpleasant in 2- and 4-month-old infants (Trainor, Tsang, and Cheung 2002).
- Hearing two of our favorite songs at once doesn’t feel better than just one; instead, it feels significantly worse.

More generally, it feels like music is a particularly interesting case study by which to pick apart the information-theoretic aspects of valence, and it seems plausible that evolution may have piggybacked on some fundamental law of qualia to produce the human preference for music. This should be most obscured with genres of music which focus on lyrics, social proof & social cohesion (e.g., pop music), and performative aspects, and clearest with genres of music which avoid these things (e.g., certain genres of classical music).

[…]

## X. A simple hypothesis about valence

To recap, the general heuristic from Section VIII was that valence may plausibly correspond to a *simple*, *atomic*, *global*, and *intuitively important* geometric property of a data structure isomorphic to phenomenology. The specific heuristics from Section IX surveyed hints from *a priori* phenomenology, hints from what we know of the brain’s computational syntax, introduced the Non-adaptedness Principle, and noted the unreasonable effectiveness of beautiful mathematics in physics to suggest that the specific geometric property corresponding to pleasure should be something that involves some sort of *mathematically-interesting patterning*, *regularity*, *efficiency*, *elegance*, and/or *harmony*.

We don’t have enough information to formally deduce which mathematical property these constraints indicate, yet in aggregate these constraints hugely reduce the search space, and also substantially point toward the following:

*Given a mathematical object isomorphic to the qualia of a system, the mathematical property which corresponds to how pleasant it is to be that system is that object’s symmetry.*

*Given a mathematical object isomorphic to the qualia of a system, the mathematical property which corresponds to how pleasant it is to be that system is that object’s symmetry.*

[…]

## XI. Testing this hypothesis today

In a perfect world, we could plug many peoples’ real-world IIT-style datasets into a symmetry detection algorithm and see if this “Symmetry in the Topology of Phenomenology” (SiToP) theory of valence successfully predicted their self-reported valences.

Unfortunately, we’re a long way from having the theory and data to do that.

But if we make two fairly modest assumptions, I think we should be able to perform some reasonable, simple, and elegant tests on this hypothesis *now*. The two assumptions are:

- We can probably assume that symmetry/pleasure is a more-or-less
*fractal*property: i.e., it’ll be evident on basically*all*locations and scales of our data structure, and so it should be obvious even with imperfect measurements. Likewise, symmetry in one part of the brain will imply symmetry elsewhere, so we may only need to measure it in a small section that need not be directly contributing to consciousness. - We can probably assume that symmetry in connectome-level brain networks/activity will roughly imply symmetry in the mathematical-object-isomorphic-to-phenomenology (the symmetry that ‘matters’ for valence), and vice-versa. I.e., we need not worry too much about the exact ‘flavor’ of symmetry we’re measuring.

So- given these assumptions, I see three ways to test our hypothesis:

**1. More pleasurable brain states should be more compressible (all else being equal).**

Symmetry implies compressibility, and so if we can measure the compressibility of a brain state in some sort of broad-stroke fashion while controlling for degree of consciousness, this should be a fairly good proxy for how pleasant that brain state is.

[…]

**2. Highly consonant/harmonious/symmetric patterns injected directly into the brain should feel dramatically better than similar but dissonant patterns.**

Consonance in audio signals generally produces positive valence; dissonance (e.g., nails-on-a-chalkboard) reliably produces negative valence. This obviously follows from our hypothesis, but it’s also obviously true, so we can’t use it as a novel prediction. But if we take the general idea and apply it to unusual ways of ‘injecting’ a signal into the brain, we should be able to make predictions that are (1) novel, and (2) practically useful.

TMS is generally used to *disrupt* brain functions by oscillating a strong magnetic field over a specific region to make those neurons fire chaotically. But if we used it on a lower-powered, rhythmic setting to ‘inject’ a symmetric/consonant pattern directly into parts of the brain involved directly with consciousness, the result should produce good feeling- or at least, *much* better valence than a similar dissonant pattern.

Our specific prediction: direct, low-power, rhythmic stimulation (via TMS) of the thalamus at harmonic frequencies (e.g., @1hz+2hz+4hz+6hz+8hz+12hz+16hz+24hz+36hz+48hz+72hz+96hz+148hz) should feel significantly more pleasant than similar stimulation at dissonant frequencies (e.g., @1.01hz+2.01hz+3.98hz+6.02hz+7.99hz+12.03hz+16.01hz+24.02hz+35.97hz+48.05hz+72.04hz+95.94hz+ 147.93hz).

[…]

**3. More consonant vagus nerve stimulation (VNS) should feel better than dissonant VNS.**

The above harmonics-based TMS method would be a ‘pure’ test of the ‘Symmetry in the Topology of Phenomenology’ (SiToP) hypothesis. It may rely on developing custom hardware and is also well outside of my research budget.

However, a promising alternative method to test this is with consumer-grade vagus nerve stimulation (VNS) technology. Nervana Systems has an in-ear device which stimulates the Vagus nerve with rhythmic electrical pulses as it winds its way past the left ear canal. The stimulation is synchronized with either user-supplied music or ambient sound. This synchronization is done, according to the company, in order to mask any discomfort associated with the electrical stimulation. The company says their system works by “electronically signal[ing] the Vagus nerve which in turn stimulates the release of neurotransmitters in the brain that enhance mood.”

This explanation isn’t very satisfying, since it merely punts the question of why these neurotransmitters enhance mood, but their approach seems to work– and based on the symmetry/harmony hypothesis we can say at least something about *why*: effectively, they’ve somewhat accidentally built a synchronized bimodal approach (coordinated combination of music+VNS) for inducing harmony/symmetry in the brain. This is certainly not the only component of how this VNS system functions, since the parasympathetic nervous system is both complex and powerful by itself, but it could be an important component.

Based on our assumptions about what valence is, we can make a hierarchy of predictions:

- Harmonious music + synchronized VNS should feel the best;
- Harmonious music + placebo VNS (unsynchronized, simple pattern of stimulation) should feel less pleasant than (1);
- Harmonious music + non-synchronized VNS (stimulation that is synchronized to a
*different*kind of music) should feel less pleasant than (1); - Harmonious music + dissonant VNS (stimulation with a pattern which scores low on consonance measures such as (Chon 2008) should feel worse than (2) and (3));
- Dissonant auditory noise + non-synchronized, dissonant VNS should feel pretty awful.

We can also predict that if a bimodal approach for inducing harmony/symmetry in the brain is better than a single modality, a trimodal or quadrimodal approach may be even more effective. E.g., we should consider testing the addition of synchronized rhythmic tactile stimulation and symmetry-centric music visualizations. A key question here is whether adding stimulation modalities would lead to diminishing or synergistic/accelerating returns.

Fantastic work, but I’m going to be quite critical here. I would be very interested to see if you can incorporate my criticisms.

Could it be that music (and symmetry) is a red herring and that pleasure is more fundamental. Could it be that the symmetry/consonance is not pleasure itself, but merely often triggers pleasure.

I don’t think you have a solid foundation of what euphoria and dysphoria are. For example you lump “anger, nausea, fear, anxiety and pain” into the category of dysphoric states. From extensive meditation I’ve come to realise that it is the suppression, or interaction, of these states with the socio-linguist & truth-evaluating part of the mind that is suffering, not the sensations themselves.

Some examples:

– Intense rage when not supressed but instead when one indulges in violence can be quite euphoric.

– nausea is only dysphoric when suppressed, usually when one is trying not to vomit, but when one allows oneself to vomit it can actually be quite euphoric.

– Fear and anxiety, again, when not suppressed, but instead if you indulge in “fight or flight” or even just “screaming” can be euphoric.

– Pain, this one has it’s obvious counterexamples in masochists, even humiliation can be euphoric to a masochist

Your pallet of positive experiences is limited by the very system of mind that is creating the dysphoria. Put another way, it’s the “belief that sensation/emotion X is bad” that makes it bad, not the sensation/emotion itself. This is why experienced meditators can self emulate. Beliefs are highly social, and linguistic, which is why the social and thought inhibiting drugs seem to be the best at causing euphoria. I would even go as far to say that morality plays a part. Anxiety grounded in “I have done something wrong” has negative valance, but the raw sensation of cortisol burning your muscles for energy is in of itself neutral – or possibly even positive.

Finally, it does seem that drugs can affect our beliefs, and even the feeling of knowing something can be hacked with drugs. Therefore a mathematical theory of valence is going to be considerably harder than you make it seem.

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