--- title: "The state of play in symmetry" authors: - name: "Cube Flipper" url: "https://twitter.com/cube_flipper" discussion-url: "https://twitter.com/cube_flipper/status/1626729482815148033" --- I am starting to realise that the word *symmetry* has been doing some heavy lifting in my writing, especially in my [previous post](https://smoothbrains.net/posts/2023-01-18-an-introduction-to-steven-lehar-part-iii.html). I owe the reader a little expansion. *Symmetry* in this context is a qualia researcher's term of art, one primarily informed by Mike Johnson's [Symmetry Theory of Valence](https://opentheory.net/2021/07/a-primer-on-the-symmetry-theory-of-valence/). He describes it succinctly in his [Principia Qualia](https://opentheory.net/principia-qualia/): > 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. A *mathematical object isomorphic to the qualia of a system* might be difficult to envision. I have previously attempted to sketch out such a prototype human *qualia state* [here](/posts/2022-10-01-an-introduction-to-steven-lehar-part-i.html#open-questions). Please note that I expect the real thing to be far more general than this: > From the top down, we have: > > - The *worldsim*, which contains: > - the *worldsheet*, a *two-dimensional [surface](https://en.wikipedia.org/wiki/Surface)* where each point has both: > - *depth*, a *scalar* value, and: > - *colour*, a *three-vector* value; and: > - the *worldfield*, a *three-dimensional [vector field](https://en.wikipedia.org/wiki/Vector_field)*. A *valence function* would thus be a mathematical function which takes such a *qualia state* as input and produces a scalar value corresponding to the state's *valence* as output. Such a function would have broad utility – it could even work as a frame-invariant [utility function](https://www.lesswrong.com/tag/utility-functions) for the welfare of conscious beings! [Qualia over QALYs](https://opentheory.net/2015/06/effective-altruism-and-building-a-better-qaly/)! This is why we might seem to have such an affection for symmetry. Mike believes that a conscious system's *symmetry* is isomorphic to its *valence*, and thus any such valence function would calculate the inherent symmetries in the system. I should be clear that there currently exists no candidate valence function that I am aware of. I would invite anyone who thinks they can come up with one to give it their best shot. Calculating the symmetry of a system could well turn out to be computationally intractable, not unlike calculating a system's [Kolmogorov complexity](https://en.wikipedia.org/wiki/Kolmogorov_complexity), but it's plausible we could find useful approximations. In this sense the concept of *symmetry* remains unquantifiable – much like the concept of *complexity* – but we can still work with it. Consensus on the state space of valence is also yet to be reached. [Andrés Gómez Emilsson](https://twitter.com/algekalipso) believes that valence will be best measured on a [logarithmic scale](https://qri.org/blog/log-scales), which [seems reasonable to me](https://en.wikipedia.org/wiki/Weber–Fechner_law). [Roger Thisdell](https://www.rogerthisdell.com), an experienced meditator, believes that there is no such thing as positive valence – that the valence scale starts at *absolute zero* and only goes down – and once had a [friendly debate with Andrés](https://qri.org/blog/classical-enlightenment-and-valence-structuralism) on this prospect. Additionally, a [total ordering](https://en.wikipedia.org/wiki/Total_order) for valence might not even be viable for the qualia state spaces we are interested in, in which case we would have to resort to a [partial ordering](https://en.wikipedia.org/wiki/Partially_ordered_set). ## Does symmetry really feel good? *Temporal symmetry* might be an intuitive notion to the practicing musician, who should be well aware of how [some intervals sound *consonant* while others sound *dissonant*](https://en.wikipedia.org/wiki/Consonance_and_dissonance) – at least, when one ignores any semantic associations and pays attention to the raw auditory phenomenology. Dyadic consonance appears to be a function of [proximity to small-integer frequency ratios](https://commons.wikimedia.org/wiki/File:Dyadic_harmonic_entropy_graph_(optimized_for_low_resolution).png). I'll leave it at this for now. Perhaps this working example will be enough for you to construct your own examples and counterexamples? For a more complete exposition, I'd recommend going straight to [Part II of Principia Qualia](https://opentheory.net/PrincipiaQualia.pdf#page=27), which covers valence: > 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). ## So why might symmetry feel good? The truth is, nobody knows. At this stage, these ideas are still primarily informed by pure phenomenological introspection. As Andrés explains in his post [Quantifying Bliss](https://qri.org/blog/quantifying-bliss), if you were to study someone's [*connectome harmonics*](https://qri.org/blog/quantifying-bliss#connectome-specific-harmonics), you might find a neural correlate of valence in the form of [*consonance dissonance noise signatures*](https://qri.org/blog/quantifying-bliss#visualizing-emotions-as-cdnss-of-states-of-consciousness) – but this still wouldn't explain *why* it feels good. That remains an open question.