The state of play in symmetry
Posted on 18 February 2023 by Cube Flipper
I am starting to realise that the word symmetry has been doing some heavy lifting in my writing, especially in my previous post. 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. He describes it succinctly in his 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. 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 where each point has both:
- depth, a scalar value, and:
- colour, a three-vector value; and:
- the worldfield, a three-dimensional 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 for the welfare of conscious beings! Qualia over QALYs! 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, 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 believes that valence will be best measured on a logarithmic scale, which seems reasonable to me. Roger Thisdell, 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 on this prospect. Additionally, a total ordering 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.
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 – 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.
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, 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, if you were to study someone’s connectome harmonics, you might find a neural correlate of valence in the form of consonance dissonance noise signatures – but this still wouldn’t explain why it feels good. That remains an open question.