The sub-algebraic picture suggests that ‘high-level computations’ can be really instantiated as sub-algebras. [...] There is some ‘objectivity’ here (or perhaps ‘pre-conditions for objectivity’), in that which coarsenings form valid commutative algebras depends on the physical system in question.
I feel like there are two kinds of coarse-graining going on in this system description, with different concerns despite being the same thing. You coarse-grain and discard information when you measure a particular C*-algebra; or you coarse-grain by selecting the right C*-algebra to reveal the preferred functional dynamics of your system.
For instance let’s say I have a digital calculator. There might be a C*-algebra corresponding to positions of electrons in the silicon chip; but there also might exist a C*-algebra capable of exposing the causal structure corresponding to integer addition, but this would be exceedingly opinionated/baroque (Claude Opus 4.7 used the phrase, “gerrymandered choice of observables”). There’s nothing which says you can’t do this. But does this happen in practice? By which metric should we favour particular operators, complexity? Symmetry? Anti-opinionatedness? Likelihood of actually being instantiated somehow? My expectation is that the default physicalist expectations around fine-graining should remain preserved, here, but happy to discuss.
The conflation to avoid making here is that a classical context is ‘a mind’ or ‘a person’ or that sort of thing. It can be much more detailed than that. It is more like a virtual world simulation that doesn’t exactly have a reductionist lowest level to it; some details are simply coarsened.
I guess this all squares with my phenomenology? I experience an internal world simulation constructed from sparse observations of the world and my body, not just a ‘mind’. Attentional modulation as choice of C*-algebra makes intuitive sense to me. I wish I had a better way of describing this, but details are clearly coarsened in the sense that while my attention is free to explore this space, it’s clear there is always some kind of compromise being made; internal constructs cast shadows; sometimes perhaps with a little serotonergic assistance one figures out how to rotate some observational basis, thus revealing habitual blind spots. Alternatively, me and Ethan Kuntz did at one point write a whole post about applying the uncertainty principle to spatial and frequency domain qualia.
A given classical context can contain multiple minds.
...unironically, tulpas? DID? 🙃
The ‘phenomena’ here are more like the phenomena of Kant than the phenomena of Chalmers: spatially three-dimensional, multi-personal.
...seems fine, but I remain uncertain what is meant by “multi-personal phenomenal contexts”. I grew tired of reading Claude explain philosophy.
You coarse-grain and discard information when you measure a particular C*-algebra; or you coarse-grain by selecting the right C*-algebra to reveal the preferred functional dynamics of your system.
Roughly I think the second kind is more general. We can consider abstract commutative C* algebras which assign functional dynamics, even if no measurement is feasible in practice.
but there also might exist a C*-algebra capable of exposing the causal structure corresponding to integer addition, but this would be exceedingly opinionated/baroque (Claude Opus 4.7 used the phrase, “gerrymandered choice of observables”). There’s nothing which says you can’t do this. But does this happen in practice?
I don’t think it’s very opinionated/baroque. Here’s where it might come up. When designing small computer chips, people care about quantum effects, because if electrons do quantum tunnelling, then that can introduce errors. Decoherence under many conditions prevents this from happening. When decoherence happens, classical descriptions are more valid. A coarse-grained commutative C* algebra for the addition dynamics would “take on specific values” due to decoherence. (Whereas other coarse-grained commutative C* algebras for the physical system might not; maybe for that sub-algebra, quantum tunnelling effects are important.) People designing small chips are going to make sure that the abstract machine dynamics correspond with coarsenings along which decoherence happens, to prevent the machine behavior from having quantum stochasticity.
Now of course there are going to be lots of natural decoherent dynamics even if the system is not engineered to create decoherence. Such as in ordinary rocks, which makes ordinary rocks poor for making quantum computers. So I’m not claiming something like “every commutative C* algebra with decoherent dynamics corresponds to a useful engineering take on the system”. It’s more like a necessary condition for classical computation than a sufficient one.
details are clearly coarsened in the sense that while my attention is free to explore this space, it’s clear there is always some kind of compromise being made
Yeah. An important part of phenomenology is that it’s coarser than physics. People don’t notice fine details on typical objects that do exist. This is one of the problems for naive forms of physicalism. Operator algebra gives an idea for how coarsenings can exist in physics, and are sometimes even essential for systems to take on well-defined values.
...unironically, tulpas? DID?
I was thinking more like, say a number of scientists work in the same lab, the lab makes quantum measurements, they see the same measurement results, there’s no Wigner’s friend ambiguity, decoherence is high. They’re operating in something like a shared abstract / computational space, which registers quantum systems the same. Now of course one can question whether this contains “the entire person” but it at least contains rich abstract physical / computational dynamics for everyone; it gets weird when considering the same body may exist in multiple non-commuting contexts (although maybe this isn’t very important).
An analogy might be a MMORPG game where multiple people can meet in the same abstract setting, which has reasonable well-defined / deterministic dynamics. Of course in this case the game itself doesn’t contain the players’ brains. But it gives an idea for how shared observations might be possible, where two scientists see the same thing; it’s not one quantum system that they make entirely different measurements of.
Contrast this with far-away aliens, who might from our perspective “be in superposition”; we cannot straightforwardly exist in the same classical context as them. (Wigner’s friend deals with similar situations, which are not separated by great distance, but are separated by causal isolation nonetheless; Wigner’s friend’s lab must be hermetically sealed, else would decohere.)
People designing small chips are going to make sure that the abstract machine dynamics correspond with coarsenings along which decoherence happens, to prevent the machine behavior from having quantum stochasticity.
I’m not claiming something like “every commutative C* algebra with decoherent dynamics corresponds to a useful engineering take on the system”. It’s more like a necessary condition for classical computation than a sufficient one.
Thanks a lot for your comprehensive response. I suspect that if we are talking past one another then this is because we are describing related yet different projects. Rather than specifying a causal structure and then verifying whether or not a given physical implementation follows it, what we are doing at our end is trying to find an unambiguous map from a physical system to the qualia we think inhabits it. In this case, the digital calculator/integer addition would be one of an infinitude of candidate maps.
I wasn’t trying to connect it to monads. I am not sure I understand the idea of monads. Perhaps I don’t believe in them. Nevertheless, non-commutative C* algebras have some aspects of “privacy” in that they cannot be exhaustively measured.
Am agnostic to whether monads are the true object corresponding to qualia (i.e. the output of the map), but C*-algebra/classical contexts seem in the ballpark.
My actual comments. First of all:
I feel like there are two kinds of coarse-graining going on in this system description, with different concerns despite being the same thing. You coarse-grain and discard information when you measure a particular C*-algebra; or you coarse-grain by selecting the right C*-algebra to reveal the preferred functional dynamics of your system.
For instance let’s say I have a digital calculator. There might be a C*-algebra corresponding to positions of electrons in the silicon chip; but there also might exist a C*-algebra capable of exposing the causal structure corresponding to integer addition, but this would be exceedingly opinionated/baroque (Claude Opus 4.7 used the phrase, “gerrymandered choice of observables”). There’s nothing which says you can’t do this. But does this happen in practice? By which metric should we favour particular operators, complexity? Symmetry? Anti-opinionatedness? Likelihood of actually being instantiated somehow? My expectation is that the default physicalist expectations around fine-graining should remain preserved, here, but happy to discuss.
I guess this all squares with my phenomenology? I experience an internal world simulation constructed from sparse observations of the world and my body, not just a ‘mind’. Attentional modulation as choice of C*-algebra makes intuitive sense to me. I wish I had a better way of describing this, but details are clearly coarsened in the sense that while my attention is free to explore this space, it’s clear there is always some kind of compromise being made; internal constructs cast shadows; sometimes perhaps with a little serotonergic assistance one figures out how to rotate some observational basis, thus revealing habitual blind spots. Alternatively, me and Ethan Kuntz did at one point write a whole post about applying the uncertainty principle to spatial and frequency domain qualia.
...unironically, tulpas? DID? 🙃
...seems fine, but I remain uncertain what is meant by “multi-personal phenomenal contexts”. I grew tired of reading Claude explain philosophy.
Roughly I think the second kind is more general. We can consider abstract commutative C* algebras which assign functional dynamics, even if no measurement is feasible in practice.
I don’t think it’s very opinionated/baroque. Here’s where it might come up. When designing small computer chips, people care about quantum effects, because if electrons do quantum tunnelling, then that can introduce errors. Decoherence under many conditions prevents this from happening. When decoherence happens, classical descriptions are more valid. A coarse-grained commutative C* algebra for the addition dynamics would “take on specific values” due to decoherence. (Whereas other coarse-grained commutative C* algebras for the physical system might not; maybe for that sub-algebra, quantum tunnelling effects are important.) People designing small chips are going to make sure that the abstract machine dynamics correspond with coarsenings along which decoherence happens, to prevent the machine behavior from having quantum stochasticity.
Now of course there are going to be lots of natural decoherent dynamics even if the system is not engineered to create decoherence. Such as in ordinary rocks, which makes ordinary rocks poor for making quantum computers. So I’m not claiming something like “every commutative C* algebra with decoherent dynamics corresponds to a useful engineering take on the system”. It’s more like a necessary condition for classical computation than a sufficient one.
Yeah. An important part of phenomenology is that it’s coarser than physics. People don’t notice fine details on typical objects that do exist. This is one of the problems for naive forms of physicalism. Operator algebra gives an idea for how coarsenings can exist in physics, and are sometimes even essential for systems to take on well-defined values.
I was thinking more like, say a number of scientists work in the same lab, the lab makes quantum measurements, they see the same measurement results, there’s no Wigner’s friend ambiguity, decoherence is high. They’re operating in something like a shared abstract / computational space, which registers quantum systems the same. Now of course one can question whether this contains “the entire person” but it at least contains rich abstract physical / computational dynamics for everyone; it gets weird when considering the same body may exist in multiple non-commuting contexts (although maybe this isn’t very important).
An analogy might be a MMORPG game where multiple people can meet in the same abstract setting, which has reasonable well-defined / deterministic dynamics. Of course in this case the game itself doesn’t contain the players’ brains. But it gives an idea for how shared observations might be possible, where two scientists see the same thing; it’s not one quantum system that they make entirely different measurements of.
Contrast this with far-away aliens, who might from our perspective “be in superposition”; we cannot straightforwardly exist in the same classical context as them. (Wigner’s friend deals with similar situations, which are not separated by great distance, but are separated by causal isolation nonetheless; Wigner’s friend’s lab must be hermetically sealed, else would decohere.)
Thanks a lot for your comprehensive response. I suspect that if we are talking past one another then this is because we are describing related yet different projects. Rather than specifying a causal structure and then verifying whether or not a given physical implementation follows it, what we are doing at our end is trying to find an unambiguous map from a physical system to the qualia we think inhabits it. In this case, the digital calculator/integer addition would be one of an infinitude of candidate maps.
Am agnostic to whether monads are the true object corresponding to qualia (i.e. the output of the map), but C*-algebra/classical contexts seem in the ballpark.