Re pagerank: This looks a lot like eigenvalues / eigenvectors, which show up a bunch in physics. (Eigenvector with high eigenvalue is like a “self-ratifying / stable generalized state”.)
Quantum mechanics involves topology of course. In operator algebra theory (Gelfand duality). And in TQFT. However the article seems to be making a leap relating quantum topology to minds and phenomenal binding. This is skipping many levels of abstraction!
I will now summarize a quantum topology approach, relevant to observers, which is not skipping nearly as many abstraction levels. We start by a quantum operator space as a C* algebra. This algebra is in general non-commutative. However, it has commutative sub-algebras. (Sub-algebra here is similar to ‘sub-group’, ‘sub-monoid’, ‘category theoretic sub-object’; has a precise characterization). These form a meet-semilattice (indicating: ‘intersection’ of commutative sub-algebras is commutative; ‘union’ is not in general commutative). The meet-semilattice structure reflects complementarity, Heisenberg uncertainty, Kochen-Specker, and so on. In PVM/POVM terms, different Hermitian operators commute when they each have a “diagonalization” (or infinite-dimensional equivalent) in a compatible basis; this is not always the case.
So we have a meet-semilattice of commutative C* sub-algebras. Then each, by Gelfand duality, is iso to a C* algebra of continuous functions S→C for a compact Hausdorff space S. Accordingly, there is a category-theoretic contravariant isomorphism between the category of commutative C* algebras and the category of compact Hausdorff spaces and continuous maps between them.
This is of course highly topological. A quantum operator algebra implies multiple classical contexts, and in general there’s no classical context containing all information from all of them. The contexts are at varying levels of fine-ness and coarse-ness. Some coarsening is necessary to get commutativity (and classicality, under the ‘commutative C* sub-algebras as classical’ interpretation.)
The sub-algebraic picture suggests that ‘high-level computations’ can be really instantiated as sub-algebras. Where sub-algebras also relate to topology through locale theory; categorical sub-objects in a category such as the category of compact regular frames. (Compare: if a group has a sub-group isomorphic to Z under addition, then the group operation implements integer addition; this is a hard mathematical constraint, not merely an interpretation.)
There is some ‘reality to wholes’ here, through sub-algebras (corresponding with quotient spaces in topology through locale-theoretic duality, Isbell). 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.
The conflation to avoid making here is that a classical context (given by a compact Hausdorff space corresponding to a commutative C* sub-algebra) 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. A given classical context can contain multiple minds (as classical reductionists expected prior to quantum mechanics). If anything, the classical ‘mind vs matter’ distinction is in a frame that makes classical assumptions; a classical context is more like a pre-requisite for ‘mind vs matter’ to be a sensible distinction. (Materialism != physicalism)
This is more my own philosophical spin than something directly implied by quantum topology, but: The ‘phenomena’ here are more like the phenomena of Kant than the phenomena of Chalmers: spatially three-dimensional, multi-personal. See also Wilfrid Sellars on phenomena; his “Empiricism and the Philosophy of Mind” is of course important background, but his “Phenomenalism” addresses multi-personal phenomenal contexts more directly.
(See Bohrification and a review for more technical details on this overall picture.)
Hi, thanks for writing this up. There’s never enough people trying to formalise these types of ideas.
This took me a while to work through given the dense jargon. Would you mind checking my understanding first? And then I’ll add another comment for the actual questions I have.
A C*-algebra is an algebra of quantum operators (with some functions like addition, multiplication, conjugation, norm, and identity).
A commutative C*-algebra has a set of operators which all commute together; for instance the position of one particle and the position of another. This makes the algebra of {x_1, x_2} a classical system.
A non-commutative C*-algebra has a set of operators in which any pair does not commute; for instance position and momentum do not commute and there will be irreducible uncertainty when you try to measure them. This makes the algebra of {x_1, p_1} a quantum system.
We are mostly concerned with commutative C*-algebras; these constitute a “way of seeing” a quantum system. There will be some inevitable coarsening of the quantum system as it is observed.
This commutative C*-algebra/will be the analog for Andrés’ monads...? It was unclear to me if Andrés’ monads or what part of these monads were intended to be quantum or classical; in my mind I substituted the instantaneous PageRank convergence for the Schrödinger equation.
These form a meet-semilattice; a partial order of commutative C*-algebras and their intersection sets. For instance, you might start with the root C*-algebra {x_1, p_1, x_2, p_2} (which is non-commutative); the first (finest-grain) level contains the sub-algebras for {x_1, x_2}, {x_1, p_2}, {x_2, p_1}, {p_1, p_2}; the second (coarsest-grain) level contains the sub-algebras for {x_1}, {p_1}, {x_2}, {p_2}.
For every commutative C*-algebra there is a corresponding topological space (or rather, “C* algebra of continuous functions S → C for a compact Hausdorff space S”. I didn’t quite grok what this object was but I’ll think about it like a topological space.)
For every non-commutative C*-algebra there is a corresponding non-commutative topological space. This is like a topological space without the notion of points? We don’t use these but I thought it was worth mentioning, in case me or Andrés wanted to think about how all this pertains to quantum rather than classical systems also.
Accordingly, there is a category-theoretic contravariant isomorphism between the category of commutative C* algebras and the category of compact Hausdorff spaces and continuous maps between them.
So you take the meet-semilattice on the left; you can map this to a graph of topological spaces on the right. In my head there is a graph of classical systems on the left and an isomorphic graph of little toruses and spheres and whatever on the right. My intuition kinda fails here also; if you take a point on the surface of a torus, what do you see this corresponding to in the corresponding classical system/C*-algebra?
A C*-algebra is an algebra of quantum operators (with some functions like addition, multiplication, conjugation, norm, and identity).
Yes, like B(H) for some Hilbert space H, bounded linear operators
A commutative C*-algebra has a set of operators which all commute together
Yes
A non-commutative C*-algebra has a set of operators in which any pair does not commute
Yes
We are mostly concerned with commutative C*-algebras
At the point of measurement, yes. We do care about the non-commutative C* algebra and there are different ways of trying to characterize it, including through its commutative sub-algebras
This commutative C*-algebra/will be the analog for Andrés’ monads...?
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.
These form a meet-semilattice; a partial order of commutative C*-algebras and their intersection sets
Yes. At least finite dimensionally, a commutative C* algebra gives a PVM. Sub-algebras give coarser PVMs.
For every commutative C*-algebra there is a corresponding topological space
Yep, by Gelfand duality. For finite dimensional Hilbert space H, B(H) gives a discrete topology over a count of elements equal to dimension of H. It’s more interesting in the infinite dimension case.
For every non-commutative C*-algebra there is a corresponding non-commutative topological space.
There are some attempts at this in non-commutative geometry, but I’m not very familiar. It at least does not give a topological space in the normal sense.
So you take the meet-semilattice on the left; you can map this to a graph of topological spaces on the right. In my head there is a graph of classical systems on the left and an isomorphic graph of little toruses and spheres and whatever on the right. My intuition kinda fails here also; if you take a point on the surface of a torus, what do you see this corresponding to in the corresponding classical system/C*-algebra?
Let’s think of the easier case, where we start with a commutative C* algebra at root. It corresponds with some topological space. It has commutative sub-algebras. These correspond with quotient spaces. There is a category theoretic reason for this: Sub-objects in the category of commutative C* algebras and homomorphisms are specified by monomorphisms, and when reversing the arrows (contravariant duality), these give epimorphisms. Epimorphisms (specifically regular epimorphisms) give quotient objects in the category of compact Hausdorff spaces and continuous maps. So there are ways of “coarsening the opens” in a topological space to get a “quotient space” which glues together some points, making them less distinguishable by opens.
It of course is a bit complicated when the root C* algebra is non commutative. Here it is a bit like an abstract object which you can take quotients of, and some of those quotients lead to topological spaces, but it isn’t a topological space (properly at least; non-commutative topology might say something) prior to quotienting. Some of the motivation here is the idea that we might be able to better understand a non commutative C* algebra by looking at which topological spaces can be found within its commutative sub-algebras.
As for specific points: Given a commutative C* algebra A, the points in the topological space are the characters, which are C* homomorphisms from A into the complex numbers. Let’s start with the finite dimension case. Let be taken as a commutative C* algebra (element wise addition / multiplication). Now the topology for is a discrete topology over n elements. A character of is a C* algebra homomorphism from into . Since C* algebra homomorphisms are complex-linear, this is a “covector” of , often represented as a row vector. Moreover, it must map the unit of (which is copies of 1) to 1, and preserve multiplication. The only possible homomorphisms here are those that read a given component, e.g. .
Conceptually, you would use to represent a classical complex-valued operator on a system with possible states. A character would accordingly be a given state; interpreted as a character, it maps an operator to its value. This is of course not very interesting on its own, but it illustrates the general idea.
A more interesting test case would be to take some commutative sub-algebra of B(H) for infinite dimension H, for example, the sub-algebra for position of one particle. Here, a point in the topological space corresponds to giving a value to position-measuring operators. That is equivalent to specifying a position. Unlike with the finite dimension case, the topology is non-trivial.
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.
Re pagerank: This looks a lot like eigenvalues / eigenvectors, which show up a bunch in physics. (Eigenvector with high eigenvalue is like a “self-ratifying / stable generalized state”.)
Quantum mechanics involves topology of course. In operator algebra theory (Gelfand duality). And in TQFT. However the article seems to be making a leap relating quantum topology to minds and phenomenal binding. This is skipping many levels of abstraction!
I will now summarize a quantum topology approach, relevant to observers, which is not skipping nearly as many abstraction levels. We start by a quantum operator space as a C* algebra. This algebra is in general non-commutative. However, it has commutative sub-algebras. (Sub-algebra here is similar to ‘sub-group’, ‘sub-monoid’, ‘category theoretic sub-object’; has a precise characterization). These form a meet-semilattice (indicating: ‘intersection’ of commutative sub-algebras is commutative; ‘union’ is not in general commutative). The meet-semilattice structure reflects complementarity, Heisenberg uncertainty, Kochen-Specker, and so on. In PVM/POVM terms, different Hermitian operators commute when they each have a “diagonalization” (or infinite-dimensional equivalent) in a compatible basis; this is not always the case.
So we have a meet-semilattice of commutative C* sub-algebras. Then each, by Gelfand duality, is iso to a C* algebra of continuous functions S→C for a compact Hausdorff space S. Accordingly, there is a category-theoretic contravariant isomorphism between the category of commutative C* algebras and the category of compact Hausdorff spaces and continuous maps between them.
This is of course highly topological. A quantum operator algebra implies multiple classical contexts, and in general there’s no classical context containing all information from all of them. The contexts are at varying levels of fine-ness and coarse-ness. Some coarsening is necessary to get commutativity (and classicality, under the ‘commutative C* sub-algebras as classical’ interpretation.)
The sub-algebraic picture suggests that ‘high-level computations’ can be really instantiated as sub-algebras. Where sub-algebras also relate to topology through locale theory; categorical sub-objects in a category such as the category of compact regular frames. (Compare: if a group has a sub-group isomorphic to Z under addition, then the group operation implements integer addition; this is a hard mathematical constraint, not merely an interpretation.)
There is some ‘reality to wholes’ here, through sub-algebras (corresponding with quotient spaces in topology through locale-theoretic duality, Isbell). 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.
The conflation to avoid making here is that a classical context (given by a compact Hausdorff space corresponding to a commutative C* sub-algebra) 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. A given classical context can contain multiple minds (as classical reductionists expected prior to quantum mechanics). If anything, the classical ‘mind vs matter’ distinction is in a frame that makes classical assumptions; a classical context is more like a pre-requisite for ‘mind vs matter’ to be a sensible distinction. (Materialism != physicalism)
This is more my own philosophical spin than something directly implied by quantum topology, but: The ‘phenomena’ here are more like the phenomena of Kant than the phenomena of Chalmers: spatially three-dimensional, multi-personal. See also Wilfrid Sellars on phenomena; his “Empiricism and the Philosophy of Mind” is of course important background, but his “Phenomenalism” addresses multi-personal phenomenal contexts more directly.
(See Bohrification and a review for more technical details on this overall picture.)
Hi, thanks for writing this up. There’s never enough people trying to formalise these types of ideas.
This took me a while to work through given the dense jargon. Would you mind checking my understanding first? And then I’ll add another comment for the actual questions I have.
A C*-algebra is an algebra of quantum operators (with some functions like addition, multiplication, conjugation, norm, and identity).
A commutative C*-algebra has a set of operators which all commute together; for instance the position of one particle and the position of another. This makes the algebra of
{x_1, x_2}a classical system.A non-commutative C*-algebra has a set of operators in which any pair does not commute; for instance position and momentum do not commute and there will be irreducible uncertainty when you try to measure them. This makes the algebra of {x_1, p_1} a quantum system.
We are mostly concerned with commutative C*-algebras; these constitute a “way of seeing” a quantum system. There will be some inevitable coarsening of the quantum system as it is observed.
This commutative C*-algebra/will be the analog for Andrés’ monads...? It was unclear to me if Andrés’ monads or what part of these monads were intended to be quantum or classical; in my mind I substituted the instantaneous PageRank convergence for the Schrödinger equation.
These form a
meet-semilattice; a partial order of commutative C*-algebras and their intersection sets. For instance, you might start with the root C*-algebra{x_1, p_1, x_2, p_2}(which is non-commutative); the first (finest-grain) level contains the sub-algebras for{x_1, x_2}, {x_1, p_2}, {x_2, p_1}, {p_1, p_2}; the second (coarsest-grain) level contains the sub-algebras for{x_1}, {p_1}, {x_2}, {p_2}.For every commutative C*-algebra there is a corresponding topological space (or rather, “C* algebra of continuous functions S → C for a compact Hausdorff space S”. I didn’t quite grok what this object was but I’ll think about it like a topological space.)
For every non-commutative C*-algebra there is a corresponding non-commutative topological space. This is like a topological space without the notion of points? We don’t use these but I thought it was worth mentioning, in case me or Andrés wanted to think about how all this pertains to quantum rather than classical systems also.
So you take the
meet-semilattice on the left; you can map this to a graph of topological spaces on the right. In my head there is a graph of classical systems on the left and an isomorphic graph of little toruses and spheres and whatever on the right. My intuition kinda fails here also; if you take a point on the surface of a torus, what do you see this corresponding to in the corresponding classical system/C*-algebra?Yes, like B(H) for some Hilbert space H, bounded linear operators
Yes
Yes
At the point of measurement, yes. We do care about the non-commutative C* algebra and there are different ways of trying to characterize it, including through its commutative sub-algebras
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.
Yes. At least finite dimensionally, a commutative C* algebra gives a PVM. Sub-algebras give coarser PVMs.
Yep, by Gelfand duality. For finite dimensional Hilbert space H, B(H) gives a discrete topology over a count of elements equal to dimension of H. It’s more interesting in the infinite dimension case.
There are some attempts at this in non-commutative geometry, but I’m not very familiar. It at least does not give a topological space in the normal sense.
Let’s think of the easier case, where we start with a commutative C* algebra at root. It corresponds with some topological space. It has commutative sub-algebras. These correspond with quotient spaces. There is a category theoretic reason for this: Sub-objects in the category of commutative C* algebras and homomorphisms are specified by monomorphisms, and when reversing the arrows (contravariant duality), these give epimorphisms. Epimorphisms (specifically regular epimorphisms) give quotient objects in the category of compact Hausdorff spaces and continuous maps. So there are ways of “coarsening the opens” in a topological space to get a “quotient space” which glues together some points, making them less distinguishable by opens.
It of course is a bit complicated when the root C* algebra is non commutative. Here it is a bit like an abstract object which you can take quotients of, and some of those quotients lead to topological spaces, but it isn’t a topological space (properly at least; non-commutative topology might say something) prior to quotienting. Some of the motivation here is the idea that we might be able to better understand a non commutative C* algebra by looking at which topological spaces can be found within its commutative sub-algebras.
As for specific points: Given a commutative C* algebra A, the points in the topological space are the characters, which are C* homomorphisms from A into the complex numbers. Let’s start with the finite dimension case. Let
Conceptually, you would use
A more interesting test case would be to take some commutative sub-algebra of B(H) for infinite dimension H, for example, the sub-algebra for position of one particle. Here, a point in the topological space corresponds to giving a value to position-measuring operators. That is equivalent to specifying a position. Unlike with the finite dimension case, the topology is non-trivial.
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.