An Effective Field Theory of Consciousness
The wave equation of Quantum Mechanics P'(U') = P(U) completely describes the Universe, or more precisely, what we think we can know about the Universe. I'm leaving out all the usual Greek letters here (P is usually "Phi").
U is a vector in Hilbert space, essentially an infinite list of "facts", including the value of every field (gravity, electromagnetic etc) at every point in the Universe. What you pay for rent is in there somewhere.
This theory becomes useful if you add another variable, K, which represents a restriction on the wave function to a domain of concern or applicability. The equation then becomes an "effective field theory", P'(U',K) = P(U,K). K will specify things like velocities much less than the speed of light, gravitational fields weaker than in a black hole etc. K may be so restrictive that things like gravity can be entirely ignored (as in a particle accelerator, where the effect of gravity is vanishingly small compared to other forces at work). Particle physicists invented the wave function and are justifiably proud of it but they rarely consider the idea that the wave function must apply to everything, not just the world of quantum mechanics. They call the function the theory of everything but they seem to think that "everything" is just fields and particles. There seems to be no reason to restrict the idea to this level of detail or this type of "fact" about the Universe.
The amazing thing about the wave function is that it takes probability distributions "in" and produces probability distributions "out". Mysteriously, we happen to find ourselves in just one of the probability states described on either side of the equation, but this can sometimes be put down to errors of measurement. We are never quite sure where we are. It's also fundamentally impossible to know exactly where we are (Heisenberg Uncertain Principle) Moreover, we definitely find ourselves in one universe rather than another (the roll of a dice will produce one particular number). This idea is a bit tricky to master, but it seems to resolve the apparent paradox between probability and measurement - the "collapse of the wave function". We all occasionally wonder how different our lives would have been if only X. It is a common perception that we have been dropped into this particular version of reality by "chance". You can gain some insight on this question by regarding the wave function as a "brute fact". It's just "real" and affords no "explanation", such as the "multi-worlds" interpretation.
It's easiest to see this with a slight rewrite : P'(U',K) - P(U,K) = Delta(K), where Delta is a huge list of differences in the Hilbert space components. Introduction of K means that "most" of the components become zero and can be ignored. For example, we can leave out the state of a snowball on Pluto without making any difference to Delta when K is any conceivable experiment performed on Earth.
This is indeed a powerful idea and it should apply to everything, including the phenomenon of consciousness. This means that the "state" of the mind should be a function of the state of the same mind an "instant" earlier whether or not we "know" the function in detail. How long an "instant"? Well we know from bran studies that an "instant" of about 1 millisecond is short enough. Perhaps we can think of our brains "calculating"[1] the wave function once per millisecond, resulting in brain waves of 1,000 Hz or less.
What sort of things go into "U"? What kind of function is P?
Let's let K restrict us to things that could be described as "memes", including memes of perception. So the effective field theory gives us the way that one set of memes produces the next. We can imagine K to be restricted to memes that are "held in the mind at the time" or "perceived". It's interesting to ask if this restriction (K) leaves anything out. This amounts to asking whether P' depends on anything other than P.
According to Hofstadter, P is all about categories and associations. So we expect P to generate a collection of "associated" memes from the collection of memes "in mind" in the previous instant. From brain studies, we know what sort of memes the brain actually produces. For example, "episodic memory" can produce a sequence of mental images - a moving picture in the brain. Our sense of location (relative to reference points) can produce a picture of where we are relative to the reference points, or a picture of where our car is in the parking lot relative to where we think we are.
With a little cleaning up and a few more examples, this may turn out to be a good "imagination pump" to help us think about what is going on in our heads (consciousness). Good examples might include "stream of consciousness" such as what happens when I walk into a room and realize I've forgotten what I'm doing here. Other examples massively provided by Hofstadter can be discussed in the light of "effective field theory of consciousness - EFTC".
EFTC can describe what we mean by the brain states called "memes" with a bit more precision. I was originally outraged by the claims made about the Blue Brain project, making a short list of why such a project hopelessly underestimated the problem of building a brain model. Quite naturally, this lead me to imagine what a brain model in silicon might look like. I think it's more productive to simply imagine that such a model is conceivable, in the same sense that the wave function assumes a lot about what its underlying facts might be with full knowledge that almost all these facts are unknowable. We can still cast our net over what is actually known about brain function to speak intelligibly about P' <= P, meaning "what we can know about the mind at one instant depends on what we can know about the mind an instant previously". The probabilistic aspect of the wave function is reflected in the approximate, fuzzy nature of memes (one of Hofstader's constant themes). What actually pops into our minds (and what we actually do) is a special case of all possible things that might have popped into our minds. The set of memes or images that actually do "pop into" our minds at any one time is not infinite, but over time, the flow of memes explores an infinite set of possible memes, including things we have never thought of before. Even things that nobody has ever thought of before.
It is important to think of "actions" as a special case of memes. Action is a sequence of 3-meme tuples: P=<things as they seem, things as I want them to seem, actions I take>. An instant later, P' is a similar tuple representing the "correction" my action has taken. All these elements have a probabilistic element (none are precise) and, as memes, are embedded in all the other "active" memes. So, for example, "things as I want them to seem" may be associated with the meme of "my job", "actions I take" may be associated with memes of tool use etc.
Hofstader's discussion of the brain as being able to host multiple "mini-minds" lets us consider the possibility that a sequence of actions may be performed without "core" memes "coming to mind". For example, we may drive down the road for a long time without thinking about the action of driving. Yet this complex action must be taking place in the brain somehow and there is no reason to give special status to memes "in mind". Hopefully, Hofstader, Dennett and others will shed some light on this issue.
Can we really know what is "in mind"? If you ask me "what are you thinking", doesn't this automatically push me into the "next instant" and trigger a sequence of memes that get progressively farther and farther from what I had "in mind" when you wondered what I was thinking? How accurate is our memory of what we were thinking? Trying to remember what was happening in a dream seems to irretrievably "burn away" the memory.
Is it possible to retrieve memories formed in the flow of consciousness associated with a "mini-mind"? Suppose I'm driving mindlessly down the road and my wife asks, How fast were you going around that last corner? or, Did you see how close you came to that red truck? Generally speaking it is sometimes possible to answer such questions (usually not). These "mini minds" seem to have their own private short term memory, such as the ability of my "mini-mind" to "keep an eye" on the speedometer, the engine sounds, cars on the road and what lane I'm in.
Returning to the subject of effective field theory, does K refer to what I'm "paying attention to" at the moment and what, if anything, could this mean? I know that it's easy to tell from the outside (watching brain waves) that a subject is "paying attention", but it's hard to define exactly what "attention" is, especially what we are talking about when we say we are "paying attention" to X. What is X?
[1] The idea of "calculating" the wave function is misleading. The wave function describes the difference between P' and P but we cannot assume (and it is generally false) that the function can be "solved" to "compute" P' from P. This is a subtle mathematical concept that becomes obvious when we start looking at the specifics of the dynamic non-linear equations that make up the "real" P of Quantum Mechanics and dynamic phenomena on all the larger scales. The difficulty arises not only in the Universe we happen to inhabit but in all conceivable Universes (it's a mathematical phenomenon).
The changes we observe are consistent with the wave function but that doesn't allow us to calculate any specific P' and P. We are stuck with measuring P' and P. If we make lots of measurements, they will turn out to be consistent with the probability distributions P' and P. What the next measurement will be is an educated guess. If we don't actually have the actual equations for P (as we do in Quantum Field Theory), it's impossible to even say that our measurements are consistent with our field theory.
The whole idea becomes useless unless we introduce some kind of model that at least approximates what we think is going on. For example, there are decent mathematical models that describe the probability that a neuron will "fire", given the state of the neuron an "instant before" and vice versa (the probability that the neuron was in a given state, given that it fired). This is an "effective field theory" that concerns itself just with what is happening in a single cell and systematically excludes a lot of things that are known to be going on within that cell but are hopefully irrelevant. Still, within its domain of applicability (and the domain of things we can measure), our results should yield observations consistent with the theory (the model). This is true even though the actual dynamic equations concerned are non-linear, which means that you can't "solve" them to "calculate" what the neuron will look like in the next instant, given what it looks like now.
It's not necessary to know how to "solve" the equations to produce intelligible and useful statements about how the system behaves over time, such as whether it goes through a repeated sequence of states (like a wave) or whether states are stable or whether they can become chaotic.
U is a vector in Hilbert space, essentially an infinite list of "facts", including the value of every field (gravity, electromagnetic etc) at every point in the Universe. What you pay for rent is in there somewhere.
This theory becomes useful if you add another variable, K, which represents a restriction on the wave function to a domain of concern or applicability. The equation then becomes an "effective field theory", P'(U',K) = P(U,K). K will specify things like velocities much less than the speed of light, gravitational fields weaker than in a black hole etc. K may be so restrictive that things like gravity can be entirely ignored (as in a particle accelerator, where the effect of gravity is vanishingly small compared to other forces at work). Particle physicists invented the wave function and are justifiably proud of it but they rarely consider the idea that the wave function must apply to everything, not just the world of quantum mechanics. They call the function the theory of everything but they seem to think that "everything" is just fields and particles. There seems to be no reason to restrict the idea to this level of detail or this type of "fact" about the Universe.
The amazing thing about the wave function is that it takes probability distributions "in" and produces probability distributions "out". Mysteriously, we happen to find ourselves in just one of the probability states described on either side of the equation, but this can sometimes be put down to errors of measurement. We are never quite sure where we are. It's also fundamentally impossible to know exactly where we are (Heisenberg Uncertain Principle) Moreover, we definitely find ourselves in one universe rather than another (the roll of a dice will produce one particular number). This idea is a bit tricky to master, but it seems to resolve the apparent paradox between probability and measurement - the "collapse of the wave function". We all occasionally wonder how different our lives would have been if only X. It is a common perception that we have been dropped into this particular version of reality by "chance". You can gain some insight on this question by regarding the wave function as a "brute fact". It's just "real" and affords no "explanation", such as the "multi-worlds" interpretation.
It's easiest to see this with a slight rewrite : P'(U',K) - P(U,K) = Delta(K), where Delta is a huge list of differences in the Hilbert space components. Introduction of K means that "most" of the components become zero and can be ignored. For example, we can leave out the state of a snowball on Pluto without making any difference to Delta when K is any conceivable experiment performed on Earth.
This is indeed a powerful idea and it should apply to everything, including the phenomenon of consciousness. This means that the "state" of the mind should be a function of the state of the same mind an "instant" earlier whether or not we "know" the function in detail. How long an "instant"? Well we know from bran studies that an "instant" of about 1 millisecond is short enough. Perhaps we can think of our brains "calculating"[1] the wave function once per millisecond, resulting in brain waves of 1,000 Hz or less.
What sort of things go into "U"? What kind of function is P?
Let's let K restrict us to things that could be described as "memes", including memes of perception. So the effective field theory gives us the way that one set of memes produces the next. We can imagine K to be restricted to memes that are "held in the mind at the time" or "perceived". It's interesting to ask if this restriction (K) leaves anything out. This amounts to asking whether P' depends on anything other than P.
According to Hofstadter, P is all about categories and associations. So we expect P to generate a collection of "associated" memes from the collection of memes "in mind" in the previous instant. From brain studies, we know what sort of memes the brain actually produces. For example, "episodic memory" can produce a sequence of mental images - a moving picture in the brain. Our sense of location (relative to reference points) can produce a picture of where we are relative to the reference points, or a picture of where our car is in the parking lot relative to where we think we are.
With a little cleaning up and a few more examples, this may turn out to be a good "imagination pump" to help us think about what is going on in our heads (consciousness). Good examples might include "stream of consciousness" such as what happens when I walk into a room and realize I've forgotten what I'm doing here. Other examples massively provided by Hofstadter can be discussed in the light of "effective field theory of consciousness - EFTC".
EFTC can describe what we mean by the brain states called "memes" with a bit more precision. I was originally outraged by the claims made about the Blue Brain project, making a short list of why such a project hopelessly underestimated the problem of building a brain model. Quite naturally, this lead me to imagine what a brain model in silicon might look like. I think it's more productive to simply imagine that such a model is conceivable, in the same sense that the wave function assumes a lot about what its underlying facts might be with full knowledge that almost all these facts are unknowable. We can still cast our net over what is actually known about brain function to speak intelligibly about P' <= P, meaning "what we can know about the mind at one instant depends on what we can know about the mind an instant previously". The probabilistic aspect of the wave function is reflected in the approximate, fuzzy nature of memes (one of Hofstader's constant themes). What actually pops into our minds (and what we actually do) is a special case of all possible things that might have popped into our minds. The set of memes or images that actually do "pop into" our minds at any one time is not infinite, but over time, the flow of memes explores an infinite set of possible memes, including things we have never thought of before. Even things that nobody has ever thought of before.
It is important to think of "actions" as a special case of memes. Action is a sequence of 3-meme tuples: P=<things as they seem, things as I want them to seem, actions I take>. An instant later, P' is a similar tuple representing the "correction" my action has taken. All these elements have a probabilistic element (none are precise) and, as memes, are embedded in all the other "active" memes. So, for example, "things as I want them to seem" may be associated with the meme of "my job", "actions I take" may be associated with memes of tool use etc.
Hofstader's discussion of the brain as being able to host multiple "mini-minds" lets us consider the possibility that a sequence of actions may be performed without "core" memes "coming to mind". For example, we may drive down the road for a long time without thinking about the action of driving. Yet this complex action must be taking place in the brain somehow and there is no reason to give special status to memes "in mind". Hopefully, Hofstader, Dennett and others will shed some light on this issue.
Can we really know what is "in mind"? If you ask me "what are you thinking", doesn't this automatically push me into the "next instant" and trigger a sequence of memes that get progressively farther and farther from what I had "in mind" when you wondered what I was thinking? How accurate is our memory of what we were thinking? Trying to remember what was happening in a dream seems to irretrievably "burn away" the memory.
Is it possible to retrieve memories formed in the flow of consciousness associated with a "mini-mind"? Suppose I'm driving mindlessly down the road and my wife asks, How fast were you going around that last corner? or, Did you see how close you came to that red truck? Generally speaking it is sometimes possible to answer such questions (usually not). These "mini minds" seem to have their own private short term memory, such as the ability of my "mini-mind" to "keep an eye" on the speedometer, the engine sounds, cars on the road and what lane I'm in.
Returning to the subject of effective field theory, does K refer to what I'm "paying attention to" at the moment and what, if anything, could this mean? I know that it's easy to tell from the outside (watching brain waves) that a subject is "paying attention", but it's hard to define exactly what "attention" is, especially what we are talking about when we say we are "paying attention" to X. What is X?
[1] The idea of "calculating" the wave function is misleading. The wave function describes the difference between P' and P but we cannot assume (and it is generally false) that the function can be "solved" to "compute" P' from P. This is a subtle mathematical concept that becomes obvious when we start looking at the specifics of the dynamic non-linear equations that make up the "real" P of Quantum Mechanics and dynamic phenomena on all the larger scales. The difficulty arises not only in the Universe we happen to inhabit but in all conceivable Universes (it's a mathematical phenomenon).
The changes we observe are consistent with the wave function but that doesn't allow us to calculate any specific P' and P. We are stuck with measuring P' and P. If we make lots of measurements, they will turn out to be consistent with the probability distributions P' and P. What the next measurement will be is an educated guess. If we don't actually have the actual equations for P (as we do in Quantum Field Theory), it's impossible to even say that our measurements are consistent with our field theory.
The whole idea becomes useless unless we introduce some kind of model that at least approximates what we think is going on. For example, there are decent mathematical models that describe the probability that a neuron will "fire", given the state of the neuron an "instant before" and vice versa (the probability that the neuron was in a given state, given that it fired). This is an "effective field theory" that concerns itself just with what is happening in a single cell and systematically excludes a lot of things that are known to be going on within that cell but are hopefully irrelevant. Still, within its domain of applicability (and the domain of things we can measure), our results should yield observations consistent with the theory (the model). This is true even though the actual dynamic equations concerned are non-linear, which means that you can't "solve" them to "calculate" what the neuron will look like in the next instant, given what it looks like now.
It's not necessary to know how to "solve" the equations to produce intelligible and useful statements about how the system behaves over time, such as whether it goes through a repeated sequence of states (like a wave) or whether states are stable or whether they can become chaotic.
Comments
Post a Comment