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"computation" is only equivalent when it's calculative, ie., when the algorithm in question is merely computing some number. The reason the LCD screen displays

"computation" is only equivalent when it's calculative, ie., when the algorithm in question is merely computing some number. The reason the LCD screen displays some output isn't because the electrical switches have some numerical state, its because they have some electrical state. The sense in which "computer" describes any system is trivial, for there to be any empirical content to computational language, we need an empirical model of the relevant algorithms the computer is performing. My kettle is also a computer: water is its state, boiling is the "computational process", and its change of state is the "number being computed". But it is only a kettle because that "calculation" which computes a number is a magnitude which is implemented by the kinetic state of the water. The sense in which "computers are equivalent" is *empirically empty*. There is no scientific content to this; it is merely a statement of pure mathematics. To use this language, of pure discrete mathematics, as-if it is informative about empirical systems *is pseudo-science*. One may as well say the brain is a geometrical system which is extended in Euclidean space, and we know topologically, that all such systems are geometrically equivalent. The world science studies (unlike that of pure mathematics), is extended in space and time, and has properties (eg., charge, mass, etc.). The number "34029348309384398" is only a frame of a video game when it names (charge, mass, extention, duration...) in a highly particular manner. Unless you have an algorithm in mind, and a model which says how its numerical content corresponds to physical properties, you arent saying anything empirical at all.

sudosysgen 4y ago
>"computation" is only equivalent when it's calculative, ie., when the algorithm in question is merely computing some number. Whoever said that computation has to be with numbers? Here we are seeing the brain as calculative, because the output of the brain is some function of it's input, is it not? Surely we can agree that this is an important, crucial, and interesting function of the brain, that is worthwhile to study? I'm not saying that this is necessarily all that the brain does, but it's an interesting and unresolved dimension of what the brain does, perhaps even the most interesting. >The reason the LCD screen displays some output isn't because the electrical switches have some numerical state, its because they have some electrical state. Sure, I don't see how that's an issue. Why does computation have to be on numerical states? It can be on any kind of state at all, even continuous states. Be it water pressure, base pairs in DNA, luminosity, anything at all that can represent data. In fact, some of the earliest algorithms were operating on lines and circles, which are neither numerical nor even discrete. >My kettle is also a computer: water is its state, boiling is the "computational process", and its change of state is the "number being computed". Sure, you could see it that way. But computation isn't the only thing your kettle is doing - and it's not the interesting part about it either. > The sense in which "computers are equivalent" is empirically empty. There is no scientific content to this; it is merely a statement of pure mathematics. To use this language, of pure discrete mathematics, as-if it is informative about empirical systems is pseudo-science. It's far from purely mathematical, nor pseudo-scientific. Sure, you could define almost anything to do some computation, but that doesn't mean the computation it is doing is worthwhile, or an interesting dimension of its operation. Certainly, however, the computational dimension of the human brain - that is, how it manipulates data - is the most interesting part of it. It's clearly informative - in this case we can conclude that the brain does irreversible computation, and thus establish various bounds on how it operates. > One may as well say the brain is a geometrical system which is extended in Euclidean space, and we know topologically, that all such systems are geometrically equivalent. Sure, we can say that. How is this helpful in this context? Understanding the brain as doing computation is certainly helpful, and perhaps understanding it as topologically equivalent to other objects is too, but I can't really see how. >Unless you have an algorithm in mind, and a model which says how its numerical content corresponds to physical properties, you arent saying anything empirical at all. Again, why does an algorithm even require a numerical content? All an algorithm needs is data, and we clearly have data going in and out, which constrains the physical system that is processing that data.
- mjburgess 4y ago
  A computation is just an implementation of a function `f: {0,1}^N-> {0,1}^M`... if not, what is the meaning of the word at all? All these phrases "manipulates data", "computation", and so on... they dont mean anything. A kettle "manipulates data". You think you're saying something empirically significant about the brain using this language, but this language has no empirical content. It is a language of pure mathematics. All of these claims are true of any system. What do we learn when we hear that "the brain is a computer" (or whatever else you wish to say). We dont learn anything. If you can provide a logical model of the algorithm the brain is performing, and a model of *how the brain implements it*, then we learn something. Saying "the brain is a computer" is basically no different than saying "it can be described, somehow, by mathematics".
  - sudosysgen 4y ago
    > A computation is just an implementation of a function `f: {0,1}^N-> {0,1}^M`... if not, what is the meaning of the word at all? Sure, that's a definition. It happens to be mathematically equivalent to the calculation of any observable signal in the real world, because there exist isomorphisms between {0,1}^N and the set of functions of maximum frequency f over time t, for example. > All these phrases "manipulates data", "computation", and so on... they dont mean anything They are certainly meaningful. > A kettle "manipulates data". Yes, it does, but in a very trivial and uninteresting way. Crucially, it does more than just manipulate data, but manipulating data is one of the things a kettle can do. > You think you're saying something empirically significant about the brain using this language, but this language has no empirical content. It is a language of pure mathematics. We certainly can say empirically significant things about the brain, since facts about the way in which it performs computations can be inferred, and from this we can infer information about how the brain must be structured. Trivially for example, we can infer that the brain must be able to have a minimum amount of outgoing total neuronal bandwidth by analyzing the makeup of outputs in can compute, and indeed we can do more. > All of these claims are true of any system. Of course, they are. But for some systems they can provide more insight than for others. The computation a kettle can do is insignificant and largely irrelevant to what interests us kettle-wise, so we don't really care. However, the way in which the brain manipulates data is much more interesting and intricate (and we can of course place lower and upper bounds on how intricate it is), and correspondingly we can learn much more. > If you can provide a logical model of the algorithm the brain is performing, and a model of how the brain implements it, then we learn something. I don't need to provide a model of the algorithm the brain is performing nor of how it is implemented to learn things. Thanks to various interesting results in computer science (in conjunction with results in the hard sciences), we can learn things about the brain without needing at all to know which algorithm it is implementing, and without knowing much of how it is implemented. At the extreme of knowing little about the implementation, we have physical lower bounds of physically possible implementations of any given computation, regardless of the algorithm. CS theory allows us to infer facts about algorithms by knowing the computation. For example, if I have a black box that inputs a list and outputs a sorted list, since I know that it is impossible to sort a list in the general case faster than n log n, and since it is impossible to know the original list from the sorted list, knowing the Landauer limit, I can infer for example a minimum power consumption. I don't need to know anything about the implementation or algorithm.

sudosysgen 4y ago

>"computation" is only equivalent when it's calculative, ie., when the algorithm in question is merely computing some number. Whoever said that computation has to be with numbers? Here we are seeing the brain as calculative, because the output of the brain is some function of it's input, is it not? Surely we can agree that this is an important, crucial, and interesting function of the brain, that is worthwhile to study? I'm not saying that this is necessarily all that the brain does, but it's an interesting and unresolved dimension of what the brain does, perhaps even the most interesting. >The reason the LCD screen displays some output isn't because the electrical switches have some numerical state, its because they have some electrical state. Sure, I don't see how that's an issue. Why does computation have to be on numerical states? It can be on any kind of state at all, even continuous states. Be it water pressure, base pairs in DNA, luminosity, anything at all that can represent data. In fact, some of the earliest algorithms were operating on lines and circles, which are neither numerical nor even discrete. >My kettle is also a computer: water is its state, boiling is the "computational process", and its change of state is the "number being computed". Sure, you could see it that way. But computation isn't the only thing your kettle is doing - and it's not the interesting part about it either. > The sense in which "computers are equivalent" is empirically empty. There is no scientific content to this; it is merely a statement of pure mathematics. To use this language, of pure discrete mathematics, as-if it is informative about empirical systems is pseudo-science. It's far from purely mathematical, nor pseudo-scientific. Sure, you could define almost anything to do some computation, but that doesn't mean the computation it is doing is worthwhile, or an interesting dimension of its operation. Certainly, however, the computational dimension of the human brain - that is, how it manipulates data - is the most interesting part of it. It's clearly informative - in this case we can conclude that the brain does irreversible computation, and thus establish various bounds on how it operates. > One may as well say the brain is a geometrical system which is extended in Euclidean space, and we know topologically, that all such systems are geometrically equivalent. Sure, we can say that. How is this helpful in this context? Understanding the brain as doing computation is certainly helpful, and perhaps understanding it as topologically equivalent to other objects is too, but I can't really see how. >Unless you have an algorithm in mind, and a model which says how its numerical content corresponds to physical properties, you arent saying anything empirical at all. Again, why does an algorithm even require a numerical content? All an algorithm needs is data, and we clearly have data going in and out, which constrains the physical system that is processing that data.

mjburgess 4y ago
A computation is just an implementation of a function `f: {0,1}^N-> {0,1}^M`... if not, what is the meaning of the word at all? All these phrases "manipulates data", "computation", and so on... they dont mean anything. A kettle "manipulates data". You think you're saying something empirically significant about the brain using this language, but this language has no empirical content. It is a language of pure mathematics. All of these claims are true of any system. What do we learn when we hear that "the brain is a computer" (or whatever else you wish to say). We dont learn anything. If you can provide a logical model of the algorithm the brain is performing, and a model of *how the brain implements it*, then we learn something. Saying "the brain is a computer" is basically no different than saying "it can be described, somehow, by mathematics".
- sudosysgen 4y ago
  > A computation is just an implementation of a function `f: {0,1}^N-> {0,1}^M`... if not, what is the meaning of the word at all? Sure, that's a definition. It happens to be mathematically equivalent to the calculation of any observable signal in the real world, because there exist isomorphisms between {0,1}^N and the set of functions of maximum frequency f over time t, for example. > All these phrases "manipulates data", "computation", and so on... they dont mean anything They are certainly meaningful. > A kettle "manipulates data". Yes, it does, but in a very trivial and uninteresting way. Crucially, it does more than just manipulate data, but manipulating data is one of the things a kettle can do. > You think you're saying something empirically significant about the brain using this language, but this language has no empirical content. It is a language of pure mathematics. We certainly can say empirically significant things about the brain, since facts about the way in which it performs computations can be inferred, and from this we can infer information about how the brain must be structured. Trivially for example, we can infer that the brain must be able to have a minimum amount of outgoing total neuronal bandwidth by analyzing the makeup of outputs in can compute, and indeed we can do more. > All of these claims are true of any system. Of course, they are. But for some systems they can provide more insight than for others. The computation a kettle can do is insignificant and largely irrelevant to what interests us kettle-wise, so we don't really care. However, the way in which the brain manipulates data is much more interesting and intricate (and we can of course place lower and upper bounds on how intricate it is), and correspondingly we can learn much more. > If you can provide a logical model of the algorithm the brain is performing, and a model of how the brain implements it, then we learn something. I don't need to provide a model of the algorithm the brain is performing nor of how it is implemented to learn things. Thanks to various interesting results in computer science (in conjunction with results in the hard sciences), we can learn things about the brain without needing at all to know which algorithm it is implementing, and without knowing much of how it is implemented. At the extreme of knowing little about the implementation, we have physical lower bounds of physically possible implementations of any given computation, regardless of the algorithm. CS theory allows us to infer facts about algorithms by knowing the computation. For example, if I have a black box that inputs a list and outputs a sorted list, since I know that it is impossible to sort a list in the general case faster than n log n, and since it is impossible to know the original list from the sorted list, knowing the Landauer limit, I can infer for example a minimum power consumption. I don't need to know anything about the implementation or algorithm.