Assuming the moderation of “beyond any possibility of doubt” I suggested in an earlier comment, I’ve already seen an example on this forum. The claim I make is:
“Achieving an intended result is not a task that necessitates either having a model or making predictions. In some cases, neither having a model nor attempting predictions are of any practical use at all.”
(NB. I have not reread my earlier post in composing the above; searching out minor differences to seize on would be to the point only in exemplifying another type of rationalisation to add to those listed below.)
One strong thread running through the responses was to interpret the word “model” so as to make the claim false by definition, a redefinition blatantly at variance with all previous uses of the word in this very forum and its parent OB. Responses of that form stopped the moment I pointed out the previous record of its use.
Another thread was to change the above claim to something stronger and argue against that instead: the claim that models and prediction are never useful.
A third was to point to models elsewhere than in the examples of systems achieving purposes without models.
These reactions are invariable. I was not surprised to encounter them here.
A fourth reaction I’ve encountered (I’m not going to reexamine the comments to see if anyone here committed this) is to claim that it works, so there must be a model. Yet when pressed, they cannot point to it, cannot even say what claim they are making about the system. It’s like hearing a Christian say “even if you’re an atheist, if you did something good it must have been by receiving the grace of God”.
One strong thread running through the responses was to interpret the word “model” so as to make the claim false by definition, a redefinition blatantly at variance with all previous uses of the word in this very forum and its parent OB. Responses of that form stopped the moment I pointed out the previous record of its use.
Richard, responses of that form stopped because it takes a long time to explain. I even had a response written up but didn’t post it because I thought it was long enough to merit a top-level post. I still have it saved, though I’ve done some reworking to make it more applicable than just as a response to your post. (I’ve just unhidden it so you guys can take a gander. What follows borrows heavily from it)
To everyone not familiar with what happened, let me explain. Richard claimed that many successful control systems don’t have “models” of their environment. Most people disagreed with that, not because of a need to shoehorn everything successful into “having a model”, but because those systems met enough of the criteria to count as “having a model” in any other context. It’s just that the whole time, Richard believed people meant something narrower when they said “model” than they really did.
So how did the other commenters use the term “model”? And how did Richard’s differ? Well, for one thing, Richard seemed to think that something has to “make predictions” to count as a model. But this is a confusion: the person using the model makes a prediction, not the model itself.
If I have a computer model of some aircraft, well, that’s just computer hardware with some switches set. It doesn’t make any prediction, yet is unambiguously a model. Rather, what happens is that the model has mutual information with the phenomenon in quesiton, and the computer apparatus applies a transformation (input/output devices) to the model that makes it meaningful to people, who then use that knowledge to explicitly specify a prediction.
All along, I suspect, people were using the “mutual information” criterion to determine whether something “has a model” of something else, and this is why I tried to rephrase Richard’s point with that more precise terminology. I think that comment clarified matters, and it showed the “meat” or Richard’s point, which I still thought was a good point, just a bit overhyped.
In contrast, Richard did not offer an equally precise definition of what he meant when he said that:
There are signals within the control system that are designed to relate to each other in the same way as do corresponding properties of the world outside. That is what a model is.
As Vladimir_Nesov noted, that definition just hides the ambiguity in the term “corresponding”. We already have a term that very precisely describes what is meant for things to “correspond” to each other; it’s called mutual information.
Note that in the time since Richard’s post, it has been very common for me to have to rephrase his point in more precise terminology in order for others to be able to make sense of it.
And I don’t think this is just an issue of arguing definitions. There’s a broader issue about whether you can helpfully carve conceptspace in a way that captures Richard’s definition of “model” but excludes things that “merely” have mutual information.
You are surprised? But obviously, any reply to the original post giving examples as sought will, by definition, raise contention.
Richard, responses of that form stopped because it takes a long time to explain.
That may have been your reason, but that does not imply that it’s everyone else’s reason—no more than your distaste for alcohol is a reason for you to disbelieve other people’s enjoyment of it.
All along, I suspect, people were using the “mutual information” criterion to determine whether something “has a model” of something else
This is flatly at variance with the uses of “model” I listed, drawn from OB/LW, and the way the word is defined in every book on model-based control. The only time people try to redefine “X is a model of Y” to mean “X has mutual information with Y” is when someone points out that systems of the sort that I described do not contain models. For some reason, people need to believe that those systems work by means of models, despite the clear lack of them, and immediately redefine the word as necessary to be able to say that. But having redefined the word, they are saying something different.
“X has mutual information with Y” is not a technical explanation of an informal concept labelled “model”. It is a completely different concept. The concept of a model, as I and everyone else outside these threads uses it, is very clear, unambiguous, and far narrower than mere mutual information. Vladimir Nesov objected to the word “correspondence” as vague; but if you want a technical elaboration of that, look in the direction of “isomorphism”, not “mutual information”.
And I don’t think this is just an issue of arguing definitions. There’s a broader issue about whether you can helpfully carve conceptspace in a way that captures Richard’s definition of “model” but excludes things that “merely” have mutual information.
Well, you have my answer to that. Conceptspace is carved along one line called “model”, and along another line called “mutual information”. Both lines matter, both have their uses, and they are in very different places. You want to erase the former or move it to coincide with the latter, but I have seen no argument for doing this.
If you want to take this on, it is no small mountain that I would have to see climbed. What it would take would be a radical reconstruction of control theory based on the concept of mutual information which eschews the word “model” altogether (because it’s taken, and there is already a perfectly good term for mutual informaation: “mutual information”), and which can be used directly for the design of control systems that are provably as good or better than those designed by existing techniques, both model-based and non-model-based. It should explain the real reason why those more primitive methods of design work (or don’t work, when they don’t), and provide better ways of making better designs.
Something like what Jaynes did for statistics. This is the level of isshokenmei at least. (ETA: no, one level higher: “extraordinary effort”.)
I do not know if this is possible. Certainly, it has not been done. When I’ve looked for information-theoretic or Bayesian analyses of control, I have found nothing substantial. Of course, I’m aware of the use of Bayesian techniques within control theory, such as Kalman filters. This is asking for the reverse inclusion. That is the substantial issue here.
All along, I suspect, people were using the “mutual information” criterion to determine whether something “has a model” of something else
This is flatly at variance with the uses of “model” I listed, drawn from OB/LW, and the way the word is defined in every book on model-based control.
No, you just asserted that people were using “model” in your sense in some posts you cited; there was nothing clear in any of the examples that implied they meant it in your sense rather than mine. And you didn’t quote from any book on model based control, and even if you did, you would still need to show how it’s not equivalent to merely having mutual information.
The only time people try to redefine “X is a model of Y” to mean “X has mutual information with Y” is when someone points out that systems of the sort that I described do not contain models.
“a simplified, abstracted representation of an object or system that presents only the information needed by its user. For example, the plastic models of aircraft I built as a kid abstract away everything except the external appearance, a mathematical model of a system shows only those dimensions and relationships useful to the model’s users,”
or
“temperature, as used by a thermostat, is a model of a system: It abstracts away all the details about the energy of individual particles in the system, except for a single scalar value representing the average of all those energies.”
So it’s clear they would count a single value that attempts to capture all critical properties of another system as a “model” of that system.
“X has mutual information with Y” is not a technical explanation of an informal concept labelled “model”. It is a completely different concept. The concept of a model, as I and everyone else outside these threads uses it, is very clear, unambiguous, and far narrower than mere mutual information.
I explained why this is false: it does not account for all the systems clearly labeled as “models” (aircraft finite element models, plastic toy models, etc.) yet only have mutual information with some phenomenon, and which the user must apply some transformation to, in order to make a prediction.
Vladimir Nesov objected to the word “correspondence” as vague; but if you want a technical elaboration of that, look in the direction of “isomorphism”, not “mutual information”.
But (as I explained before), isomorphism is not what you want here. Everyone accepts that models don’t have to be perfect representations. In contrast, “isomorphism” means a one-to-one mapping, which would indeed be a perfect model. “Mutual information” is more general than that: it includes isomorphisms, but also cases where the best mapping isn’t always correct, and where the model doesn’t include all aspects of the phenomenon.
And I don’t think this is just an issue of arguing definitions. There’s a broader issue about whether you can helpfully carve conceptspace in a way that captures Richard’s definition of “model” but excludes things that “merely” have mutual information.
Well, you have my answer to that. Conceptspace is carved along one line called “model”, and along another line called “mutual information”.
Er, that’s not how carving conceptspace works. The task of helpfully carving conceptspace is to show how your cuts don’t split things with significant relevant similarities. I claim you do so when you say a model “must make predictions”. This would count a computer model of an aircraft as “not a model”.
You’re missing the point of the problem when you say what you did here.
Both lines matter, both have their uses, and they are in very different places. You want to erase the former or move it to coincide with the latter, but I have seen no argument for doing this.
No, what I’m saying is that to be a model, something must have (nontrivial) mutual information with some other phenomenon. But “model” is most often used to connote a case where some human, with whom you can debate, will apply the necessary interpretation to the physical instantiation of model so as to tell you what its prediction is.
Still, something “has a model” whether or not some human is actually applying the necessary interpretation. The domino computer I linked contains a model of binary addition, even before someone realizes it. A computer’s hardware can have a model of an aircraft, even if someone throws it in the trash. In fact, the whole field of computation is basically identifying which physical systems already contain models of some kind of computation, and which we can therefore rely on, given some interpretation, to consistently give us the correct answer.
I do not find it helpful to say, “this thing over here explicitly outputs a prediction, so it’s a model, but this thing over here is just entangled with the phenomenon, so it doesn’t have a model”. Both are models, and the problem is on our end in the inability to harness the correlation to make what we consider a prediction.
When I’ve looked for information-theoretic or Bayesian analyses of control, I have found nothing substantial. Of course, I’m aware of the use of Bayesian techniques within control theory, such as Kalman filters. This is asking for the reverse inclusion. That is the substantial issue here.
Sorry, I don’t see it. The only problem is your arbitrary distinction between model-based controllers vs. non-model based, when really, both are model-based. As I said when I rephrased your claim, the substantive issue is how much of a given system needs to be modeled, and I already accept your claim that a model needn’t include everything about its environment, and that further, people typically overestimate how much must be modeled.
That is what we are really talking about, and I already agree with you there. All that remains is your arbitrary re-assignment of some things as “models” and others not, which is fruitless.
No, you just asserted that people were using “model” in your sense in some posts you cited; there was nothing clear in any of the examples that implied they meant it in your sense rather than mine. And you didn’t quote from any book on model based control, and even if you did, you would still need to show how it’s not equivalent to merely having mutual information.
With respect to the links I provided to earlier postings on OB/LW I shall only say that I have reviewed them and stand by the characterisation I made of them at the time (which went beyond mere assertion that they agree with me). To amplify my claim regarding books on model-based control theory, the following notes are drawn from the books I have to hand which include an easily identified statement of what the authors mean by a model. All of them are talking about a system that is specifically similar in structure to and not merely entangled with the thing modelled. At this point I think it is up to you to show that these things are equivalent. As I said at the end of my last comment, this would be a highly non-trivial task, a complete reconstruction of the content of books such as these. (It is too large to do in the columns of Less Wrong, but I look forward to reading it, whoever writes it.)
1. Brosilow & Joseph “Techniques of Model-Based Control”
Page 10, Figure 1.6, “Generic form of the model-based control strategy.” This is a block diagram in which one block is labelled “Process”, and another “Model”; the Model is a subsystem of the control system, designed to have the same input-output behaviour as the Process which the control system is to control. Ding!
2. Marlin, “Process Control”. Page 584, section 19.2, “The Model Predictive Control Structure”.
Here the author introduces the eponymous control method, in which a model of the process to be controlled is constructed and used to predict its future behaviour, in order to overcome the problem that (in the motivating example) the process contains substantial transport lags (a common situation in process control). The model is, as in the previous reference, a mathematical scheme designed to have the same input-output-relation as the real process, and is used by the controller to predict the future values of some of the variables. Ding!
3. Goodwin, Graebe, and Salgado, “Control System Design”.
Pages 29-30, section 2.5: (paraphrased slightly) “Let us also assume that the output is related to the input by a known functional relationship of the form y = f(u)+d, where f is a transformation that describes the input-output relations in the plant. We call a relationship of this type a model.” Ding!
Another block diagram as in Brosilow & Joseph. Ding!
5. Leigh, “Control Theory” (2nd. ed.)
Chapter 6, “Mathematical modelling”.
Sorry, no nuggets to quote, you’ll have to read it yourself. But it’s a whole chapter about models in the above sense. This, in fact, is a book I’d recommend as an introduction to control theory in general, which is why I mention it, despite it not lending itself to concise quotation. Ding!
The example that comes to mind here is tumble-and-travel chemotaxis.
For those not familiar with it, it’s how e coli (and many other bacteria) get to places where the chemical environment favors them. From an algorythmic perspective, it senses the current pleasantness of the chemical environment (more food, less poison) as a scalar, compares that pleasantness to its general happiness level (also a scalar), is more likely to go straight if the former is higher and more likely to tumble if the latter is, and updates its happiness in the direction of the pleasantness. The overall effect is that it goes straight when things are getting better and randomly turns when they’re getting worse, which does a passable job of going toward food and away from danger. The environment consists of its location and an entire map, but its memory is a single scalar.
I’m not sure what you’re saying about systems like this. That they exist? Of course. This one is well studied. That they outperform model-based systems? Certainly if you include the energy cost of building and running a more complex system. Probably not if you don’t, though I can’t prove it.
Or are you claiming that this sort of system can solve arbitrarily complex problems? Maybe, but you’ll need to do more than assert that.
Or are you claiming that this sort of system can solve arbitrarily complex problems?
You mean, that I have a solution to strong AI? No, not at all. Just the italicised claim, in opposition to the idea that anything that succeeds at funnelling reality through a desired path must be using a model.
As a moderate modeler I’m going to admit that I would prefer if it turned out there’s a simple way to prove that thermostats and such can be convincingly reinterpreted as having a model, but I’m not going to lose any sleep if it turns out not to be true.
That summarizes exactly why I tried to unearth the actual substance of the claim that a system “has no model”, i.e. what testable implication did his claim have? And that I think I successfully did in the comment I linked.
The implication was that, basically, you don’t need to know everything about your environment to build a working controller, and so you probably overestimate how much you have to know about it.
There was such strong reaction to Richard’s claim because people associated different concepts with models than Richard did. Like with the “tree falling makes a sound?” debate, the correct approach is to identify the substance of the dispute, and that’s exactly what I did.
If I wanted to nitpick or argue, I’d nitpick based on the meaning of “intended”. (I think I stayed silent during that discussion. On a side note, I suspect that human brains do have a built-in capacity to model the physics of ballistics, air resistance included, because we can throw objects to hit a target.)
Anyway, if we want a “model-free” designer and optimization process, we can always go point to our “friend” the alien god, which certainly doesn’t have models or make predictions, yet it works.
As far as I can tell, only way to call evolution an intelligence, you have to add in the whole system in which the evolution works(The biosphere). If we take “mutual information” to be basis for “model”, evolution actually has absolutely accurate model of the biosphere, the biosphere itself. It’s just that evolution uses this model in a very very very suboptimal way.
The reason behind combining the process and the system it works in is quite simple, I believe. Evolution is simply a result of the biosphere doing the biosphere-thing, just as our intelligence is a result of our brain doing the brain-thing, all according to the laws of physics. Take the biosphere(or the brain) away, and that “intelligence” is gone.
Assuming the moderation of “beyond any possibility of doubt” I suggested in an earlier comment, I’ve already seen an example on this forum. The claim I make is:
“Achieving an intended result is not a task that necessitates either having a model or making predictions. In some cases, neither having a model nor attempting predictions are of any practical use at all.”
(NB. I have not reread my earlier post in composing the above; searching out minor differences to seize on would be to the point only in exemplifying another type of rationalisation to add to those listed below.)
One strong thread running through the responses was to interpret the word “model” so as to make the claim false by definition, a redefinition blatantly at variance with all previous uses of the word in this very forum and its parent OB. Responses of that form stopped the moment I pointed out the previous record of its use.
Another thread was to change the above claim to something stronger and argue against that instead: the claim that models and prediction are never useful.
A third was to point to models elsewhere than in the examples of systems achieving purposes without models.
These reactions are invariable. I was not surprised to encounter them here.
A fourth reaction I’ve encountered (I’m not going to reexamine the comments to see if anyone here committed this) is to claim that it works, so there must be a model. Yet when pressed, they cannot point to it, cannot even say what claim they are making about the system. It’s like hearing a Christian say “even if you’re an atheist, if you did something good it must have been by receiving the grace of God”.
Oh geez.
Richard, responses of that form stopped because it takes a long time to explain. I even had a response written up but didn’t post it because I thought it was long enough to merit a top-level post. I still have it saved, though I’ve done some reworking to make it more applicable than just as a response to your post. (I’ve just unhidden it so you guys can take a gander. What follows borrows heavily from it)
To everyone not familiar with what happened, let me explain. Richard claimed that many successful control systems don’t have “models” of their environment. Most people disagreed with that, not because of a need to shoehorn everything successful into “having a model”, but because those systems met enough of the criteria to count as “having a model” in any other context. It’s just that the whole time, Richard believed people meant something narrower when they said “model” than they really did.
So how did the other commenters use the term “model”? And how did Richard’s differ? Well, for one thing, Richard seemed to think that something has to “make predictions” to count as a model. But this is a confusion: the person using the model makes a prediction, not the model itself.
If I have a computer model of some aircraft, well, that’s just computer hardware with some switches set. It doesn’t make any prediction, yet is unambiguously a model. Rather, what happens is that the model has mutual information with the phenomenon in quesiton, and the computer apparatus applies a transformation (input/output devices) to the model that makes it meaningful to people, who then use that knowledge to explicitly specify a prediction.
All along, I suspect, people were using the “mutual information” criterion to determine whether something “has a model” of something else, and this is why I tried to rephrase Richard’s point with that more precise terminology. I think that comment clarified matters, and it showed the “meat” or Richard’s point, which I still thought was a good point, just a bit overhyped.
In contrast, Richard did not offer an equally precise definition of what he meant when he said that:
As Vladimir_Nesov noted, that definition just hides the ambiguity in the term “corresponding”. We already have a term that very precisely describes what is meant for things to “correspond” to each other; it’s called mutual information.
Note that in the time since Richard’s post, it has been very common for me to have to rephrase his point in more precise terminology in order for others to be able to make sense of it.
And I don’t think this is just an issue of arguing definitions. There’s a broader issue about whether you can helpfully carve conceptspace in a way that captures Richard’s definition of “model” but excludes things that “merely” have mutual information.
You are surprised? But obviously, any reply to the original post giving examples as sought will, by definition, raise contention.
That may have been your reason, but that does not imply that it’s everyone else’s reason—no more than your distaste for alcohol is a reason for you to disbelieve other people’s enjoyment of it.
This is flatly at variance with the uses of “model” I listed, drawn from OB/LW, and the way the word is defined in every book on model-based control. The only time people try to redefine “X is a model of Y” to mean “X has mutual information with Y” is when someone points out that systems of the sort that I described do not contain models. For some reason, people need to believe that those systems work by means of models, despite the clear lack of them, and immediately redefine the word as necessary to be able to say that. But having redefined the word, they are saying something different.
“X has mutual information with Y” is not a technical explanation of an informal concept labelled “model”. It is a completely different concept. The concept of a model, as I and everyone else outside these threads uses it, is very clear, unambiguous, and far narrower than mere mutual information. Vladimir Nesov objected to the word “correspondence” as vague; but if you want a technical elaboration of that, look in the direction of “isomorphism”, not “mutual information”.
Well, you have my answer to that. Conceptspace is carved along one line called “model”, and along another line called “mutual information”. Both lines matter, both have their uses, and they are in very different places. You want to erase the former or move it to coincide with the latter, but I have seen no argument for doing this.
If you want to take this on, it is no small mountain that I would have to see climbed. What it would take would be a radical reconstruction of control theory based on the concept of mutual information which eschews the word “model” altogether (because it’s taken, and there is already a perfectly good term for mutual informaation: “mutual information”), and which can be used directly for the design of control systems that are provably as good or better than those designed by existing techniques, both model-based and non-model-based. It should explain the real reason why those more primitive methods of design work (or don’t work, when they don’t), and provide better ways of making better designs.
Something like what Jaynes did for statistics. This is the level of isshokenmei at least. (ETA: no, one level higher: “extraordinary effort”.)
I do not know if this is possible. Certainly, it has not been done. When I’ve looked for information-theoretic or Bayesian analyses of control, I have found nothing substantial. Of course, I’m aware of the use of Bayesian techniques within control theory, such as Kalman filters. This is asking for the reverse inclusion. That is the substantial issue here.
No, you just asserted that people were using “model” in your sense in some posts you cited; there was nothing clear in any of the examples that implied they meant it in your sense rather than mine. And you didn’t quote from any book on model based control, and even if you did, you would still need to show how it’s not equivalent to merely having mutual information.
No, as others pointed out, they normally use “model” to mean e.g.
or
So it’s clear they would count a single value that attempts to capture all critical properties of another system as a “model” of that system.
I explained why this is false: it does not account for all the systems clearly labeled as “models” (aircraft finite element models, plastic toy models, etc.) yet only have mutual information with some phenomenon, and which the user must apply some transformation to, in order to make a prediction.
But (as I explained before), isomorphism is not what you want here. Everyone accepts that models don’t have to be perfect representations. In contrast, “isomorphism” means a one-to-one mapping, which would indeed be a perfect model. “Mutual information” is more general than that: it includes isomorphisms, but also cases where the best mapping isn’t always correct, and where the model doesn’t include all aspects of the phenomenon.
Er, that’s not how carving conceptspace works. The task of helpfully carving conceptspace is to show how your cuts don’t split things with significant relevant similarities. I claim you do so when you say a model “must make predictions”. This would count a computer model of an aircraft as “not a model”.
You’re missing the point of the problem when you say what you did here.
No, what I’m saying is that to be a model, something must have (nontrivial) mutual information with some other phenomenon. But “model” is most often used to connote a case where some human, with whom you can debate, will apply the necessary interpretation to the physical instantiation of model so as to tell you what its prediction is.
Still, something “has a model” whether or not some human is actually applying the necessary interpretation. The domino computer I linked contains a model of binary addition, even before someone realizes it. A computer’s hardware can have a model of an aircraft, even if someone throws it in the trash. In fact, the whole field of computation is basically identifying which physical systems already contain models of some kind of computation, and which we can therefore rely on, given some interpretation, to consistently give us the correct answer.
I do not find it helpful to say, “this thing over here explicitly outputs a prediction, so it’s a model, but this thing over here is just entangled with the phenomenon, so it doesn’t have a model”. Both are models, and the problem is on our end in the inability to harness the correlation to make what we consider a prediction.
Sorry, I don’t see it. The only problem is your arbitrary distinction between model-based controllers vs. non-model based, when really, both are model-based. As I said when I rephrased your claim, the substantive issue is how much of a given system needs to be modeled, and I already accept your claim that a model needn’t include everything about its environment, and that further, people typically overestimate how much must be modeled.
That is what we are really talking about, and I already agree with you there. All that remains is your arbitrary re-assignment of some things as “models” and others not, which is fruitless.
With respect to the links I provided to earlier postings on OB/LW I shall only say that I have reviewed them and stand by the characterisation I made of them at the time (which went beyond mere assertion that they agree with me). To amplify my claim regarding books on model-based control theory, the following notes are drawn from the books I have to hand which include an easily identified statement of what the authors mean by a model. All of them are talking about a system that is specifically similar in structure to and not merely entangled with the thing modelled. At this point I think it is up to you to show that these things are equivalent. As I said at the end of my last comment, this would be a highly non-trivial task, a complete reconstruction of the content of books such as these. (It is too large to do in the columns of Less Wrong, but I look forward to reading it, whoever writes it.)
1. Brosilow & Joseph “Techniques of Model-Based Control”
Page 10, Figure 1.6, “Generic form of the model-based control strategy.” This is a block diagram in which one block is labelled “Process”, and another “Model”; the Model is a subsystem of the control system, designed to have the same input-output behaviour as the Process which the control system is to control. Ding!
2. Marlin, “Process Control”. Page 584, section 19.2, “The Model Predictive Control Structure”.
Here the author introduces the eponymous control method, in which a model of the process to be controlled is constructed and used to predict its future behaviour, in order to overcome the problem that (in the motivating example) the process contains substantial transport lags (a common situation in process control). The model is, as in the previous reference, a mathematical scheme designed to have the same input-output-relation as the real process, and is used by the controller to predict the future values of some of the variables. Ding!
3. Goodwin, Graebe, and Salgado, “Control System Design”.
Pages 29-30, section 2.5: (paraphrased slightly) “Let us also assume that the output is related to the input by a known functional relationship of the form y = f(u)+d, where f is a transformation that describes the input-output relations in the plant. We call a relationship of this type a model.” Ding!
4. Astrom and Wittenmark, “Adaptive Control”
Page 20, Chapter 1, “Model-Reference Adaptive Systems”
Another block diagram as in Brosilow & Joseph. Ding!
5. Leigh, “Control Theory” (2nd. ed.)
Chapter 6, “Mathematical modelling”.
Sorry, no nuggets to quote, you’ll have to read it yourself. But it’s a whole chapter about models in the above sense. This, in fact, is a book I’d recommend as an introduction to control theory in general, which is why I mention it, despite it not lending itself to concise quotation. Ding!
Ding! Ding! Ding! Ding! Ding!
The example that comes to mind here is tumble-and-travel chemotaxis.
For those not familiar with it, it’s how e coli (and many other bacteria) get to places where the chemical environment favors them. From an algorythmic perspective, it senses the current pleasantness of the chemical environment (more food, less poison) as a scalar, compares that pleasantness to its general happiness level (also a scalar), is more likely to go straight if the former is higher and more likely to tumble if the latter is, and updates its happiness in the direction of the pleasantness. The overall effect is that it goes straight when things are getting better and randomly turns when they’re getting worse, which does a passable job of going toward food and away from danger. The environment consists of its location and an entire map, but its memory is a single scalar.
I’m not sure what you’re saying about systems like this. That they exist? Of course. This one is well studied. That they outperform model-based systems? Certainly if you include the energy cost of building and running a more complex system. Probably not if you don’t, though I can’t prove it.
Or are you claiming that this sort of system can solve arbitrarily complex problems? Maybe, but you’ll need to do more than assert that.
You mean, that I have a solution to strong AI? No, not at all. Just the italicised claim, in opposition to the idea that anything that succeeds at funnelling reality through a desired path must be using a model.
As a moderate modeler I’m going to admit that I would prefer if it turned out there’s a simple way to prove that thermostats and such can be convincingly reinterpreted as having a model, but I’m not going to lose any sleep if it turns out not to be true.
That summarizes exactly why I tried to unearth the actual substance of the claim that a system “has no model”, i.e. what testable implication did his claim have? And that I think I successfully did in the comment I linked.
The implication was that, basically, you don’t need to know everything about your environment to build a working controller, and so you probably overestimate how much you have to know about it.
There was such strong reaction to Richard’s claim because people associated different concepts with models than Richard did. Like with the “tree falling makes a sound?” debate, the correct approach is to identify the substance of the dispute, and that’s exactly what I did.
If I wanted to nitpick or argue, I’d nitpick based on the meaning of “intended”. (I think I stayed silent during that discussion. On a side note, I suspect that human brains do have a built-in capacity to model the physics of ballistics, air resistance included, because we can throw objects to hit a target.)
Anyway, if we want a “model-free” designer and optimization process, we can always go point to our “friend” the alien god, which certainly doesn’t have models or make predictions, yet it works.
As far as I can tell, only way to call evolution an intelligence, you have to add in the whole system in which the evolution works(The biosphere). If we take “mutual information” to be basis for “model”, evolution actually has absolutely accurate model of the biosphere, the biosphere itself. It’s just that evolution uses this model in a very very very suboptimal way.
The reason behind combining the process and the system it works in is quite simple, I believe. Evolution is simply a result of the biosphere doing the biosphere-thing, just as our intelligence is a result of our brain doing the brain-thing, all according to the laws of physics. Take the biosphere(or the brain) away, and that “intelligence” is gone.