You may already have seen Jochen’s essay Four Verses from the Daodejingan entry in this year’s FQXi competition. It’s a thought-provoking piece, so here are a few of the ones it provoked in me. In general I think it features a mix of alarming and sound reasoning which leads to a true yet perplexing conclusion.

In brief Jochen suggests that we apprehend the world only through models; in fact our minds deal only with these models. Modelling and computation are in essence the same. However, the connection between model and world is non-computable (or we face an infinite regress). The connection is therefore opaque to our minds and inexpressible. Why not, then, identify it with that other inexpressible element of cognition, qualia? So qualia turn out to be the things that incomprehensibly link our mental models with the real world. When Mary sees red for the first time, she does learn a new, non-physical fact, namely what the connection between her mental model and real red is. (I’d have to say that as something she can’t understand or express, it’s a weird kind of knowledge, but so be it.)

I think to talk of modelling so generally is misleading, though Jochen’s definition is itself broadly framed, which means I can’t say he’s wrong. In his terms it seems anything that uses data about the structure and causal functioning of X to make predictions about its behaviour would be a model. If you look at it that way, it’s true that virtually all our cognition is modelling. But to me a model leads us to think of something more comprehensive and enduring than we ought. In my mind at least, it conjures up a sort of model village or homunculus, when what’s really going on is something more fragmentary and ephemeral, with the brain lashing up a ‘model’ of my going to the shop for bread just now and then discarding it in favour of something different. I’d argue that we can’t have comprehensive all-purpose models of ourselves (or anything) because models only ever model features relevant to a particular purpose or set of circumstances. If a model reproduced all my features it would in fact be me (by Leibniz’ Law) and anyway the list of potentially relevant features goes on for ever.

The other thing I don’t like about liberal use of modelling is that it makes us vulnerable to the view that we only experience the model, not the world. People have often thought things like this, but to me it’s almost like the idea we never see distant planets, only telescope lenses.

Could qualia be the connection between model and world? It’s a clever idea, one of those that turn out on reflection to not be vulnerable to many of the counterarguments that first spring to mind. My main problem is that it doesn’t seem right phenomenologically. Arguments from one’s own perception of phenomenology are inherently weak, but then we are sort of relying on phenomenology for our belief (if any) in qualia in the first place. A red quale doesn’t seem like a connection, more like a property of the red thing; I’m not clear why or how I would be aware of this connection at all.

However, I think Jochen’s final conclusion is both poignant and broadly true. He suggests that models can have fundamental aspects, the ones that define their essential functions – but the world is not under a similar obligation. It follows that there are no fundamentals about the world as a whole.

I think that’s very likely true, and I’d make a very similar kind of argument in terms of explanation. There are no comprehensive explanations. Take a carrot. I can explain its nutritional and culinary properties, its biology, its metaphorical use as a motivator, its supposed status as the favourite foodstuff of rabbits, and lots of other aspects; but there is no total explanation that will account for every property I can come up with; in the end there is only the carrot. A demand for an explanation of the entire world is automatically a demand for just the kind of total explanation that cannot exist.

Although I believe this, I find it hard to accept; it leaves my mind with an unscratched itch. If we can’t explain the world, how can we assimilate it? Through contemplation? Perhaps that would have been what Laozi would have advocated. More likely he would have told us to get on with ordinary life. Stop thinking, and end your problems!

 

 

31 Comments

  1. 1. Matt says:

    Ah! There is the carrot-in-itself, but not (one assumes) the carrot-for-itself.

  2. 2. SelfAwarePatterns says:

    I personally like talking about models for awareness, although I’m usually fine if someone wants to talk in terms of representations, image maps, or use some other terminology. But I fully agree that the models are not exhaustive. They’re sparse, fragmentary, gappy, and filled with hacks and kludges. Evolution does what works, what’s adaptive, not what makes for a clean engineering diagram.

    The models work because their adaptive function is prediction, rather than accuracy. (Some neuroscientists, psychologists, and philosophers only talk about prediction and eschew any talk of models, representations, etc, but the predictions have to be formed in *some* manner.)

    That said, I can’t say I understand Szangolies’ argument that the relation between the object and the model is not computable. If so, then the relation between my face and the model of it in my laptop’s facial recognition system wouldn’t be computable, which makes no sense since there is obviously an engineering model of that relationship. (Is he saying my laptop has qualia?) If the relationship between the laptop’s model and external object can be modeled and computed, then I can’t see why the relationship between my mental models and the outside world can’t be as well.

  3. 3. Tom says:

    Well, in principle a carrot can be described by all its parts, properties and all its relations to everything else. That would be a complete description. It goes without saying that such a description is beyond our reach. Fortunately, it is usually satisfactory to have just a very partial description that focuses on some useful relations: the carrot’s color, shape, edibility, location (in my pantry?) etc. The carrot’s relations to the planet Neptune or to the second world war are usually uninteresting.

    And then there is also something about the carrot that is in principle indescribable — that which has all those relations that are described, namely the carrot (in) itself (as opposed to its parts, properties and relations to other things).

    As for the fundamental, by “fundamental” I usually mean something that is extremely general (abstract) so that it is instantiated in everything – for example (the property of having an) identity or (the property of having a) relation.

  4. 4. Paul Topping says:

    The “Four verses” paper lost me in the introduction. I see each species having a mix of instinct-driven vs sense-of-self-driven behavior. There’s no phase transition needed. At least such a thing would need to be proven.

    As far as modelling goes, it takes the definition too literally. It conjures up the old Homunculus point of view with its talk of a model needing to be perceived by some other part of the brain. From a computational (and computer science) point of view, this is taking the concept too narrowly. Many software systems model some aspects of an external reality. That just means the program’s states correlate in some way with a part of reality. The internal model is not necessarily a miniature version of the external world. It’s structure can be quite different. I’ll admit that I have no good examples of this … must think.

  5. 5. Paul Torek says:

    The way that can be followed is not the Way.

    Jochen’s conclusion about qualia (as reported by Peter; I haven’t read the original) seems similar to my own view. To wit, qualia are features of our internal mechanisms linking our models to the world. For example, the qualia of cold and hot are reported to “us” (the Global Workspace of the executive system, roughly speaking) independently of our judgments of actual physical temperature. For example, after training, you could probably tell that a water bath is 35 Celsius with each hand, even though one had been soaking in hot water beforehand and the other in cold. The qualia from the two hands are quite different. The world-model (“35 Celsius”) is the same.

  6. 6. mjgeddes says:

    Well, see my comments to Jochen in other thread. I don’t buy the claim that the connection between ‘world’ and ‘models’ is non-computable. All models are incomplete and never ‘bottom out’ , true, but this is just the nature of science – it applies to any scientific model – the weather, cars, etc. Phenomenological properties are no different, and thus just as applicable to modelling as everything else.

    Consciousness itself I think is a self-model of a dynamical system carried to three levels of recursion. All the confusion about consciousness I think comes from the fact that in the everyday world we’re just not familiar with complex dynamical systems. Consciousness is a *dynamical system* , a dynamical pattern of information extended over time. Closest analogy is a weather system- think hurricane or tornado. We can model a tornado, so we can model consciousness.

    A dynamical system is characterized by it’s thermodynamic properties (energy, entropy, information, complex), and I have no doubt that it’s possible to define consciousness in those terms. And no, we don’t need a perfect definition- perfect models or definitions are indeed unobtainable, but this isn’t really a problem for science.

    In fact, if ‘information is fundamental’, as I think, then, indeed, we can in fact view everything as a model (including the process of modeling itself).

    See my ultimate ‘Model of Model of Models’ here:
    http://www.zarzuelazen.com/CoreKnowledgeDomains2.html

    (I think the recursion stops at 3 levels, and this is what avoids an infinite regress).

  7. 7. David Duffy says:

    https://www.researchgate.net/publication/228948706_The_Natural_Metaphysics_of_Computing_Anticipatory_Systems

    might be worth a read, given Rosen and Whitehead are brought up. It seems to me that the
    the model qua formal system must be running on a substrate – together these make up the
    the “real” model, which is metaphysical in Rossiter and Heather’s terminology. The FS cannot completely predict itself in their formulation.

  8. 8. Jochen says:

    Thanks for again giving some blog-space to my ruminations, Peter, I really appreciate reading your (and everyone’s) thoughts!

    I’ll come back with some more detailed replies, but let me just try and clarify a few bits and pieces that haven’t really gotten the attention they needed in the essay, in part due to character count restrictions:

    Regarding modeling, maybe I should have chosen a different terminology, but I merely followed Rosen here. It turns out that, on this reading, it really is quite difficult to think about engaging with the world in terms that do not, ultimately, boil down to ‘modeling’ in Rosen’s sense: as long as the states of your mind (or brain) are in some correspondence with the world as it is perceived, you’ve got a ‘model’ of the world. That’s basically all there’s to it.

    One might suggest something like that we’re in touch with the world generally, that perception ‘reaches out’ and gets us a direct line to what’s out there; but of course, such an account has to content with the fact that frequently, our perceptions fail to be veridical—as in hallucinations, or more ordinary misperceptions, like mistaking one person for another. What was our perception ‘in touch’ with there? It seems like there ought to be some mediator between our experience and the world, and I can’t think of any that wouldn’t fall under the term ‘model’ as I use it. But as always, that may be saying more about my limitations than the world.

    As for Leibniz and similar worries about the in-principle inadequateness of models, first of all, there may of course be more than one source of such a mismatch between model and object—I simply chose to focus on computation as a limiting factor. But one has to be careful with following one’s intuition here, I think: for instance, it seems obvious that a given structure can’t contain its full description within itself—but it’s actually wrong. Fractals contain substructures that exactly mirror the complete fractal, so it seems that a fractal universe would at least potentially contain many complete models of itself. This isn’t in conflict with Leibniz’ law anymore than having two cubes identical in every respect, yet at half a meter’s distance from one another is.

    The other thing I don’t like about liberal use of modelling is that it makes us vulnerable to the view that we only experience the model, not the world.

    Well, we only ever experience what our senses tell us—that, I think, doesn’t really change even if we abandon the modeling-account. Whether those impressions constrain a model, or build up a perception of the world in other ways is a secondary concern here, I think.

    Finally, regarding qualia: I think they seem exactly like connections—after all, they bring properties of objects external to my mind into my mind. They bridge the gap between mind and world; it’s through my experience that I know a rose as being red, smelling rose-y, and so on. What else should a connection seem like? It’s like looking through a telescope: you see stars, not lenses. But it’s the lenses that make you capable of doing so.

    Plus, it gives qualia a role to play, i.e. drags them out of epiphenomenal hiding from the world.

    When Mary sees red for the first time, she does learn a new, non-physical fact, namely what the connection between her mental model and real red is. (I’d have to say that as something she can’t understand or express, it’s a weird kind of knowledge, but so be it.)

    (Slight correction: I don’t think Mary learns a non-physical fact, at least, not in an ontological sense—indeed, my whole project is in part an attempt to defend monism, although if you call it ‘materialism’ or something else isn’t much of an issue for me. To me, the world is physical, it’s just turned out that physics doesn’t give an exhaustive account of the physical—it’s sort of the distinction McGinn draws between physicalism and physics-alism.)

    You’re right that that Mary obtains a weird kind of knowledge, but to me, this seems like a good thing: after all, knowledge of qualia is a weird, inexpressible kind of knowledge—just witness all the circumlocution on the subject, ‘what-it’s-like-ness’, ‘redness of red’, and so on. Indeed, that the possession of such a weird kind of knowledge falls out of the whole approach is what suggested the identification, to me, in the first place!

  9. 9. mjgeddes says:

    Actually Peter I do think that ‘all we ever see is a model’. This claim becomes easier to swallow when you consider optical illusions. For instance take a look at these famous ones here:

    http://blog.visme.co/best-optical-illusions/

    Your conscious perceptions are all models, not how the illustrations actually look at all.

  10. 10. Peter says:

    You’re not alone! Lots of people, many of them cleverer than me, have supposed that the possibility of error, in illusions, mirages, and so on, showed that we really only experience sense data (or some intermediary thing). If we we really see the thing, how could we be wrong about it? How could we see a thing that in fact does not exist?

    I think the error is not between thing seen and the seeing person, but in the seeing person’s beliefs about what they are seeing. There is indeed a sense in which my perceptions can’t be wrong; falsity is a property of propositions, not perceptions.

    Now in vision there’s so much pre-processing that often our unconscious mind actually presents a preferred interpretation, so we are almost given the false belief. But even so, I think it’s too radical to deny that we’re seeing the picture.

  11. 11. SelfAwarePatterns says:

    Another reason for concluding that we only have access to the models is that the available bandwidth in the optic isn’t sufficient to convey a full resolution camera like picture to the brain in real time. It appears that what’s transmitted are changes. If so, then our perceived vision is a construction updated by the limited information streaming in from the retinas.

    Peter, as you note, all of this far precedes any conscious perception. We can’t introspect it, no matter how hard we try.

    Of course, saying we *only* have access to the model presupposes there is some alternative. Perception has to be built somewhere before it can be utilized. And “access to” implies that there’s an entity separate from the models accessing them, when in reality it’s one part of the system utilizing another part of the system’s information.

  12. 12. Paul Topping says:

    I don’t really see what the problem is. We now have self-driving cars with vision systems that makes mistakes. Its algorithms are designed to expect certain input data which they process and use to make decisions. These algorithms are far from perfect and can be fooled by unexpected input data. They also suffer from programming mistakes.

    Humans have a similar setup, just different hardware and software. The hardware and software were designed by evolution but we all know that is not a process that leads to perfect designs. Our hardware and software algorithms can be fooled by unexpected input and bugs in the algorithm, or just flaky hardware and software in the particular individual.

  13. 13. Jochen says:

    Selfawarepatterns:

    That said, I can’t say I understand Szangolies’ argument that the relation between the object and the model is not computable.

    Well, think of it in terms of the understanding of language. You might understand a Chinese text by translating it into English. If the language of thought-hypothesis is true, you might understand the English, in turn, by translating it into Mentalese, the language your brain speaks. But the buck must stop here: you can’t understand Mentalese by yet further translating it; otherwise, you’d just get into an infinite regress of translations, without ever understanding anything. Consequently, Mentalese must not be understood by translation, and the way (whatever it be) that the brain understands Mentalese grounds our ability to understand Chinese by translation into English (and so forth).

    Now, it’s similar with computations. The sequence of states a system traverses can be mapped onto a formal object, such as an algorithm, a computable function, or what have you. In a sense, we ‘translate’ the state sequence into that algorithm. But how does this translation work? Well, one thing taking in data of one kind (the states of the system) and putting out data of another kind (the algorithm) is a computer. So we suppose that it’s by computation that this mapping between physical and formal object is accomplished.

    But then, the computation furnishing the mapping itself needs to be grounded in some physical system—there must be a computer performing the computation. But then, there must be a mapping taking the states of that system to those of the appropriate computation. How is this mapping supposed to be implemented? As with the translation above, if we again answer ‘by computation’, we run into an infinite regress. So it can’t be computation that ultimately underlies the mapping. Consequently, in order to perform computation at all, we need to ground it in non-computational operations; likewise, in order to translate and understand, understanding can’t be furnished by translation.

    So that’s why mental computation needs to be grounded in the noncomputational, while the relation between your face and its digital image is perfectly computational: it’s just like how the relation between Chinese and English text is one of translation, but the relation between Mentalese and your understanding thereof can’t be.

    Of course, there are other good reasons to believe the world isn’t computational. One is simply that there’s no good reason to think that it should be. Another is that there’s lots of things that fall into place if you stipulate this: if we’re trying to apprehend a non-computational world by computational means, for instance, we should perceive the world as following a deterministic law, that is interspersed with random events—simply because every noncomputable function can be represented as a computation plus a string of random numbers. This is, of course, exactly what we see.

    But moreover, a computational world would be an epistemic tragedy: just think about how a denizen of a simulation ever could find out what ‘hardware’, so to speak, the world runs on. They couldn’t, of course: whether it’s a PC running Windows or Linux, or a clever contraption of levers and switches, thanks to computational universality, all would be capable of running the simulation. So computationalism would mean that the fundamental layer of the world is forever closed off to us. We could give up on things like finding a final theory—or otherwise, declare any theory we have to be that final theory: for any theory capable of describing a computer running our simulation is adequate as a physical theory of everything, with the right initial conditions (the ‘program’). So, electromagnetism is the theory of everything!

    ————————————–

    Paul Topping:

    As far as modelling goes, it takes the definition too literally. It conjures up the old Homunculus point of view with its talk of a model needing to be perceived by some other part of the brain.

    Actually, if anything, my definition of modeling is overly broad—all that’s needed is, as you say, some sort of correlation between the model and the object. Looking at the model, you must be capable of extracting information about the state of the object.

    And yes: this does bring up the homunculus; my argument against computationalism is merely a formal version thereof. It can’t be models/computation all the way down, and hence, we must ground our engagement with the world otherwise. But since this grounding can’t itself be modeled, it seems mysterious to us.

    ——————————–

    mjgeddes:

    I don’t buy the claim that the connection between ‘world’ and ‘models’ is non-computable.

    Well, it’s not merely a claim—I give a detailed argument; if the connection were computable, we’d never bottom out. And I don’t think it’s acceptable to simply go, well, there’s probably gonna be a regress one way or another, so let’s just say ‘everything is information’ and go for an early lunch.

    ————————–

    Peter:

    I think the error is not between thing seen and the seeing person, but in the seeing person’s beliefs about what they are seeing.

    That’s interesting, but I don’t really see how you can pry apart perceptions and beliefs about perceptions. Is there a difference between seeing something and believing to see something (isn’t seeing believing, as they say?)? Can I falsely believe I have a headache, and what’s the difference to actually having a headache?

    Besides, ultimately, even on my view, modeling isn’t all that’s going on; after all, the whole purpose of the argument is to show that our perceptions or experiences can’t be grounded in modeling. So you might also view my argument as a reductio of the proposition that all cognition is modeling.

    But I think I need to think about this issue a little more.

  14. 14. Jochen says:

    I meant to address this part earlier:

    A demand for an explanation of the entire world is automatically a demand for just the kind of total explanation that cannot exist.

    Although I believe this, I find it hard to accept; it leaves my mind with an unscratched itch. If we can’t explain the world, how can we assimilate it?

    In a sense, the entire thing is nothing but an incompleteness theorem for physics (and other ways of modeling the world); thus, at worst, it leaves us in the same predicament mathematicians have been in for going on 90 years now. They’ve coped, and so will we: while there’s no single, one-size-fits-all explanation for everything, there are still explanations for any given thing. Our epistemic picture of the world is bound to be more of a patchwork than a grand tapestry, but then, what have we really lost?

  15. 15. Jochen says:

    That’s interesting, but I don’t really see how you can pry apart perceptions and beliefs about perceptions.

    Maybe having beliefs about perceptions involves having second order states that have perceptions as their content; but if so, then I think that in some sense, my modeling really only concerns second order states, as well. I think that when, for instance, we see a book as a book, that involves having a model of the book; but it may be that one can ‘strip away’ the higher order, leaving us with a kind of simple perceptual consciousness, like when we’re seeing the book, but not really attending to that perception.

    So maybe in the essay, I hastily identified ‘being conscious’ with ‘having higher order states’, but in retrospect, it’s not clear that one can’t be conscious without having any particular thing of which one is conscious—a sort of ‘zoned out’, meditative state perhaps. But I don’t think that’s a threat to my ideas otherwise.

  16. 16. SelfAwarePatterns says:

    Jochen #13,
    I’m grateful for the thoughtful reply. BTW, sorry for referencing you by your last name. I didn’t initially pick up that you, the Jochen who posts here, was the author.

    First, I should note that I don’t agree that it’s obvious that the universe can be divided between computational and non-computational components. Certainly we can’t compute all of it, but that may simply be a limitation of our vantage point.

    My philosophy of mathematics is empirical. I think mathematics is grounded in patterns we observe in the world. So I wouldn’t say that the universe is mathematics so much as mathematics is an (attempted) model of the universe. When we run into something we can’t currently model with it, we tend to expand mathematics to do so. Newton invented calculus to deal with gravity. Einstein had to make use of tensors to understand general relativity; had he attempted to do so before tensors had been developed, he would have been forced to invent them.

    In my mind, this explains the “unreasonable effectiveness” of mathematics. Granted, it does leave the question open of what is doing the computation? But then our understanding of something is always in terms of its more primitive underpinnings. Eventually we always reach a layer we can’t understand.

    The thing is, anything that can be modeled mathematically can be interpreted to be computing those mathematics. Which implies that most, if not all, of the universe is computational. Now, it’s often not productive to do that interpretation. The interpretive effort to see a rock or a pond as doing computation would be silly. The computation to energy ratio needs to be high enough that the interpretation is convenient (doesn’t require a lot of energy).

    So, you ask where are the mappings or translations implemented? I’m not quite sure what you’re asking here, since the implementation exists in front of us, either in the camera I/O system in my laptop or in our peripheral nervous system. It seems like what you’re really asking is, where were the mappings or translations come from?

    In a designed computer, they’re often designed in other computers, or in the engineer’s mind. But in an evolved system, they’re implemented by natural selection. Granted, it’s implementation without comprehension, but that’s what evolution does. It only succeeds because of the large amounts of time it has to work with.

    I suppose you could argue that the mapping between the model and the object is one of those cases where the computational interpretation isn’t productive. I’d grant that it’s far more complicated than what my laptop is doing, and that we don’t have a full accounting of that model yet, but it strikes me as overly pessimistic to assume we never will.

    I’m somewhat pessimistic that we’ll ever have a “final theory.” There may always be a layer we don’t understand. For instance, what is energy? Space? Time? I suspect any answers would have components which would represent new unknowns. Turtles all the way down.

  17. 17. Stephen says:

    It seems to me that mapping between the physical world and a model is typically a symbol assignment for sensor data to something the model can work with. As such, it is really just a part of the model itself. If it is treated as separate, then it is a trivial model, being just a declarative equivalency. No further understanding of the mapping can be found by modelling it, so there is no infinite regression of models.

  18. 18. Jochen says:

    Selfawarepatterns:

    First, I should note that I don’t agree that it’s obvious that the universe can be divided between computational and non-computational components.

    This makes me think that maybe we’re using the terms ‘computational’ and ‘noncomputational’ differently, because there’s a sharp mathematical distinction between them. Computational, roughly, is anything that could be output by a Turing machine, even in the limit of it running forever; noncomputational is anything that can’t be. So, for instance, the set of halting computations is noncomputational: no Turing machine exists that could output all its members; that’s just the unsolvability of the halting problem.

    Many more noncomputational objects than computational objects exist in mathematics. The set of computable real numbers is of vanishing measure in the set of real numbers—‘almost all’ real numbers are noncomputable in the sense that if you picked a real number at random, the probability that it’s a noncomputable real is (exactly!) 1. There are only as many computable numbers as there are natural numbers, and there are many more real numbers than natural numbers.

    The same goes for functions, say, for definiteness, from the natural numbers to the natural numbers—everything a computer can do can be framed in these terms, because we can think of the initial and final states of the computer as a finite binary string, which codes for a natural numbers; it’s computation is then a function taking a binary (natural) number and outputting another. Almost all of these functions are noncomputable—in fact, there are as many such functions as there are real numbers, and again, only as many computable functions as there are natural numbers.

    So what is computable and what’s not isn’t a feature of our vantage point, or a human limitation; it’s not that these are things we don’t yet know how to compute, but rather, that no possible computer could compute them. And then to surmise that our world is computational would be to say that it is confined to an infinitely small space of mathematical possibility—and all I’m saying is that maybe there’s no reason for such a confinement.

    I think mathematics is grounded in patterns we observe in the world.

    I basically agree here—more accurately, I think that mathematics is ultimately the abstract science of structure. Structure, to my mind, is that which an object and its model have in common. A favorite example is the set of my paternal ancestors and the books of varying thickness on my shelf: I can associate an ancestor with a book such that if a book is thicker than another, then the person associated with that book is an ancestor of that associated to another. Consequently, I need only compare book thickness in order to see whether John is an ancestor of Jim.

    That’s possible because both the set of my paternal ancestors and the set of books obey a certain structure: a total well-ordering. If I included maternal ancestors, there would no longer be such an ordering; rather, we’d have a partial order, and consequently, I would have to include something to keep track of that (like using books in different shelves, for example) into my model.

    Computers are then universal models in that basically any kind of structure can be imbued onto them. Or, I should rather say, any computable structure—as argued above, there are mathematical objects such that no computer can reproduce them.

    The thing is, anything that can be modeled mathematically can be interpreted to be computing those mathematics. Which implies that most, if not all, of the universe is computational.

    This is at least somewhat open to interpretation. On the usual interpretation of what it means for something to be ‘computational’, it’s wrong: as computational is defined by what a Turing machine can do, there are mathematical objects that are non-computational, and then, it’s at least possible for here to be systems that can be modeled mathematically, but that can’t be called ‘computational’. A certain class of such (hypothetical) systems are generally called ‘hypercomputers’.

    On the other hand, one may think about this as a counterexample to the Church-Turing thesis: it turns out that Turing machines really didn’t do the job of capturing all that can be computed, as there are systems that can compute things no TM can compute. This, however, would trivialize the thesis of computability: by such a definition, everything is trivially computable, because we simply call everything any system ever could do ‘computation’.

    When people talk about ‘computationalism’, they generally mean the first kind of interpretation: that everything in the world could be simulated by a Turing machine. That’s what my arguments are directed against: only a certain subset of the world is computational, and only that subset is directly amenable to being modeled; hence, anything not in that subset is not directly accessible to model-based reasoning.

    I’m not quite sure what you’re asking here, since the implementation exists in front of us, either in the camera I/O system in my laptop or in our peripheral nervous system.

    The implementation doesn’t exist in either of those systems; it’s a function mapping states of one system to states of another. Similarly, the translation itself is neither the Chinese nor the English text, but instead, the way one is connected to the other. In translating, we perform some work: look up words, apply rules of grammar, and so on. I’m curious about how that same work is performed in modeling, or computation.

    A part of what makes this so difficult is that our computing systems are designed to be readily interpreted. It’s the same with language: you don’t typically notice the words you read right now as words, as symbols, but rather, you directly and immediately grasp their meaning. They are transparent to you, but that transparency hides a great deal of effort: after all, it’s by no means self-evident that the word ‘dog’ maps to a certain kind of furry four-legged barking creature—if that were the case, then everybody would just immediately understand it; but actually, learning languages can be rather difficult.

    Likewise, the way a computer presents its output—via pictures, or text, or sound—is structured such as to be near-immediately meaningful. But that meaning does not come from the output itself, just as the meaning of a text is not within that text itself—it’s instead constructed by the interpreting mind.

    But if that’s the case, then the way the mind itself creates its meaning must be different—otherwise, we’d have an infinite regress. And it’s here that the noncomputability of the connections between (mental) model and object comes in.

  19. 19. Jochen says:

    Stephen:

    It seems to me that mapping between the physical world and a model is typically a symbol assignment for sensor data to something the model can work with. As such, it is really just a part of the model itself.

    This is essentially saying that there are symbols such that they carry their meaning on their sleeve—i.e. whose semantics is given by their syntax. Generally, this is thought to be impossible—it’s the reason that it’s typically not possible to translate a text that has been written in a forgotten language: the text (the model) is still present, but its translation (the mapping) has been lost; so that mapping is not inherent in the model itself. The security of codes also hinges on this impossibility.

    Also, you can use one and the same model for different objects: the stack of books I described above could model just as well the set of my maternal ancestors, or the kids in a class, or the different versions of Windows. Given only the model, it is in general impossible to figure out what its object is; consequently, the mapping between it and its object is not part of the model.

    In fact, this is something that can be proven mathematically: as Newman first pointed out (what’s today called ‘Newman’s problem’), any given set of N objects can be imbued with the structure of any other system of N objects—so all that a given model tells you about its object is its cardinality (and even there, only giving a bound: the object could have a lesser cardinality, if certain elements of the model are identified with one another).

    In order to speak of modeling, it does not suffice to have access to the model system—you need that system and the mapping between it and the object; only then can you use to model to extract information about the object.

  20. 20. Tom Clark says:

    Jochen in 8:

    “…knowledge of qualia is a weird, inexpressible kind of knowledge—just witness all the circumlocution on the subject, ‘what-it’s-like-ness’, ‘redness of red’, and so on. Indeed, that the possession of such a weird kind of knowledge falls out of the whole approach is what suggested the identification, to me, in the first place!”

    I’m not sure we have knowledge of qualia as basic simples-in-themselves, e.g., red, since we can’t further describe them. If you can’t articulate a non-relational fact about red even to yourself, then what special “first-person” knowledge do you have of it? This in a way makes sense since the epistemic regress has to end somewhere in descriptions, so we can think of qualia as the front-line, not further decomposable, cognitively impenetrable surds in terms of which of objects are discriminated perceptually in consciousness. Red works perfectly well as a way to discriminate objects (thus know facts about them) without itself being knowable in anything but relational terms.

    Perhaps it’s the case that any sufficiently ramified, representationally recursive modeling system ends up with front-line terms of representation that end up as qualitative for the system, that is, terms about which the system can’t articulate any but relational facts. Such relational facts (e.g., red is more like orange than blue) would be available to any system with similar representational capacities, thus are not “first-person” facts.

  21. 21. SelfAwarePatterns says:

    Jochen #18,
    I like your description of mathematics as an abstract science of structure. I would just note that, per many physicists, mathematical structures are only an approximation of structures in the world. However, they’re always tightening these approximations, so that they become increasingly effective at predicting the real world versions.

    Computation can be divided into two perspectives: abstract computation and concrete computation. Abstract computation is the mathematical formalism you discuss. A Turing machine is an abstract concept. Concrete computation is what takes place in actual physical systems. Concrete computation is never a perfect replica of abstract computation, only an approximation. Strictly speaking, there are no physical Turing machines. Only constructed systems that approximate it to some level of effectiveness.

    If a physical system is dynamic and has a large enough number of states which affect and are affected by its environment, whether those states are discrete (digital) or continuous (analog), I think it can non-trivially be interpreted as a computational system. Analog computers (which are not Turing machines) are a technological example, and nervous systems (also not Turing machines) are a natural one.

    We don’t see analog computers much anymore. They used to be needed to do computations that digital systems couldn’t. But as digital systems have become more powerful, that is, as the resolution of their discrete states has increased, their ability to approximate the processing of analog systems has reached a point that, for most purposes, the analog systems aren’t needed. (It’s worth noting that analog systems themselves can’t perfectly reproduce each other’s processing, including, due to wear and tear, their own from the past.)

    Are there things that Turing machines can’t compute? Absolutely. But given sufficient resources, they can effectively approximate the processing of many of those computations, effective enough for most purposes. My face is as analog a system as anything else. But the model of my face in my laptop is a digital one. It’s an effective approximation of the analog reality.

    In other words, the divide you describe may be interesting in an academic sense, but both evolution and successful engineering work in terms of effectiveness. In that sense, there’s nothing stopping the interface between the object and the model from being computational to an approximation at some level of effectiveness.

    While abstract systems might be vulnerable, within their formalism, to the infinite regress you describe, concrete systems reduce to their physics, and can be considered in purely physical terms (albeit with more work since doing so is operating at a lower level of abstraction), where the interpretation issues seem moot. Put another way, the formal function of a physical system will always be a matter of interpretation relative to some other goal seeking system (such as us), but the actual actions of that physical system are what they are regardless.

    Not that things don’t eventually get very weird in physical systems 🙂

  22. 22. Jochen says:

    Tom:

    Red works perfectly well as a way to discriminate objects (thus know facts about them) without itself being knowable in anything but relational terms.

    I’m skeptical about this—to me, it seems that there needs to be some non-relational anchor upon which relations supervene. Ted Sider (to make the exactly opposite point) has made the example of a plain that’s halve red and halve blue. He claims that there is an objectively right way to describe the structure of the plain, a way that ‘carves at the joints’: namely, it’s the one along the dividing line between red and blue.

    It would seem to be a mistake to take any other ‘cut’ through the plain, and referring to the two sides by the predicates ‘bred’ and ‘rue’ (the argument is in the sample of Writing the Book of the World here). The division into ‘red’ and ‘blue’ part gets at the true structure of the plain; the division into ‘bred’ and ‘rue’ doesn’t.

    What Sider, to me, seems to miss is that the former only is the true structure of the world by virtue of being realized in terms of the non-structural, intrinsic facts about what color the parts of the plain actually are. Relationally, the predicates ‘red’ and ‘blue’ are indistinguishable from ‘bred’ and ‘rue’, and if there were nothing beyond those relations, both descriptions should be considered on equal footing. Certainly, and on pain of yet another infinite regress, we can’t further analyze ‘red’ in terms of relations that would justify us elevating it above ‘bred’ in terms of describing Sider’s plain.

    Again, this touches on Newman’s problem: all that pure structure ever tells us about a domain is its cardinality. In my opinion, it thus needs something to pick out the true structure of that domain, and my hypothesis is that these are qualia, playing sort of the role of intrinsic properties, that makes a give model a model of a particular object system, and not of every system with a given cardinality.

  23. 23. Jochen says:

    Selfawarepatterns:

    If a physical system is dynamic and has a large enough number of states which affect and are affected by its environment, whether those states are discrete (digital) or continuous (analog), I think it can non-trivially be interpreted as a computational system. Analog computers (which are not Turing machines) are a technological example, and nervous systems (also not Turing machines) are a natural one.

    This I would think goes against the spirit in which computationalism is usually taken. Neural networks and analog computers aren’t Turing machines, but they’re both (in the limit) computationally universal—i.e. they could be replaced by a Turing machine, or a physically realizable approximation, without functional difference. They’re TM equivalent computational paradigms. Indeed, it’s just the fact that every computer that we’ve so far been able to think up ends up being (in the limit) equivalent to a Turing machine that’s motivated the Church-Turing thesis, namely, that Turing machines characterize the set of functions that can actually be computed. In this sense, the difference between TMs and neural nets doesn’t matter for computability.

    Computationalism now holds that only physical systems exist (including the entire universe) that are equivalent to a Turing machine, and moreover, that they are wholly exhausted by their functional description—i.e. that all we need to know about them is what they compute.

    It’s in this spirit that I think the world is non-computational. It may be so in several ways: one, there may be physical systems that are capable of behavior no Turing machine could match, and thus, that can be said to ‘compute’ a noncomputable function. On the other hand, it may be that the computational description simply doesn’t fully capture the character of physical systems. There may be physical properties that don’t reduce to information, to syntactic, symbolic structures.

    I think both is very likely right (and I’m not sure they’re ultimately really different): behavior according to a noncomputable function would seem like computable behavior plus random intermissions to an agent using computational models—which is what we see, with quantum mechanics. Properties that don’t reduce to structure would seem to be ineluctably intrinsic, incommunicable and inutterable—which is what we get with qualia. Furthermore, as I said above, we don’t really have any good reason to think that the world only permits computation (that isn’t equally well explained by the fact that our models of the world are computable). So just drop this prejudice, and it seems that whole swaths of mysterious behavior suddenly becomes far less so.

    This also has the advantage of making our picture of the world more parsimonious. So we just drop a questionable assumption, and lots of stuff seems to fall into place. Seems a bargain to me!

    My face is as analog a system as anything else. But the model of my face in my laptop is a digital one.

    This is often given as an argument, but it ultimately falls short—it’s the same as saying that a vinyl record contains information that can’t be captured on a CD. But that’s wrong: as long as the signal is finite, an analog signal can be exactly replicated by a digital data structure, thanks to the Nyquist-Shannon theorem. There’s ultimately no difference between digital and analog as far as computing (over finite domains) is concerned.

    While abstract systems might be vulnerable, within their formalism, to the infinite regress you describe, concrete systems reduce to their physics, and can be considered in purely physical terms (albeit with more work since doing so is operating at a lower level of abstraction), where the interpretation issues seem moot.

    It’s exactly in concrete physical systems that the issue becomes important: again, it’s on par with translation, and translation is also important between actual texts. So there is a question of how an orrery comes to model the solar system; and this question has no (Turing-) computable answer.

  24. 24. Stephen says:

    Jochen @19

    I’m happy to go along with the idea that the mapping isn’t part of the model. It’s just a matter of definition, in my opinion. As you point out, the model without the mapping is quite useless, so they are tightly linked.

    “it’s typically not possible to translate a text that has been written in a forgotten language: the text (the model) is still present, but its translation (the mapping) has been lost; so that mapping is not inherent in the model itself.”

    Perhaps the issue is that multiple models and mappings are being conflated. In the text of a forgotten language example you give, there are two models and mappings. One is the text model and mappings itself and the other is your personal model and mappings of the text. In the case of Linear B, no one understood how to translate it until someone in the 1950’s deciphered it by examining the text and modern Greek. What this means is that the mapping of the forgotten text language existed, it was just not part of anyone’s personal model and mapping until it was “discovered”. Codes can be cracked.

    In any case, what hasn’t been addressed (at least it isn’t clear to me) is why a declarative equivalency (mapping) is subject to being further modeled thereby resulting in infinite regress. Perhaps it is just being confused with creating a personal model?

  25. 25. mjgeddes says:

    Jochen and Stephen,

    There’s no infinite regress with computational modelling. Just postulate a ‘principle of ultra-finite recursion’ – the modelling is ‘good enough for all practical purposes’ once some finite number of levels been reached. I think 3 levels is good enough.

    i.e

    (1) Language A models some sensory data (or code) X (map)
    (2) Language B models language A (map of the map)
    (3) Language C models language B (map of the map of the map)

    STOP RECURSION

    Principle of ultra-finite recursion: ‘Infinite recursion can always be approximated to any degree of accuracy with only 3 levels of recursion’

  26. 26. mjgeddes says:

    What is consciousness then in the computational model? It’s precisely language C, the third level of self-reflection (recursion)!

    So I think Jochen is indeed correct that consciousness is indeed the connection between world and model and what ultimately grounds meaning, but it can be entirely computational! Because by the principle of ultra-finite recursion, 3 levels of recursion is enough to approximate infinite recursion to any desired degree of accuracy.

  27. 27. Jochen says:

    Stephen:

    In any case, what hasn’t been addressed (at least it isn’t clear to me) is why a declarative equivalency (mapping) is subject to being further modeled thereby resulting in infinite regress.

    Well, the further mapping is due to trying to find an explanation of how the mapping in the original case works. So, say you have an orrery: clearly, it models the solar system. But how does it come to do so? How does its configuration come to represent that of the solar system? There is an interpretative act here, and this is what we want to understand. And I believe that such understanding always involves creating a model—sort of a mental simulation of what’s to be understood. If you have such a model of something, you understand it—you can ‘play back’ its behavior, answer counterfactuals about it (i.e. what would happen if the object were subject to such-and-such conditions) and so forth.

    So trying to understand how a model is connected to its object involves creating a model of how this connection works. Does this make things any more clear?

    ——————————–

    mjgeddes:

    Just postulate a ‘principle of ultra-finite recursion’ – the modelling is ‘good enough for all practical purposes’ once some finite number of levels been reached. I think 3 levels is good enough.

    Well, the problem is that a mapping on the nth level depends on a computation, which itself involves a mapping on the (n+1)st level—and without that level, there simply is no nth level mapping. Consequently, there is no third level if there isn’t a fourth, and so forth; after all, that’s what makes this a problem.

    Alternatively, you could mean that, say, the third-level mapping is qualitatively different from those that it grounds—i.e. that it’s not computational. But that’s just my proposal.

  28. 28. Stephen says:

    Jochen

    What I am trying to say is that the mapping “model object x is equivalent to real object y” has no properties other than the one equivalency, no behaviours and no intrinsic meaning. All of that is contained in the model. There is just nothing to understand about it.

    If the little sphere representing earth in the orrery was moved to be the second planet from the sun, it would be an error in the model, not the mapping. If the same sphere was presented as a cube instead of a sphere, it would also be an error in the model. If there was a superfluous mapping of a sphere representing a planet that did not exist, if it appeared in the orrery it would again be an error in the model.

    Whew. I think I’m tapped out on this one. 🙂

  29. 29. Jochen says:

    Stephen:

    What I am trying to say is that the mapping “model object x is equivalent to real object y” has no properties other than the one equivalency, no behaviours and no intrinsic meaning.

    Well, you could say the same about computer programs: they all really boil down to a mapping between the starting state x and the stopping state y (a partial mapping, to account for non-halting computations, but still). So every computation is trivial: you need only provide a lookup table such that every possible starting state is associated with the right stopping state, and you’re done. Likewise, every translator can be replaced by a big book containing every possible phrase in, say, Chinese, and its equivalent in English.

    Of course, these things are practically impossible: a computation that accepts an input of ~34 characters in length already needs a lookup table with more entries than there are atoms in the observable universe. So this isn’t a very practical way to do computation, or translation.

    Sure, if there were a language that differs from English in merely substituting different words, leaving all other rules the same, then one could provide a dictionary that just translates every word. But that’s not in general how languages work.

    And neither do models work by just every element of the model being mapped to an element of the object. The ‘errors’ you quote are only errors if you (erroneously) assume that there is only one right mapping between the elements of the model and those of the object. But that’s not the case: you could without logical problems map the second planet to the Earth, and the third to Venus—then, the model would not have the same order of planets, but there’s no reason to require that it should. You could still read of important information, if you keep the ratio of orbits, only flipping it for the Earth/Venus case, or if you keep the orbit times right; it would merely add a trivial bit of complexity to the operation needed to extract the information (i.e. the mapping).

    Likewise, you could claim that ‘the quick brown fox jumps over the lazy dog’ and ‘the quick brown fox jumps over the lazy cat’ are two different sentences, with one of them being wrong, but you could also adapt your translation such that the second sentence comes from a language that is identical to English in every respect, except that ‘cat’ means dog.

    Or you could use cubes to represent planets—indeed, you could encode additional information that way, such as its mass in terms of its edge length. You could use an additional bead to represent the relative position of the star nearest to the sun in the night sky; or you could use it to represent the sun’s position relative to the galactic center.

    In the end, a model is best thought of as a kind of cipher, which has to be decoded in order to yield information about the object. It’s simply not the case that only trivial codes, where say every letter is exchanged for a different one, are the only ones allowed—and indeed, it can’t actually be like that, since all that our brains have to build models with are neuron firing patterns. There’s no obvious mapping between such patterns and the relative positions of the planets, for example.

    But if that’s the case, then you generally have to put a little more work into the decoding; and how exactly that’s accomplished is the topic of my essay.

  30. 30. John Davey says:

    There is a something of a problem regarding everything as a model – namely that a model must exist inside a head in the first place. We are back to the “head inside the head” it seems to me.

    if we have say – instinct – based upon a “model” – then we have to ask ourselves how the model comes about, into being, in the first place. Models are, by definition, observer-relative, so we must be born with an observer in our head in the first place. So the fundamental cognitive question remains.

    For me, I think models are a higher order mental feature – a value added feature of the homo sapiens brain. But our fundamental cognitive processes are inherited from worms and small creatures that scuttle through forests. I think at some point models emerged from the evolutionary swamp – but as products of cognition, not sources of them.

    JBD

    JBD

  31. 31. Jochen says:

    John Davey:

    Models are, by definition, observer-relative, so we must be born with an observer in our head in the first place.

    I don’t see why. I don’t intend for there to be some entity in the head perceiving my model, modeling it itself, and so on; rather, having the model is the perception—there’s no further mediation.

    Basically, we have qualia. This isn’t model-based, and they’re not something I explain, but take as given—albeit, if my argumentation is right, their properties seem to be well explained by the impossibility of modeling them.

    Qualia connect us with things out there in the world. We don’t have a red-experience, we experience the redness of something—a rose, say. These experiences are the building blocks from which models are created. They’re the map between the structure of the mind—equivalently, the brain—and the world outside that makes my mental structure, neuron-firing pattern, or whatever, into a model of the outside world. No further observer in the head necessary.

    Have you ever noticed how, only after some seconds have passed, suddenly the fact that the church bells are ringing enters your awareness, but you can nevertheless tell how many rings their have been? That’s in my view explained by the qualia of the ringing bells being introduced into a model of the world: you had the phenomenal experience first, then used it to construct a representation of the outside world.

    Or take another example: listening to a voice. Ordinarily, you will be paying attention to what is said—i.e. to the meaning of the spoken words. But it’s possible to instead shift your attention to how it’s being said—the diction, speed, the uhs and uhms and ahs you normally wouldn’t even notice.

    What’s changed here is a change in how you model the world—the same building blocks, phenomenal experiences, differently arranged, thus bringing the structure of your mind-stuff into correspondence with a different structure out there in the world.

    There’s a place where the buck stops, and that’s at the model of the outside world in the head; nothing further is needed. Indeed, that model can’t itself be modeled—this is where the infinite regress would come in. I’m forced to conclude that the mental model can’t be grounded in the way that exterior models (orrerys and so on) are grounded, because doing so would indeed lead to vicious regress; but by concluding that there must be something else at play there, I get out of it.

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