Computational functionalism probably can't explain phenomenal consciousness
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These algorithms are useful maps of the brain and mind. But is computation also the territory? Is the mind a program? Such a program would need to exist as a high-level abstraction of the brain that is causally closed and fully encodes the mind.
I said it in one of your previous posts but I’ll say it again: I think causal closure is patently absurd, and a red herring. The brain is a machine that runs an algorithm, but algorithms are allowed to have inputs! And if an algorithm has inputs, then it’s not causally closed.
The most obvious examples are sensory inputs—vision, sounds, etc. I’m not sure why you don’t mention those. As soon as I open my eyes, everything in my field of view has causal effects on the flow of my brain algorithm.
Needless to say, algorithms are allowed to have inputs. For example, the mergesort algorithm has an input (namely, a list). But I hope we can all agree that mergesort is an algorithm!
The other example is: the brain algorithm has input channels where random noise enters in. Again, that doesn’t prevent it from being an algorithm. Many famous, central examples of algorithms have input channels that accept random bits—for example, MCMC.
And in regards to “practical CF”, if I run MCMC on my computer while sitting outside, and I use an anemometer attached to the computer as a source of the random input bits entering the MCMC run, then it’s true that you need an astronomically complex hyper-accurate atmospheric simulator in order to reproduce this exact run of MCMC, but I don’t understand your perspective wherein that fact would be important. It’s still true that my computer is implementing MCMC “on a level of abstraction…higher than” atoms and electrons. The wind flowing around the computer is relevant to the random bits, but is not part of the calculations that comprise MCMC (which involve the CPU instruction set etc.). By the same token, if thermal noise mildly impacts my train of thought (as it always does), then it’s true that you need to simulate my brain down to the jiggling atoms in order to reproduce this exact run of my brain algorithm, but this seems irrelevant to me, and in particular it’s still true that my brain algorithm is “implemented on a level of abstraction of the brain higher than biophysics”. (Heck, if I look up at the night sky, then you’d need to simulate the entire Milky Way to reproduce this exact run of my brain algorithm! Who cares, right?)
2I think causal closure of the kind that matters here just means that the abstract description (in this case, of the brain as performing an algorithm/computation) captures all relevant features of the the physical description, not that it has no dependence on inputs. Should probably be renamed something like "abstraction adequacy" (making this up right now, I don't have a term on shelf for this property). Abstraction (in)adequacy is relevant for CF I believe (I think it's straight-forward why?). Randomness probably doesn't matter since you can include this in the abstract description.
Right, what I actually think is that a future brain scan with future understanding could enable a WBE to run on a reasonable-sized supercomputer (e.g. <100 GPUs), and it would be capturing what makes me me, and would be conscious (to the extent that I am), and it would be my consciousness (to a similar extent that I am), but it wouldn’t be able to reproduce my exact train of thought in perpetuity, because it would be able to reproduce neither the input data nor the random noise of my physical brain. I believe that OP’s objection to “practical CF” is centered around the fact that you need an astronomically large supercomputer to reproduce the random noise, and I don’t think that’s relevant. I agree that “abstraction adequacy” would be a step in the right direction.
Causal closure is just way too strict. And it’s not just because of random noise. For example, suppose that there’s a tiny amount of crosstalk between my neurons that represent the concept “banana” and my neurons that represent the concept “Red Army”, just by random chance. And once every 5 years or so, I’m thinking about bananas, and then a few seconds later, the idea of the Red Army pops into my head, and if not for this cross-talk, it counterfactually wouldn’t have popped into my head. And suppose that I have no idea of this fact, and it has no impact on my life. This overlap just exists by random chance, not part of some systematic learning algorithm. If I got magical brain surgery tomorrow that eliminated that specific cross-talk, and didn’t change anything else, then I would obviously still be “me”, even despite the fact that maybe some afternoon 3 years from now I would fail to think about the Red Army when I otherwise might. This cross-talk is not randomness, and it does undermine “causal closure” interpreted literally. But I would still say that “abstraction adequacy” would be achieved by an abstraction of my brain that captured everything except this particular instance of cross-talk.
Two thoughts here
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I feel like the actual crux between you and OP is with the claim in post #2 that the brain operates outside the neuron doctrine to a significant extent. This seems to be what your back and forth is heading toward; OP is fine with pseudo-randomness as long as it doesn't play a nontrivial computational function in the brain, so the actual important question is not anything about pseudo-randomness but just whether such computational functions exist. (But maybe I'm missing something, also I kind of feel like this is what most people's objection to the sequence 'should' be, so I might have tunnel vision here.)
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(Mostly unrelated to the debate, just trying to improve my theory of mind, sorry in advance if this question is annoying.) I don't get what you mean when you say stuff like "would be conscious (to the extent that I am), and it would be my consciousness (to a similar extent that I am)," since afaik you don't actually believe that there is a fact of the matter as to the answers to these questions. Some possibilities what I think you could mean
- I don't actually think these questions are coherent, but I'm pretending as if I did for the sake of argument
- I'm just using consciousness/identity as fuzzy categories here because I assume that the realist conclusions must align with the intuitive judgments (i.e., if it seems like the fuzzy category 'consciousness' applies similarly to both the brain and the simulation, then probably the realist will be forced to say that their consciousness is also the same)
- Actually there is a question worth debating here even if consciousness is just a fuzzy category because ???
- Actually I'm genuinely entertaining the realist view now
- Actually I reject the strict realist/anti-realist distinction because ???
Thanks!
I feel like the actual crux between you and OP is with the claim in post #2 that the brain operates outside the neuron doctrine to a significant extent.
I don’t think that’s quite right. Neuron doctrine is pretty specific IIUC. I want to say: when the brain does systematic things, it’s because the brain is running a legible algorithm that relates to those things. And then there’s a legible explanation of how biochemistry is running that algorithm. But the latter doesn’t need to be neuron-doctrine. It can involve dendritic spikes and gene expression and astrocytes etc.
All the examples here are real and important, and would impact the algorithms of an “adequate” WBE, but are mostly not “neuron doctrine”, IIUC.
Basically, it’s the thing I wrote a long time ago here: “If some [part of] the brain is doing something useful, then it's humanly feasible to understand what that thing is and why it's useful, and to write our own CPU code that does the same useful thing.” And I think “doing something useful” includes as a special case everything that makes me me.
I don't get what you mean when you say stuff like "would be conscious (to the extent that I am), and it would be my consciousness (to a similar extent that I am)," since afaik you don't actually believe that there is a fact of the matter as to the answers to these questions…
Just, it’s a can of worms that I’m trying not to get into right here. I don’t have a super well-formed opinion, and I have a hunch that the question of whether consciousness is a coherent thing is itself a (meta-level) incoherent question (because of the (A) versus (B) thing here). Yeah, just didn’t want to get into it, and I haven’t thought too hard about it anyway. :)
1The most obvious examples are sensory inputs—vision, sounds, etc. I’m not sure why you don’t mention those.
Obviously algorithms are allowed to have inputs, and I agree that the fact that the brain takes in sensory input (and all other kinds of inputs) is not evidence against practical CF. The way I'm defining causal closure is that the algorithm is allowed to take in some narrow band of inputs (narrow relative to, say, the inputs being the dynamics of all the atoms in the atmosphere around the neurons, or whatever). My bad for not making this more explicit, I've gone back and edited the post to make it clearer.
Computer chips have a clear sense in which they exhibit causal closure (even though they are allowed to take in inputs through narrow channels). There is a useful level of abstraction of the chip: the charges in the transistors. We can fully describe all the computations executed by the chip at that level of abstraction plus inputs, because that level of abstraction is causally closed from lower-level details like the trajectories of individual charges. If it wasn't so, then that level of abstraction would not be helpful for understanding the behavior of the computer -- executions would branch conditional on specific charge trajectories, and it would be a rubbish computer.
random noise enters in
I think this is a big source of the confusion, another case where I haven't been clear enough. I agree that algorithms are allowed to receive random noise. What I am worried about is the case where the signals entering the from smaller length scales are systematic rather than random.
If the information leaking into the abstraction can be safely averaged out (say, we just define a uniform temperature throughout the brain as an input to the algorithm), then we can just consider this a part of the abstraction: a temperature parameter you define as an input or whatever. Such an abstraction might be able to create consciousness on a practical classical computer.
But imagine instead that (for sake of argument) it turned out that high-resolution details of temperature fluctuations throughout the brain had a causal effect on the execution of the algorithm such that the algorithm doesn't do what it's meant to do if you just take the average of those fluctuations. In that case, the algorithm is not fully specified on that level of abstraction, and whatever dynamics are important for phenomenal consciousness might be encoded in the details of temperature fluctuations, not be captured by your abstraction.
I’m confused by your comment. Let’s keep talking about MCMC.
- The following is true: The random inputs to MCMC have “a causal effect on the execution of the algorithm such that the algorithm doesn't do what it's meant to do if you just take the average of those fluctuations”.
- For example, let’s say the MCMC accepts a million inputs in the range (0,1), typically generated by a PRNG in practice. If you replace the PRNG by the function
return 0.5(“just take the average of those fluctuations”), then the MCMC will definitely fail to give the right answer.
- For example, let’s say the MCMC accepts a million inputs in the range (0,1), typically generated by a PRNG in practice. If you replace the PRNG by the function
- The following is false: “the signals entering…are systematic rather than random”. The random inputs to MCMC are definitely expected and required to be random, not systematic. If the PRNG has systematic patterns, it screws up the algorithm—I believe this happens from time to time, and people doing Monte Carlo simulations need to be quite paranoid about using an appropriate PRNG. Even very subtle long-range patterns in the PRNG output can screw up the calculation.
The MCMC will do a highly nontrivial (high-computational-complexity) calculation and give a highly non-arbitrary answer. The answer does depend to some extent on the stream of random inputs. For example, suppose I do MCMC, and (unbeknownst to me) the exact answer is 8.00. If I use a random seed of 1 in my PRNG, then the MCMC might spit out a final answer of 7.98 ± 0.03. If I use a random seed of 2, then the MCMC might spit out a final answer of 8.01 ± 0.03. Etc. So the algorithm run is dependent on the random bits, but the output is not totally arbitrary.
All this is uncontroversial background, I hope. You understand all this, right?
executions would branch conditional on specific charge trajectories, and it would be a rubbish computer.
As it happens, almost all modern computer chips are designed to be deterministic, by putting every signal extremely far above the noise floor. This has a giant cost in terms of power efficiency, but it has a benefit of making the design far simpler and more flexible for the human programmer. You can write code without worrying about bits randomly flipping—except for SEUs, but those are rare enough that programmers can basically ignore them for most purposes.
(Even so, such chips can act non-deterministically in some cases—for example as discussed here, some ML code is designed with race conditions where sometimes (unpredictably) the chip calculates (a+b)+c and sometimes a+(b+c), which are ever-so-slightly different for floating point numbers, but nobody cares, the overall algorithm still works fine.)
But more importantly, it’s possible to run algorithms in the presence of noise. It’s not how we normally do things in the human world, but it’s totally possible. For example, I think an ML algorithm would basically work fine if a small but measurable fraction of bits randomly flipped as you ran it. You would need to design it accordingly, of course—e.g. don’t use floating point representation, because a bit-flip in the exponent would be catastrophic. Maybe some signals would be more sensitive to bit-flips than others, in which case maybe put an error-correcting code on the super-sensitive ones. But for lots of other signals, e.g. the lowest-order bit of some neural net activation, we can just accept that they’ll randomly flip sometimes, and the algorithm still basically accomplishes what it’s supposed to accomplish—say, image classification or whatever.
1I'm not saying anything about MCMC. I'm saying random noise is not what I care about, the MCMC example is not capturing what I'm trying to get at when I talk about causal closure.
I don't disagree with anything you've said in this comment, and I'm quite confused about how we're able to talk past each other to this degree.
Yeah duh I know you’re not talking about MCMC. :) But MCMC is a simpler example to ensure that we’re on the same page on the general topic of how randomness can be involved in algorithms. Are we 100% on the same page about the role of randomness in MCMC? Is everything I said about MCMC super duper obvious from your perspective? If not, then I think we’re not yet ready to move on to the far-less-conceptually-straightforward topic of brains and consciousness.
I’m trying to get at what you mean by:
But imagine instead that (for sake of argument) it turned out that high-resolution details of temperature fluctuations throughout the brain had a causal effect on the execution of the algorithm such that the algorithm doesn't do what it's meant to do if you just take the average of those fluctuations.
I don’t understand what you mean here. For example:
- If I run MCMC with a PRNG given random seed 1, it outputs 7.98 ± 0.03. If I use a random seed of 2, then the MCMC spits out a final answer of 8.01 ± 0.03. My question is: does the random seed entering MCMC “have a causal effect on the execution of the algorithm”, in whatever sense you mean by the phrase “have a causal effect on the execution of the algorithm”?
- My MCMC code uses a PRNG that returns random floats between 0 and 1. If I replace that PRNG with
return 0.5, i.e. the average of the 0-to-1 interval, then the MCMC now returns a wildly-wrong answer of 942. Is that replacement the kind of thing you have in mind when you say “just take the average of those fluctuations”? If so, how do you reconcile the fact that “just take the average of those fluctuations” gives the wrong answer, with your description of that scenario as “what it’s meant to do”? Or if not, then what would “just take the average of those fluctuations” mean in this MCMC context?
MCMC is a simpler example to ensure that we’re on the same page on the general topic of how randomness can be involved in algorithms.
Thanks for clarifying :)
Are we 100% on the same page about the role of randomness in MCMC? Is everything I said about MCMC super duper obvious from your perspective?
Yes.
If I run MCMC with a PRNG given random seed 1, it outputs 7.98 ± 0.03. If I use a random seed of 2, then the MCMC spits out a final answer of 8.01 ± 0.03. My question is: does the random seed entering MCMC “have a causal effect on the execution of the algorithm”, in whatever sense you mean by the phrase “have a causal effect on the execution of the algorithm”?
Yes, the seed has a causal effect on the execution of the algorithm by my definition. As was talked about in the comments of the original post, causal closure comes in degrees, and in this case the MCMC algorithm is somewhat causally closed from the seed. An abstract description of the MCMC system that excludes the value of the seed is still a useful abstract description of that system - you can reason about what the algorithm is doing, predict the output within the error bars, etc.
In contrast, the algorithm is not very causally closed to, say, idk, some function f() that is called a bunch of times on each iteration of the MCMC. If we leave f() out of our abstract description of the MCMC system, we don't have a very good description of that system, we can't work out much about what the output would be given an input.
If the 'mental software' I talk about is as causally closed to some biophysics as the MCMC is causally closed to the seed, then my argument in that post is weak. If however it's only as causally closed to biphysics as our program is to f(), then it's not very causally closed, and my argument in that post is stronger.
My MCMC code uses a PRNG that returns random floats between 0 and 1. If I replace that PRNG with return 0.5, i.e. the average of the 0-to-1 interval, then the MCMC now returns a wildly-wrong answer of 942. Is that replacement the kind of thing you have in mind when you say “just take the average of those fluctuations”?
Hmm, yea this is a good counterexample to my limited "just take the average of those fluctuations" claim.
If it's important that my algorithm needs a pseudorandom float between 0 and 1, and I don't have access to the particular PRNG that the algorithm calls, I could replace it with a different PRNG in my abstract description of the MCMC. It won't work exactly the same, but it will still run MCMC and give out a correct answer.
To connect it to the brain stuff: say I have a candidate abstraction of the brain that I hope explains the mind. Say temperatures fluctuate in the brain between 38°C and 39°C. Here are 3 possibilities of how this might effect the abstraction:
- Maybe in the simulation, we can just set the temperature to 38.5°C, and the simulation still correctly predicts the important features of the output. In this case, I consider the abstraction causally closed to the details temperature fluctuations.
- Or maybe temperature is an important source of randomness for the mind algorithm. In the simulation, we need to set the temperature to 38+x°C where, in the simulation, I just generate x as a PRN between 0 and 1. In this case, I still consider the abstraction causally closed to the details of the temperature fluctuations.
- Or maybe even doing the 38+x°C replacement makes the simulation totally wrong and just not do the functions its meant to do. The mind algorithm doesn't just need randomness, it needs systematic patterns that are encoded in the temperature fluctuations. In this case, to simulate the mind, we need to constantly call a function temp() which simulates the finer details of the currents of heat etc throughout the brain. In this case, in my parlance, I'd say the abstraction is not causally closed to the temperature fluctuations.
I think the simplest objection to your practical CF part is that (here and further, phenomenal) consciousness is physiologically and evolutionarily robust: an infinite number of factors can't be required to have consciousness because the probability of having an infinite number of factors right is zero.
On the one hand, we have evolutionary robustness: it seems very unlikely that any single mutation could cause Homo sapiens to become otherwise intellectually capable zombies.
You can consider two extreme possibilities. Let's suppose that Homo sapiens is conscious and Homo erectus isn't. Therefore, there must be a very small number of structural changes in the brain that cause consciousness among a very large range of organisms (different humans), and ATP is not included here, as both Homo sapiens and Homo erectus have ATP.
Consider the opposite situation: all organisms with a neural system are conscious. In that case, there must be a simple property (otherwise, not all organisms in the range would be conscious) common among neural systems causing consciousness. Since neural systems of organisms are highly diverse, this property must be something with a very short description.
For everything in between: if you think that hydras don't have consciousness but proconsuls do, there must be a finite change in the genome, mRNAs, proteins, etc., between a hydra egg and a proconsul egg that causes consciousness to appear. Moreover, this change is smaller than the overall distance between hydras and proconsuls because humans (descendants of proconsuls) have consciousness too.
From a physiological point of view, there is also extreme robustness. You need to be hit in the head really hard to lose consciousness, and you preserve consciousness under relatively large ranges of pH. Hemispherectomy often doesn't even lead to cognitive decline. Autism, depression, and schizophrenia are associated with significant changes in the brain, yet phenomenal consciousness still appears to be here.
EDIT: in other words, imagine that we have certain structure in Homo sapiens brain absent in Homo erectus brain which makes us conscious. Take all possible statements distinguishing this structure from all structures in Homo erectus brain. If we exclude all statements, logically equivalent to "this structure implements such-n-such computation", we are left... exactly with what? We are probably left with something like "this structure is a bunch of lipid bubbles pumping sodium ions in certain geometric configuration" and I don't see any reasons for ion pumping in lipid bubbles to be relevant to phenomenal consciousness, even if it happens in a fancy geometric configuration.
1If we deny practical computational functionalism (CF), we need to pay a theoretical cost:
1. One such possible cost is that we have to assume that the secret of consciousness lies in some 'exotic transistors,' meaning that consciousness depends not on the global properties of the brain, but on small local properties of neurons or their elements (microtubules, neurotransmitter concentrations, etc.).
1a. Such exotic transistors are also internally unobservable. This makes them similar to the idea of soul, as criticized by Locke. He argued that change or replacement of the soul can't be observed. Thus, Locke's argument against the soul is similar to the fading qualia argument.
1b. Such exotic transistors should be inside the smallest animals and even bacteria. This paves the way to panpsychism, but strong panpsychism implies that computers are conscious because everything is conscious. (There are theories that a single electron is the carrier of consciousness – see Argonov).
There are theories which suggest something like a "global quantum field" or "quantum computer of consciousness" and thus partially escape the curse of exotic transistors. The assume global physical property which is created by many small exotic transistors.
2 and 3. If we deny exotic transistors, we remain either with exotic computations or soul.
"Soul" here includes non-physicalist world models, e.g., qualia-only world, which is a form of solipsism or requires the existence of God who produces souls and installs them in minds (and can install them in computers).
Exotic computations can be either extremely complex or require very special computational operations (strange loop by Hofstadter).
I'm on board with being realist about your own consciousness. Personal experience and all that. But there's an epistemological problem with generalizing - how are you supposed to have learned that other humans have first-person experience, or indeed that the notion of first-person experience generalizes outside of your own head?
In Solomonoff induction, the mathematical formalization of Occam's razor, it's perfectly legitimate to start by assuming your own phenomenal experience (and then look for hypotheses that would produce that, such as the external world plus some bridging laws). But there's no a priori reason those bridging laws have to apply to other humans. It's not that they're assumed to be zombies, there just isn't a truth of the matter that needs to be answered.
To solve this problem, let me introduce you to schmonciousness, the property that you infer other people have based on their behavior and anatomy. You're conscious, they're schmonscious. These two properties might end up being more or less the same, but who knows.
Where before one might say that conscious people are moral patients, now you don't have to make the assumption that the people you care about are conscious, and you can just say that schmonscious people are moral patients.
Schmonsciousness is very obviously a functional property, because it's something you have to infer about other people (you can infer it about yourself based on your behavior as well, I suppose). But if consciousness is different from schmonsciousness, you still don't have to be a functionalist about consciousness.
In Solomonoff induction, the mathematical formalization of Occam's razor, it's perfectly legitimate to start by assuming your own phenomenal experience (and then look for hypotheses that would produce that, such as the external world plus some bridging laws). But there's no a priori reason those bridging laws have to apply to other humans.
You can reason that a universe in which you are conscious and everyone else is not is more complex than a universe in which everyone is equally conscious, therefore Solomonoff Induction privileges consciousness for everyone.
If consciousness is not functional, then Solomonoff induction will not predict it for other people even if you assert it for yourself. This is because "asserting it for yourself" doesn't have a functional impact on yourself, so there's no need to integrate it into the model of the world - it can just be a variable set to True a priori.
As I said, if you use induction to try to predict your more fine-grained personal experience, then the natural consequence (if the external world exists) is that you get a model of the external world plus some bridging laws that say how you experience it. You are certainly allowed to try to generalize these bridging laws to other humans' brains, but you are not forced to, it doesn't come out as an automatic part of the model.
If consciousness is not functional, then Solomonoff induction will not predict it for other people even if you assert it for yourself.
Agreed. But who's saying that consciousness isn't functional? "Functionalism" and "functional" as you're using it are similar sounding words, but they mean two different things. "Functionalism" is about locating consciousness on an abstracted vs. fundamental level. "Functional" is about consciousness being causally active vs. passive.[1] You can be a consciousness realist, think consciousness is functional, but not a functionalist.
You can also phrase the "is consciousness functional" issue as the existence or non-existence of bridging laws (if consciousness is functional, then there are no bridging laws). Which actually also means that Solomonoff Induction privileges consciousness being functional, all else equal (which circles back to your original point, though of course you can assert that consciousness being functional is logically incoherent and then it doesn't matter if the description is shorter).
I would frame this as dual-aspect monism [≈ consciousness is functional] vs. epiphenomenalism [≈ consciousness is not functional], to have a different sounding word. Although there are many other labels people use to refer to either of the two positions, especially for the first, these are just what I think are clearest. ↩︎
You can also phrase the "is consciousness functional" issue as the existence or non-existence of bridging laws (if consciousness is functional, then there are no bridging laws). Which actually also means that Solomonoff Induction privileges consciousness being functional, all else equal.
Just imagine using your own subjective experience as the input to Solomonoff induction. If you have subjective experience that's not connected by bridging laws to the physical world, Solomonoff induction is happy to try to predict its patterns anyhow.
Solomonoff induction only privileges consciousness being functional if you actually mean schmonsciousness.
You're using 'bridging law' differently from I was, so let me rephrase.
To explain subjective experience, you need bridging-laws-as-you-define-them. But it could be that consciousness is functional and the bridging laws are implicit in the description of the universe, rather than explicit. Differently put, the bridging laws follow as a logical consequences of how the remaining universe is defined, rather than being an additional degree of freedom.[1]
In that case, since bridging laws do not add to the length of the program,[2] Solomonoff Induction will favor a universe in which they're the same for everyone, since this is what happens by default (you'd have a hard time imagining that bridging laws follow by logical necessity but are different for different people). In fact, there's a sense in which the program that SI finds is the same as the program SI would find for an illusionist universe; the difference is just about whether you think this program implies the existence of implicit bridging laws. But in neither cases is there an explicit set of bridging laws that add to the length of the program.
Most of Eliezer's anti zombie sequence, especially Zombies Redacted can be viewed as an argument for bridging laws being implicit rather than explicit. He phrases this as "consciousness happens within physics" in that post. ↩︎
Also arguable but something I feel very strongly about; I have an unpublished post where I argue at length that and why logical implications shouldn't increase program length in Solomonoff Induction. ↩︎
Chalmer’s fading qualia [...]
Worth noting that Eliezer uses this argument as well in The Generalized Anti-Zombie Principle, as the first line of his Socrates Dialogue (I don't know if he has it from Chalmers or thought of it independently):
Albert: "Suppose I replaced all the neurons in your head with tiny robotic artificial neurons that had the same connections, the same local input-output behavior, and analogous internal state and learning rules."
He also acknowledges that this could be impossible, but only considers one reason why (which at least I consider highly implausible):
Sir Roger Penrose: "The thought experiment you propose is impossible. You can't duplicate the behavior of neurons without tapping into quantum gravity. That said, there's not much point in me taking further part in this conversation." (Wanders away.)
Also worth noting that another logical possibility (which you sort of get at in footnote 9) is that the thought experiment does go through, and a human with silicon chips instead of neurons would still be conscious, but CF is still false. Maybe it's not the substrate but the spatial location of neurons that's relevant. ("Substrate-indendence" is not actually a super well-defined concept, either.)
If you do reject CF but do believe in realist consciousness, then it's interesting to consider what other property is the key factor for human consciousness. If you're also a physicalist, then whichever property that is probably has to play a significant computational role in the brain, otherwise you run into contradicts when you compare the brain with a system that doesn't have the property and is otherwise as similar as possible. Spatial location has at least some things going for it here (e.g., ephaptic coupling and neuron synchronization).
For example, consciousness isn’t a function under this view, it probably still plays a function in biology.[12] If that function is useful for future AI, then we can predict that consciousness will eventually appear in AI systems, since whatever property creates consciousness will be engineered into AI to improve its capabilities.
This is a decent argument for why AI consciousness will happen, but actually "AI consciousness is possible" is a weaker claim. And it's pretty hard to see how that weaker claim could ever be false, especially if one is a physicalist (aka what you call "materialist" in your assumptions of this post). It would imply that consciousness in the brain depends on a physical property, but that physical property is impossible to instantiate in an artificial system; that seems highly suspect.
A failure of practical CF can be of two kinds:
- We fail to create a digital copy of a person which have the same behavior with 99.9 fidelity.
Copy is possible, but it will not have phenomenal consciousness or, at least, it will be non-human or non-mine phenomenal consciousness, e.g., it will have different non-human qualia.
What is your opinion about (1) – the possibility of creating a copy?
I argue that computation is fuzzy, it’s a property of our map of a system rather than the territory.
This is false. Everything exists in the territory to the extent to which it can interact with us. While different models can output a different answer as to which computation something runs, that doesn't mean the computation isn't real (or, even, that no computation is real). The computation is real in the sense of it influencing our sense impressions (I can observe my computer running a specific computation, for example). Someone else, whose model doesn't return "yes" to the question whether my computer runs a particular computation will then have to explain my reports of my sense impressions (why does this person claim their computer runs Windows, when I'm predicting it runs CP/M?), and they will have to either change their model, or make systematically incorrect predictions about my utterances.
In this way, every computation that can be ascribed to a physical system is intersubjectively real, which is the only kind of reality there could, in principle, be.
(Philosophical zombies, by the way, don't refer to functional isomorphs, but to physical duplicates, so even if you lost your consciousness after having your brain converted, it wouldn't turn you into a philosophical zombie.)
Could any device ever run such simulations quickly enough (so as to keep up with the pace of the biological neurons) on a chip small enough (so as to fit in amongst the biological neurons)?
In principle, yes. The upper physical limit for the amount of computation per kg of material per second is incredibly high.
Following this to its logical conclusion: when it comes down to actually designing these chips, a designer may end up discovering that the only way to reproduce all of the relevant in/out behavior of a neuron, is just to build a neuron!
This is false. It's known that any subset of the universe can be simulated on a classical computer to an arbitrary precision.
The non-functionalist audience is also not obliged to trust the introspective reports at intermediate stages.
This introduces a bizarre disconnect between your beliefs about your qualia, and the qualia themselves. Imagine: It would be possible, for example, that you believe you're in pain, and act in all ways as if you're in pain, but actually, you're not in pain.
Whatever I denote by "qualia," it certainly doesn't have this extremely bizarre property.
But since we’re interested in the phenomenal texture of that experience, we’re left with the question: how can we assume that octopus pain and human pain have the same quality?
Because then, the functional properties of a quale and the quale itself would be synchronized only in Homo sapiens. Other species (like octopus) might have qualia, but since they're made of different matter, they (the non-computationalist would argue) certainly have a different quality, so while they funtionally behave the same way, the quale itself is different. This would introduce a bizarre desynchronization between behavior and qualia, that just happens to match for Homo sapiens.
(This isn't something that I ever thought would be written in net-upvoted posts about on LessWrong, let alone ending in a sequence. Identity is necessarily in the pattern, and there is no reason to think the meat-parts of the pattern are necessary in addition to the computation-parts.)
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1The non-functionalist audience is also not obliged to trust the introspective reports at intermediate stages.
This introduces a bizarre disconnect between your beliefs about your qualia, and the qualia themselves. Imagine: It would be possible, for example, that you believe you're in pain, and act in all ways as if you're in pain, but actually, you're not in pain.
I think "belief" is overloaded here. We could distinguish two kinds of "believing you're in pain" in this context:
- Patterns in some algorithm (resulting from some noxious stimulus) that, combined with other dispositions, lead to the agent's behavior, including uttering "I'm in pain."
- A first-person response of recognition of the subjective experience of pain.
I'd agree it's totally bizarre (if not incoherent) for someone to (2)-believe they're in pain yet be mistaken about that. But in order to resist the fading qualia argument along the quoted lines, I think we only need someone to (1)-believe they're in pain yet be mistaken. Which doesn't seem bizarre to me.
(And no, you don't need to be an epiphenomenalist to buy this, I think. Quoting Block: “Consider two computationally identical computers, one that works via electronic mechanisms, the other that works via hydraulic mechanisms. (Suppose that the fluid in one does the same job that the electricity does in the other.) We are not entitled to infer from the causal efficacy of the fluid in the hydraulic machine that the electrical machine also has fluid. One could not conclude that the presence or absence of the fluid makes no difference, just because there is a functional equivalent that has no fluid.”)
I think "belief" is overloaded here. We could distinguish two kinds of "believing you're in pain" in this context:
(1) isn't a belief (unless accompanied by (2)).
But in order to resist the fading qualia argument along the quoted lines, I think we only need someone to (1)-believe they're in pain yet be mistaken.
That's not possible, because the belief_2 that one isn't in pain has nowhere to be instantiated.
Even if the intermediate stages believed_2 they're not in pain and only spoke and acted that way (which isn't possible), it would introduce a desynchronization between the consciousness on one side, and the behavior and cognitive processes on the other. The fact that the person isn't in pain would be hidden entirely from their cognitive processes, and instead they would reflect on their false belief_1 about how they are, in fact, in pain.
That quale would then be shielded from them in this way, rendering its existence meaningless (since every time they would try to think about it, they would arrive at the conclusion that they don't actually have it and that they actually have the opposite quale).
In fact, aren't we lucky that our cognition and qualia are perfectly coupled? Just think about how many coincidences had to happen during evolution to get our brain exactly right.
(It would also rob qualia of their causal power. (Now the quale of being in pain can't cause the quale of feeling depressed, because that quale is accessible to my cognitive processes, and so now I would talk about being (and really be) depressed for no physical reason.) Such a quale would be shielded not only from our cognition, but also from our other qualia, thereby not existing in any meaningful sense.)
Whatever I call "qualia," it doesn't (even possibly) have these properties.
(Also, different qualia of the same person necessarily create a coherent whole, which wouldn't be the case here.)
Quoting Block: “Consider two computationally identical computers, one that works via electronic mechanisms, the other that works via hydraulic mechanisms. (Suppose that the fluid in one does the same job that the electricity does in the other.) We are not entitled to infer from the causal efficacy of the fluid in the hydraulic machine that the electrical machine also has fluid. One could not conclude that the presence or absence of the fluid makes no difference, just because there is a functional equivalent that has no fluid.”
There is no analogue of "fluid" in the brain. There is only the pattern. (If there were, there would still be all the other reasons why it can't work that way.)
(1) isn't a belief (unless accompanied by (2))
Why not? Call it what you like, but it has all the properties relevant to your argument, because your concern was that the person would "act in all ways as if they're in pain" but not actually be in pain. (Seems like you'd be begging the question in favor of functionalism if you claimed that the first-person recognition ((2)-belief) necessarily occurs whenever there's something playing the functional role of a (1)-belief.)
That's not possible, because the belief_2 that one isn't in pain has nowhere to be instantiated.
I'm saying that no belief_2 exists in this scenario (where there is no pain) at all. Not that the person has a belief_2 that they aren't in pain.
Even if the intermediate stages believed_2 they're not in pain and only spoke and acted that way (which isn't possible), it would introduce a desynchronization between the consciousness on one side, and the behavior and cognitive processes on the other.
I don't find this compelling, because denying epiphenomenalism doesn’t require us to think that changing the first-person aspect of X always changes the third-person aspect of some Y that X causally influences. Only that this sometimes can happen. If we artificially intervene on the person's brain so as to replace X with something else designed to have the same third-person effects on Y as the original, it doesn’t follow that the new X has the same first-person aspect! The whole reason why given our actual brains our beliefs reliably track our subjective experiences is, the subjective experience is naturally coupled with some third-person aspect that tends to cause such beliefs. This no longer holds when we artificially intervene on the system as hypothesized.
There is no analogue of "fluid" in the brain. There is only the pattern.
We probably disagree at a more basic level then. I reject materialism. Subjective experiences are not just patterns.
1Why not?
Because it's not accompanied by the belief itself, only by the computational pattern combined with behavior. If we hypothetically could subtract the first-person belief (which we can't), what would be left would be everything else but the belief itself.
if you claimed that the first-person recognition ((2)-belief) necessarily occurs whenever there's something playing the functional role of a (1)-belief
That's what I claimed, right.
Seems like you'd be begging the question in favor of functionalism
I don't think so. That specific argument had a form of me illustrating how absurd it would be on the intuitive level. It doesn't assume functionalism, it only appeals to our intuition.
I'm saying that no belief_2 exists in this scenario (where there is no pain) at all. Not that the person has a belief_2 that they aren't in pain.
That doesn't sound coherent - either I believe_2 I'm in pain, or I believe_2 I'm not.
I don't find this compelling, because denying epiphenomenalism doesn’t require us to think that changing the first-person aspect of X always changes the third-person aspect of some Y that X causally influences.
That's true, but my claim was a little more specific than that.
The whole reason why given our actual brains our beliefs reliably track our subjective experiences is, the subjective experience is naturally coupled with some third-person aspect that tends to cause such beliefs. This no longer holds when we artificially intervene on the system as hypothesized.
Right, but why think it matters if some change occurred naturally or not? For the universe, everything is natural, for one thing.
I reject materialism.
Well... I guess we have to draw the line somewhere.
I think a missing critical ingredient to evaluating this is why simulating the brain would cause consciousness. Realizing why it must makes functionalism far more sensical as a conclusion. Otherwise it's just "I guess it probably would work":
Suzie Describes Her Experience
- Suzie is a human known to have phenomenal experiences.
- Suzie makes a statement about what it's like to have one of those experiences—"It's hard to describe what it feels like to think. It feels kinda like....the thoughts appear, almost fully formed..."
- Suzie's actual experiences must have a causal effect on her behavior because: when we discuss our experience, it always feels like we're talking about our experience. If the actual experience wasn't having any effect on what we said, then it would have to be perpetual coincidence that our words lined up with our experience. Perpetual coincidence is impossible.
Replacing Neurons Generally
- We know that regardless of whatever low level details cause a neuron to fire, it ultimately resolves into a binary conclusion—fire or do not fire
- Every outward behavior we perform is based on this same causal chain. We have sensory inputs, this causes neurons to fire, some of those cause others to fire, eventually some of those are motor neurons and they cause vocal cords to speak or fingers to type.
- If you replace a neuron with a functional equivalent, whether hardware or software, assuming that it fires at the same speed and strength as the original neuron, and given the same input it will either fire or not fire as the original would have - then the behavior would be exactly the same as the original. It's not a guess this is true, it's a fact of physics. This is true whether they were hardware or software equivalents.
Replacing Specifically Suzie's Neurons Specifically While She Describes Her Experience
- We have already established that Suzie's experience must have a causal effect on honest self-report of experience.
- And we also established that all causal effects of behaviour resolve at the action potential scale and abstraction level. For instance, if quantum weirdness happens on a smaller scale - it only has an effect on behaviour if it somehow determined whether or not a neuron fired. Our hardware or software equivalents would be made to account for that.
- Not to mention there's not really good reason to suppose that tiny quantum effects are orchestrating large scale neuronal pattern alterations. I'm not sure the quantum consciousness people are even arguing this. I think there focus is more on attempting to find consciousness in the quantum realm, than to say that quantum effects are able to drastically alter firing patterns
- So if Suzie's experience has a causal effect, and the entire causal chain is in neuron action potential propagation, then that must mean that experience is somehow contained in the patterns of this action potential propagation, and it is independent of the substrate, so it is something about what these components are doing, rather than the components themselves
I think you're conflating creating a similar vs identical conscious experience with a simulated brain. Close is close enough for me - I'd take an upload run at far less resolution than molecular scale.
I spent 23 years studying computational neuroscience. You don't need to model every molecule or even close to get a similar computational and therefore conscious experience. The information content of neurons (collectively and inferred where data is t complete) is a very good match to reported aspects of conscious experience.
I don't like this writing style. It feels like you are saying a lot of things, without trying to demarcate boundaries for what you actually mean, and I also don't see you criticizing your sentences before you put them down. For example, with these two paragraphs:
Surely there can’t be a single neuron replacement that turns you into a philosophical zombie? That would mean your consciousness was reliant on that single neuron, which seems implausible.
The other option is that your consciousness gradually fades over the course of the operations. But surely you would notice that your experience was gradually fading and report it? To not notice the fading would be a catastrophic failure of introspection.
If you're aware that there is a map and a territory, you should never be dealing with absolutes like, "a single neuron..." You're right that the only other option (I would say, the only option) is your consciousness gradually fades away, but what do you mean by that? It's such a loose idea, which makes it harder to look at it critically. I don't really understand the point of this thought experiment, because if it wasn't phrased in such a mysterious manner, it wouldn't seem relevant to computational functionalism.
I also don't understand a single one of your arguments against computational functionalism, and that's because I think you don't understand them either. For example,
In the theoretical CF post, I give a more abstract argument against the CF classifier. I argue that computation is fuzzy, it’s a property of our map of a system rather than the territory. In contrast, given my realist assumptions above, phenomenal consciousness is not a fuzzy property of a map, it is the territory. So consciousness cannot be computation.
You can't just claim that consciousness is "real" and computation is not, and thus they're distinct. You haven't even defined what "real" is. Besides, most people actually take the opposite approch: computation is the most "real" thing out there, and the universe—and any consciouses therein—arise from it. Finally, how is computation being fuzzy even related to this question? Consciousness can be the same way.
331In response to the two reactions:
- Why do you say, "Besides, most people actually take the opposite approch: computation is the most "real" thing out there, and the universe—and any consciouses therein—arise from it."
Euan McLean said at the top of his post he was assuming a materialist perspective. If you believe there exists "a map between the third-person properties of a physical system and whether or not it has phenomenal consciousness" you believe you can define consciousness with a computation. In fact, anytime you believe something can be explicitly defined and manipulated, you've invented a logic and computer. So, most people who take the materialist perspective believe the material world comes from a sort of "computational universe", e.g. Tegmark IV.
- Soldier mindset.
Here's a soldier mindset: you're wrong, and I'm much more confident on this than you are. This person's thinking is very loosey-goosey and someone needed to point it out. His posts are mostly fluff with paradoxes and questions that would be completely answerable (or at least interesting) if he deleted half the paragraphs and tried to pin down definitions before running rampant with them.
Also, I think I can point to specific things that you might consider soldier mindset. For example,
It's such a loose idea, which makes it harder to look at it critically. I don't really understand the point of this thought experiment, because if it wasn't phrased in such a mysterious manner, it wouldn't seem relevant to computational functionalism.
If you actually want to know the answer: when you define the terms properly (i.e. KL-divergence from the firings that would have happened), the entire paradox goes away. I wasn't giving him the answer, because his entire post is full of this same error: not defining his terms, running rampant with them, and then being shocked when things don't make sense.
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1I reacted locally invalid (but didn't downvote either comment) because I think "computation" as OP is using it is about the level of granularity/abstraction at which consciousness is located, and I think it's logically coherent to believe both (1) materialism[1] and (2) consciousness is located at a fundamental/non-abstract level.
To make a very unrealistic analogy that I think nonetheless makes the point: suppose you believed that all ball-and-disk integrators were conscious. Do you automatically believe that consciousness can be defined with a computation? Not necessarily -- you could have a theory according to which a digital computer computing the same integrals is not consciousness (since, again, consciousness is about the fine-grained physical steps, rather than the abstracted computational steps, and a digital computer calculating performs very different physical steps than a ball-and-disk integrator doing the same). The only way you now care about "computation" is if you think "computation" does refer to low-level physical steps. In that case, your implication is correct, but this isn't what OP means, and OP did define their terms.
as OP defines the term; in my terminology, materialism means something different ↩︎
If you believe there exists "a map between the third-person properties of a physical system and whether or not it has phenomenal consciousness" you believe you can define consciousness with a computation.
I'm not arguing against the claim that you could "define consciousness with a computation". I am arguing against the claim that "consciousness is computation". These are distinct claims.
So, most people who take the materialist perspective believe the material world comes from a sort of "computational universe", e.g. Tegmark IV.
Massive claim, nothing to back it up.
This person's thinking is very loosey-goosey and someone needed to point it out.
when you define the terms properly (i.e. KL-divergence from the firings that would have happened)
I think I have a sense of what's happening here. You don't consider an argument precise enough unless I define things in more mathematical terms. I've been reading a lot more philosophy recently so I'm a lot more of a wordcell than I used to be. You are only comfortable with grounding everything in maths and computation, which is chill. But my view is that maths and computation are not the only symbols upon which constructive discussion can be built.
If you actually want to know the answer: when you define the terms properly (i.e. KL-divergence from the firings that would have happened), the entire paradox goes away.
I'd be excited to actually see this counterargument. Is it written down anywhere that you can link to?
1But my view is that maths and computation are not the only symbols upon which constructive discussion can be built.
I find it useful to take an axiom of extensionality—if I cannot distinguish between two things in any way, I may as well consider them the same thing for all that it could affect me. Given maths/computation/logic is the process of asserting things are the same or different, it seems to me to be tautologically true that maths and computaiton are the only symbols upon which useful discussion can be built.
I'm not arguing against the claim that you could "define consciousness with a computation". I am arguing against the claim that "consciousness is computation". These are distinct claims.
Maybe you want to include some undefinable aspect to consciousness. But anytime it functions differently, you can use that to modify your definition. I don't think the adherents for computational functionalism, or even a computational universe, need to claim it encapsulates everything there could possibly be in the territory. Only that it encapsulates anything you can perceive in the territory.
There is an objective fact-of-the-matter whether a conscious experience is occurring, and what that experience is. It is not observer-dependent. It is not down to interpretation. It is an intrinsic property of a system.
I believe this is your definition of real consciousness? This tells me properties about consciousness, but doesn't really help me define consciousness. It's intrinsic and objective, but what is it? For example, if I told you that the Serpinski triangle is created by combining three copies of itself, I still don't know what it actually looks like. If I want to work with it, I need to know how the base case is defined. Once you have a definition, you've invented computational functionalism (for the Serpinski triangle, for consciousness, for the universe at large).
I think I have a sense of what's happening here. You don't consider an argument precise enough unless I define things in more mathematical terms.
Yes, exactly! To be precise, I don't consider an argument useful unless it is defined through a constructive logic (e.g. mathematics through ZF set theory).
If you actually want to know the answer: when you define the terms properly (i.e. KL-divergence from the firings that would have happened), the entire paradox goes away.
I'd be excited to actually see this counterargument. Is it written down anywhere that you can link to?
Note: this assumes computational functionalism.
I haven't seen it written down explicitly anywhere, but I've seen echoes of it here and there. Essentially, in RL, agents are defined via their policies. If you want to modify the agent to be good at a particular task, while still being pretty much the "same agent", you add a KL-divergence anchor term:
This is known as piKL and was used for Diplomacy, where it's important to act similarly to humans. When we think of consciousness or the mind, we can divide thoughts into two categories: the self-sustaining (memes/particles/holonomies), and noise (temperature). Temperature just makes things fuzzy, while memes will proscribe specific actions. On a broad scale, maybe they tell your body to take specific actions, like jumping in front of a trolley. Let's call these "macrostates". Since a lot of memes will produce the same macrostates, let's call them "microstates". When comparing two consciousnesses, we want to see how well the microstates match up.
The only way we can distinguish between microstates is by increasing the number of macrostates—maybe looking at neuron firings rather than body movements. So, using our axiom of reducibilityextensionality, to determine how "different" two things are, the best we can do is count the difference in the number of microstates filling each macrostate. Actually, we could scale the microstate counts and temperature by some constant factor and end up with the same distribution, so it's better to look at the difference in their logarithms. This is exactly the cross-entropy. The KL-divergence subtracts off the entropy of the anchor policy (the thing you're comparing to), but that's just a constant.
So, let's apply this to the paradox. Suppose my brain is slowly being replaced by silicon, and I'm worried about losing consciousness. I acknowledge there are impossible-to-determine properties that I could be losing; maybe the gods do not let cyborgs into heaven. However, that isn't useful to include in my definition of consciousness. All the useful properties can be observed, and I can measure how much they are changing with a KL-divergence.
When it comes to other people, I pretty much don't care if they're p-zombies, only how their actions effect me. So a very good definition for their consciousness is simply the equivalence class of programs that would produce the actions I see them taking. If they start acting radically different, I would expect this class to have changed, i.e. their consciousness is different. I've heard some people care about the substrate their program runs on. "It wouldn't be me if the program was run by a bunch of aliens waving yellow and blue flags around." I think that's fine. They've merely committed suicide in all the worlds their substrate didn't align with their preferences. They could similarly play the quantum lottery for a billion dollars, though this isn't a great way to ensure your program's proliferation.
In response to the two reactions:
- Why do you say, "Besides, most people actually take the opposite approch: computation is the most "real" thing out there, and the universe—and any consciouses therein—arise from it."
Euan McLean said at the top of his post he was assuming a materialist perspective. If you believe there exists "a map between the third-person properties of a physical system and whether or not it has phenomenal consciousness" you believe you can define consciousness with a computation. In fact, anytime you believe something can be explicitly defined and manipulated, you've invented a logic and computer. So, most people who take the materialist perspective believe the material world comes from a sort of "computational universe", e.g. Tegmark IV.
I'm happy to grant that last sentence for the sake of argument, but note that you originally just said "most people," full stop, without the massively important qualifier "who take the materialist perspective."
Given that Euan begins his post with an axiom of materialism, it's referenced in the quote I'm responding to, and I'm responding to Euan, not talking to a general audience, I think it's your fault for intepreting it as "most people, full stop".
I don't really understand the point of this thought experiment, because if it wasn't phrased in such a mysterious manner, it wouldn't seem relevant to computational functionalism.
I'm sorry my summary of the thought experiment wasn't precise enough for you. You're welcome to read Chalmers' original paper for more details, which I link to at the top of that section.
I also don't understand a single one of your arguments against computational functionalism
I gave very brief recaps of my arguments from the other posts in the sequence here so I can connect those arguments to more general CF (rather than theoretical & practical CF). Sorry if they're too fast. You are welcome to go into the previous posts I link to for more details.
and that's because I think you don't understand them either.
What am I supposed to do with this? The one effect this has is to piss me off and make me less interested in engaging with anything you've said.
You can't just claim that consciousness is "real"
This is an assumption I state at the top of this very article.
and computation is not
I don't "just claim" this, this is what I argue in the theoretical CF post I link to.
You haven't even defined what "real" is.
I define this when I state my "realism about phenomenal consciousness" assumption, to the precision I judge is necessary for this discussion.
most people actually take the opposite approch: computation is the most "real" thing out there, and the universe—and any consciouses therein—arise from it
Big claims. Nothing to back it up. Not sure why you expect me to update on this.
how is computation being fuzzy even related to this question? Consciousness can be the same way.
This is all covered in the theoretical CF post I link to.
and that's because I think you don't understand them either.
What am I supposed to do with this? The one effect this has is to piss me off and make me less interested in engaging with anything you've said.
Why is that the one effect? Jordan Peterson says that the one answer he routinely gives to Christians and atheists that piss them off is, "what do you mean by that?" In an interview with Alex O'Conner he says,
So people will say, well, do you believe that happened literally, historically? It's like, well, yes, I believe that it's okay. Okay. What do you mean by that? That you believe that exactly. Yeah. So, so you tell me you're there in the way that you describe it.
Right, right. What do you see? What are the fish doing exactly? And the answer is you don't know. You have no notion about it at all. You have no theory about it. Sure. You have no theory about it. So your belief is, what's your belief exactly?
(25:19–25:36, The Jordan B. Peterson Podcast - 451. Navigating Belief, Skepticism, and the Afterlife w/ Alex O'Connor)
Sure, this pisses off a lot of people, but it also gets some people thinking about what they actually mean. So, there's your answer: you're supposed to go back and figure out what you mean. A side benefit is if it pisses you off, maybe I won't see your writing anymore. I'm pretty annoyed at how the quality of posts has gone down on this website in the past few years.
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