I think the computational equivalence argument is quite compelling:
The argument appeals to the fact that the same computation occurs each time. In addition, it relies on the idea that if what goes on in the head and gives rise to the mind is Turing-style computation, then the phenomenal component of lifetime welfare must be the same whenever the same underlying computational processes are reproduced, regardless of elapsed time. A Turing machine model of computation, after all, has nothing in it corresponding to the flow of time. The machineās computation is defined in terms of the sequence of configurations yielded by the starting configuration. Thereās nothing in the model corresponding to the amount of time the machine spends in a given configuration or requires when transitioning from one configuration to another. If the mind is essentially Turing machine-style computation, the time the computation needs in order to complete when physically instantiated ought to be irrelevant to the character of mind, and so to the phenomenal component of lifetime welfare.
You reject the above argument, saying:
Clearly, conscious experience unfolds in time, and any fully adequate account of consciousness as an empirical phenomenon needs to be able to account for this. On some views, temporal properties of conscious experience end up playing an essential role in determining the representational content of consciousness, because experience represents temporal properties in the world based on a mirroring principle: an experience of change requires a change in experience, and, more generally, any experience representing any temporal property must itself instantiate the property it represents (Phillips 2014). However, we need not agree with this controversial position in order to recognize the more basic point that atemporal models of the basis of consciousness should be presumed to be incomplete.
However, I am not convinced conscious experience unfolds in time. Simulations of digital minds would presumably be run in a digital computer, so I would intuitively guess their conscious experience could be the sum of discrete/ādigital experiences instead of the integral of a continuous experience.
More broadly, ādigital physics is a speculative idea that the universe can be conceived of as a vast, digital computation device, or as the output of a deterministic or probabilistic computer programā. As an example, mechanics can be described with time as a dependent rather than independent variable.
Relatedly, I liked the discussion between Joscha Bach and Spencer Greenberg in this podcast about whether the universe is discrete of continuous:
[JOSCHA:] So a different perspective that I have on the world is that, for instance, the notion of continuous space as a computer scientist doesnāt make a lot of sense. Because itās not actually computable. Iām not able to build some kind of letters that have an infinite density and compute transitions in it at infinite resolution that have a finite number of steps. I can define this in abstract mathematics, but the languages that are required to define it have contradictions of the nature that Gƶdel has discovered. So the only thing that me and mathematicians can ever do is to work this finite view of lattices when we want to describe some continuous space. And what we mean by continuous space in physics and mathematics, ultimately, is a space that is composed of too many locations to count. And the objects that are moving to this space might be consisting of too many parts to count. As a result, you need to use operators that converge in the limit, and a set of operators over too many parts to count that converge in the limit is roughly geometry. Itās a particular kind of trick of computing things. And some of the stuff in geometry is not computable in the sense that youāre able to get to a perfect result. So imagine that you try to do a rotation of an object in your computer with finite resolution. If you donāt preserve the original object, and you do this a number of times, then the object will lose its shape. It will fall apart because of rounding errors. And if you want to get rid of the rounding errors, you need to use tricks. You need to store the original shape of the object, and we load it from time to time, or something like this. So in practice, these things matter. They donāt matter in this kind of mathematics, where you can perform infinitely many steps in a finite amount of time. But in any practical sense, this doesnāt work. So this is basically the transition that my own mind has made from the mathematical tradition that existed before the last century and the one that was invented in the last one. Actually, constructive mathematics is much older than this. But in classical mathematics, constructive mathematics, I think, was seen as a Viet aberration. And from the perspective of computation, itās part of mathematics that actually works.
SPENCER: Okay, I think Iām beginning to home in on our philosophical differences. I think one thing is Iām not that confident that the universe is computable. So when you say, āWell, you canāt really have an infinitely fine grid, you canāt have continuous space.ā Iām not that confident in that. Iām not saying that the universe is definitely not computable. I just feel undecided on that question. I feel like youāre more confident itās computable. Is that right?
JOSCHA: So do you think that universe exists?
SPENCER: Sure. And yeah, in some definitions it exists, absolutely.
JOSCHA: So what does exist mean?
SPENCER: Thatās a tough one. [laughs] It is thereā¦ The stuff happening.. Yeah, I donāt know how to define existence. Do you have a better definition?
JOSCHA: I donāt know. From my own perspective, for something to exist, it needs to be implemented. And something exists to the degree that itās implemented. Thatās also true for highly abstract objects: tables exist ākinda, sortaā. They exist as long as you squint very hard, but there are borderline cases where itās not clear whether itās a table or not. And when you zoom in very hard, itās just all a bunch of atoms. And so at which point does the table start, and other things end? Itās not that clear. So the table exists to the degree that itās implemented. It exists in a certain context, in a certain cause range description. And for coarse grained objects, I think itās completely obvious that they only exist to the degree that theyāre implemented. So, you could say that the financial system exists to a certain degree of approximation to the degree to which it is actually implemented. There is a part of the financial system that is a fiction, that is not actually implemented. And that is changing under our eyes and is melting away and so on. But there is a part that is rock-hard implemented, and that is not a fiction. But itās an approximation that changes from time to time. And the physical universe, I think, in order to exist ā for instance, to say that electrons exist, the electron needs to be implemented in some sense. ā So you could say, āIām not sure if the universe exists, but electrons exist.ā So I can talk about them, because I can measure them, I can interact with them, and so on. They exist to the degree that they are implemented. What does it mean for an electron to be implemented? It means that you have to have a type of particle that has a spin like this, and they charge like that. And spin and charge are defined as interactions with other things that play out in this way. So electrons are a particular way to talk about patterns of information. To say that the universe exists means that a certain causal structure exists that gives rise to the observations that I make in a regular fashion. And this, to me, means there is an implementation of some sort. And I can talk about the existence of the universe to the degree that Iām able to discover a language in which I can talk about its existence. So the inconvenient thing is, if I am unable to describe what existence means, then it could imply that existence doesnāt mean anything and the universe doesnāt actually exist.
I may go listen to the podcast if you think it settles this more, but on reading it Iām skeptical of Joschaās argument. It seems to skip the important leap from āimplementedā to ācomputableā. Why does the fact that our universe takes place in an incomputable continuous setting mean itās not implemented? All it means is that itās not being implemented on a computer, right?
Why does the fact that our universe takes place in an incomputable continuous setting mean itās not implemented?
I do not think we have any empirical evidence that the universe is:
Continuous, because all measurements have a finite sensitivity.
Infinite, because all measurements have a finite scale.
Claiming the universe is continuous or infinite requires extrapolating infinitely far from observed data. For example, to conclude that the universe is infinite, people usually extrapolate from the universe being pretty flat locally to it being perfectly flat globally. This is a huge extrapolation:
Modelling our knowledge about the local curvature as a continuous symmetrical distribution, even if the best guess is that the universe is perfectly flat locally, there is actually 0 % chance it has zero local curvature, 50 % it has negative, and 50 % it has positive.
We do not know whether the curvature infinitely far away is the same as the local one.
In my mind, claiming the universe is perfectly flat and infinite based on it being pretty flat locally is similar to claiming that the Earth is flat and infinite based on it being pretty flat locally.
Sorry, I shouldnāt have used the phrase āthe fact thatā. Rephrased, the sentence should say āwhy would the universe taking place in an incomputable continuous setting mean itās not implementedā. I have no confident stance on if the universe is continuous or not, just that I find the argument presented unconvincing.
Thanks, Vasco! Itās possible that weāre just reading different things into the idea that āconscious experience unfolds in timeā? For example, thereās a sense in which thatās fully compatible with thinking that experience is discrete as opposed to continuous if by that we mean that the content of consciousness changes discontinuously or that consciousness proceeds in short-lived bursts against the backdrop of surrounding unconsciousness. Is the view youāre proposing that our experiences have no location or extension in time? I think all Iām saying here is that that view is false, so there might otherwise be no disagreement. Itās also worth noting that I take the falsity of that sort of view to be a presupposition of the argument Iām criticising in the paper, since it assumes that adjusting the clock speed of the simulation hardware results in experiences that fill different amounts of objective time.
Itās interesting to me that you refer to (CPU) clock speed. If my understanding is correct, when you change the clock speed of a CPU, you donāt actually change the speed at which signals propagate through the CPU, you just change the length of the delay between consecutive propagations. (Technically, changes in temperature or voltage could have small side-effects on propagation speed, but letās ignore those for the sake of argument.) It seems to me that the length of the delay is not morally relevant, for the same reason that the length of a period of time during which I am unconscious is not morally relevant, all else being equal. I am curious if you agree, and if so, whether that changes any of your practical conclusions.
For what itās worth, it seems to me that both digital and biological minds are discrete in an important sense, regardless of whether physics is continuous. Indeed, for a digital simulation of a biological mind to even be possible, it has to rely on a discrete approximation being sufficient. But I think Iād have trouble making that argument precise to your satisfaction, so for now the thought experiment will have to do. Also, thank you for the post, I found it quite thought-provoking!
Thanks for following up! Sorry for my lack of clarity. Here is an attempt to explain how I am thinking:
Time is discrete, and therefore conscious/āunconscious experience is a sequence of discrete conscious/āunconscious states.
The objective duration of an experience is proportional to the number of states comprising it.
For the same reason that it does not make sense to talk about accelerating/ādecelerating e.g. the sequence of integer numbers, it does not make sense to talk about accelerating/ādecelerating experiences.
So, strictly speaking, it is not possible to have āsimulated minds that have the same experiences but run through those same experiences at different objective speedsā. If 2 minds have the same experiences, their objective duration will necessarily be the same.
However, casually speaking, an experiences can be said to be accelerated (decelerated) if it was obtained by running the original n (1/ān) times as fast. For example, for a mind of 1 bit where 0 and 1 represent unconsciousness and consciousness, one can have:
An original experience comprised of 4 states: o1 = 0; o2 = 1; o3 = 0; o4 = 1.
An accelerated experience comprised of 2 states, corresponding to running the original 2 times as fast: a1 = o1 + o2 = 1; a2 = o3 + o4 = 1.
A decelerated experience comprised of 8 states, corresponding to running the original 50 % as fast: d1 = o1 = 0; d2 = o1 = 0; d3 = o2 = 1; d4 = o2 = 1; d5 = o3 = 0; d6 = o3 = 0; d7 = o4 = 1; d8 = o4 = 1.
The welfare of an experience is the sum of the welfare of the states comprising it. The way I defined accelerated and decelerated experiences above, if states 0 and 1 have welfare of 0 and 1, decelerating the experience would increase welfare:
The original and accelerated experiences would each have a welfare of 2.
The decelerated experience would have a welfare of 4.
The intensity of an experience is the sum of the absolute welfare of the states comprising it. Higher computation rates are associated with greater intensity.
The felt duration of an experience is a property of the current state, but felt duration is not independent of past states. Longer felt duration is associated with greater intensity.
Thanks! I think that makes sense. I discuss something slightly similar on pp. 21 ā 22 in the paper (following the page numbers at the bottom), albeit just the idea that you should count discrete pain experiences in measuring the extensive magnitude of a pain experience, without any attempt to anchor this in a deeper theory of how experience unfolds in time.
Maybe one thing Iām still a bit unsure of here is the following. We could have a view on which time is fundamentally discrete, rather than continuous. There are physical atoms of time and how long something goes on for is a matter of how many such atoms itās made up of. But, on its face, those atoms neednāt correspond to the āframesā into which experiences are divided, since that kind of division among experiences may be understood as a high-level psychological fact. Similarly, the basic time atoms neednāt correspond to discrete steps in any physical computation, except insofar as we imagine fundamental physics as computational. Thus, experiential frames could be composed of different numbers of fundamental temporal atoms, and varying the hardware clock-speed could lead to the same physical computation being spread over more or fewer time atoms. This seems to give us some sense in which experiences and physical computation unfolds in time, albeit in discrete time. However, I took it you wanted to rule that out, and so probably Iāve misunderstood something about how youāre thinking about the relationship between the fundamental time atoms and computations/āexperiential frames, or Iāve just got totally the wrong picture?
Thus, experiential frames could be composed of different numbers of fundamental temporal atoms, and varying the hardware clock-speed could lead to the same physical computation being spread over more or fewer time atoms. This seems to give us some sense in which experiences and physical computation unfolds in time, albeit in discrete time. However, I took it you wanted to rule that out, and so probably Iāve misunderstood something about how youāre thinking about the relationship between the fundamental time atoms and computations/āexperiential frames, or Iāve just got totally the wrong picture?
Interesting! I think you got my picture right, but I am assuming one experiential frame always corresponds to one temporal atom, because oneās mind, which is a physical system, will be in a certain state for each temporal atom. However, since temporal atoms are super short (the Planck time is 5.39*10^-44 s), I guess the vast majority of experiential frames is pretty empty, having welfare close to 0. I suppose it would be possible to accelerate/ādecelerate a given experience by orderly elimating/āadding a bunch of empty experiential frames.
What you described seems analogous to what I have in mind if I interpret your experiential frames as ones with welfare meaningfully different from 0. If these are packed closer together (further apart), the experience will be accelerated (decelerated).
Thanks for sharing, Andreas!
I think the computational equivalence argument is quite compelling:
You reject the above argument, saying:
However, I am not convinced conscious experience unfolds in time. Simulations of digital minds would presumably be run in a digital computer, so I would intuitively guess their conscious experience could be the sum of discrete/ādigital experiences instead of the integral of a continuous experience.
More broadly, ādigital physics is a speculative idea that the universe can be conceived of as a vast, digital computation device, or as the output of a deterministic or probabilistic computer programā. As an example, mechanics can be described with time as a dependent rather than independent variable.
Relatedly, I liked the discussion between Joscha Bach and Spencer Greenberg in this podcast about whether the universe is discrete of continuous:
I may go listen to the podcast if you think it settles this more, but on reading it Iām skeptical of Joschaās argument. It seems to skip the important leap from āimplementedā to ācomputableā. Why does the fact that our universe takes place in an incomputable continuous setting mean itās not implemented? All it means is that itās not being implemented on a computer, right?
Interesting point.
I do not think we have any empirical evidence that the universe is:
Continuous, because all measurements have a finite sensitivity.
Infinite, because all measurements have a finite scale.
Claiming the universe is continuous or infinite requires extrapolating infinitely far from observed data. For example, to conclude that the universe is infinite, people usually extrapolate from the universe being pretty flat locally to it being perfectly flat globally. This is a huge extrapolation:
Modelling our knowledge about the local curvature as a continuous symmetrical distribution, even if the best guess is that the universe is perfectly flat locally, there is actually 0 % chance it has zero local curvature, 50 % it has negative, and 50 % it has positive.
We do not know whether the curvature infinitely far away is the same as the local one.
In my mind, claiming the universe is perfectly flat and infinite based on it being pretty flat locally is similar to claiming that the Earth is flat and infinite based on it being pretty flat locally.
Sorry, I shouldnāt have used the phrase āthe fact thatā. Rephrased, the sentence should say āwhy would the universe taking place in an incomputable continuous setting mean itās not implementedā. I have no confident stance on if the universe is continuous or not, just that I find the argument presented unconvincing.
Thanks, Vasco! Itās possible that weāre just reading different things into the idea that āconscious experience unfolds in timeā? For example, thereās a sense in which thatās fully compatible with thinking that experience is discrete as opposed to continuous if by that we mean that the content of consciousness changes discontinuously or that consciousness proceeds in short-lived bursts against the backdrop of surrounding unconsciousness. Is the view youāre proposing that our experiences have no location or extension in time? I think all Iām saying here is that that view is false, so there might otherwise be no disagreement. Itās also worth noting that I take the falsity of that sort of view to be a presupposition of the argument Iām criticising in the paper, since it assumes that adjusting the clock speed of the simulation hardware results in experiences that fill different amounts of objective time.
Itās interesting to me that you refer to (CPU) clock speed. If my understanding is correct, when you change the clock speed of a CPU, you donāt actually change the speed at which signals propagate through the CPU, you just change the length of the delay between consecutive propagations. (Technically, changes in temperature or voltage could have small side-effects on propagation speed, but letās ignore those for the sake of argument.) It seems to me that the length of the delay is not morally relevant, for the same reason that the length of a period of time during which I am unconscious is not morally relevant, all else being equal. I am curious if you agree, and if so, whether that changes any of your practical conclusions.
For what itās worth, it seems to me that both digital and biological minds are discrete in an important sense, regardless of whether physics is continuous. Indeed, for a digital simulation of a biological mind to even be possible, it has to rely on a discrete approximation being sufficient. But I think Iād have trouble making that argument precise to your satisfaction, so for now the thought experiment will have to do. Also, thank you for the post, I found it quite thought-provoking!
Thanks for following up! Sorry for my lack of clarity. Here is an attempt to explain how I am thinking:
Time is discrete, and therefore conscious/āunconscious experience is a sequence of discrete conscious/āunconscious states.
The objective duration of an experience is proportional to the number of states comprising it.
For the same reason that it does not make sense to talk about accelerating/ādecelerating e.g. the sequence of integer numbers, it does not make sense to talk about accelerating/ādecelerating experiences.
So, strictly speaking, it is not possible to have āsimulated minds that have the same experiences but run through those same experiences at different objective speedsā. If 2 minds have the same experiences, their objective duration will necessarily be the same.
However, casually speaking, an experiences can be said to be accelerated (decelerated) if it was obtained by running the original n (1/ān) times as fast. For example, for a mind of 1 bit where 0 and 1 represent unconsciousness and consciousness, one can have:
An original experience comprised of 4 states: o1 = 0; o2 = 1; o3 = 0; o4 = 1.
An accelerated experience comprised of 2 states, corresponding to running the original 2 times as fast: a1 = o1 + o2 = 1; a2 = o3 + o4 = 1.
A decelerated experience comprised of 8 states, corresponding to running the original 50 % as fast: d1 = o1 = 0; d2 = o1 = 0; d3 = o2 = 1; d4 = o2 = 1; d5 = o3 = 0; d6 = o3 = 0; d7 = o4 = 1; d8 = o4 = 1.
The welfare of an experience is the sum of the welfare of the states comprising it. The way I defined accelerated and decelerated experiences above, if states 0 and 1 have welfare of 0 and 1, decelerating the experience would increase welfare:
The original and accelerated experiences would each have a welfare of 2.
The decelerated experience would have a welfare of 4.
The intensity of an experience is the sum of the absolute welfare of the states comprising it. Higher computation rates are associated with greater intensity.
The felt duration of an experience is a property of the current state, but felt duration is not independent of past states. Longer felt duration is associated with greater intensity.
Am I making any sense?
Thanks! I think that makes sense. I discuss something slightly similar on pp. 21 ā 22 in the paper (following the page numbers at the bottom), albeit just the idea that you should count discrete pain experiences in measuring the extensive magnitude of a pain experience, without any attempt to anchor this in a deeper theory of how experience unfolds in time.
Maybe one thing Iām still a bit unsure of here is the following. We could have a view on which time is fundamentally discrete, rather than continuous. There are physical atoms of time and how long something goes on for is a matter of how many such atoms itās made up of. But, on its face, those atoms neednāt correspond to the āframesā into which experiences are divided, since that kind of division among experiences may be understood as a high-level psychological fact. Similarly, the basic time atoms neednāt correspond to discrete steps in any physical computation, except insofar as we imagine fundamental physics as computational. Thus, experiential frames could be composed of different numbers of fundamental temporal atoms, and varying the hardware clock-speed could lead to the same physical computation being spread over more or fewer time atoms. This seems to give us some sense in which experiences and physical computation unfolds in time, albeit in discrete time. However, I took it you wanted to rule that out, and so probably Iāve misunderstood something about how youāre thinking about the relationship between the fundamental time atoms and computations/āexperiential frames, or Iāve just got totally the wrong picture?
Interesting! I think you got my picture right, but I am assuming one experiential frame always corresponds to one temporal atom, because oneās mind, which is a physical system, will be in a certain state for each temporal atom. However, since temporal atoms are super short (the Planck time is 5.39*10^-44 s), I guess the vast majority of experiential frames is pretty empty, having welfare close to 0. I suppose it would be possible to accelerate/ādecelerate a given experience by orderly elimating/āadding a bunch of empty experiential frames.
What you described seems analogous to what I have in mind if I interpret your experiential frames as ones with welfare meaningfully different from 0. If these are packed closer together (further apart), the experience will be accelerated (decelerated).