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?)
I 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.
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.)
(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 ???
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. :)
The 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.
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.
I’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 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?)
I 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
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.)
(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 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.
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. :)
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.
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.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?
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)+cand sometimesa+(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.
I’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:
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?Thanks for clarifying :)
Yes.
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.
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.