"Are the subsequent experiences of the copies "mine" relative to this self? If so, then it is certain that "I" will experience both drawing a red ball and drawing a blue ball, and the question seems meaningless. I feel that I may be missing a simple counter-example here."

No. Assume you have already been copied and you know you are one of the software versions. (Some proof of this has been provided). What you don't know is whether you are in a red ball simulation or a blue ball simulation. You do know that there are a lot of (identical - in the digital sense) red ball simulations and one blue ball simulation. My view on this is that you should presume yourself more likely to be in the red ball simulation.

Some people say that the probability is 50/50 because copies don't count. I would make these points:

1. sensitivity, which you clearly know about.
2. it is hard to say where each program starts and ends. For example, we could say that the room with each with red ball simulation computer in it is a simulation of a room with a red ball simulation computer in it - in other words, the physical environment around the computer could validly be considered part of the program. It is trivial to argue that a physical system is a valid simulation of itself. As each computer is going to be in a slightly different physical environment, it could be argued that this means that all the programs are different, even if the digital representation put into the box by the humans is the same. The natural tendency of humans is just to to focus on the 1s and 0s - which is just a preferred interpretation.
3. Humans may say that each program is "digitally" the same but we might interpret the data slightly differently. For example, one program run may have a voltage of 11.964V in a certain switch at a certain time. Another program run may have a voltage of 11.985V to represent the same binary value. It could be argued that this makes them different programs, each of which is simulating a computer with an uploaded mind on it with different voltages in the switches (again, using the idea that a thing is also a computer simulation of that thing if we are going to start counting simulations).

I just think that when we try to go for 50/50 (copies don't count) we can get into a huge mess that a lot of people can miss. While I don't think you agree with me, I think maybe you can see this mess.

"While this is also a valid and interesting scenario to consider, I don't think it "deals with the objection". The idea that "which computer am I running on?" is a meaningful question for someone whose experiences have multiple encodings in an environment seems pretty central to the discussion."

I think the suggested scenario makes it meaningful. There is also the issue of turning off some of the machines. If you know you are running on a billipn identical machines, and that 90% of them are about to be turned off then it could then become an important issue for you. It would make things very similar to what is regarded as "quantum suicide".

We can also consider another situation:

You have a number of computers, all running the same program, and something in the external world is going to affect these computers, for example a visitor from the outside world will "login" and visit you - we could discuss the probability of meeting the visitor while the simulations are all identical.

"This is why I think I/O is important, because a mind may depend on a subjective environment to function. If this is the case, removal of the environment is basically removal of the mind."

I don't know if I fully understood that - are you suggesting that a reclusive AI or uploaded brain simulation would not exist as a conscious entity?

As you asked me about Permutation City (Greg Egan's novel) before, I will elaborate on that a bit.

The "dust hypothesis" in Permutation City was the idea that all the bits of reality could be stuck together in different ways, to get different universe. The idea here is that every interpretation of an object, or part of an object, that can be made, in principle, by an interpretative algorithm, exists as an object in its own right. This argument applies it to minds, but I would clearly have to claim it applies to everything to avoid being some kind of weird dualist. It is therefore a somewhat more general view. Egan's cosmology requires a universe to exist to get scrambled up in different ways. With a view like this, you don't need to assume anything exists. While a lot of people would find this counter-intuitive, if you accept that interpretations that produce objects produce real objects, there is nothing stopping you producing an object by interpreting very little data, or no data at all. In this kind of view, even if you had nothing except logic, interpretation algorithms that could be applied in principle with no input - on nothing at all - would still describe objects, which this kind of cosmology would say would have to exist as abstractions of nothing. Further objects would exist that would be abstractions of these. In other words, if we take the view that every abstraction of any object physically exists as a definition of the idea of physical existence, it makes the existence of a physical reality mandatory.

"Of course, this leads to the problem of interpretation, which suggests to me that "information" and "algorithm" may be ill-defined concepts except in terms of one another. This is why I think I/O is important, because a mind may depend on a subjective environment to function."

and I simply take universal realizability at face value. That is my response to this kind of issue. It frees me totally from any concerns about consistency - and the use of measure even makes things statistically predictable.

"As long as the simulations are identical and interact identically (from the simulation's point of view) with the external world, I don't think the above question is meaningful. A mind doesn't have a geographical location, only implementations of it embedded in a coordinate space do. So A, B, and C are not disjoint possibilities, which means probability mass isn't split between them."

I dealt with this objection in the second article of the series. It would be easy to say that there are two simulations, in which slightly different things are going to happen. For example, we could have one simulation in which you are going to see a red ball when you open a box and one where you are going to see a blue ball. We could have lots of computers running the red ball situation and then combine them and discuss how this affects probability (if at all).

"The more redundancy in a particular implementation of a version you, then the more likely it is that that implementation is causing your experiences."

Does this mean that if we had a billion identical simulations of you in a VR where you were about to see a red ball and one (different) simulation of you in a VR where you are about to see a blue ball, and all these were running on separate computers, and you did not know which situation you were in, you would not think it more likely you were going to see a red ball? (and I know a common answer here is that it is still 50/50 - that copies don't count - which I can answer if you say that and which is addressed in the second article - I am just curious what you would say about that.)

" see this the other way around. The more redundancy in a particular implementation, the more encodings of your own experiences you will expect to find embedded within your accessible reality, assuming you have causal access to the implementation-space. If you are causally disconnected from your implementation (e.g., run on hypothetical tamper-proof hardware without access to I/O), do you exist with measure zero? If you share your virtual environment with millions of other simulated minds with whom you can interact, do they all still exist with measure zero?"

I am not making any suggestion that there is any connection between measure, redundancy and whether or not you are connected to I/O. Whether you are connected to I/O does not interest me much. However, some particularly low measure situations may be hard to connect to I/O if they are associated with very extreme interpretations.

"Less measure" is only meant to be of significance statistically, not subjectively. For example, if you could exist in one of two ways, one with measure X and one with measure of 0.001X, I would say you should think it more likely you are in the first situation. In other words, I am agreeing (if you are arguing for this) that there should be no subjective difference for the mind in the extreme situation. I just think we should think that that situation corresponds to "less" observers in some way.

My own argument is actually a justification of something a bit like the dust hypothesis in "Permutation City". However, there are some significant differences, so that analogy should not apply too much. I would say that the characters in Greg Egan's novel undergo a huge decrease in measure, which could cause philosophical issues - though it would not feel different after it had happened to you.

I think we should consider this in terms of measure because there are "more ways to find you" in some situations than in others. It is almost like you have more minds in one situation than another - though there are no absolute numbers and really it should be considered in terms of density. If you want to see why I think measure is important, this first article may help: http://www.paul-almond.com/Substrate1.htm.

I think Max Tegmark made an argument for that - and I find it more convincing.

But I wasn't trying to argue that "low level" does mean "close to the machine". That, however is a way it is often expressed. I merely listed that as one idea of "low level". If I had not mentioned that in the article someone would have simply said "A low level language is close to the machine" and thought that dealt with it, so I had to deal with it out of completeness. I was not saying that "low level" as "close to the machine" was a formal, official idea - and I actually argued that it isn't. I was after a language which is, as far as possible, free from prejudice towards particular applications and I was arguing that it can be non-trivial to get one. You might dispute my use of the word "low level" for this, but I would say that this is largely a semantic issue and that there is still a need for knowing that we can get a language with these properties. What I was proposing was a way of taking two languages, and testing them against each other without any reference to any third language, any hardware or any physics to determine which of them is most free of any prejudice towards particular uses - in a way, which of them is as close as possible to being free of any information content.

I think it is possible and inevitable (though I am unsure of timescale). I think it has some risks (I think these are understated by some people who make false analogies between simple systems and ones with minds which may be designed to adapt to an environment and which may be given simple goals and make more sophisticated goals to satisfy these, which humans may not even have specified) and would need extreme caution, but I don't think these risks are avoided in any way if only dangerous people are left to do it. I would also say - please don't view me as authoritative in any way on this.

This is an approach I considered back in 1990something actually, and at the time I actually considered it correct. I get the idea. We say that the "finding algorithm" somehow detracts from what is running. The problem is, this does not leave a clearly defined algorithm as the one being found. if X is found by F, you might say that all that runs is a "partial version of X" and that X only exists when found by F. This, however, would not just apply to deeply hidden algorithms. I could equally well apply it your brain. I would have to run some sort of algorithm, F, on your brain to work out that some algorithm corresponding to you, X, is running. Clearly, that would be nothing like as severe as the extreme situations discussed in that article, but what does it mean for your status? Does it mean that the X corresponding to you does not exist? Are you "not all there" in some sense?

Here is a thought experiment:

A mind running in a VR system (suppose the two are one software package to make this easier) gradually encrypts itself. By this I mean that it goes through a series of steps, each intended to make it slightly more difficult to realize that the mind is there. There is no end to this. When does the mind cease to exist? When it is so hard to find that you would need a program as long as the one being hidden to find it? I say that is arbitrary.

You suggest that maybe the program running the mind just exists "partially" in some way, which I fully understand. What would the experience be like for the mind as the encryption gets more and more extreme? I say this causes issues, which are readily resolved if we simply say that the mind's measure decreases.

I can also add a statistical issue to this, which I have not written up yet. (I have a lot to add on this subject. It may be obvious that I need to argue that this applies to everything, and not just minds, to avoid some weird kind of dualism.).

Suppose we have two simulations of you, running in VRs. One is about to look in a box and see a red ball. The other will see a blue ball. We subject the version that will see the blue ball to some process that makes it slightly harder to find. You don't know which version you are. How much will you expect to see a blue ball when you look in the box? Do you say it is 50/50 that you will see a red ball or a blue ball? We keep increasing the "encryption" a bit each time I ask the question. If your idea that somehow the mind is only "partial" by needing the finding algorithm to find it is right, I suggest we end up with statistical incoherency. We can only say that the probability is 50/50 when the situations are exactly the same, but that will never be the case in any real situation. For any situation, one mind will need a bit more finding than the other.

In other words, if you think the length of the finding algorithm makes the algorithm running a mind somehow "partial", in a statistical question in which you had two possibilities, one in which your mind was harder to find than the other, and you don't know which situation you are in, when would you eliminate the "partial" mind as a possibility? If you say, "Never. As the encryption increases I would just say I am less and less likely to be in that situation" you have effectively agreed with me by adopting an approach where each mind is as valid as the other (you accept either as a candidate for your situation but treat them differently with regard to statistics - which is what I do). If you say that one mind cannot be a candidate for your situation then you have the issue of cut-off point. What cut-off point? When would you say, “This mind is real. This mind is only partial so cannot be a candidate for my experience. Therefore, I am the first mind?”

I would point out that I do not ignore these issues. I address them by using measure. I take the view that a mind which takes more finding exists with less measure, because a smaller proportion of the set of all possible algorithms that could be used to find something like it will find something like it.

Finally, this only deals with one issue. There is also the issue of combining computers in the statistical thought experiments that I mentioned in the first article of that series. My intention in that series is to try to show that these various issues demand that we take a particular view about minds and reality to maintain statistical coherency.

Either name is fine (since it is hardly a secret who I am here).

Yes, I see the problem, but this was very much in my mind when I wrote all this. I could have hardly missed the issue. I would have to accept it or deny it, and in fact I considered it a great deal. It is the first thing you would need to consider. I still maintain that there is nothing special about this algorithm length. I actually think your practical example of buying the computer, if anything counts against it. Suppose you sold me a computer and it "allegedly" ran a program 10^21 bits long, but I had to use another computer running a program that was (10^21)+1 bits long to analyze what it was doing and get any useful output. Would I want my money back? Of course I would. However, I would also want my money back if I needed a (10^21)-1 bit program to analyze the computer – and so would you. As a consumer, the thing would be practically useless anyway. In one case I am having to do all the computers job, and a tiny bit more, just to get any output. In the other case I am having to do a tiny bit less than the computer's job to get any output: it would hardly make a practical difference. There is no sudden point at which I would want my money back: I would want it back long before we got near 10^21 bits. Can you show that 10^21 bits is special? I would say that to have it as special you pretty much have to postulate it and I want to work with a minimum of postulates: it is my whole approach, though it causes some conclusions I hardly find comfortable.

You have mentioned Occam’s razor, but we may disagree on how it should be applied. What Occam originally said was probably too vague to help much in these matters, so we should go with what seems a reasonable “modernization” of Occam’s razor. I do not think Occam’s razor tells us to reduce the amount of stuff we accept. Rather, I think it tells us to reduce the amount of stuff we accept as intrinsically existing. I would not, for example, regarding Occam's razor as arguing against the many-worlds interpretation of quantum mechanics, as many people would. I would say that Occam's razor would argue against having some arbitrary wavefunction collapse mechanism if we need not assume one.

I would also say, as well, that this does not resolve the issue of combining computers and probability that I raised in the first article. My intention was to put a number of such issues together and show that we needing to do the sort of thing I said to get round difficult issues.

I am just someone who has an interest in these issues Carl, and they are all written in a private capacity: I am not, for example, anyone who works at a university. I have worked as a programmer, and as a teacher of computing, in the past.I think machineslikeus describes me as an "independent researcher" or something like that... which means, I suppose, that I write articles.

I hope it is okay for me to reply to all these. Right, yes, that is my position steven. When the interpreter algorithm length hits the length of the algorithm it is finding, nothing of any import happened. Would we seriously say, for example, that a mind corresponding to a 10^21 bit computer program would be fine, any enjoying a conscious existence, if it was "findable" by a 10^21 bit program, but would suddenly cease to exist if it was findable by only a 10^21+1 bit program? I would say, no. However, I can understand that that is always how people see it. For some reason, the point at which one algorithmic length exceeds the other is the point at which people think things are going too far.