As I keep trying to point out, I think your definition of “successor relation” and its relationship to what is somehow a “valid” or “right” consciousness, is incoherent and internally inconsistent. And particularly open to ambiguous interpretation. This is why I keep trying to get you to settle down and discuss some very simple cloning examples. But you keep jumping all over the place. Regardless of your opinion of what has “passed me by”, I am happy that you now find it appropriate to continue discussing the cloning example.
Then, I have no reason to believe in quantum mechanics, or in any scientific theory: if every successor rule is the right one, then, for every one such that it yields the statistical predictions of quantum mechanics, there are equally right ones that don’t. The fact that we observe quantum statistics is thus completely unexplained in your theory.
In the clone example, there are very rare strings of successors that see p=1.0, just as when you flip a coin you may have a lucky streak and see p=1.0. The density of strings of successors is such that the statistical predictions are equivalent to a binomial distribution with p=0.5. The statistical predictions of QM are no different. Yes, there are strings of successors that don’t observe QM statistics, just as there are in the Copenhagen collapse model. The point is that you are statistically more likely to follow QM statistics. This is just a question of understanding statistics. In the binomial case of the clone example, that’s what it means to say you have a binomial distribution of p=0.5, that there is such and such a probability of finding yourself to measure p=0.4 or p=0.1, depending on the number of trials.
The fact that you are getting confused about this leads me to further push that you understand the clone example. Do you agree or disagree that in the clone example the p=0.5 statistics are not “completely unexplained”??
For p = 0.5, this is indeed right, and follows from the simple fact that in the total ensemble of all possible strings of A and B, both occur equally often. But note that even this already entails an assumption about the successor relation: that it obeys the ‘counting’ statistics for strings. A successor relation is perfectly well imaginable in which splits are effectively biased, and independently so from the quantum statistics.
Also, the argument does not hold for unequal probabilities of receiving A or B.
YES!!!
(although I would word it differently: “it follows from the simple fact that after N clonings each possible string of n A’s and k B’s has a multiplicity given by the Nth row of pascal’s triangle”)
I’m not sure what you are saying here. In the cloning example, the counting statistics are unambiguous. After, say, 2 clonings, there are 3 types of clones. One type has two A’s, one type has one A and one B, and one type has two B’s. There is one clone with two A’s, two clones with one A and one B, and one clone with two B’s. The counting statistics are completely unambiguous, no different from the kind that might be used in settling a Monty-hall type problem. There is a 1/4 chance of finding yourself to have two A’s, a 1/2 chance to find yourself with one A and one B, and a 1/4 chance of finding yourself to have two B’s.
If you think that in this example there “splits can be biased” then I think you are confusing yourself. The splits can only be “biased” by there being a different number of clones produced at each cloning step, in which case you simply have to re-do the math to determine the different probability distribution that results.
Yes it does. Keeping true to the analogy, unequal probabilities result from some number of clones at each cloning step, and an unequal number of the receiving A’s or B’s. For example, suppose that after the cloning there are three copies, two receive card A, and one receives card B. After, say, two clonings, there are the following states:
{AA,AA,AB,AA,AA,AB,BA,BA,BB}
There is a 4/9 chance of getting two A’s
There is a 4/9 chance of getting one A and one B
There is a 1/9 chance of getting two B’s
After 3 clonings there are the following states:
{AAA,AAA,ABA,AAA,AAA,ABA,BAA,BAA,BBA
AAA,AAA,ABA,AAA,AAA,ABA,BAA,BAA,BBA
AAB,AAB,ABB,AAB,AAB,ABB,BAB,BAB,BBB}
There is a 8/27 chance of getting three A’s
There is a 12/27 chance of getting two A’s and one B
There is a 6/27 chance of getting one A and two B’s
There is a 1/27 chance of getting three B’s
And so on.
In the large N limit the probability is maximum at 2/3 B’s and 1/3 A’s, as you would expect.
[Edit: I math error fixed]
The last line of my last post should have said:
“In the large N limit the probability is maximum at 2/3 A’s and 1/3 B’s, as you would expect.”
I want to point out that you keep ignoring (in addition to the other very clear ‘yes’ or ‘no’ question I have repeatedly asked you) what I think amounts to a clear demonstration of the internal inconsistency of your logic:
Your logic that consciousness is contingent upon there not being “ambiguity of identification” or “ambiguity of successor relation” implies that by adding clones to the universe in such a way that successor relations are no longer one-to-one, you can invalidate the experience of the original, which is now on equal footing with the clones. You could point to the fact that the original was not cloned, and wrongly argue that the cloning process is not validly causal, but then you would be rejecting the fact that transport from (x1,y1,z1,t1) to (x2,y2,z2,t2) is, in your opinion, a valid successor relation, since the process of cloning is equivalent to the transport process without destruction of the original version of the state. On the other hand if you reject that transport from (x1,y1,z1,t1) to (x2,y2,z2,t2) is a valid successor relation, then you are rejecting that Newtonian mechanics (or physical simulation of Newtonian mechanics) provides a valid successor relation, since the time evolution of a state is equivalent to the cloning of the state at (x1,y1,z1,t1) and the transport of the state to (x1+dx,y1+dy,z1+dz,t1+dt), and the destruction of the original at (x1,y1,z1,t1).
Only by your fiat. A valid successor relation for the case of one splitting is that (using my previous example) c3 is the successor of c1, and c4, c5 and c6 are the successors of c2. Let c1 be the mind that received A originally, and c2 the mind that received B. Then, if c3 and c5 received A, c4 and c6 B, we obviously have the states {AA, BB, BB, BA}, in violation of quantum mechanics. The correct quantum statistics would only obtain for the successor relation in which c3 and c4 succeed c1, and c5 and c6 succeed c2; but as I have now repeatedly pointed out, there is nothing about the physical evolution that singles out this successor relation among all possibilities.
As for your later example with the different number of minds, this again only obtains if you presume that somehow every state is outfitted with just the right number or measure or minds in order to get the quantum statistics out—again presupposing the quantum statistics in the attempt to derive them.
The way you’re reasoning is a well-known fallacy in the attempts to outfit many-worlds with the right probabilities. Take again Hemmo and Pitowsky:
Here, the μ[sub]i[/sub] are the probabilities assigned to a set of mutually exclusive outcomes of a measurement.
If you’re talking about this:
[QUOTE=you]
if you are cloned at (x1,y1,z1,t1) and emerge at (x2,y1,z1,t1), the original copy having been destroyed (“transferred”), then are they identified?
[/QUOTE]
then that’s about as much a straight yes-or-no question as ‘when did you stop beating your girlfriend?’. So I’ve given you the only answer I can give without further qualifications, which I repeat here for your benefit: if there is an unambiguous successor relation between the two, then yes; if there isn’t, then who the hell knows? ‘Identity’ simply ceases to make sense here.
Regarding your other bit:
[QUOTE=you]
This is why I keep pointing to the clone example. By adding a clone, you would have that the newly added ambiguity of identification would subtract from the conscious reality of the original. This makes no sense. This is a good analogy because it is exaclty what is happening in both the clone example and in the MWI. If you pruned away the tree such that there was only one copy at any given time, then there would be identification in the sense that pleases you. This is because pruning away the tree randomly is exactly equivalent to what is done in random collapse models. The implication is that by adding back the branches, something is lost.
[/QUOTE]
I’m not subtracting anything from the conscious reality of the original, and the fact that you could think I am suggests to me that we’re reading this thread through very different glasses. I’m not even appealing to consciousness: all my arguments work the same if the clones are zombies. Consciousness is not special; it’s physical after all.
What I’m saying is that without a notion of mental evolution, of transtemporal identifiability, without a successor relation, there’s no meaning to talk about one clone being the future version of another—something so simple that it appears a mere tautology to me. If I am a being at some point in time, and there are two beings at some later point in time, and there’s no sense in which one of these beings is a successor to me, then there’s no sense in which I am any of these future beings, and no sense in which any of this future beings once was me. The same if there’s only one future being without a successor relation.
And yet in this thread it remains to me remarkably elusive what you mean by asserting that “there’s no meaning”. Ie what are the practical consequences of there being “no meaning to talk about” something, if it in fact occurs? Do you mean that the clones have no conscious experience? I mean, we have constructed an example in which this cloning happens. How do your assertions of “there being no meaning” translate to the clones not having conscious experience? Because if they do, then they prove my point about probabilities arising in the MWI. It would seem that you are now saying that the clones do have conscious experience, since you just said:
And yet if the clones have conscious experience, then my analogy shows what I set out to show, that probabilities arise naturally in the MWI.
What I keep pointing out is that if you are a being at some point in time, and there are two beings at some later point in time, they can both be a successor to you. They can both be clones, for example, produced through some deterministic physical evolution. They are both valid successors. But what your argument seems to indicate is that if there are two clones, there is no identification, and therefore no meaning to discussing what they will experience (as I point out above, this is baffling to me – what to you mean there is no meaning to discuss their experience – do you deny they have an experience? If not, why is there no meaning in discussing it?). And yet, as I have pointed out, if you remove one of them, then you don’t seem to have a problem. Somehow the addition of a clone makes it no longer meaningful to discuss the conscious experience of each clone, despite the fact that you agree that they have a conscious experience.
How so? I can’t lead you through a chain of logic unless you are able to agree or disagree to a given statement. If there is some ambiguity, please help me shore it up, rather than do everything you can to prevent us from making progress. I understand that you are frustrated, but this response is extremely unproductive. I am doing my best in good faith to understand your position and expose its logical consequences, and you seem to be purposefully evasive. It is already obvious that we get nowhere if I point out the logical inconsistency starting from your general statement, so why not help me apply it to a specific example? Your general statement has the disadvantage of being definitionally ambiguous. What exactly qualifies as an unambiguous successor relation? This is why I am providing a specific example, to see if you think it qualifies as an unambiguous successor relation.
By ‘there’s no meaning to talk about (one mind being the successor of another)’ I simply mean that there’s no sense in which a mind in the future is the future version of a mind in the past, without a successor relation (which is really a trivial claim—it’s the same in physics, that there’s no sense in which a state is the future state of a system if there’s no physical evolution yielding that state).
Be that as it may, I’ve done my best to answer your question. How can you expect me to answer yes or no to a question that’s not a binary choice, but whose answer depends on further information?
In any case, seeing how you again omit the relevant portion of my post, I’d like to remind you that I’m still waiting for an answer (any answer—I don’t insist on setting the options you have to choose between for you) to my question:
Perhaps some additional layer of generality makes this even more obvious. In order to generate any possible branching probability—i.e. in order to realize all possible probability distributions in accord with experience such that in the (now normalized) state a|A> + b|B>, it is in fact the case that |a|[sup]2[/sup] of the time, |A> is observed, and |b|[sup]2[/sup], |B> is observed—you would have to have a continuous infinity of minds supervening on the physical state. That is, if |x> is the state s[sub]1[/sub], and s[sub]2[/sub] is a|A> + b|B>, in order to observe the correct quantum statistics, |a|[sup]2[/sup] of the minds supervening on |x> would be associated with the minds supervening on a|A> + b|B> and observing |A>, and |b|[sup]2[/sup] would be associated to the minds observing |B>. Do you agree?
But then, the possible successor relations are just all possible ways of associating the infinitely many minds supervening on |x> to the infinitely many minds supervening on a|A> + b|B>. Do you agree?
Not all of these functions will ensure that in fact |a|[sup]2[/sup] minds will end up in the state observing |A>, and |b|[sup]2[/sup] in the state observing |B>. In particular, the rule ‘all end up in |A>’ is a perfectly valid successor relation. Do you agree?
The physical evolution does not fix the successor relation (see above). Do you agree?
Hence, the physical evolution does not fix the particular successor relation yielding the correct quantum probabilities. (Now I know you don’t agree here, so I won’t bother asking.)
Aahhhhhhh! First of all, you are all over the place! What I mean by that is all of a sudden you are jumping to “in violation of quantum mechanics”. The clone example is not meant to be quantum mechanics!! It is meant to show that which you initially seemed to object to: that probabilities can arise naturally from MWI!
That said…
I deny that it matters, however in the cloning example, the successor relation is explicitly in which c3 and c4 succeed c1, and c5 and c6 succeed c2: c3 and c4 are produced from the cloning of c1, and c5 and c6 are produced from the cloning of c2.
Also, it is completely by your fiat that these “successor relations” should have any say as to what the quantum statistics are. At the end of the day you have {AA, BB, BB, BA}. An experimentalist finding himself at step N=2 does not have access to “successor relations”. He only has access to AA, BB, BB, or BA. There is obviously a fundamental disconnect here.
But this is why I keep at it, trying to get you to study the clone example carefully. There is no “measure” that I am massaging here. It is just counting statistics. Not “quantum counting statistics”. Just basic counting statistics. You have states {AA,AB,BA,BB}. What is the probability of a state with memory AA? 1/4. What is the probability of a state with memory BB? 1/4. The clone example is not meant to reproduce QM. It is meant to show how statistics arise completely naturally from a cloning mechanism that is in good analogy with the MWI.
(Note that I wrote this before your latest post appeared; but it seems it stays on topic nonetheless.)
To aid visualization a little, I’ve whipped up some (admittedly somewhat crude) drawings.
In the first one, what’s at the bottom is the physical state of the system, undergoing unitary evolution, as depicted by the black arrows. Above the state, the little thought bubbles are minds that supervene on each state. The minds are linked by a successor relation, indicated by dashed lines. Each mind has a content, its ‘conscious awareness’, though it could just as well be some pointer indicating a certain state; ‘A’ indicates ‘finding himself in stat |A>’, ‘B’ conversely indicates ‘finding himself in state |B>’. The minds are linked by a possible successor relation, indicated with black dashed lines. In this case, the successor relation is the right one for a fifty/fifty split. The experiences—by which I just mean: histories of being in some state, making some observation, etc.—of the minds are, in turn, AA, AB, BA, and BB. Clearly, this gives the correct quantum probabilities. (Pic here.)
The second picture is essentially the same as the first, with a crucial difference: the successor relation depicted has changed. The new experiences of the minds are AA, BB, BB, and BA. Clearly, this is not in accordance with the quantum prediction. But also, the physical evolution has not changed; neither have the states, nor the minds that supervene on them, nor their mental content. Hence, the physical evolution does not determine the successor relation. (Pic here.)
This means one simple thing: that based on the physical state and evolution alone, each mind cannot consider themselves as having had any particular experience (as in, sequence of observations). Nor does memory somehow magically save the day: memory depends on information being passed to some successor; if the successor can’t be uniquely defined, then neither can the information be passed on. Memory does not create succession, it depends on it.
And I guess that’s a ‘no’ regarding answering my questions?
By providing or explaining what further information is necessary.
I did respond to that. Here
I haven’t seen your recent posts until now. I had my edit window open in a backgrounded tab during a 2 hour meeting, and then posted a response to an earlier post. Chill out. I’m doing my best. You have been ignoring many of my questions too
But this still doesn’t answer my question. What does it matter that “there’s no sense in which a mind in the future is the future version of a mind in the past”? Suppose you are one of the clones in the clone example. You go through the cloning machine, get card A, then go through the cloning machine again, get card B. This clone’s experience is real. How is your assertion that “there’s no sense in which a mind in the future is the future version of a mind in the past” have any affect on this poor clone’s conscious experience?
Furthermore, I think that your particular definition of what is and is not a valid successor relation is incoherent. I have many times tried to point out why, but you seem to selectively ignore those parts of my posts. I’ll try again.
You seem to think that if we start out with state c1, and then the state evolves through physical law to two copies of itself, call them c2 and c3, that there is no valid successor relation. But this is internally inconsistent, because if you take away c3, you would say that it is a valid successor relation. But the existence of c3 should have no effect on the conscious experience of c2.
And yet you may say, as you have done, that no, the conscious experience is unaffected. Then I point you to the clone example, where you have the same situation. If the conscious experience of both clones c2 and c3 are valid, then so are their memories. If their memories are valid, then the statistics are valid.
First of all, I am extremely unhappy going back to the quantum probabilities and bypassing the clone example. I see it as you bullying the argument into territory that you find more comfortable, even though I think objectively the clone example is simpler and clearer and there is less room for potential misunderstanding. I also think that in the clone example I can clearly show that your logic is internally inconsistent, but you are being purposefully uncooperative in making your opinions clear enough to pin you down.
That said, in the spirit of good will, I will still answer your question. Not all of it yet, but I will leave the whole thing intact and we can fill it in as the answers progress.
With you so far.
Not with you any more, because I am not absolutely sure you didn’t make an editing mistake. You are saying that s[sub]1[/sub] = |x> (where |x> has not been previously defined)? And s[sub]2[/sub] = a|A>+b|B>?
Thanks for putting up the drawings, those are nice. Back to the argument:
Memory does save the day! You forgot to draw the memories on the little clouds! In the clone example I thought this was obvious:
Clone 1, who has memory A, gets cloned again. The clone still has memory A. It was not magically erased. The clone that still has memory A, now gets card B. The clone now has memory of card A and card B. The cloning process passes on the memory by definition of cloning. How are we miscommunicating about this???
If my theory is correct, then the next post will be both a Half Man Half Wit and iamnotbatman post, simultaneously.
Half Man Half notbatman?