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prase comments on How Many Worlds? - Less Wrong Discussion

2 Post author: smk 14 December 2011 02:51PM

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Comment author: argumzio 14 December 2011 05:49:37PM * -2 points [-]

Uncountably many. Consider that on the scale of the Omniverse (which contains only this one particular universe among uncountably many) the probability for any event is 1. It is also so, because it is absurd to suppose there is a universe in which something, if there be anything, does not exist. Furthermore, even if the probability for an event in our universe were 0 that would in no way serve as an impediment to its occurring in the long run.

Comment author: prase 14 December 2011 06:52:33PM 0 points [-]

The answer is only true if the measured quantity has continuous spectrum, therefore not applying to the only explicitly mentioned example of the cat. Furthermore I don't follow your subsequent reasoning.

Comment author: argumzio 14 December 2011 07:43:17PM * -1 points [-]

Taking the universe as a QM event most definitely implies there are uncountably many universes. The OP very clearly asked for non-standard instances of the question, and a generalization of the question most certainly applies thereto.

I certainly hope others do not continue to down-vote what they don't grasp, because LW will only be the worse off for it. (Not implying you down-voted, but if you weren't, then the one who did obviously hasn't the wherewithal to state an outright objection.)

Edit: if you don't "follow", at least state in what exactly you don't follow so that I can actually provide something to your explicit satisfaction.

Comment author: prase 14 December 2011 09:17:37PM * 0 points [-]

I certainly hope others do not continue to down-vote what they don't grasp, because LW will only be the worse off for it.

I was the first person to downvote. Not because I don't grasp, but because I believe your explanation is in the best too brief to be generally intelligible. My negative opinion can be, of course, due to my stupidity, but as for my downvoting strategy, my own judgment is all I can rely upon. (My judgment also tells me that you appear a bit oversensitive to downvoting.)

state in what exactly you don't follow

From the former comment:

Consider that on the scale of the Omniverse

I don't see how it is relevant. Quantum branching doesn't require Omniverse. That alone makes your argument seemingly irrelevant. But let's proceed.

the probability for any event is 1

I have no clear idea what a probability of event happening in the Omniverse means. Could you elaborate? (Possible issues: From an observer-independent point of view, the event either happens or not. The observers are restricted to their own universes, how do they construct probabilities over events in different universes? If the generic word "event" is replaced by the actual specification of the event, is the number of universe included - i.e. do you replace it by "two protons collide at given x,y,z,t" or rather "two protons collide at given x,y,z,t in universe #554215"? How do you solve the apparent problem that the given definition of the event may not have sense in some universes, e.g. if the universe happens to be one-dimensional and have no protons in it for the example given above? If you simply mean "for any event, we can imagine a universe that contain it", why did you start speaking about probabilities?)

It is also so, because it is absurd to suppose there is a universe in which something, if there be anything, does not exist.

Is this supposed to justify the previous claim, i.e. that the probability of any event in Omniverse is 1? If so, I don't regard "each universe contains something, therefore any event has probability 1 in the Omniverse" a valid inference, whatever interpretation of both the premise and the conclusion I can imagine.

Furthermore, even if the probability for an event in our universe were 0 that would in no way serve as an impediment to its occurring in the long run.

What is "long run"? Does it mean "in other universes" (that would make sense, but the choice of words "long run" to denote that seems bizarre) or does it mean "sometimes later in this universe" (that would be the natural interpretation of "long run", but then the statement says "p(the event happens) = 0 and the event can happen", which is a contradiction).

And of all that, how does anything imply, or even relate to, the "uncountably many" answer you gave at the beginning?

From the immediate parent:

Taking the universe as a QM event most definitely implies there are uncountably many universes.

This is an assertion without explanation. I even don't understand what do you mean by "taking the universe as a QM event".

The OP very clearly asked for non-standard instances of the question

From the single sentence the OP consists of, could you quote the section where it very clearly asks for non-standard instances of the (which?) question?

Comment author: argumzio comment score below threshold [+] (12 children)

Comment author: argumzio 14 December 2011 09:53:24PM -4 points [-]

I was the first person to downvote. Not because I don't grasp, but because I believe your explanation is in the best too brief to be generally intelligible. My negative opinion can be, of course, due to my stupidity, but as for my downvoting strategy, my own judgment is all I can rely upon. (My judgment also tells me that you appear a bit oversensitive to downvoting.)

Good enough for me. The sensitivity is merely a measure of my newness to LW. But, again, the sensitivity wasn't unwarranted granted your complete lack of explanation for the objection "I don't follow".

I don't see how it is relevant. Quantum branching doesn't require Omniverse. That alone makes your argument seemingly irrelevant. But let's proceed.

No, it doesn't. The question posted by the OP implied the relevance of MWI of QM. Note, in order for QM to hold any relevance to us, it must be interpreted in some way. Yes, let's proceed.

I have no clear idea what a probability of event happening in the Omniverse means.

You obviously aren't familiar with the concept (for which I cannot be held accountable). In any event, I'll explain it briefly: the omniverse is that state of affairs in which all possibilities are realized. Hence, that any event should obtain therein is an absolute certainty.

Is this supposed to justify the previous claim, i.e. that the probability of any event in Omniverse is 1? If so, I don't regard "each universe contains something, therefore any event has probability 1 in the Omniverse" a valid inference, whatever interpretation of both the premise and the conclusion I can imagine.

No, not particularly. However, even if it were so, consider this: tell me of a universe in which nothing exists. Does it make sense to posit something of which there is nothing? Equivalently: There isn't anything of the universe. But there is a thing, namely, the universe.

What is "long run"? Does it mean "in other universes" (that would make sense, but the choice of words "long run" to denote that seems bizarre) or does it mean "sometimes later in this universe" (that would be the natural interpretation of "long run", but then the statement says "p(the event happens) = 0 and the event can happen", which is a contradiction).

This is the standard understanding of what objective probability teaches: given any universe you please, a given probability of an event is supposed to hold for a particular situation in the case that one were to observe all cases (for all time). Thus, the "long run" considers a particular situation for all time. If you flip a coin, you will not observe an outcome of 50% heads and 50% tails, but were you to flip this coin for eternity, the net result is just such an outcome.

And of all that, how does anything imply, or even relate to, the "uncountably many" answer you gave at the beginning?

I'm not sure how you'd pose this question seriously. For one, the MWI and nature of QM decoherence shows a state of information as unrelated instances of a general state of things (in a coherent superposition). That there are uncountably many universes (as inhabited by any observer you please) in which the cat is alive, and so too for the cat being dead. The "cat" could even be an infinite variety of other objects, for all we damn well know.

I even don't understand what do you mean by "taking the universe as a QM event".

Then you obviously aren't familiar with MWI. Even Penrose and Hawking agree that QM applied to the universe implies MWI.

From the single sentence the OP consists of, could you quote the section where it very clearly asks for non-standard instances of the (which?) question?

Are you being obtuse to justify your down-vote or something? This is ridiculous. Now I have to justify my answer to the OP to you? Absurd. But I'll play along, quoting OP:

...what about non-50/50 scenarios...

I think that the universe is a "non-50/50 scenario", but I guess you can make the case it isn't.

Comment author: VincentYu 15 December 2011 10:34:52PM 2 points [-]

I have no clear idea what a probability of event happening in the Omniverse means.

You obviously aren't familiar with the concept (for which I cannot be held accountable). In any event, I'll explain it briefly: the omniverse is that state of affairs in which all possibilities are realized. Hence, that any event should obtain therein is an absolute certainty.

The word 'omniverse' does not represent a recognized concept in mainstream physics. You give a definition for it and implicitly imply in your root comment that MWI implies the existence of an omniverse,

Consider that on the scale of the Omniverse [...],

but provide no justification for this.

What is "long run"? Does it mean "in other universes" (that would make sense, but the choice of words "long run" to denote that seems bizarre) or does it mean "sometimes later in this universe" (that would be the natural interpretation of "long run", but then the statement says "p(the event happens) = 0 and the event can happen", which is a contradiction).

This is the standard understanding of what objective probability teaches: given any universe you please, a given probability of an event is supposed to hold for a particular situation in the case that one were to observe all cases (for all time). Thus, the "long run" considers a particular situation for all time. If you flip a coin, you will not observe an outcome of 50% heads and 50% tails, but were you to flip this coin for eternity, the net result is just such an outcome.

You are either using different definitions of "long run" or making contradictory statements across your comments. Here you state that this specific outcome will obtain in the long run, but in your root comment you argued that any alternative outcome can obtain in the long run:

[E]ven if the probability for an event in our universe were 0 that would in no way serve as an impediment to its occurring in the long run.

And of all that, how does anything imply, or even relate to, the "uncountably many" answer you gave at the beginning?

I'm not sure how you'd pose this question seriously. For one, the MWI and nature of QM decoherence shows a state of information as unrelated instances of a general state of things (in a coherent superposition). That there are uncountably many universes (as inhabited by any observer you please) in which the cat is alive, and so too for the cat being dead. The "cat" could even be an infinite variety of other objects, for all we damn well know.

You use the phrase "uncountably many" without providing justification. I can substitute this phrase with "countably infinitely many" and the structure and strength of your arguments would not be changed. Provide justification for why the cardinality of the natural numbers is not enough. (This was Prase's point in eir reply to your root comment, which you did not address.)

I even don't understand what do you mean by "taking the universe as a QM event".

Then you obviously aren't familiar with MWI. Even Penrose and Hawking agree that QM applied to the universe implies MWI.

This response is not constructive. Provide references. Also, you changed context from

taking the universe as a QM event

QM applied to the universe,

without clarifying what you meant by the first phrase, which I cannot parse in a way that makes sense.

From the single sentence the OP consists of, could you quote the section where it very clearly asks for non-standard instances of the (which?) question?

Are you being obtuse to justify your down-vote or something? This is ridiculous. Now I have to justify my answer to the OP to you? Absurd. But I'll play along, quoting OP:

...what about non-50/50 scenarios...

I think that the universe is a "non-50/50 scenario", but I guess you can make the case it isn't.

First, your tone unnecessarily escalates the hostility in this comment thread. Second, a binary quantum event in which the final quantum states have unequal probabilities is standard. It is the opposite, where the probabilities are equal, which requires specific preparations, because we would need to make sure that the square of the modulus of the probability amplitude of both states are equal.

Comment author: argumzio 15 December 2011 10:58:18PM -2 points [-]

The word 'omniverse' does not represent a recognized concept in mainstream physics.

If The Road to Reality (from which the term omniverse, or "omnium", originally sprung) is not "mainstream", then pray tell what is.

[E]ven if the probability for an event in our universe were 0 that would in no way serve as an impediment to its occurring in the long run.

This is a technical aspect of the discussion, and is not contradictory. The point should be clear if one considers the possibility of flipping 100 heads in a row on a fair two-sided coin. For all intents and purposes, the probability is 0, but that it may happen is not in the least prevented or negated were we to consider an infinite ("long run") flipping of coins. Pretty straightforward and not contradictory.

I can substitute this phrase with "countably infinitely many" and the structure and strength of your arguments would not be changed.

Had I devoted the energy to a full-length discussion of the topic, this probably wouldn't be an issue, but (in general) it should be clear that the number of such worlds (or universes) should be uncountably infinite, not countably infinite. That is, the cardinality would be on the order of Aleph-1, at the very least. And I seriously doubt that had any bearing on prase's original point.

This response is not constructive. Provide references. Also, you changed context from ... without clarifying what you meant by the first phrase, which I cannot parse in a way that makes sense.

I guess you could read on the topic, if you're interested. I've already suggested at least two (namely, Hawking and Penrose). Do I really have to do all the work? I need to eat and making a living.

First, your tone unnecessarily escalates the hostility in this comment thread.

There is no "tone" here. That is a mind-projection fallacy. If anyone liberated of mammalian instinct can read what I say without imputing emotional overtones thereto, then it should be obvious that my points consist in reasoned discourse without torrents of bluster at all. It's almost as if you people wish to say, "yeah, we can see you holding that 9mm, just waiting to bust a cap, and the foam dripping from your mouth". It's really rather cute.

Your last two sentences are interesting, but I'm currently short on time. Grant me that I will return to respond to them later. Thank you.

Comment author: VincentYu 16 December 2011 12:26:46AM * 0 points [-]

If The Road to Reality (from which the term omniverse, or "omnium", originally sprung) is not "mainstream", then pray tell what is.

First, words and phrases become recognized in mainstream physics when they become widely used in publications, not when one well-known physicist uses them. There are 15 results on Google Scholar for a search of 'omniverse' within physics, and of those results, none has been cited more than three times.

Second, even within The Road to Reality - for which I have the first edition as an ebook - the word 'omnium' appears only six times in 1094 pages, where they appear within six consecutive pages (p. 784-9) in a single chapter (ch. 29). The index gives only one page reference (p. 783) for this word.

ETA: You disregarded my claim that "you implicitly imply in your root comment that MWI implies the existence of an omniverse [...] but provide no justification for this." This was a main point.

This is a technical aspect of the discussion, and is not contradictory. The point should be clear if one considers the possibility of flipping 100 heads in a row on a fair two-sided coin. For all intents and purposes, the probability is 0, but that it may happen is not in the least prevented or negated were we to consider an infinite ("long run") flipping of coins. Pretty straightforward and not contradictory.

I was taking what you wrote literally, because you remarked at least twice ([1], [2]) that you dislike the lack of technical sophistication in discussions here, from which I concluded that you must mean what you write when you use technical terms. Under this assumption of literal meaning, I contend that there is a contradiction in the two statements that you wrote.

I have nothing further to add to this line of discussion.

Had I devoted the energy to a full-length discussion of the topic, this probably wouldn't be an issue, but (in general) it should be clear that the number of such worlds (or universes) should be uncountably infinite, not countably infinite. That is, the cardinality would be on the order of Aleph-1, at the very least. And I seriously doubt that had any bearing on prase's original point.

But this is the main point in contention! Recall that your answer to Smk's question ("How many worlds?") is

Uncountably many.

Prase and I pointed out that some of your subsequent reasoning and justification for this answer are unclear or incorrect. An argument for your answer is what I would like to see. You state that this is "clear", but again, one of the main purposes of this comment thread is to establish whether your answer is correct or not!

I guess you could read on the topic, if you're interested. I've already suggested at least two (namely, Hawking and Penrose). Do I really have to do all the work? I need to eat and making a living.

I am reasonably well-read in Hawking's and Penrose's texts in popular science. (I assume you are not referring to their original contributions to physics because other physicists are better known for their contributions to MWI.) I still cannot parse your first phrase ("taking the universe as a QM event"). I think I understand what you mean by your second phrase ("QM applied to the universe"). Is the first phrase supposed to have to same meaning as the second phrase?

There is no "tone" here. That is a mind-projection fallacy. If anyone liberated of mammalian instinct can read what I say without imputing emotional overtones thereto, then it should be obvious that my points consist in reasoned discourse without torrents of bluster at all. It's almost as if you people wish to say, "yeah, we can see you holding that 9mm, just waiting to bust a cap, and the foam dripping from your mouth". It's really rather cute.

Then I must remind you that all commenters on Less Wrong are human, with the exception of Clippy. One of the purposes of this comment thread is to establish which claims are correct. If your arguments are correct, then you have nothing to lose by being more persuasive, and I claim that your tone was overly aggressive and not persuasive for most purposes.

Comment author: argumzio 16 December 2011 03:28:38AM -1 points [-]

You disregarded my claim that "you implicitly imply in your root comment that MWI implies the existence of an omniverse [...] but provide no justification for this." This was a main point.

I don't need to justify what is common knowledge. Take note of Tegmark, if you and the other down-voters care to.

Under this assumption of literal meaning, I contend that there is a contradiction in the two statements that you wrote.

Wow, so you really think your strawman is sufficient as grounds for objection to what I've claimed as correct? I didn't require sophistication of others here. That's pure nonsense. But by all means, try to impute meaning into my posts where it wasn't.

An argument for your answer is what I would like to see. You state that this is "clear", but again, one of the main purposes of this comment thread is to establish whether your answer is correct or not!

I have. It is quite clear. And the only objections I've seen consist in mere definitional confusions on the part of the "objectors" or who don't seem to demonstrate an understanding of the claims I made, but instead contend that I'm merely being "hostile" and not persuasive enough.

Is the first phrase supposed to have to same meaning as the second phrase?

Not necessarily the same "meaning" but more or less the same pragmatic thrust.

If your arguments are correct, then you have nothing to lose by being more persuasive, and I claim that your tone was overly aggressive and not persuasive for most purposes.

You make an interesting, and fallacious, claim, and continue to hide behind smoke and mirrors by suggesting that I haven't answered your so-called objections.

Going back to your last post:

It is the opposite, where the probabilities are equal, which requires specific preparations...

What exactly is "it"? I'm referring to the universe, not the cat's being dead or alive. What exactly is the relevance of the probabilities being equal, in any case? Does that even impinge on anything I've said, or even anything anyone else has said? Not obviously so.

Comment author: VincentYu 16 December 2011 06:44:33AM * 0 points [-]

I am responding to Argumzio's comment in several separate replies. This is my first reply.

I don't need to justify what is common knowledge. Take note of Tegmark, if you and the other down-voters care to.

I assume that you are referring to Tegmark's ideas on his multiverse hierarchy and his ultimate ensemble. If I am incorrect, correct me, and point out which of Tegmark's ideas you are trying to use. Tegmark's speculative ideas are certainly common knowledge within the physics community. They also fail to justify your claim that MWI implies an omniverse.

Your definition of the omniverse and your subsequent uses of this concept does not clearly indicate whether you mean a Level III multiverse or a Level IV multiverse in Tegmark's terminology, so I will provide rebuttals to both cases. I shall be referring to Tegmark's most recent elaborations of his multiverse hierarchy in arXiv:0905.1283v1 (2009).

Suppose that you wish to claim that your omniverse is equivalent to a Level III multiverse. Then you have trouble because Tegmark counts at most a countably infinite number of worlds. In particular, Tegmark states that

At the quantum level, there are 10 to the $10^{118}$ universes with temperatures below $10^8$ kelvins. That is a vast number, but a finite one.

Tegmark's calculations for this are in Footnote 5 on p. 4. The obvious extension of this calculation (by scaling the temperature) shows that there is a finite number of universes below any temperature. This implies a countable number of universes even if we grant an unbounded temperature, because we can easily get a bijection with a subset of $\mathbb{N}$ by enumerating the universes below any arbitrary temperature.

So this does not work.
Suppose that you wish to claim that your omniverse is equivalent to a Level IV multiverse. Then I fail to see where Tegmark claims that MWI implies an omniverse. On the contrary, Tegmark is careful to distinguish between a Level III multiverse (MWI) and a Level IV multiverse.

Furthermore, it is not clear to me how Tegmark's Level IV multiverse can be equivalent to your omniverse. Tegmark defines the Level IV multiverse as one in which

mathematical existence and physical existence are equivalent, so that all mathematical structures exist physically as well.

This is not equivalent to your definition of the omniverse, where

the omniverse is that state of affairs in which all possibilities are realized. Hence, that any event should obtain therein is an absolute certainty.

Tegmark makes no mention of events occurring within the Level IV multiverse, while the context within which you defined the omniverse mentions only "events", not mathematical structures. Nota bene that Tegmark does mention quantum events occurring, but only in the Level III multiverse, which I have already concluded is different from your omniverse.

I no longer believe that you are throwing names of well-known physicists in good faith. Thrice you have done this:

Then you obviously aren't familiar with MWI. Even Penrose and Hawking agree that QM applied to the universe implies MWI.
I guess you could read on the topic, if you're interested. I've already suggested at least two (namely, Hawking and Penrose). Do I really have to do all the work? I need to eat and making a living.
I don't need to justify what is common knowledge. Take note of Tegmark, if you and the other down-voters care to.

Not once have you provided any reference to go with the names. Of the single reference that you gave in this thread, to The Road to Reality, it was erroneous justification for the word 'omniverse' being recognized in mainstream physics.

I welcome any refusal to give arguments that have already been given elsewhere. But if you are going to name names, then provide references. I should not have to say "I assume that you are referring to Tegmark's ideas on [...]"; I should instead be able to say "I agree with section A in Tegmark (2009), but..."

[...], if you and the other down-voters care to.

For what it's worth, I never downvote replies to my comments; I recognize that this disincentivizes replies. However, I have indeed downvoted your root comment and your replies to Prase.

continue this thread »

Comment author: prase 14 December 2011 10:20:24PM * 4 points [-]

You obviously aren't familiar with the concept

Are you being obtuse to justify your down-vote or something? This is ridiculous.

I'm not sure how you'd pose this question seriously.

Then you obviously aren't familiar with MWI.

For your information, I am familiar with both concepts, I pose all my questions seriously and I don't need to justify my downvotes. I also consider your debating style condescending and generally hostile. This prevents me from continuing in this debate.

Comment author: Luke_A_Somers 15 December 2011 08:54:02PM * 2 points [-]

Quite. I agree with argumzio and find the failure to consider other reasons for disagreement grating.

edited to clarify: his failure to consider other reasons.

Comment author: prase 16 December 2011 11:31:47AM 1 point [-]

His failure or my failure? If the latter: I find it difficult to understand argumzio's arguments and as I have already said, I find discussion with him unpleasant. Perhaps you can restate his arguments in different words and show me what is his (and your) position. Then, if there is some disagreement, I will consider and address it.

Comment author: taf 15 December 2011 04:16:30AM * -1 points [-]

The sensitivity is merely a measure of my newness to LW.

Don't sweat it. I don't think much of this nonsense "karma" thing. It's a total joke but makes sense only for those who regard the "wisdom" of the mass as somehow reflective of a post's quality. A post should be judged according to its merits, not the "points" accorded to it by (anonymous) persons who can't provide a justification for their vote.

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