Re: Variations in measure
Wei writes: If you think about it more, I think you'll realize that the greater number of observer-moments observing flying rabbits or similar happenings can't make up for the much smaller measure of each such observer-moment. Unfortunately right now I can't find a way to easily articulate the reasoning behind that conclusion. Here is an example. Suppose we had a universe which was a CA system like Conway's Life game, but more complex. It still has a fairly simple program to represent its functions and so will have generally high measure. Now suppose we modify that program to be, follow the normal rules except at position X, always set the cell to 0. This represents a flying rabbit universe, one which has relatively simple laws of physics but where there is an exception. If the universe is very large, then to specify X will take a large number of bits. Hence the flying rabbit universe program is much larger than the simple universe program, and its measure is much less. This is the explanation I accepted for why we are not in a flying rabbit universe. (I am assuming the universal distribution as a measure, where the measure of an n-bit minimal program is 2^(-n).) However if you consider all possible universes of this type, that is, all possible values of X, then there are 2^n of these if X is n bits long, exactly countering the loss in measure due to the size of X. The collection of this kind of flying rabbit universes has only modestly less measure than the simple universe. The only decrease is due to the size of the except at position and set to 0 clauses, which might be only a few bits long. And this is only one possible kind of exceptional universe. If we consider the various other special-case exceptions to the normal rule then the collective measure of all of these will come even closer to the simple case. This suggests that the simplicity explanation against flying-rabbit universes is not strong, because the total collection of flying-rabbit universes is close in measure to the simple universe to which they rerpesent exceptions. That's the problem as I see it. Hal
Re: Variations in measure
[EMAIL PROTECTED] wrote:
Wei writes:
If by flying-rabbit you mean any deviation from simplicity, then I agree
with you. Notice that our own universe is full of quantum randomness, but
we don't see any pattern to the randomness. Similarly, an observer in a
Conway's life universe may observe these anomolies that you described, but
most observers would perceive them as random fluctuations rather than
flying rabbits.
The universes where the deviations form patterns meaningful to their
observers would collectively have a very small measure compared to the
universes where the deviations are perceived as random, because in the
former case the programs to generate the meaningful deviations would have
to contain information about what kinds of deviations would be meaningful
to the observers, and that would make them much longer than programs that
simply generate random deviations.
Russell Standish sent me private mail referring to his article at
http://parallel.hpc.unsw.edu.au/rks/docs/occam/, where he made a similar
argument. However I am not completely convinced.
Parenthetically, I don't see that the presence of quantum randomness
in our universe is relevant. If we assume that many-worlds is the true
physics of our universe, then in fact our universe is deterministic and is
not full of quantum randomness. Even if we do have quantum randomness,
that would not be like the situation I am describing, where you have a
universe which is almost entirely lawful and has some kind of extremely
rare exception.
From the viewpoint of my paper Occam's Razor paper, QM is not the
true physics of the universe. It is just that any observer is
unlikely to be able to distinguish the behaviour of er world from one
described by QM. That is the result of the last section of that paper.
I agree however that you (and Russell) are right that one would not
literally expect to see a flying rabbit or a materializing dragon.
The information content of such a manifestation would be large, and most
miracles which used a similar quantity of information would be random
in their effects, and probably unnoticeable.
I hadn't noticed until now that Wei Dai agrees with my argument in
Occam's razor...
Nevertheless I think there could be exceptions to the laws of nature which
have major, observable effects while being relatively concise to specify.
Going back to my CA example, in some CA worlds if you had a cell fixed
in the 1 state, that could have dramatic macroscopic effects. It might
appear to be continually radiating the equivalent of energy, for example.
In such a situation, you might have conservation of energy throughout
the entire universe, except at this one location it would be violated.
A rather poor choice of example - our universe appears to have a
violation of exactly this sort at its origin. But then, that is
required of the Anthropic Principle, otherwise we would be here to
argue about it :)
More seriously, any undergraduate will be able to demonstrate the
failure of conservation of energy. I did it several times - even at
high school. However, the reason this is not worthy of a Nobel prize
is that experimental error is a more likely explanation for the
experimental results, than that the conservation law broke down. It
would require a really massive violation of the magnitude of the
afore-mentioned dragon to convince the Nobel Prize committee...
Now of course, with more sophisticated experimental and statistical
techniques one can increase the sensitivity of the test by many
orders of magnitude (ie reduce the amount of extra information
required for a magical universe). Of course this can be done so far,
that the violating universe is no longer considered magical. For
example, if some experimenter should show that mass/energy was violated on
the scale of 10^{-20} (lets say), then it is unlikely that people
would say the universe was not regular, and that science failed. The
researcher might get the Nobel prize, but that would probably be the
limit of the discovery's impact on the methodology of science.
Incidently, experiments were conducted in the 1980s to detect
violations of the baryon conservation no, which were expected to be of
the order of 10^{-32}/year. In the event, the violations were not
detected, ruling a particular class of GUT.
The collection of all universes which have this kind of violation of the
laws of nature could, by my argument, have measure not much less than
that of a universe which had the simpler laws of physics which allowed
for no such violation. Inhabitants of such a universe who have not yet
stumbled upon the magic location might think that their observations
give them reason to believe that the laws of physics hold everywhere.
But they are wrong. There is a significant probability that violations
of this sort exist. Occam's razor is not as sharp as they believe.
Hal
I would agree with you. Occam's razor is
Re: Variations in measure
[EMAIL PROTECTED] wrote: Wei writes, quoting Hal In general, one might expect those minds with less observational power and less specific knowledge and understanding of the universe to have larger measure. Yes, but that doesn't mean you should be surprised if you find yourself having more observational power and more knowledge, because the set of sharp minds can have greater measure than the set of dull minds even if individual sharp minds has less measure than individual dull minds. Does this have any implications for the use of the all-universe hypothesis to explain and predict our observations? What kinds of implications did you have in mind? What is the right question to ask in terms of relating measure of an observer-moment to our likelihood of experiencing it? Equivalently, what can we hope to explain via the concept of observer-moments that vary in measure? It seems that the general statement that we would expect to be in a high-measure observer-moment is not true, if the number of low-measure observer moments is high. We are not more likely to live in a simple universe than in a complex one, if the number of possible complex universes is correspondingly larger. And the larger number seems plausible when there is greater complexity, as in the example above of more complex minds existing in higher numbers. Hence the all universe principle does not easily explain the absence of flying rabbits, because while flying-rabbit universes are more complex and of lower measure, there are so many more ways to come up with complex universes. It seems that the explanatory power of the principle is less than I had realized. Hal What it does explain is the outcomes of events chosen at random - eg our birth moment, or the beginning of the universe. These are relatively simple. It does predict that complex moments (eg our present minds or the present state of the universe), are unlikely to appear out of nowhere. They are far more likely to appear as a result of some evolutionary process that delivers the complex moment from some simple moment. This, I believe, succinctly sums up the debate on the ASSA vs the RSSA we had earlier. Cheers Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
Re: Variations in measure
Wei writes, quoting Hal In general, one might expect those minds with less observational power and less specific knowledge and understanding of the universe to have larger measure. Yes, but that doesn't mean you should be surprised if you find yourself having more observational power and more knowledge, because the set of sharp minds can have greater measure than the set of dull minds even if individual sharp minds has less measure than individual dull minds. Does this have any implications for the use of the all-universe hypothesis to explain and predict our observations? What kinds of implications did you have in mind? What is the right question to ask in terms of relating measure of an observer-moment to our likelihood of experiencing it? Equivalently, what can we hope to explain via the concept of observer-moments that vary in measure? It seems that the general statement that we would expect to be in a high-measure observer-moment is not true, if the number of low-measure observer moments is high. We are not more likely to live in a simple universe than in a complex one, if the number of possible complex universes is correspondingly larger. And the larger number seems plausible when there is greater complexity, as in the example above of more complex minds existing in higher numbers. Hence the all universe principle does not easily explain the absence of flying rabbits, because while flying-rabbit universes are more complex and of lower measure, there are so many more ways to come up with complex universes. It seems that the explanatory power of the principle is less than I had realized. Hal
Re: Variations in measure
On Sat, Dec 08, 2001 at 12:57:16PM -0800, [EMAIL PROTECTED] wrote: For example, suppose he took a drug which made his mental processes become confused. He was no longer sure of basic facts about himself and the universe. This mental state would no longer be bound to one specific universe. Instead, a large collection of distinct universes could be consistent with this mental state. These observer-moments might therefore have larger measure, since they would correspond to a larger part of the multiverse. I think this is a common occurance. Every time you forget something, a post-forgetting observer-moment would have larger measure than a pre-forgetting observer-moment. And similarly, every time you observe something new, a post-observation observer-moment would have smaller measure than a pre-observation observer-moment. In general, one might expect those minds with less observational power and less specific knowledge and understanding of the universe to have larger measure. Yes, but that doesn't mean you should be surprised if you find yourself having more observational power and more knowledge, because the set of sharp minds can have greater measure than the set of dull minds even if individual sharp minds has less measure than individual dull minds. Does this have any implications for the use of the all-universe hypothesis to explain and predict our observations? What kinds of implications did you have in mind?
Re: Variations in measure
Russel wrote: Saibal Mitra wrote: Hal wrote: One of the concepts we have explored is that all universes and hence all minds exist, but that some observer-moments have greater measure than others. This may help to explain why we observe the kind of universe that we do, because we must be observer-moments that have relatively large measure. I wonder if it would be possible for the measure of an individual to vary over the course of his lifetime. We do expect the measure to fall as he ages, as he comes to occupy fewer and fewer universes. However there may be other ways that his measure could change. For example, suppose he took a drug which made his mental processes become confused. He was no longer sure of basic facts about himself and the universe. This mental state would no longer be bound to one specific universe. Instead, a large collection of distinct universes could be consistent with this mental state. These observer-moments might therefore have larger measure, since they would correspond to a larger part of the multiverse. In general, one might expect those minds with less observational power and less specific knowledge and understanding of the universe to have larger measure. Does this have any implications for the use of the all-universe hypothesis to explain and predict our observations? Yes it does. In particular it explains why we are of finite age, contrary to what one would naively expect from qti. As I have written some time ago qti needs to be modified precisely because of the effect you describe above. The analogy with the universal prior favoring simpler universes is interesting. Saibal Are you implying that we will not see some arbitrary large age because our minds will become confused (senile perhaps), and so our self-perceived age might slip back? Or are you saying that the effect of measure decreasing as a function of psychological time implies that we must start from a simple nascent state of age 0, then experience all intermediate states before reaching some enormous age? This later statement is entirely consistent with the conventional form of QTI. The former is an interesting point, but I'm not entirely sure how to formalise it properly (perhaps as a corollory of the second law of thermodynamics?). I mean it in the former sense. We could become senile and become identical to a younger person (probably a baby at sleep) and that way evade death, or it could happen as a result of massive head injuries. I think that the probability of ``surviving´´ in this discontinuous way (on the long run) is far larger than in a continuous way, as the conventional QTI seems to imply. Saibal
