Brent, It sounds like you are saying that probability is useful because it allows us to predict things-- we convert (past) relative frequencies to (future) subjective beliefs. This cannot be denied. But I don't feel like it answers very much... to understand what t means to "predict", I need to understand time already, which is what is being questioned here... What does it mean for a prediction to be more or less reasonable, if all possible futures in fact occur? How does it help me to take the past experimental frequencies, if I know (or at least believe) that all alternatives will take place?
>> Mathematically, though, a real-values time variable doesn't eliminate >> moments, it just makes an infinite number of them between any other >> two, with a particular mathematical structure. So the question of what >> makes them "stick together" remains. >> > They come with a topology which is about the only concept of sticking > together I can imagine. So anything with a topology counts as time?? That doesn't sound right. Or are you saying it is necessary, rather then sufficient? --Abram On Sat, Dec 20, 2008 at 12:54 AM, Brent Meeker <[email protected]> wrote: > > Abram Demski wrote: >> Brent, >> >> I'm not sure how the comment about real numbers effects my basic >> argument. One interesting objection I got from someone not on this >> list was that time isn't composed of moments at all, only intervals-- >> a "moment" is an imaginary thing that we get by considering >> arbitrarily small intervals. >> > This is the same as assuming reals. Real numbers can be defined in > terms of intervals marked by rationals > > http://planetmath.org/encyclopedia/DedekindCuts.html > >> Mathematically, though, a real-values time variable doesn't eliminate >> moments, it just makes an infinite number of them between any other >> two, with a particular mathematical structure. So the question of what >> makes them "stick together" remains. >> > They come with a topology which is about the only concept of sticking > together I can imagine. > > >> Obviously, one reason I think that I am traveling through time is >> because I remember the past (but can only guess at the future). But >> "remembering the past" is an experience that takes time, spanning many >> moments, making this a little tangled. The multiverse complicates >> things further: even supposing that only the possible worlds implied >> by quantum mechanics exist (that is, no alternative physics, just all >> possible quantum states) it is quite possible for me to remember the >> future. It's merely improbable. But if all possible alternatives >> actually occur, I don't know what probability means. (Even if there >> are literally more alternatives down the probable paths, does this >> make it more probable that I experience the more probable result? What >> would that mean?) >> > I think probability is useful because it has different interpretations, > relative frequency, degree of rational belief, measure, propensity, > etc. So you may estimate the propensity of throwing snake eyes by > throwing many trials (relative frequency) and then base you bets on the > results (degree of rational belief). So in the case of QM you can look > at the Born rule as defining a measure and then reinterpret it as a > degree of rational belief in order to inform your decisions. The > problem is that the Born rule seems to still have to be adopted as a > separate axiom, thus reintroducing the problem Everett intended to solve. > > Brent >> --Abram >> >> On Thu, Dec 18, 2008 at 7:21 PM, Brent Meeker <[email protected]> >> wrote: >> >>> Abram Demski wrote: >>> >>>> [Sorry if this is a duplicate, I think that I did not send correctly >>>> the first time.] >>>> >>>> Bruno, everyone, >>>> >>>> I've decided that it will be more productive/entertaining to post my >>>> various concerns as a new topic. >>>> >>>> What is time? >>>> >>>> >>> Time is what you read on a clock. >>> >>>> I'm going to ask a bunch of questions; for the sake of brevity, I'm >>>> going to skip my arguments (which would mostly be reasons why >>>> particular answers don't work). I'll argue once someone replies. >>>> >>>> If all possible universes exist, does that mean every possible moment, >>>> >>>> >>> What do you mean by "possible"? Do you mean nomologically possible - >>> which might be very restrictive but we don't know? Or do you mean >>> logically possible - just not instantiating a contradiction "X and >>> not-X"? Or something inbetween? >>> >>> >>>> or every possible timeline of moments? If "moments" is the answer, >>>> then how are the moments connected? >>>> >>> If time is a real variable (which QM assumes), moments automatically >>> inherit the topology of the reals. >>> >>> >>>> How would it matter, since the >>>> moments already are what they are? If "timeline" is the answer, then >>>> there is a similar question of how it matters. >>>> >>>> If there is a physical universe, then is there some sort of basic >>>> physical connection behind time? >>>> >>>> If the universe is mathematical in nature, then what is the >>>> mathematical connection between moments? What sort of mathematical >>>> connection counts as time? >>>> >>>> If (as was recently suggested, in connection with relativity) time >>>> cannot really be divided into individual moments, then what is it? >>>> >>>> >>> In physics, it's a variable in the equations that determines the causal >>> topology. >>> >>>> Why do we experience time passing? >>>> >>>> Is it legitimate to think as if the next moment we experience will be >>>> chosen randomly in some sense? Does probability or randomness have a >>>> role to play in the flow of time? >>>> >>>> >>> Randomness would seem to give a sense to the direction of time. That's >>> why physicist who are loathe to give up time-symmetry in their equations >>> tend to favor Everett's interpretation of QM. >>> >>> >>>> In connection with UDA: what is the meaning of a first-person >>>> probability due to uncertainty of the future? Is there any sense in >>>> which such estimates can be more or less accurate if all possible next >>>> moments do in fact occur? >>>> >>>> >>> Good question. It's the same as asking how the Born rule arises in >>> Everett's interpretation of QM. >>> >>> Brent >>> >>> >>>> Hope that sparks some thought... >>>> >>>> -- >>>> Abram Demski >>>> Public address: [email protected] >>>> Public archive: http://groups.google.com/group/abram-demski >>>> Private address: [email protected] >>>> >>>> >>>> >>> >> >> >> >> > > > > > -- Abram Demski Public address: [email protected] Public archive: http://groups.google.com/group/abram-demski Private address: [email protected] --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
