Brent, That does sound interesting. But even if we construct real numbers in terms of intervals of rational numbers, we would still be taking rational-valued moments as basic... I suppose it would be possible to define things starting with intervals, though. But what properties define an interval of time? With each moment we can associate a definite physical state. With an interval, we could associate an average... this average could be taken as basic, constraining sub-intervals so that their averages (weighted by length) must equal the total. But that seems quite strange... of course it is not the only possible way of defining things.
--Abram On Sun, Dec 21, 2008 at 12:24 AM, Brent Meeker <meeke...@dslextreme.com> wrote: > > Abram Demski wrote: >> 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 >> > No, I'm saying that the time that appears in physics is a variable that > takes real values and so it has the topology of the real line. That > topology is continuous so every "moment" has other moments arbitrarily > close to it which are well ordered. When I think about this it seems to > capture the idea of "sticking together". If I pick any two times there > is a dense set of times joining them. Of course time also includes the > idea of direction. Most fundamental theories of physics are time > symmetric and the "arrow of time" is tied to expansion of the universe > by statistics. > > Bertrand Russell wrote a paper in 1935, which is reprinted in "Logic and > Knowledge" 1956 which considers how instants (i.e. moments) are > logically constructed from events (which have non-zero durations). He > shows that "...the existence of instants requires hypotheses which there > is no reason to suppose true..." It's rather technical, but you might > find it interesting. I think Russell is right to regard events > (intervals) as fundmental and instants as idealized constructs. > > Brent > > > > -- Abram Demski Public address: abram-dem...@googlegroups.com Public archive: http://groups.google.com/group/abram-demski Private address: abramdem...@gmail.com --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---