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 <meekerdb.domain.name.hidden> 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-demski.domain.name.hidden
Public archive: http://groups.google.com/group/abram-demski
Private address: abramdemski.domain.name.hidden
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Received on Sun Dec 21 2008 - 10:20:00 PST