RE: Processes and Causality
Chris,
That is the intention:
>It seems to me that we want a definition of space and time that allows us to
>keep some/most of our intuitions of the mereo-topology of space and time
>(and space-time).
Section 2 of the paper defines the four-dimensional space-time
continuum together with local mappings to four-dimensional
Euclidean (flat) space. That supports all of Newtonian
mechanics, Einstein's special and general relativity, and
everything that engineers have been designing and building.
Then Section 3 defines discrete processes with clocks (which
correspond to all the measuring instruments that have ever
been built from Stonehenge to the latest atomic clocks). And
then it defines mappings for embedding discrete processes into
continuous processes so that the numbers assigned to the ticks
of the clocks can be correlated (synchronized) with coordinate
x4 of the continuous processes.
>In your scheme of things how would you identify the extension of the
>concept/class/property (take your pick) 'instants' - of time?
The continuous coordinate system defines spatial points and
instants. If that corresponds to your intuition of "reality",
you can accept them. I prefer to think of events as more "real"
than the hypothetical continuum and consider the ticks to be
more accessible than the coordinate system. But since there
is a mapping between the two, you can take your pick.
>It would seem to me to be the class (or whatever) of slices of the
>space-time continuum that are orthogonal to the time dimension (for a
>selected frame of reference). This would include only one tick from each of
>the possible clocks.
In terms of the continuous processes, a time slice is a cross
section of the space-time continuum for a fixed value of x4.
In terms of the discrete processes, you need to supplement
the definitions with a predicate simul(x,y), which corresponds
to the observation that event x is simultaneous with event y.
I mentioned simul(x,y) in the informal discussion, which relates
it to a vertical line drawn through all the events and states
of a timing diagram, such as Figure 2 of the paper. Perhaps
I should add another definition to make simul(x,y) part of the
formalism rather than the informal commentary.
>If you do not intend something like this, I would be interested in how you
>would interpret the kinds of things we see in business databases; dates,
>days of the week, time in hours and seconds, etc..
I believe that my interpretation corresponds to what you
have in mind.
>BTW do you realise that the body of some of your messages (this one, for
>example) are arriving as attachments.
Yes. That is why I prefer the Unix mail facilities, which let
me copy a file directly into the e-mail. Since I switched from
west.poly.edu to bestweb.net, I have been using kludgy GUIs.
I plan to start logging into the bestweb.net server and use
the full power of FreeBSD, but I haven't yet switched over all
my goodies.
John