Re: Time as a Lattice of Partially-Ordered Causal Events or Moments

From: Tim May <tcmay.domain.name.hidden>
Date: Mon, 2 Sep 2002 23:07:06 -0700

On Monday, September 2, 2002, at 09:22 PM, Osher Doctorow wrote:

> From: Osher Doctorow osher.domain.name.hidden, Mon. Sept. 2, 2002 9:29PM
>
> It is good to hear from a lattice theorist and algebraist, although I
> myself
> prefer continuity and connectedness (Analysis - real, complex,
> functional,
> nonsmooth, and their outgrowths probability-statistics and
> differential and
> integral and integrodifferential equations; and Geometry).
> Hopefully, we
> can live together in peace, although Smolin and Ashtekar have been
> obtaining
> results from their approaches which emphasize discreteness (in my
> opinion
> built in to their theories) and so there will probably be quite a
> battle in
> this respect at least intellectually.


I'm not set one way or the other about discreteness, especially as the
level of quantization is at Planck length scales, presumably. That is,
10^-34 cm or so. Maybe even smaller. And the Planck time is on the
order of 10^-43 second.

One reason discrete space and time isn't ipso facto absurd is that we
really have no good reason to believe that smooth manifolds are any
more plausible. We have no evidence at all that either space or time is
infinitely divisible, infinitely smooth. In fact, such infinities have
begun to seem stranger to me than some form of loops or lattice points
at small enough scales.

Why, we should ask, is the continuum abstraction any more plausible
than discrete sets? Because the sand on a beach looks "smooth"? (Until
one looks closer.) Because grains of sand have little pieces of quartz
which are smooth? (Until one looks closer.)

But, more importantly, the causal set (or causal lattice) way of
looking at things applies at vastly larger scales, having nothing
whatsoever to do with the ultimate granularity or smoothness of space
and time. That is, a set of events, occurrences, collisions, clock
ticks, etc. forms a causal lattice. This is true at the scale of
microcircuits as well as in human affairs (though there we get the
usual "interpretational" issues of causality, discussed by Judea Pearl
at length in his book "Causality").

You say you prefer continuity and connectedness....this all depends on
the topology one chooses. In the microcircuit case, the natural
topology of circuit elements and conductors and clock ticks gives us
our lattice points. In other examples, set containment gives us a
natural poset, without "points."

(In fact, of course mathematics can be done with open sets, or closed
sets for that matter, as the "atoms" of the universe, with no reference
to points, and certainly not to Hausdorff spaces similar to the real
number continuum.)

The really interesting things, for me, are the points of intersection
between logic and geometry.


--Tim May
(.sig for Everything list background)
Corralitos, CA. Born in 1951. Retired from Intel in 1986.
Current main interest: category and topos theory, math, quantum
reality, cosmology.
Background: physics, Intel, crypto, Cypherpunks
Received on Mon Sep 02 2002 - 23:07:32 PDT