Shane,
> Unfortunately, neither ancient nor modern physics defines the universe as
a closed (limited in time and space) system. Orthodox modern physics
defines the universe as originating in a "big bang." Even that plurality of
physicists unwilling to embrace a Big Banger have to wrack their brains to
come up with some origin for that event (they look for a "singularity," for
"strings," for multiple "dimensions," or for a "multiverse"), and however
nonsensical all such speculations are they all have to postulate something
"outside" the universe to account for its very existence. So modern physics
is talking about an open universe. Ancient physics, and heterodox modern
physics, looks explicitly at an open universe, limitless ("infinite") in
space and time. Plato's Timaios talks poetically of the universe as the
*partial* ordering of a "matrix," a "receptacle for becoming." The
statement by Herakleitos that I like to use as a signature tag ("This
cosmos did none of gods or men make, but it always was and is and shall be:
an everlasting fire, kindling in measures and going out in measures") is a
virtually explicit statement of heterodox modern physics's
universe--energetic plasma permeated by currents of cosmic electricity that
sometimes concentrate it into stars, planets, molecules, atoms, etc.,
sometimes explodes those material concentrations back into plasma and
radiant energy.
>
> Practical, as opposed to theoretical, physics and economics deal with
partially closed systems--systems, with their own internal dynamical laws,
that are always subject to modification from external sources of energy.
The first law of thermodynamics is stated as:
d(E_p + E_k) = 0
That is, the *total* quantity of energy in the universe, both potential and
kinetic, is constant. Because the entire universe is included. No energy
can come from outside, because there's no outside. Can the universe be
"infinite" in time/space and yet contain a constant amount of
matter/energy? A mass that occupies an infinite space has to be unbounded.
No? But does unbounded means variant (as opposed to constant)?
I once asked a related question to a young Cuban physicist (UH professor,
member of the Cuban Academy of Sciences, trained in the Soviet Union) how
he visualized the idea in the Soviet philosophy manual that the universe
was infinite yet knowable. I don't remember his answer exactly, but with
time I came to believe that he meant to say that the key to it was in
Cantor's proof that the cardinality of certain infinite sets varies. E.g.,
R (the set of real numbers) contains an order of infinity "higher" than the
infinity of N (the set of natural numbers), etc. The time/space
cardinality of the universe may have a twist (or several twists) -- if I
can put it that way.
One way to visualize this is by analogy to the Moebius strip. It is an
object in R^3, yet it has a single boundary or edge as an object in R^2 (a
surface). Topologically, it is both an object in R^3 and in R^2, depending
on where you situate yourself. If you're the proverbial ant walking on its
surface, you think it's all R^2. If you're an outside observer, it is
"obviously" an R^3 object. In a way (though this is different) it's as if
an object in a R^n set and its projection on a R^{n-1} set were both true
in physical space/time. How come? Through a transformation with a rather
simple mathematical representation. Wikipedia has all that. But who knows
really?
Anyway, FWIW, my way of reconciling these two seemingly contradictory
properties of the universe (its qualitative boundedness or unity, and its
quantitative infinity), both consistent with our modern understanding of
things, is that the universe may have a twisted time/space cardinal system.
(Ask me about how I reconcile in my head the seemingly conflicting
discreteness and continuity of the universe!)
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