Re: Philosophy specifies: organisms process information


"r norman" <r_s_norman@xxxxxxxxxxxx> wrote in message news:80im239r4shpludij70ijudiof9pq2fv51@xxxxxxxxxx
On Sun, 22 Apr 2007 03:02:15 GMT, "Perplexed in Peoria"
<jimmenegay@xxxxxxxxxxxxx> wrote:


"r norman" <r_s_norman@xxxxxxxxxxxx> wrote in message news:ctdl23t1eomlvhvoq6r1lmn1kjcopdcc9j@xxxxxxxxxx
On Sat, 21 Apr 2007 21:04:16 -0400, r norman <r_s_norman@xxxxxxxxxxxx>
wrote:

On Sun, 22 Apr 2007 00:15:50 GMT, "Perplexed in Peoria"
<jimmenegay@xxxxxxxxxxxxx> wrote:


And it was my claim that that Newtonian clockwork universe, with completely
reversible time, can be looked at in the way specfified by Boltzman, in
which case it has a 2LOT and irreversible time. Time's Arrow is (painful
as it sounds) in the eye of the beholder.

The second law is a probabilistic law. The Newtonian clockwork
universe is absolutely completely reversible.

Consider a closed volume with gas molecules starting with all the
molecules crammed into one corner of the volume, the remaining space
being empty vacuum. Let time expire and you end up with the
molecules distributed quite uniformly in the volume. Now freeze time,
recording the position and velocity of every molecule. (No Heisenberg
here, we are talking Newtonian mechanics). Now keep every particle in
exactly the same location but reverse the sign of every velocity (in
other words, mimic running time backwards, but "real" time is
actually going forwards). You will find that the molecules end up all
crammed back into the corner of the volume. But, you declaim, entropy
says it can't happen! Wrong! Entropy says it has only a very small
probability of happening. You just picked a very particular starting
condition that made it happen. Time is reversible in a Newtonian
system; entropy is reversible in a Newtonian system.

Here is the proper way to interpret the second law. Consider, again,
a situation with all the molecules distributed in one corner. How
many different configurations are there that look quite
indistinguishable, all with the molecules crammed in that corner?
There are a lot; call the number n. Now consider the ensemble of all
of these configurations, all released to run their time course. In
almost every single one of them, the molecules will end up uniformly
distributed. That is, with probability exceptionally close to one
(but not exactly one) the system will move to a uniformly distributed
state. There will be n examples of this uniformly distributed state
each one being the result of each one of the starting conditions.

Now consider the reverse situation. Consider a system with the
molecules uniformly distributed. How many configurations of this
state are there? There are N, a number enormously larger than n. Now
if you use each as a starting condition and run the system
"backwards", with a probably exceptionally close to one (but not
exactly one) the system will stay in a uniformly distributed state.
However there is a tiny number of starting configurations that will
result in the molecules ending up all crammed into a corner. How many
of this special type of configuration are there? There are, in fact,
n. But n is much much smaller than N so the probability of starting
in one of these instead of one of the others is very close to zero.
In other words, the probability of reversing entropy is close to zero
and the probability of it increasing is close to one.

The second law says that, with probability close to one, a system will
move from low entropy to high entropy. It does not say that time is
irreversible, only that the chances of finding a way to do it is close
to zero. But allowing the movie of reality to play out and then
reversing it is specifically a way of finding one of those
exceptionally rare instances when entropy goes backwards.


I should add that if you take my scenario starting with all the
molecules in a corner, let it run until they are uniform and then
start the replay with all the molecules going with negative velocity
you end of with the molecules in a corner only if you do the replay
absolutely accurately. If even one of those molecules moves even the
slightest distance, or gets started with even the tiniest error in
velocity, then you have a completely different situation and it stays
uniform with no decrease in entropy.

Yes. And that contradicts what I said ... how?


Perhaps I misinterpreted what you said as implying that the clockwork
universe is irreversible.

I said that the clockwork reversible universe, when viewed in the way
Boltzman suggests, is seen to be irreversible. As you point out, that
irreversibility is only a probability thing. It is probable that entropy
will increase, but there do exist some rare system states that lead to a
decrease in entropy.

I also have stated elsewhere that this 'emergence' of a prefered direction
of time in the passage to the thermodynamic limit is an example of spontaneous
symmetry breaking, and hence is a cononical example of an 'emergent property'.
Involving 'hidden epistemology' as do all cases of emergence.

The 'hidden epistemology', in this case, arises because we specify the boundary
conditions - the motions of the atoms constituting the walls containing the
gas molecules - only statistically, even though we are pretending that we
know exactly the motions of each gas molecule. Microscopic unpredictability
leaks into a closed system through its boundary - regardless of the direction
of entropy flow. And once the closed system has soaked up unpredictability
from the surroundings, then an increase in the entropy of system+surroundings
is statistically inevitable.

Modern physics, though, has found an
asymmetry in the direction of time in the kaon decay I mentioned
earlier so there may be some "objective physical reality" to it.

Right. But now you are departing from the Newtonian clockwork universe.
And, as far as we know, kaon decay has nothing to do with the thermodynamic
Time's Arrow. Kaon decay seems to be a different arrow in Time's quiver.

.

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