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Rock Garden, Ryoan-ji: japan-guide.com


Temporal Sequences
Sketches on a mildy alternate reality model.


2020-1-9

A really thought provoking idea to me is how "much" entropy effects
our world.  It effects our world so much, it seems to me, that you can
really only define time "locally" which respect to a specific point you
picked in time.  For example, in computer simulations of waves, the
form of the wave can be well defined just after the wave starts, but
after awhile, this wave looks like all other waves no matter what
shape of wave you start out with.  This is entropy at work.

Henri Bergson spoke of time in a subjective way.  It's a way of
viewing time more compatible with quantum theory or as some physicists
used to refer to it as wave mechanics.  This is strikingly obvious
when you observe the propagation of waves, especially observing
dispersion of waves in time.  If you try to model wave propagation
using sequences of numbers, then the sequence is only significant
in its behavior at the beginning of the sequence.  If you then
model the sequence as binary tree structure containing information,
the most of the model deals with the sequence when the sequence starts.
This is inherently dynamical in nature.  You can refer to this type
of dynamicity as ergodic.  You can refer to this type of tree as
a prefix tree or trie.

This fact of time being actually significant only at certain points
in time leads one to think that the "duration" of time is important.
I think duration is important only because you "distinguish"
experience at points in time.  Now, with respect to physics, time is
a complimentary aspect of energy.  We experience "energy" when our
sensory organs feel changes in the energy fields around us.  If you
try to simulate energy changes in waves on a digital computer, you
can use a model which is based very generally on pulses.  A good
example is computing the energy fields in classical heat distributions
using differential equations and Fourier series.

Bergson sort of tried to give importance to how time forms a kind of
memory of past events.  I made this mistake also (I maybe wrong here
about Bergson, but time is not "an accumulation").  I'm guessing
that Bergson was wrong here.  You really cannot experience the "flow"
of time in the continuous sense with a ticking wall clock without memory.
Bergson refers to memory incorrectly in his temporal accumulation
hypothesis.  Bergson might have been right if he said temporal events
could be correlated, connected or tied together using memory. It's a
very subtle point (but I may be wrong).  Without memory there would
be no way to transfer state information in temporal events.  You
can't just assume that time carries that much information over a
long duration. [3] 

For awhile, I tried to see how I could extrapolate temporal information
over long sequences.  I didn't get anywhere.  Waves, as dynamic sequences,
are ergodic.  So I don't think you can build models solely on the nature
of time because most of this kind of thinking Bergson makes is meaningless
with respect to the physical world.  It has significance if you apply
this kind of thinking to how human-beings think.

The fact that energy propagation is ergodic leads me to think that
time as conceived in relation to Einstein's relativity is really
very geometrical ... purely geometrical in which the math of
Minkowski works to perfection.  The stuff of "waves" happens inside
the geometry of space-time.  (I might REALLY be wrong here!)  I'm
basing this on intuition, but I thought about this alot.

So time takes on two views: (1) that of a subjective view like Bergson's
and (2) that of on objective view like Einstein's.  I think both are
correct.

The above paragraphs are obviously full of mistakes.  It's up to
you to work it out also.  I expect you to think this through
for yourself.  It's too important not to think it out for yourself.
The treasures here are obvious to me.

I greatly admire Satosi Watanabe's work on time.  He showed
that there are processes in Nature in which you can predict things
happening in the future, but not in the past.  Entropy or ergodicity
determines the flow of time, and retrodiction.  This work on
prediction and retrodiction [1], reminds me of Bergson's work,
but Satosi Watanabe was an incredible mathematician.  Professor
Watanabe mathematically showed how time is intertwined "within"
or emerges from entropy.  When I attended his classes, I was just
mesmerized with his skill in mathematics.  There was no one I've
met in person that could do math like he did.

Both Bergson and Watanabe were poets.

Anyway, retrodiction is an important concept because it shows
how entropy works in Nature.  Another great work on entropy is
Alekandr Khinchin's work in which he brilliantly summarizes what
erogodicity is.  In his conclusion to his great book [2] he say:

      The channel we are given is a noisy channel.
      This means that we cannot determine the sequences
      of symbols sent at the channel input from the
      sequences received at the channel output;
      because of noise, two different sequences at the
      channel input can give rise to the same sequence
      at the output.
      
This to me is incredible.  I'm sure it is to you also.  If not try
to understand the above quote by reading it over.  It's worth it.
The quote above by Khinchin is really, in essence, simple.

The math in his book, however, is not so understandable because
of its complexity.  I think you can read through the stuff on
this webpage without formal math training if you're good at
using your imagination or intuition.  Even if you do know lots
of math, you'd still need to use your intuition to understand
the world.  So if you have questions, just send me an e-mail.

The stuff above has multiple levels, and confuses me.
Any comments are welcomed.







[1]  Time and the Probabilistic View of the World, Satosi Watanabe,
     p. 527, in The Voices of Time, ed. J. T. Fraser., 1966.

[2]  Alekandr Khinchin, Mathematical Foundations of Information Theory,
     Dover Publications, Inc.  1957, p. 117.

[3]  I think Bergson is correct in saying memory needs a connection
     to time, as in: if time is substance, and memory is form.