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

Temporal Sequences
Sketches on a mildy alternate reality model.

updated: 2021-12-23      

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.  Using ergodicity and tries with time ordered
sequences to describe events, you are sort of viewing time from the
point of view of discrete duration, not a continuum.  In fact,
using only time ordered sequences in a trie, you can get by
without a continuum.  This is kind of like the quantum mechanical
view of the world.

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.  I also think this is a rather "subjective"
view of time like how Bergson described duration.

Bergson sort of tried to give importance to how time forms a kind of
memory of past events.  Most people would agree that you cannot
experience the "flow" of time in the continuous sense with a ticking
wall clock without memory.  You need to be aware of each instant
of a tick.  Bergson view of memory is rather close to how
Alfred Whitehead liked to think about processes.  I think Bergson
was correct to give time a special significance.

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 rely on models built solely on
the nature of duration because most of this kind of thinking Bergson
makes is incomplete with respect to the physical world.  You also
need Einstein's space-time in a continuum for a full description of the
world.  (May this will change with new theories in the future.)

The fact that energy propagation is ergodic leads me to think that
time as conceived in relation to Einstein's relativity is really
geometrical; purely geometrical in which the math of Minkowski works
to perfection.  The stuff of "waves" happens inside the geometry of
space-time; inside of E = mc2 in a geometrical sense.  The quantum
mechanical sense would be inside the substance of a "primordial"
field of waves where you can only measure outcomes statistically.

So time takes on two views: (1) that of a subjective view like Bergson's
and (2) that of an objective view like Einstein's.  The fact that
you need both has been really confusing for me.  Thinking about
duration has led me across many disasterous paths full of mistakes.
It's been a great source of confusion for me surely because I've
made too many unnecessary, prejudicial assumptions about time.

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 mechanism.
     The word memory should be more like a verb.

     The ancient Vedic texts says that memory is the machinery embedded
     in time which leads to Karma, the result.  The temporal evolution
     of the cosmos depends on the "memory" or Karma in past events.
     Memory in hindu sanskrit is "smriti" which connotates a meaning like
     the natural order of things.
     What's a really important to note is that the use of the word
     "memory" might be a source of confusion, and that we may be
     befter off not using that word.  It would probably make a
     debate on time like that between Bergson and Einstein

     In modern biology, the temporal evolution depends on the mechanism
     inside coded DNA.  We don't need to use the word memory in any
     description of evolution if we focused on the mechanism of
     what produced the event or object.

     But in human terms, the word memory is real and not merely mechanism.