"Waves"














Great Wave, Hokusai: theculturetrip.com

Beauty to a Machine

For the past 15 years, in my spare time, I've been an avid gardener
building Japanese gardens.  I've gotten a feel for the practice of Zen,
by building rock and water gardens.

Muso Soseki was a Rinzai Zen priest who built the Moss Garden in Japan in
the 13th century.  Like Soseki, Shunmyo Masuno is a Soto Zen priest who
builds Zens gardens today.  In the book "Zen Gardens: The complete works
of Shunmyo Masuno", [1] you become deeply aware of the ancient art of
creating beautiful spatial relationships among Japanese garden elements.
Rocks, water features and miniature trees are abstracted by greatly
simplifying these items into symbolic paradigms representing mountains,
oceans and forests.  A Zen garden is a pattern of abstracted symbols.

A Zen garden is a place of mediation.  It's usually an area isolated from
the rest of the yard containing natural forestry.  The Zen garden is
extremely sparse compared to natural scenery.  Its purpose is to empty
the mind, and to feel peaceful.

In the foreword to "Zen Gardens", [2] Shigeru Uchida talks about the
design themes of a Zen garden.  He transforms the subject of Zen gardens
such as rocks, water features, bonsai, and miniature man made symbols
like lanterns into "objects with precedence."  He says,

       "... formerly a relationship firstly had independent
       content, and it was thought that within that content,
       that relationship came into being.

       ... relationship as precedent is predicate logic.
  
       Depending on the situation things fall into and the
       circumstances, even if they are the same, they create
       different meanings.  

The rest of Shigeru Uchida's narration is an excellent attempt to describe
the meaning and mysteries of Zen through how the mind associates and gives
meaning to the relationship of Zen garden elements.  He says through the
Zen mediator in the garden, that the gardens elements actively become the
"modifier" or operators [3] in forming relationships inside the Zen
mediators mind.  This to me is a highly active form of observation
- not passive at all. [4]

Intense beauty comes from a rich but precise flow of information.  You
want as little information as possible, but enough to focus on.  In terms
of the flow of entropy in time, you're trying to get the principal
components of the description. [5]  This is entropy which is minimized, or
entropy which has been descreased so that the description's relationships
(its order or complexity with respect to the mediator's mind) has been
maximized.

A beautiful Zen painting is usually never pure emptiness, and usually
never filled with clutter.  It's most likely at the degree to which the
observer's mind can calmly, in a relaxed state, understand the subject
matter the observer (or priest) is focused on.  The observer must be
encoding the information at the brain's optimal processing speed. [6]
  
Observation of two or three dimensional pictures is different from hearing
single dimensional audio signals.  Two dimensional temporal signals are
geometrically or exponentially harder to decode than temporal audio
signals because there is no formal grammar to process two dimensional
signals.  With audio signals you can use the grammar of speech, like
those proposed by Norm Chomsky.  This gives you a tremendous advantage
since you can form rules and heuristics to break down computational
complexity.  With two dimensional signals, you have to use state machines.
Carrying the state of the elements of multi-dimensional signals without
rules (rewriting rules or heuristics) becomes n-p complete - in other
words, impossible, in practice.

Observation of the two or three dimensional Zen garden requires the
observer to use his intuitive sense.  Intuition is an important sense
related to the processes of elevating incomplete knowledge in the
primitive mind.  It's a hunch, a gut feeling, and is related to
generating emotion.  I think, in some "sense", the observer using his
intuition is the way the observer processes incomplete information which
is intinsically multi-dimensional.  We can sort of say that intuition is
used in multi-dimensional processing of incomplete knowledge which is
related to a uncertain or probabilistic, if I can say probabilistic,
type of knowledge. [7]

So the Zen priests have optimized their act of observation.  This act of
harmonizing the mind, our organic "syntactic" neural machine, leads to
quieting the mind in mediators.  Beside the act of pure observation, it's
likely that the priests are doing lots of introspection.  This is why
Zen gardens are so beautiful for many people.




Rock Garden, Ryoan-ji: japan-guide.com
[1] Zen Gardens: The Complete Works of Shunmyo Masuno, by Mira Locher Tuttle Publishing, 2012. [2] Ibid., page 8. [3] I use the word operators in the sense of computer language operators like Lisp operators. [4] Throughout the ages, I can hear Zen masters telling their meditating students in a Zen garden to "quietly watch." And they also "observe with intense introspection." [5] Eigenvalues [6] MIT Technology Review, 2009 My intution tells me the brain processes sequential visual information at about 2 lines of text per second from reading material. I guess 15 bits per word in 2 lines of text containing on average 20 words is at least 300 bits per second. But we can be listening to music, scratching our head and more at the same time. So the multi-processing brain is incredible. In the article, they don't claim any "upper bound" on this information rate. I don't think anybody can. It depends on too many factors. [7] I never really delved into the intuitionistic logic of Brouwer or Heyting because, maybe, I never had an "intuitive" "feel" for that kind of math. Hence I had no ground to stand on in pursuing a study in this field. In physics, in school, we studied the math of Hilbert. I was prejudiced this way. However, during the last couple of years, I've started reading more stuff on self-evaluating or self-referential systems ... more on the intuitionistic BHK logic which focuses on time, a core interest of mine, with respect to constructing neural networks. An advanced neural network requires self-awareness. To build this self-aware part requires a "grammar' or a concrete, programmable language. I also now sort of know the mistakes in my thinking, from years ago, about Russells views against Bergson on time. Bergson's views of time seems more "correct" to me now ... probably because of the problems I'm encountering moving forward on the development of neural networks. I also made mistakes critizing Russell athough I admire him alot. I should really have embraced Bergson's ideas years ago, however incorrect his ideas were in many instances. Brouwer is also someone I should have studied years ago. Definitely, my big mistake. Anyway I like Kolmogorov's work on sequences, so BHK logic would be a natural area, or place, for me to go now. Actually I did lots of study on Bergson years ago, especially reading his debate with Einstein. I was so prejudiced then. I guess I needed to get to this point in developing neural nets to know this.



Home->Waves/Articles




Articles

Zen Gardens -
Beauty to a Machine 2019-12-29

Structure of the Machine -
Dimensionality Reduction
Using Prefix Trees
2019-12-31

Multi-dimensional Sequences
2020-1-2

Temporal Sequences
2020-1-4