Zen
and the new Mathematics.
(objective reality, number theory, artificial intelligence, & semantics.)
This section is
presented "as is" for reflection.
Have fun.
The polymath Douglas Hofstadter (b.1945)
- a devoted exponent
of formal logical realism,
wrote in 1997 in a work on Typographic Number Theory (TNT), objective and
Artificial
Intelligence, pattern recognition,..(amongst many other subjects)...
The amazing thing about language is how imprecisely we use it
but still manage to get away with it.
Relying on words to lead you to the truth
is like relying on
an incomplete formal system
to lead you to the truth.
A formal system, no matter how powerful, cannot lead to all truths.
The dilemma of mathematicians is What else is there to rely on but formal
systems ?
The dilemma of the Zen people is What else is there to rely on but words ?
Mumon (1183-1260) in his 48 koans called the "Gateless Gate",
states the dilemma
very clearly :
"It cannot be expressed with words, and it cannot be expressed without words".
When you study Bongard (pattern recognition) problems,
you realize that the elusive sense of patterns which we humans inherit from our
genes
involves all the mechanisms of representation of (objective) knowledge,
including
nested contexts, conceptual skeletons and conceptual mapping,
slipability, descriptions, meta-descriptions and their interactions,
fission and fusion of symbols, multiple representations
(along different dimensions and different levels of abstraction),
default expectations, and more.
The semantic aspects of "form" in patterns
cannot be tested for in predictable lengths of time
(as is also the case for TNT string theoremhood),
because an objects meaning is not localized within the object itself.
As time passes more meaning unfolds, forever.
Typographic Number Theory (TNT) can talk about itself ("perceive")
but it cannot jump out of ("transcend") itself.
A computer program can modify itself ("perceive")
but cannot violate ("transcend") its own instructions.
Self transcendence is the central them of Zen. but
Zen is a system, and cannot be its own meta-system.
There is always something outside of Zen, which
cannot be fully understood or described within Zen.
Gŏdel's Incompleteness theorem, Church's Undecideability theorem,
Turing's Halting theorem, and Tarski's Truth theorem all have the flavor -
"To seek self-knowledge is to embark on a journey which
will always be incomplete, cannot be charted on any map,
will never halt, cannot be described."
I would say that we are all in the same boat as the Zen master who,
after contradicting himself several times in a row,
said to the confused student : I cannot understand myself.
Propositional Calculus states that (either/or is the same as if not/then) so :
"Either a cloud is hanging over the mountain, or the moonlight is penetrating
the waves."
is the same as :
"If a cloud is not hanging over the mountain, then the moonlight is penetrating
the waves."
This may not be
Enlightenment,
but it is the best that the Propositional Calculus has to offer.
Zen is holism carried to its logical extreme.
If holism claims that things can only be understood as
wholes and not the sum of their parts,
Zen goes one further in maintaining that the world cannot be
broken into parts at all.
To divide the world into parts is to be deluded,
and to miss enlightenment.
Enlightenment and Endarkenment must concede each other.
This is the tao of Zen.
bob harbinson
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bob harbinson and Silver Pipe Productions S.A.
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