Unconventional knowledge
by Kenichi Morita
Distinguishing between
“conventional computing” and “unconventional computing” is not so easy, since
the notion of unconventional computing is rather vague. Some scientist may want
to give a rigorous definition of it. But, if he or she does so, then
unconventional computing will become less attractive. The very vagueness of the
concept stimulates one's imagination, and thus is a source of creation.
In this short essay,
related to such a problem, we consider thinking styles of the West and the
East. We examine several possibilities of ways by which we can recognize
various concepts in the world, and acquire enlightenment from the nature. At
first, we begin with the two categories of knowledge in Buddhism. They are
“discriminative knowledge” and “non-discriminative knowledge” (however, as we
shall see below, discrimination between “discriminative knowledge” and
“non-discriminative knowledge” itself is not important at all in Buddhism).
Although it is very difficult to explain them, in particular non-discriminative knowledge, by words, here
we dare to give some considerations on them.
Discriminative knowledge is just the set-theoretic one. Namely, it is a
knowledge acquired by classifying things existing in the world. For example, the discriminative knowledge on
“cat” is obtained by distinguishing the objects that are cats from the objects
that are not cats. Therefore, what we can argue based on discriminative knowledge
is a relation among the sets corresponding to various concepts, e.g., the set
of cats is contained in the sets of animals, and so on. Knowledge described by
an ordinary language (or a mathematical language like a logic formula) is of
this kind, since “words” basically have a function to distinguish certain
things from others.
Non-discriminative knowledge, on the other hand, is regarded as the true wisdom
in Buddhism. But, it is very difficult to explain it in words, since words can
be used for describing discriminative knowledge. Therefore, the only method by
which we can express it is using a negative sentence like “Non-discriminative
knowledge is not a knowledge that is obtained by distinguishing certain things
from others.”
Actually, non-discriminative
knowledge is recognized neither by words, nor by thinking, nor by act.
Moreover, it is not even recognizable. This is because all acts such as
recognizing, thinking, and explaining some objects necessarily accompany
discrimination between the self (i.e., actor) and the object. In Buddhism,
everything is empty, i.e., it has no reality in the world in its essence.
Hence, there is nothing to be discriminated, and there is a truth that can be
gotten without discriminating things. Furthermore, such a truth (non-discriminative
knowledge) itself is also empty, and thus does not exist. It may sound
contradictory, but this is caused by explaining it by ordinary words.
There is no doubt that
discriminative knowledge brings practical convenience to our daily life.
Today's science also relies on discriminative knowledge. There, objects to be
studied are clearly identified, and their properties are described precisely.
By this, science brought us a great success. However, discrimination is
considered as a kind of “biased view” in Buddhism. Thus, we should note that such
a knowledge is a “relative” one. Namely, when we state a scientific truth, we
can only say like “If we assume a certain thing is distinguishable from others
based on some (biased) viewpoint, then we can conclude so-and-so on it.” We
should thus be careful not to overestimate the descriptive power of languages.
It is well known that from
the end of 19th century the foundation of mathematics has been formalized
rigorously with the utmost precision. It is, of course, based on discriminative
knowledge. However, at the same time, problems and limitations of such a
methodology were also disclosed. A paradox by Bertrand Russell on the set theory
is the most famous one, which first appeared in Nachwort of the Frege's book
(Frege, 1903). Russell's paradox is as follows:
Let R be the set of all
sets each of which does not contain itself as a member.
Is R a member of itself or
not? In either case, it contradicts the definition of R.
Due to this paradox, the
naive set theory had to be replaced by some sophisticated ones such as the type
theory. The incompleteness theorem by Kurt Gödel (1931) also shows a limitation
of a formal mathematical system. He proved that in every formal system in which
natural numbers can be dealt with, there exists a “true” formula that cannot be
proved in this system. He showed it by composing a formula having the
meaning “This formula is unprovable.”
Nagarjuna is a Buddhist
priest and philosopher who lived in India around 150 - 250 AD. He is
the founder of Madhyamaka school
of Buddhism, where he
developed the theory of emptiness. In his book Vigrahavyavartani (The
Dispeller of Disputes) (Westerhoff, 2010), he pointed out “very logically”
that false thinking will be caused by relying only on discriminative knowledge.
This book is written in the following form. First, philosophers of other
schools who believe every concept has a substance (here, we call them
philosophical realists) present objections against those of Madhyamaka school.
Then, Nagarjuna refutes all of them.
While philosophers of
Madhyamaka school assert every concept has no substance (but they assert
“nothing” as we shall see below), the opponents (philosophical realists) say as
follows (Westerhoff, 2010):
If the substance of all things is not to be found
anywhere, your assertion which is devoid of substance is not able to refute
substance. (Verse 1)
Moreover, if that statement exists substantially,
your earlier thesis is refuted. There is an inequality to be
explained, and the specific reason for this should be given. (Verse2)
Nagarjuna says:
If I had any thesis, that fault would apply to me.
But I do not have any thesis, so there is indeed no fault for me. (Verse 29)
To that extent, while all things are empty, completely
pacified, and by nature free from substance, from where could a thesis come?
(Commentary by Nagarjuna on Verse 29)
That is, without saying “all
things are empty,”all things are empty by nature, and hence the Nagarjuna's
assertion itself is also empty.
We can see that the
observation “If all things are empty, then the assertion ‘all things are empty’
cannot exist” resembles the second incompleteness theorem:
“If a formal system in which natural numbers can be
dealt with is consistent, then consistency of the system cannot be proved in
the system” by Gödel (1931).
However, methodologies for
obtaining the above observations are quite different. In the former case,
non-discriminative knowledge played the crucial role, and thus the observation
itself is again empty.
Nagarjuna launches a
counterattack against philosophical realists, who claim “all things have
substances", by the following objection:
The name “non-existent” what is this, something
existent or again non-existent? For if it is existent or if it is nonexistent,
either way your position is deficient. (Verse 58)
It is clear that the above
argument is analogous to Russell's paradox. By this, Nagarjuna pointed out that
philosophical realists who rely only on discriminative knowledge have a logical
fault. However, as stated in
Verse 29, Nagarjuna asserts nothing in his book.
It will be reasonable to
regard discriminative knowledge as conventional knowledge. Then, how is
non-discriminative knowledge? Although this kind of knowledge has been argued
by philosophers and Buddhists for a very long time, we can say neither
conventional nor unconventional. Probably, it is meaningless to make such a
distinction. Instead, we consider a question: Can we use non-discriminative
knowledge for finding a new way of scientific thinking, and for giving a new
methodology of unconventional computing? Since current scientific knowledge is
very far from non-discriminative knowledge, it looks quite difficult to do so. However,
it will really stimulate our imagination, and may help us to widen the vista of
unconventional computing.
I have been studying
reversible computing and cellular automata (Morita, 2008) for more than 30
years. Through the research onthese topics, I tried to find novel ways of
computing, and thus I think they may be in the category of unconventional
computing. Besides the scientific research, I was interested in Buddhism
philosophy. In 1970's and 80's, I read Japanese translations of several sutras
and old texts of Buddhism. They are, for example, Prajnaparamita Sutra (Sutra of Perfection of Transcendent Wisdom),
and Vimalakirti-nirdesa Sutra
(Vimalakirti Sutra), as well as Vigrahavyavartani
(The Dispeller of Disputes). All of them discuss emptiness of various
concepts and things in the world, but assert nothing. I was greatly impressed
by these arguments, which themselves are empty. Although my research results
are, of course, given in the form of discriminative knowledge, and thus in the
purely Western style, I think such a thought somehow influenced me on my
research when exploring new ways for unconventional computing.
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