Download matrix of complementarity for metagenetic

Symmetry Festival 2009. Abstracts. Budapest 2009.
MATRIX OF COMPLEMENTARITY
FOR METAGENETIC
Kamil Bakhtiyarov
Professor of Mathematics, Doctor of Philosophy., Logic (Moscow, RUSSIA).
Email: [email protected]
Abstract. The letters of a genetic code are taken for a sample: A (adenine) as a
maximum, u (uracil) as a weak minimum, and also the inverted letters: V as a minimum, n
as a weak maximum. The Matrix of Complementarity, columns of which represent
complementary pairs, has been constructed under laws of creation of a living organism.
The complete block Ψ characterizes dependence on Last Name-dominants A and V; and
the split block (↓↑) – dependence on First Name-dominants columns ↓ and ↑.
Isomorphism of matrices of a genetic code and mental types shows
predisposition of characters, in many respects determined by their genetic code.
Keywords: complementarity, dominants, isomorphism, genetic code, mental types.
Stabilité – première condition du bonheur public.
Comment s’accomode-t-elle avec la perfectibilité indefinite.
А.S.Pouchkin
The author offers the Matrix of Complementarity which uses the complementary
pairs instead of contrasts of the traditional Square Of Opposition to overcome the infinite
discontinuity (of second kind) for one of its values.
Four values underlie the Square of Opposition which has a point of an infinite
break point between + ∞ and – ∞. Belnap interpreted the uncertainty 0/1 as None (neither
truth, nor false), and the infinity 1/0 as a nonsense, Both (both truth and false). (Belnap
N.D. 1976). The author thinks if to use the value 1 as the true label it would be natural to
use the opposite magnitude as the false label, a negative number –1. Then the logic zero
can be used for the uncertainty, and inverse magnitude would be the logic infinity, the
nonsense (Bakhtiyarov K.I. 2003, 2005). Thus, we receive two pairs of the oppositions: by
the sign the values are +1 and –1, and by the magnitude they are zero 0 and infinity 1/0 =
2
± ∞. Then use of the zero by computer by default will correspond to uncertainty. It is
better than false presumptions.
Under the approach based on the Square of Opposition and a principle of
antecedence of the outgoing the cycles arise causing «the epicycles of the sixes and
nines» (for numbers of hydrogen bonds) in the codon table (Petoukhov S.V. 2001, 2008).
To overcome these artificial artefacts it was necessary to introduce a natural disposition of
the complementary pair elements opposite to each other and to introduce a principle of
autecedence of the incoming. The Matrix of Complementary is offered to be constructed
under the laws of living organism creation, using a natural disposition of the
complementary pair elements. As a complementary pair we consider letter A (adenine) as
a maximum sign, and the letter U (uracyl) as a weak minimum sign. For another
complementary pair we accept the similar inverse signs: the letter V as a minimum sign
(cytosine), and the letter n as a weak maximum sign (guanine) (Bakhtiyarov K.I. 2007,
2008).
We have The Matrix of Complementary for the cardinal points (on the left) and
the Square of Opposition for properties (on the right) which differ by the disposition of
elements.
n
A
n
A
V
u
u
V
The Square of Opposition is an artificial logic design generating paranoiac
infinite amplitude of oscillations."castling" of its elements makes the bridge between
artificial intelligence and natural intelligence (NI). It suggests a way to create the artificial
intelligence (AI). The Square of Opposition (on the right) is the artificial logic
construction causing the discontinuity of second kind. In case of transposition of elements
or "castling" in the lower row we have The Matrix of Complementary (on the left) that is
free of this nonsense. It allows to restore the course of nature that ensures the continuous
development, similar to monthly or annual cycle, characteristic for biological and Mental
processes. The Square of Opposition looks like a table but comes to the linear scale what
becomes obvious if we perform projecting operation.
3
The matrix consists of 4 units, each of which is it a miniature, operating as the
fractal multiplier. Considering the type of pairs (x1, x2) = (First Name, Second Name) we
accept the primacy of the surname (the second name). We have two dominant surnames:
vowel *A (liberalism top is polygamous, opened) and consonant *V (the conservatism
crater is monogamous, closed). Non-dominant surnames n, u: with vowel names A *, u* aura of gold pair - adjoin the block of vowels and with consonant names V *, n* - volensnolens to the block of consonants. Complemtary pairs organise combinations of the strong
character with the gentle one.
The matrix Ψ = (↓↑)are columns of complementary pairs ↓ and ↑:
n
A
– monogamous consonants, ↑=
↓=
V
– polygamous vowels.
u
n
A
V
u
Non-Kronecker (left) tensor matrix square Ψ =
(↓↑) n
nn
An n A AA
gly STOP, arg/ser glu/asp
Vn
un
arg STOP, trp/cys gln/his STOP/tyr
nV
AV nu
lys/asn
ΨA
=
ΨV
results in Ψ2 =
VA uA
Au
ala
thr
val
ile, met/ile
VV uV Vu uu
pro
ser
leu
leu/phe
(↓↑)u
The bold letters mean "polygamous" cells (the left table), generating the codones rich with
amino acids (the right table). The problem on structural isomorphism of mental,
physiological and natural phenomena was considered in antiquity. Since Hippocrates four
temperaments were selected similar to aggregate state of substance.
01) Fire-passion, "summer", fire. Actors histeroids (A).
02) Earth-power, "winter", ice. Power epileptids (V).
03) Water-potion, "autumn", water. Scientists schizoids (u).
04) Air-media, "spring", steam. Media cycloids (n).
n
x’y
V
x’y’
A
xy
u xy’
Actually the table is a two-letter logic diagram by L. Carroll. For offered matrix
classification the indexing of columns is from the left to the right, what means xy in the first
4
quadrant, x’y in the second quadrant, xy ’ in the third quadrant, x’y ’ in the fourth quadrant
of the Cartesian coordinate plane.
Isomorphism of matrices of a genetic codes and mental types shows the
propensity of the characters in many respects defined by their genetic code. The Matrix of
Complementary for psychological types
nn.Manipulator
Goebbels
Vn.Informant
Pavlic Morozov
nV.Politican
Lenin
VV.Leader
Ceasar
An.Showman
Chaplin
un.Commentator
Engels
AV.ArtLeader
Nero
uV. Critic
Iudushka Golovlev
nA.Artist
Shalyapin
VA.Producer
Meierkhold
nu. Fantast
Wells
Vu.Methodologist
L'Hôpital
AA. Lover
Don Juan
uA. Art Critic
Bakhrushin
Au.Teacher
Socrates
uu.Scientist
Leibniz
:
The microlevel of kinds (subdivisiona) resembles the macrolevel of types (units) that
generates the fractality (the self-similarity) of the structure of the basic table. The matrix
consists of 4 units, each of which is it a miniature, operating as the fractal multiplier.
Logic positional dominance facilitates the qualitative leap as the positional notation at
highest levels does not need new letters. The genetic code allowed us to glance at knowhow of the Nature and to learn the formation principles for the new things. The Matrix of
Complementary will allow to overcome the discontinuity (of second kind) between
natural and an artificial intelligence.
REFERENCES
Bakhtiyarov K.I. (2003) Algebra of logic for the computer// Tezisy 4-oi Mejdunarodnoi konferencii
"Smirnovskie chteniya". Moscow,. pp. 25-27. (in Russian).
Bakhtiyarov K.I. (2005) Logical Multidimensionality (vectorial and matrix models) // The Bulletin of the
Moscow State University, series 7, Philosophy, № .5, p. 85-95 (in Russian).
Bakhtiyarov K.I. (2007) Alphabet of Universal Language // Smirnov’s Readings on Logic. Proseedings 5-th
Conference. Мoscow, p. 21-23 (in Russian).
Bakhtiyarov K.I. (2008) Principles of Universal Language (positional dominance and fractality) //
The Oppositions and Paradoxes. Мoscow, p. 216-233 (in Russian).
Belnap N.D. (1976) How a Computer Should Think. Contemporary Aspects of Philosophy Proceedings of the
Oxford International Symposium.
Petoukhov S.V. (2001) The Biperiodic Table of Genetic Code and Number of Protons. Moscow (in Russian).
Petoukhov S.V. (2008) The Matrix Genetics, Algebrases of Geneic Code, Noise Immunity. Moscow
(in Russian).