  Algebraic properties of the genetic code are analyzed. The investigations of
the genetic code on the basis of matrix approaches ("matrix genetics") are
described. The degeneracy of the vertebrate mitochondria genetic code is
reflected in the black-and-white mosaic of the (8*8)-matrix of 64 triplets, 20
amino acids and stop-signals. This mosaic genetic matrix is connected with the
matrix form of presentation of the special 8-dimensional Yin-Yang-algebra and
of its particular 4-dimensional case. The special algorithm, which is based on
features of genetic molecules, exists to transform the mosaic genomatrix into
the matrices of these algebras. Two new numeric systems are defined by these
8-dimensional and 4-dimensional algebras: genetic Yin-Yang-octaves and genetic
tetrions. Their comparison with quaternions by Hamilton is presented. Elements
of new "genovector calculation" and ideas of "genetic mechanics" are discussed.
These algebras are considered as models of the genetic code and as its possible
pre-code basis. They are related with binary oppositions of the Yin-Yang type
and they give new opportunities to investigate evolution of the genetic code.
The revealed fact of the relation between the genetic code and these genetic
algebras is discussed in connection with the idea by Pythagoras: "All things
are numbers". Simultaneously these genetic algebras can be utilized as the
algebras of genetic operators in biological organisms. The described results
are related with the problem of algebraization of bioinformatics. They take
attention to the question: what is life from the viewpoint of algebra?
