Board NUMBER , GEOMETRY AND NATURE

Number is one of the most fundamental concepts not only in mathematics, but in general natural science as well. It may be primary even in comparison with such global categories as time, space, substance, matter, and field. That is why editing the first issue of the journal " Hypercomlex numbers in geometry and physics " the editorial board sincerely hopes that articles not only on numbers in general, but primarily the works that reveal their organic connection with the real world will find here their true scope. The concept of number in its most general meaning unifies not only common numbers that all of us know from school, but also such objects as the quaternion, the octave, the matrices, etc. Without denying the importance of numbers of all types, let us well emphasize the class chain that has the following shape: natural → integer → rational → real → complex. At the same time our aim is to found the possibility of extending the given above classification to numbers of high dimensionality, including those that obey commutative-associative multiplication. At first sight this plan seems to be absolutely unproductive, for in algebra there exists the Frobenius theorem that claims that multy-component numbers, as being structures subjected to arithmetic properties, end with the complex numbers. At the same time a special stress is laid on the fact that in the according algebras there are no the so-called divisors of zero. Of course, if we take into consideration the real and complex numbers, treating them as the standard, the zero divisor seems to be redundant. Nevertheless, from the point of view of physics and the pseudo-Euclidean geometry closely connected thereto, the zero divisor is one of the most natural objects, for the world lines of the light rays are related to it. The fact that the pseudo-Euclidean planes may be juxtaposed with the algebra of the commutative associative double numbers which have the zero divisors, may serve as the best proof of it. Habitual claims, that the double numbers are too primitive and cannot act as a real competitor to the complex, do not seem to be well-founded, as it would mean in terms of geometry that the Euclidean spaces are more important than the pseudo-Euclidean spaces. Long ago geometricians came to an agreement that both types of space have right to exist; therefore, that is why it is impossible to divide the …