The reality is this phenomenon, which manifests itself constantly through our sensations. Unlike feelings, they play a pioneering role in the understanding and determination of it.Knowing the finer border between unreality (virtuality, film, social networks, dreams ... etc.)and reality; between the two worlds, the first is well deduced from the second.But, what can we say more concretely about this reality, that our minds swim there just like afish in its environment?
Considering this questioning, it is undoubtedly possible to give aninfinity of answers. This reality, to which it is almost impossible to renounce those wetransmit our various senses, seems to be made only of mathematics.Indeed, reality is nothing but various mathematical objects, in this sense characterized byspaces; sizes; measurements; surfaces; lengths; distances; circles; cubes; spheres; polytopes;matrices; systems; sets ... etc.
Life itself is mathematical, for nothing but our hopes of life are intervals of time, a period, amathematical measure. Our senses tells us mathematically, a spider is often scary, because itsshape through our eyes, we feel a danger, similar for the hearing, the touch, the taste and thesmell in various contexts ... In this case, how are we going to unravel the mysteries ofmathematics?
We live in mathematical spaces and always use mathematical objects. To livewithout mathematics is compared to a lifeless body, since nothingness is also a mathematicalobject (empty space). Whatever the position of the object, it seems to belong to a space. Weknow the Euclidean space; hermitian or prehilbertian, which are also algebraic objects. Wehave always learned that a linear application or linear transformation of elements belonging toa vector space (ring, abelian group, body, ... etc.) is delimited by a starting set (which givesthe antecedent values) and a set of arrived (the images or result of the transformation of thevariable elements).
In dimensions 0, 1, 2 and 3, objects change shape and easily perceptibleby the eye. At the limit, any object in dimension greater than 3 is hardly observable.Geometry is the more simplified representation of the numerical or matrix complex of mathematics. A mathematical object is formalized by this transformation on elements identifiable by sets and characterized by stops. Having a base or several vertices, displacement or mobility in search of an ideal environment in a space, amounts to changingfrom one position to another (vector space). To do this, we will need a locomotion, which is nothing but a base consisting of the family ofelements (eigenvectors associated with the values or solutions of the system) free andgenerative made possible by the diagonalization (or triangulation and through the transitionmatrix (or base change), which consists in bringing a set (endomorphism) back into a diagonal(trigonal) matrix.
The latter results in homothety (displacement on the same direction) orrotation (from one direction to another) in the whole of the vector space. Indeed,geometrically, to move is to go from one point to another represents a distance. In reality, itamounts to calculating the determinant (or invertible) of a matrix with the unit matrix of thesame dimension with an unknown. The new position is known by the values of these fixedunknowns in the set and which will allow the setting up of the elements (vectors) of the base.One manages to move in a space, while changing base by the financial means of thediagonalization. Mathematics, as a particle of knowledge, main pillar of the demonstrationand thus defines the essence of science. Therefore, could we, in this case, merge allknowledge into a single discipline of super mathematics?
Abdi-Basid ADAN, 2018.
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