Primera álgebra de magnitudes*

The equations of Physics do not simply relate numbers, vectors or tensors of a mathematical nature, but rather dyadic quantities formed with these components linked to various units that indicate quantities of natural magnitudes. So, why do we operate with the dyadic entities of Physics as if they were pure mathematical elements? Doesn't this fiction suppose an aberration that debases all scientific knowledge? Some authors have warned of this critical gap, which hides such a fundamental pillar from Physics. Pre-eminent physicists such as Clerk Maxwell or Max Planck, among other classics, can be cited. All of them expressed in their own way the scruples aroused by the traditional and unjustified way of operating with physical quantities and their units. Here such a remarkable arithmeticization paradox of Physics is discovered, described and solved and a rigorous and coherent algebra is constructed for the quantities of magnitudes.The First Algebra of Magnitudes resolves the false hypothesis of the International System of Units, consisting of negligently assuming that physical magnitudes have a multiplicative abelian group structure. It cannot be like that, as demonstrated in this work.Finally, the logical and unappealable path that leads from the algebra of magnitudes to the dysmetric spaces is revealed, which are studied in greater depth in the second volume of this work. Dysmetry is a powerful new tool for accurately representing the physical phenomena of a variable universe. This new Physics welcomes a multitude of innovations, which will undoubtedly be appreciated by many enterprising researchers.