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In this book we develop step by step the FIRST ALGEBRA OF MAGNITUDES, the specific dyadic algebra for physical quantities, in order to rectify the sloppy hypothesis of «arithmetization» of Physics, normalized by the International System of Units in sections 2.1, 5.2 , 5.4.1 and 5.4.6 of his brochure SI, which is tolerated by a clueless scientific community.
With dyadic algebra, full meaning is given to the meanings of the laws, equations and compound units of Physics, a sense that we all neglect today . As a culmination, the «DYSMETRIC» FORECAST is reached, with innumerable and far-reaching implications for the enrichment of physical models and the development of infinite innovations.
In this way, the trap of «arithmetizing» Physics in which we all easily fall, even the most reputable and award-winning scientists, is ended. Except for one in the entire history of Physics, which was Newton, the only one who operated with magnitudes through the affinity of physical quantities with the elements of geometry, teaching us that, although Physics is not «arithmetizable», on the other hand it is it can be «geometrized». It seems incredible, but it is a grotesque fact that nowadays no one cares about what is really done when operating with physical magnitudes or what is the full meaning of the composite magnitudes or of the analytical formulations, which underlie all of Physics, for what no one should take a step without first having clarified this knowledge. On the contrary, it turns out that operations apparently as elementary as the multiplication of a meter by a kilogram have no arithmetic explanation, because no one identifies what the multiplier of that product is, which does not multiply numbers, but rather dyads or quantities of length and mass. Despite which, it seems that no one is bothered by such a ridiculous embarrassment. Can one call himself a physicist who cannot rigorously define this simple operation and does not care? Can a science be called Physics that lacks a coherent algebra to operate with its fundamental elements, the quantities of physical phenomena? The truth is that the defect is too gross not to take it into account.
All this as a consequence of the fact that the current arithmetic hypothesis that postulates the abelian multiplicative group structure for the magnitudes is impossible. Such a structure is only valid for internal additive laws, it is not valid for external multiplicative laws. Obviously, this situation is shameful and pernicious for Physics, it is unsustainable and must be corrected as soon as possible.
The dyadic algebra of magnitudes, in addition to giving meaning to the laws, equations, and compound magnitudes, reveals striking consequences, such as the non-existence of inverse elements of physical units, since heterogeneous multiplicative dyadic operations are not internal composition laws, but external. In turn, it naturally leads to «dysmetry», which makes it possible to represent the infinite physical realms of empty space and which radically transforms the vision of physical constants, incompatible in an absolute sense with «dysmetric» spaces, including the number pi and the speed of light.
