New Understanding of Time Based on the Concept of Areal Multitudes
The article puts forward a new ontology of the Time of Nature based on the following statements: 1) there is a multitude that we call “Time”; 2) this multitude consists of an inﬁnite number of individual elements that we call “Instants”; 3) all the elements of the given multitude have a following feature: if one element is REAL, all the other elements of the multitude are UNREAL; 4) we shall call the multitudes of such type “AREAL MULTITUDES.” It was discovered that the elementary areal ratio is a logical law of contradiction: A and NON-A form together an areal multitude of two elements. In other words, if A is real, NON-A is unreal, but we see that this NON-A does not disappear, because without it, A is logically impossible. Nevertheless, if A exists, NON-A does not exist in reality. Thus, NON-A exists only as a possibility, it is “areal.” Formulating the law of contradiction, Aristotle, and all the logicians after him, constantly underlined the fact that A and NON-A cannot be in the same ratio at the same time. We would like to rearrange accents: in our formulation AREALITY is a particular logical ratio that simulates the Time of Nature. An inﬁnite multitude of instants of Time is an areal multitude, because reality of the Present instant makes all the other instants of this inﬁ nite multitude unreal. We determine that the inﬁnite areal multitude is also the multitude of normalizations of the numerical axis and suggest it as a model of Time. The new model determines the Time order as a symbolic sequence where the instants are the symbols of normalizations represented as unequal, actual inﬁnitesimals. This approach allows us to detect periodization related to the mathematical constant e (Euler’s number) on the inﬁ nite multitude of Time. The given unconventional conclusion is indicative of appropriateness of the proposed model.