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    • Aion and Chronos

    Consider a concept of time composed of Aion and Chronos:
    Chronos: the time that pass, the pulsations, the seconds that scroll, the beating of our heart and before us that of our mother.
    Aion: the pure moment of time, time of the events, a time both too early and too late, a point on the arrow of time.

    Ordinal and cardinal functions of the numbers:
    There are apples on the table.
    1, 2, 3, 4, 5, 6. I count apples, the numbers have an ordinal function, the action to count is held in the Chronos.
    There are thus 6 apples. 6 take a cardinal function, we are not located more in the Chronos, we are in another time : the Aion.

    In our vision of the natural numbers, in the vision of the fundamental theorem of the arithmetic, in the decomposition into weight * level with jump = 0, we are in the Aion.
    To replace the natural numbers in the Chronos, it is enough to consider the decomposition into weight * level + jump with jump = 1.
    We did not see the difference until now because the two decompositions give the same result (with a different offset): the sieve of Eratosthenes. It's because the jump is constant, the pulsation is regular.

    In Aion, the prime numbers are primes, they are of level 1, that's all.
    How to see in a new way prime numbers ?
    By considering them in the Chronos, by analyzing them by the decomposition into weight * level + jump. In this case the jump is not constant, the pulsation is irregular.
    There are "prime numbers" and "multiples" among the prime numbers ("prime numbers" and "multiples" remain to be defined in this case).

    The numbers have only one Aion but several Chronos. To decompose a number into weight * level + jump, we must specify the time in which it is located. Is the number in the Aion or the Chronos ? And if it is in the Chronos, in which Chronos is it ?
    11 in Aion: 11 is prime, is of level 1.
    11 in the Chronos of natural numbers: 11 has a weight of 2: 11 = 2 * 5 + 1.
    11 in the Chronos of prime numbers: 11 has a weight of 3: 11 = 3 * 3 + 2.

    Chronos gives us the intuition of time and there even our intuition of the numbers.

    Good discovery of the decomposition and good thoughts,

    Rémi Eismann.