Every whole [natural] number is detached from the others, it possesses its own individuality
To my mind, however, this viewpoint omits the fourth, irrational, “just-so-ness” of individual natural integers.
This element has certainly been recognized time and again, but no one quite knows what to make of it.
Henri Poincare, for instance, says:
“Every whole [natural] number is detached from the others, it possesses its own individuality, so to speak; each one of them forms a kind of exception, for which reason also general theorems of number theory are but seldom forthcoming.”
Nevertheless, this individual aspect of number appears to contain the mysterious factor that enables it to organize psyche and matter jointly.
The number one possesses these unique qualities to a particular degree.
In contradistinction to all other numbers it does not multiply by itself, or reduce itself by division because it is the divisor of all other numbers. It is the only number that yields more by addition with itself than by multiplication with itself ( 1 + 1 = 2, but 1 X 1 = 1).
The well-known number of Mersenne (2′ – 1) (p = prime number) and that of Fermat (2 2• +1 ) cannot be formulated without one.
The number one also forms the marginal number of Pascal’s triangle:
Nevertheless, this individual aspect [just-so-ness] of number appears to contain the mysterious factor that enables it to organize psyche and matter jointly. Marie-Louise von Franz, Number and Time, Page 60-61
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