Creatio ex nihilo

“Abstraction is everybody’s zero but nobody’s nought.”
~ Robert Smithson

 

Zero is believed to have been invented as a number like other numbers by the Indians, somewhere between the fifth and ninth centuries. The idea of ‘null space’ or the ‘void’ was known and used by earlier cultures, but the Indians were the first to produce a symbol that could be utilized in mathematical calculations to represent the void. When we consider numbers today, it is appropriate for us to begin with zero as the unique numerical symbol for nothingness – indeed, when we derive mathematical operations from set theory this is exactly how we do start, with zero as the symbol for the empty set.

If the first number is zero, denoting nothingness, then the second number – one – denotes identity. In set-theoretic terms, it is the set which can have only one possible element (the set of the empty set, in fact). This set-theoretic interrelation between nothingness and oneness is mirrored in the symbolism of the taijitu, and the doctrine of creatio ex nihilo – something out of nothing.

The existence of zero and of one as numbers generates the concept of category; a unitary entity having more than one component subentities. The simplest structure of category is duality – the category that has exactly two elements, as ‘one and zero.’ The numerical symbol for duality is two.

Three elaborates this concept of category further into the more general plurality. Where twoness denotes a paradigm of either/or, a binary system within which ‘one’ may acceptably and completely be defined as ‘not-zero,’ threeness opens a doorway – a Gateless Gate, indeed – onto countable infinities of paradigm in which each element is uniquely itself and cannot be defined in terms of any other element (although it can be defined in terms of all other elements, with reference to the established concepts of nothingness, identity, and duality).

Four, being both the sum and the product and the power of two twos, embodies divisibility. This is a further elaboration upon plurality – with the addition of fourness, we now find that there exist some plural entities which are both entities in themselves and unions of lesser entities. We can, of course, derive numbers along the real number line by defining mathematical operators that utilize this principle more generally – indeed, we could do that when we had only zeros and ones to play with – but fourness is the philosophical symbol that uniquely develops this concept.

These, then, are the numbers which symbolize the essential concepts of being: nothingness, identity, duality, plurality, and divisibility. You probably already realized this, but we have just derived another expression for the Law of Fives.