Novel Numbers

Here is a new and novel idea about numbers, or I think it is new.  There is some debate about whether numbers, or which numbers, are ontological ‘things’. This is Mathematical Realism.   Perhaps only Prime Numbers have a life of their own, so to speak, as composite numbers can be assembled from them.  Fractions are created out of the prime numbers because they can be represented as a polynomial and even the transcendental numbers can be written as an infinite sum of numbers.  Philosophers from Kripke to Russell and with ever expanding, complex, new Number Theory, have grappled with accepting the ‘a priori’ truth of even the Number ‘One’ and from it the Number Line by assuming that non-existence has the ontological status of a number, called ‘zero’ to which One can be endlessly added.  But nothing is nothing, and we are imagining a continuum that in reality can only approach non-existence from either side but can never ‘not be’ because even the idea of something is a form of existence with ontological presence even if devoid of ‘substance’.  The Prime Numbers do appear to have real-world existence beyond our use of language and the ability to label things in useful ways.  Now, here is my new and novel idea.  It came to me while thinking of the pentagram, the five-pointed star that can be assembled into two different, regular three-dimensional objects.  The square root of five is an important number in this, so it occurred to me that perhaps it is the square root of five that is the real world phenomenon, not the integer five itself.  Then I thought how the square root of two is the length of the diagonal of a square.  That makes it exist in the real world in a fundamental way, as a length that exists for itself.  The number two, on the other hand, is a mental construct by people to count when there are a precise quantity of a multiplicity of single objects.  I say, ‘I have two hands,’ but I just have a hand and have another hand, the ‘twoness’ of my hands, their duality, is all in human imagination.  A similar argument for the diagonal of a cube that are the square root of three.  So, it is the square roots of numbers that are special,and exist in the real world in a way that our counting integers do not.