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The Natural Natural Numbers and How Many God’s Do You Want?

August 11, 2011

There is a trivial disagreement between mathematicians: some begin the natural numbers at 1 and others at 0.  I’m going to say the natural numbers begin at 0, acknowledging my background in logic and computers, but I shall call the natural natural numbers those natural numbers which are positive.  Thus the natural natural numbers begin at 1.  Now, if you have three rocks in your hand and you show it to a young child, they will see three rocks.  Remove a rock and they see two rocks.  Remove one more and they see one rock, but remove the last rock and they see a hand, not zero rocks.   Zero is natural to the advanced thinker, but not to a child, so it is not as natural as 1, 2, 3, 5 or 7.  I shall call {1,2,3,5,7} the intuitive basis for the natural numbers, and 0 cannot be represented exactly without reference to inverse operations which are, again, relatively unintuitive to a child’s mind.  So how do we actually represent zero?  Well, basically what we do is to pick a ridiculously large NN number that we will never count to and designate that number the number before 1 and name it Zero (or Zorro if you want to get dramatic with it).  So, in our intuitive model, 0=1+2^3^5^7 where ^ denotes raising to the power of.  If this is not big enough, add a prime so that 0=1+2^3^5^7^11.  We can guarantee that this number is not even, and is not a Mersennes prime either (because the exponent of 2 is non-prime).  Now, with my childlike intuitive model of the natural natural numbers, I’m going to enter the great atheist debate.  The other person, who we shall call Doctor Dorking, believes that 0 is not the successor of any number and believes this with all the fervour of a religious fundamentalist.  He will try to hang or shoot anybody who tries to prove the non-existence of his beloved 0-that-comes-before-all-positive and we don’t, for everybody’s safety, want to push him too far.

Me: So do you believe in God?

Dork: No! Absolutely not!

Me: Well, if I were to ask you to put a number to it, how many would that be?

Dork: Zero!  Absolutely Zero.

Me: Hmmm… but there is no real Zero, only numbers too big to count.  What you are really telling me is that you have more gods than you can count and you’ve given up counting.

Dork: What??

Me:  Well, I prefer to have a Universal God who is one and all that is Godlike.  This makes things much simpler.  For example, I don’t have to ask the question: which God?  Or to try and apply existential quantifiers together with negation to get statements such as ‘God does not exist’.  I like it simple.  Do you have a simple explanation of you Zero God?

Dork:  But I don’t believe in any god, let alone a God of Zero.

Me: Can you tell me one thing, anything, that you fundamentally do believe in.

Dork:  Well, I believe in evolution.  That and selfish genes.

Me: Well then, Evolution and Selfish Genes are your Gods then.  How many Selfish Genes are there, and how many Evolutions?  Are they single and Universal, or many and distinct?

Dork:  ?????

I really don’t know where, as a fundamentalist atheist, Dorking will go next.  Any thoughts?

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