The Game of Math
ne of my most vivid childhood memories is driving my mother () distraction by asking the ‘why’ question. Most children go through this phase:
Me: “Why is a sponge wet?”
My mother: “Because it has soaked up water.”
Me: “Why has it soaked up water?”
My mother: “Because it has small holes in it”
Me: “But what makes water wet?”
My mother: “Because it is made of wet stuff” a bit weak now.
Me: “What is wet stuff?”
You can ramble on indefinitely unpeeling a never-ending onion. Sometimes, if you are unlucky, you may get stuck in a loop. For example, “where did the chicken come from?” “An egg, “and where did the egg come from?”..
Mathematics breaks this cycle!
In mathematics, there is no danger of an infinite number of ‘why’ questions because at its core are a clearly defined set of absolute rules called axioms. You cannot ask the ‘why’ question of an axiom. It is a RULE!
Starting from an absolute minimum of fundamental rules everything else is built up so that no step requires any leap of faith nor generates any contradiction. Let me give you a concrete example and, in the process, show you how numbers are defined.
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