What is One?

Let's start at the very beginning. What is '1'? The obvious answer is that it is the first number. But is it? (See '0' next). Or is it even a number? Y'see every other number you can count on your fingers, toes, abacus etc etc, is made up of lots of '1's. So there is a school of thought that '1' isn't actually a number, but is instead the building blocks of all numbers.

One can now wander off down a long and winding path that is a career in Number Theory. Note that that is a sensible academic discipline which attracts seriously minded professional people dedicated to deep study and contemplation. Numerology is NOT to be confused with Number Theory. THAT is a nutty mystical system (in the loosest possible sense) of superstitions which attracts people with serious mental health issues dedicated to deep confusion and picking lucky lottery numbers.

Let us not wander down that path though. For our purposes here, let us instead contemplate 1 as a unit of something. The concept of a unit of something is a tricky one, and one which was never satisfactorily explained to me in school. For length, for instance, you have to decide what "units" you are working in - which is not quite the same as saying [imperial] or [metric]. No, the units will be miles or kilometres, yards or metres, inches or centimetre and so on. You need to get this bit right so that if you measure length 2 and add a length 3, what you get is a total length of 5. If you add 2 metres to 3 miles you do not get 5 of anything, you get a mess, and your probe fails to enter orbit. As I said though, this is not just imperial versus metric. If you add 2 metres to 3 kilometres, again you do not end up with 5 of anything.

So when you are deciding on which units you are using to measure you are really deciding an absolute reference length. ALL other lengths you are going to be measuring are then multiples (or maybe fractions) of that reference length. That means that you can do normal maths on these lengths - addition or multiplication for instance - and you will get sensible answers WHICH ARE themselves multiples or fractions of the SAME reference length.

I remember being very confused in school trying to answer the question "How many square centimetres are in a cubic centimetre?". I kept imagining pieces of paper cut into squares a centimetre on each side and then stacked one on top of the other, and being confused because I could not work out how many would fit to a cubic centimetre. I now know that I was confused about this because I was dealing with two completely different units. A cubic centimetre is a unit in its own right, and is not some multiple of units of square centimetres. There is no exchange rate. A cubic centimetre is a unit of volume and represents a cube (funny that) with sides which are one centimetre in length. A square centimetre is a unit of area and is a square with sides which are one centimetre in length. No one had properly explained the concept of units to me.

So 1 can be seen as the ultimate unit. Even centimetres can be broken down into smaller divisions. For instance a centimetre is actually one hundredth of a metre, which in turn is actually the distance travelled by light in a vacuum in roughly one three hundred thousandth of a second. But 1 does not need to be broken down any more, nor can it be. It is the absolute basic unit, from which everything else is referenced. So when I say I am adding 83 to 32, I actually MEAN I am adding 83 ones to 32 ones.

At a very basic level, and I LIKE very basic levels, 1 is the basic unit which every other thing is measured relative to. It therefore represents the difference between something and nothing. Which takes us neatly on to...