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Somebody had to do it first. It need not have happened. That prehistoric person did not need to count to survive. They had enough problems to deal with every day. They did it to try and make sense of their tough life. Inside that prehistoric mind there was a link between three things:

  • the real object they looked at,

  • the imagined idea in their head that tomorrow could be better,

  • the scratch in the bone.

These three things have nothing obvious in common. It took a great leap of the imagination to join them up for the first time. Counting is probably the first and greatest invention. It was like the pebble that started the landslide. So big did that landslide become that caught up in it are all the arts, sciences and games of humankind. That prehistoric person deserves a statue. If he or she did not start counting you would certainly not be here today reading this book in your comfy surroundings.

We have today, in museums, several of the ancient bones with lines of scratches in them. From the list above that is the only thing we do have. The first thing in the list – the objects – we can make a good guess at. The second thing in the list – why they did it – well, why else would they have done it? Whatever the truth it was held in the mind of the person who made the scratches. Any link between the three things died when they did, thousands of years ago.

(If you look at the list above you will see the first thing is a real object. The second thing is an idea – something you can’t touch or see. Who knows what that was? The scratch, the number 1, the link, is somewhere between these two. Numbers are both real things and things in our mind. Or are they neither?).

The scratch - we have that. The object we can guess at. Buy why, oh why, did they do it? That middle bit – what urged them on - is the key to understanding numbers. After all, that prehistoric person invented counting. If anyone can understand numbers surely they can.

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