A philosopher might tell you that mathematics exists beyond the physical realm, independent of human thought. Or another might say that mathematics is really our mind's attempt to impose order on a disordered universe.
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Certainly, the number ten predates humans and the first creature that theoretically could count on its 'fingers' was a primitive fish.
In the Devonian period there was a proliferation of fishes, giving it the name The Age of Fishes. In the late Devonian (393-359 million years ago) the first tetrapods (four limbs) appeared, ready to invade the land. Among them was Elpistostege watsoni.
That creature had articulating digits in the fin that were ancient precursors to our fingers.
With five digits on each hand, the obvious thing for us is a counting system based on the number ten.
Not everyone agrees, however, because in New Guinea, the Oksapmin people use a base-27 counting system. To do that, they use a few more body parts such as their nose, wrist and ears.
Computers, on the other hand (pardon the pun), use the binary system that only needs the digits zero and one.
However, making larger numbers means stringing long sequences together, so that decimal 201 becomes an unmanageable 011001001 in binary. Great for computers, not so good for humans.
Still, base-10 is the dominant system used in everyday language.
The use of base-10 goes back a long way, to the Ancient Egyptians and the Greeks. Of course there are Roman numerals and, as any long-suffering school kid will know, doing mathematics with those is near impossible. Instead, we use Arabic numbers, where the position of each digit signifies ones, tens, hundreds, etc.
That, in turn, requires the use of the digit zero as a place holder. The history of zero is long and complicated, having appeared in various forms in places such as China and India. Ptolemy used a symbol for zero in AD 150.
Who would've thought, one of the greatest advances in mathematics was the invention of nothing. It did, however, pose a philosophical conundrum. How could something represent nothing? Does nothing really exist?
Pythagoras had a special fondness for the number ten because it could be formed into a triangle called the 'tetractys' by arranging ten points in four rows: one, two, three, and four points in each row. These can be read as musical ratios, giving 4:3 (perfect fourth), 3:2 (perfect fifth) and 2:1 (octave).
These embody "the harmony of the cosmos, the ascent to the divine and the mysteries of the divine realm".
You could spend tens of years mulling over these things, which would match our fondness for measuring the passing of time in decades.
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