[Ian Scott (OP)]

Have we found all the numbers?

Pythagorus thought of "perfection" insofar as all numbers could be seen a P/Q with P and Q being non divisible integers. His student Hispassus proved him wrong with the square root of 2 and was sent to an ocean grave to learn better! This revelation called forth irrational numbers.

I wonder why we add - commerce suggests the need to equate income and expense. But why multiply?

Did numbers come before the need to say Tax as a percentage or did we feel some inherent duty to seek out multiplication - did the Romans though with their clumsy MCXIV... system?

Do we limit ourselves the same way with four binary operators - a field in the real number system. Are there higher binary operators beyong +,-,*,/ and will these present new numbers as yet undiscovered?



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[RD]

Are there higher binary operators beyond +,-,*,/ ... ?

http://en.wikipedia.org/wiki/Logical_connective#Binary_relations

[Ian Scott (OP)]

Thanks RD

http://ian.r.scott.tripod.com/inventing_numbers.htm

If you are interested in conjecture...

Ian

[blakestyger]

Practical to the last, Homo sapiens is probably likely to have first used numbers to account for stuff. What are thought to be tally marks appear on bone artifacts ca, 30 000 BCE - this is probably the birth of accountancy. []

Sadly, the recorded language of the Minoans, Linear B (which was deciphered by Michael Ventris in the 1950s), turned out to be almost exclusively lists of wool, sheep, chariot wheels and who owed what to whom.
Not a word of poetry or heroic deeds done - just plain bloody accounting!

Whatever we may like to imagine or wish for, the origins of these things is probably most likely to be just down-to-earth prosaic. 

[Ian Scott (OP)]

Nice comments blakestyger