Question

Various historical aspect of number

Answer 1

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Great question. Agree with all prior definitions. My definition of numbers: the letters in an alphabet used by mathematics. Whereas all other languages use arbitrary symbols (letters), to construct words, that have assigned meanings (ie: english, french, spanish, basque....), math symbols are limited to quantities, and the logical operations (ie: grammar) that can be performed with or upon them. A quantity is something we observe, that appears to have a boundary - without a boundary, no quantity could exist. For example, where does an apple begin or end? At it's skin - but when you examine the skin of an apple under greater and greater magnification, the boundary begins to be more ambiguous - never-the-less, an inch away from the skin of an apple is clearly, by common sense, no longer that apple. One of the unique values that ordinary language has is that it permits the transmission of complex, symbolic ideas. Numbers are specific to quantity alone - one apple, one proton, one dog - are all the "same" in that regard - "one". This notion turns out to be incredibly useful in describing reality. Spookily so. Theoretical math, with no apparent connection to reality, but only to it's own rules (grammar), has often been found to be useful in solving real problems, many years later. Why this should be so is a great mystery. Animals clearly have the capacity to count, but how this developed, and whether it's conscious or genetically programmed, is another great mystery. All languages including math, are used to construct mental maps of aspects of reality. As symbolic descriptions, they are of necessity (so far at least), only partial, but pragmatically useful, descriptions of reality.

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Answer 2

Here is your answer,

In the long history of the number π, there have been many twists and turns, many inconsistencies that reflect the condition of the human race as a whole. Through each major period of world history and in each regional area, the state of intellectual thought, the state of mathematics, and hence the state of π, has been dictated by the same socio-economic and geographic forces as every other aspect of civilization. The following is a brief history, organized by period and region, of the development of our understanding of the number π. 

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