history-page2 - Prehistoric Tallies OF-topic by denition...

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Numbers and Counting General Counting is arguably the most fundamental/primitive mathematical action. Modern science of combinatorics. Counting arrangements. E.g., how many ways can 67 be written as the unordered sum of positive integers? More generally, assessing the quantity of objects in a collection. In competition for most basic with assessing the magnitude of a physical quantity. · DiFerence is discreteness versus continuity. · Parallel to time versus space. · Which do we see ±rst in children? Story of comparing hairs on two animals · 1-to-1 correspondence · cardinality 1-to-1 correspondence with · physical tokens (pebbles, ±nger-positions) · sounds · written symbols (numerals) Natural Numbers = N = { 1 , 2 , 3 , 4 , 5 , 6 ,... } (abstract quantity, not the symbol)
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Unformatted text preview: Prehistoric Tallies OF-topic by denition Claims are: Speculative Tentative Unconvincing Calinger: far more fundamental than language Not terribly advanced animals have ability to count into the high single digits. Anecdote about crows being able to count to ve but not six. The canonical (but not only) work is The Number Sense by Stanislas Dehaene. or the historic era, we now address the question, what numeral systems did various ancient civilizations develop and when? In a bow to history over heritage, we look at: Mesopotamia Egypt Indus Valley Yellow River Greek Mesoamerican Roman Independence? Still a matter of dispute....
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.

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