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Notes on video lecture:
The Birth of Arithmetic
Notes taken by Edward Tanguay on September 28, 2016 (go to class or lectures)
Choose from these words to fill the blanks below:
flat, imagination, pebbles, banking, trade, Besserat, marks, Greeks, money, incommensurables, wet, multiplication, abstraction, agreement, indentations, distances, pyramids, modern, land, area, notched, real, moon, sheep, Principia, foundational
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arithmetic
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led to              mathematics
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addition, subtraction,                             , division
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originally just addition and subtraction
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counting
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35,000 BCE or earlier
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piles of               
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notches on bones and sticks
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               bones have been found
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perhaps for
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seasons
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phases of the         
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monetary system
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the first evidence we have for abstract numbers was           
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Sumeria
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5,000 BCE
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the invention of numbers for monetary purposes
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you didn't have numbers until you needed money
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needed fro human transaction of goods and salaries
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the essential reason why numbers came about was               
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bankers applied money to trade
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today, bankers apply banking to figments of the                       
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but back then numbers were applied to actual physical goods
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but not quite
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the moment you introduce money, you immediately have something fictitious that depends on human                   
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1971 Denise Schmandt-                
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clay tokens from Sumeria, ca 5000 BCE
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at burial sites and ruins of homes
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tokens for things people would           
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represented goods, e.g. tokens that looked like tokens
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Sumerian society was getting complex
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you had tokens that represented the           
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how to keep tokens secure
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bankers kept tokens
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took sheet of        clay and sealed them
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to show worth, they would impress the tokens on the wet clay
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your worth is represented by the           
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layers of                        developing
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then realized you didn't need the tokens inside, it's all about the                         
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then realized they just needed a          tablet with abstract markings
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measuring
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building                 
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seeing how much          you owned
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counting
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natural numbers
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measuring
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just thought of as units, not thought of as numbers, but were quantities, lengths, volumes
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but          seems to be more complicated
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the              tried to combine them
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discovered that the square root of two was irrational
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pushed them apart again
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because of the                                 
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only at the end of the 19th century was this done in a system of numbers called the real numbers
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the natural numbers were regarded as                         
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the human cognitive system captures both
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natural numbers
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counting
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real numbers
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lengths, areas
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in the                   , Newton
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he's not talking about numbers, but quantities (         numbers)
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calculus wasn't applied to numbers of                    and areas

Ideas and Concepts:

On the origin of mathematics and the nature of money via this morning's Mathematical Thinking class: "The invention of numbers was for monetary purposes. We generally don't see humans using numbers and arithmetic until they needed money, e.g. for transactions of goods or for recording salaries, and so one of the first professions using numbers was that of banking. One might say that bankers today apply numbers to figments of the imagination, and that back then numbers were applied to actual physical goods. But not quite:The moment you introduce money, you immediately have something fictitious that depends on human agreement."
The Birth of Arithmetic