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