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C O U R S E 
A Brief History of Humankind
Dr. Yuval Noah Harari, The Hebrew University of Jerusalem
C O U R S E   L E C T U R E 
The Human Brain's Outsourcing of Mathematics
Notes taken on October 5, 2013 by Edward Tanguay
throughout history, in order to build a large kingdom or city or modern state, humans needed (1) enough food, (2) an imagined order, and (3) techniques for storing large amounts of information
up until the agricultural revolution, all information needed was stored in the human brain
but as societies grew larger and larger, two things happened
1. amounts of necessary information also grew which had to be stored
e.g. a town of 5,000 requires much more information processing than a band of 50 people
2. the human brain was ill-adapted for the kind of information that needed to be stored
monotonous mathematical data, or numbers
foragers had little use for numbers, they needed to more remember shapes, qualities and behavior patterns of thousands of species, and habits and relations of several dozen band members
foragers had little need for large numbers, e.g. didn't need to remember the number of fruits on each tree in the forest
if someone like Hammurabi (1792 BC - 1750 BC) wanted to maintain an empire, he needed to collect collect taxes from hundreds of thousands of people, you need to collect data about payments that were made, income and possession of people, about debts and fines, about discounts and exemptions
human brains have a very hard time dealing with this this amount of numbers and mathematical complexity
this mental limitation severely constrained the size of collectives after the agricultural revolution
once societies got to a certain size, humans hadn't developed the mathematical concepts yet to deal with this large number of people
before this, human social networks remained relatively small
Sumerians (4500 BC - 2400 BC)
present-day Southern Iraq
they were the first people to solve this mathematical challenge
around 4000 BC, larger kingdoms began to grow
between 3500 BC and 3000 BC some unknown Sumerian geniuses invented a new system for storing and processing information outside the brain, and this new system was custom-built to manage large amounts of mathematical data, in this way the Sumerians freed their social order from the limitations of the human brain and opened the way for the appearance of larger cities and kingdoms and empires. This data-processing system that the Sumerians invented was called "writing".
instead of using neurons in the brain, they used material signs of all kinds and shapes.
writing was invented not in order to write poetry or philosophy or history, since all of this could be done in your brain, but one thing you cannot do in your brain is to store and process a large set of mathematical data, this is the original purpose for which writing was created
so if you are looking for the first words of wisdom from our Sumerian ancestors 5000 years ago, you are in for a disappointment
one of the first texts in history on a clay tablet:
"29,086 measures of barley where received over the course of 37 months"
the first author in history was an accountant
most early writings were: the payment of taxes, the accumulation and ownership of property
after the appearance of writing, we begin to hear history through the voices of its protagonists
as time went by, writing became more sophisticated was used for other purposes: laws, poetry, philosophy, sacred scriptures
however, even long after the invention of writing, for the most part even today the most basic function of writing is to store administrative information and mathematical data which cannot be stored and processed in the human brain
it was this administrative use of writing that was essential to the functioning of large societies
in fact, the dominant language of the world today is not English or Mandarin, but mathematics, the language of numbers: all states, companies, states or institutions, no matter if they primarily speak English, German, Spanish or Mandarin, all use the language of numbers to record and process data
every piece of information that can be translated into numbers is stored, spread and processed with amazing speed and efficiency, a person who wishes to influence the decisions of countries, companies and international organizations, must not only learn to speak English or Mandarin, but more importantly the language of numbers
there are entire fields of knowledge such as physics, chemistry and engineering that have already lost almost all connection with the spoken human spoken language and are maintained almost solely in mathematical script
e.g. this is the equation for calculating the acceleration of mass i under the influence of gravity according to the theory of relativity
when most people see such an equation, they usually panic and freeze like a deer caught in the headlights of an oncoming vehicle, but this reaction is quite natural and is not a result of lack of intelligence or lack of curiosity, it is simply that, with rare exceptions, human brains are incapable of thinking through concepts like relativity or quantum mechanics.
physicists manage to engage with these ideas and theories by setting aside the traditional human way of thinking and learn instead to think with the help of external data processing systems such as mathematical writing and computers
crucial parts of the thought process in physics take place not in the head of the physicist but on blackboards, or paper, or in computers, because you can't do it in your head, it's not built for it
more recently, mathematical writing has given rise to an even more revolutionary writing system, the binary script which consists of only two signs: zero and one.
scientists are working on intelligent systems which are based on numbers only, and so, the move from the human mind to written number systems to computer systems, to a new kind of intelligence