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The History of Mathematics
In 3000-2000 BC, the Babylonians developed the place-value system. Thus
123 was different from 321 for the first time! I wonder when grammar —
the idea that word-order matters in sentences — was invented. Gorillas
don’t understand grammar, but dolphins and humans do. In my Classical Latin
studied, I remember the word order being more fixed than in English.
The Babylonians — like most all cultures that achieved competence in
math in the entire world’s history — used base-60 for everything. We still
use base-60 in minutes and seconds, and base-12 in months, hours and inches.
Obviously base-12 is far superior to base-10. Only stupid indoctrinated
ignoramuses would think for a fraction of a second that base-10 is better
for any purpose. While the ignoramus is thinking during that second, I
would point out to him/her that there are sixty of those seconds in a minute,
sixty one-second-thoughts per minute, 3600 just-a-seconds, hold-on-a-seconds,
and I’ll-be-with-you-in-a-seconds in an hour. Is 10 evenly divisible by
4? I thought not. How often do we divide by 5 in carpentry? Or business?
Will a pizza parlor cut your pizza into 10 pieces? Do most people call
that big coin a “quarter”, showing a desire to divide by four, an operation
possible in base-12 and base-60, but not base-10 (recall that ten won’t
divide by four!). Or do they call it a “twenty-five-cent piece”, showing
a preference for the dollar divided by hundredths? Aha!!! I thought as
much. It’s not just a syllable thing either. “Penny” has two syllables,
but “cent” has one. What do people call those little copper-zinc coins?
Pennies! From the British base-12 based coining system!!! So you see!
60 is divisible by 1, 2, 3, 4, and 5 since 60=1×2×3×4×5. Sexagesimal
is better than decimal because every right-thinking person would rather
have sex than dec.
The Babylonians were the first to form multiplication tables. They
did +, -, ×, ÷, square, cube, and extraction of any root! All this
was happening over 4000 years ago. Can you calculate the 13th root of 2
with a rock and a sharp stick?
The early Babylonians lacked a system to carry the 60 over into the
next number place since they didn’t have a way of noting empty space, which
we do with zeroes, so there was some confusion. They eventually invented
a symbol, like 0, as a place holder. The Hindus later brought the 0 into
the decimal system in the 400s. The Babylonians were able to solve multivariable
sets of linear equations, and even solve fourth-order equations.
In the 1600s, a place-valued decimal number system began to be adopted
in Europe. The Arabs had known about the weird Hindu decimal system for
some time, but decided to ignore it since it was not convenient at all
for doing astronomical observation and prediction, for which base-60 was
far more useful.
In the 500s, in Bagdad, the Persians began to seek out Greek mathematical
texts and also learned Indian astronomical techniques. al-Khwarizmi (died
850) is the guy from whom we get the names algorithm and algebra. The story
they told me in school about it being named after an Arab mathematician’s
daughter, Al-Jabra, is unsubstantiated. The term algebra was taken from
his work Kitab al-jabr wa al-maqabalah. This work was a simple translation
into Arabic of what he had learned of ancient Mesopotamian mathematics.
Renee Descartes invented analytic geometry. This was the first time
that anyone had used algebraic equations to describe spatial relationships.
Quiz
to test your reading comprehension
So here are the answers to the quiz. You can supply the questions.
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The Arabs did not invent algebra around 600 AD. The Mesopotamians did around
2000 BC. (Arguably, they lived in the same town, but at different times.)
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The Arabs did not invent base-10. They preferred base-60, but knew that
in India, base-10 was used.
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Base-10 was used by the Indians a long time ago but didn’t make it to Europe
until the 17th century.
Bonus Questions
to test your understanding
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What practical purpose did finding any root of a number fulfill for the
Mesopotamians in 2000 BC?
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Why did the Mesopotamians need to solve multivariable linear equations
in 2000 BC?
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Give an example of a problem that needed to be solved in 2000 BC which
would use a fourth-order equation.
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October 15, 1582 was a Friday. What day was October 4, 1582? What day was
October 9, 1582?
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