March 05, 2017 Sunday
Bedtime Story
Sapir-Whorf Hypothesis in Mathematical Notation
We had discussed fractals last night in relation to the increase
in the size of Roman numbers.
You can imagine that when Archimedes calculated the number of
grains it would take to fill the entire universe (as per his calculation it was
1063), it would have been impossible to write that down in those
letters-for-numbers format.
This famous paper of Archimedes goes by the name of “The Sand
Reckoner”, and is claimed by many to be the first research-expository paper.
Besides the problem of size, this idea of using the letters-for-numbers
prevented these civilizations from developing or inventing the idea of symbolic
variables.
In linguistics, this problem is popularly known as the Sapir-Whorf
hypothesis.
The hypothesis proposes that the very structure of a language
affects its speakers’ world view or cognition.
So the inability to invent symbolic variables for numbers was a
huge limiting factor for development of mathematics.
Take for instance polynomials.
Diophantus of Alexandria somewhere around 250 AD studied
polynomial equations using these letters-for-numbers system.
Besides it being extremely hard to understand, in the terms that
Diophantus wrote these equations, it hindered the extensibility of his
polynomial equations.
For mathematics to really flower, it needed the modern
mathematical notation of numbers which originated in India between the first
century and fourth century A.D.
It remains unknown the Hindu or the Hindus who pioneered this
remarkable system of notation.
This novel notation evolved very slowly and tediously starting
from first century AD to sixth century AD.
Even as late as in 300 AD the first three numbers were represented
with a single horizontal stroke, double horizontal strokes and triple horizontal
strokes respectively.
Four was represented with the + sign.
It was only around 700 to 800 AD that the numbers began to have a
semblance to the modern Hindu numerals.
It spread to the West via the works of Arabic mathematicians.
Two of the Arab mathematicians that are given most credit for this
favor to the West are Mohommed ibn-Musa al-Khwarizmi and Al-Kindi.
They published their books somewhere around 800 AD and by 1000 AD
the Indian number system was firmly established and very popular at least in
the Arab world.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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