September 11, 2019 Wednesday
Bedtime Story
Understanding the Power of Geometric Progression
We will quickly run through the two
mathematical problems concerned with geometric progression tonight (but not
with their solutions) that you might be familiar with.
This is merely to demonstrate the power of
geometric series and progression that is exploited in finance and money
creation by the commercial banks.
First is the wheat and chessboard problem
which states that if a chessboard were to have wheat placed upon each square
such that one grain were placed on the first square, two on the second, four on
the third, and so on (doubling the number of grains on each subsequent square),
how many grains of wheat would be on the chessboard at the finish?
As legend goes (as recorded by Shafi’I
scholar Ibn Khallikan) this problem arose when a vizier of an Indian King by
the name of Sissa Ben Dahir presented a very fine handcrafted chess board (and
perhaps he was the inventor of the game for he certainly was a brilliant man)
to the King in return for which the King wished to reward him.
As a reward the vizier asked that he merely
wanted as many grains of rice as is proposed in the problem.
The King was taken aback and mentally
scoffed at the vizier considering him stupid as to ask for such a triviality
when he could have gotten so much more had he simply opened his mouth for
anything else.
The King of course did not mind it and
readily accepted to give him so.
The prize seemed to be easy enough in the
beginning and the King seemed to be pleased.
The first signs of trouble started when the
King’s men started to place the rice grains on the second half of the
chessboard meaning the 33rd square.
The term “second half of the chessboard”
was coined by Raymond Kurzweil – a MIT graduate who is currently director of
engineering at Google.
It was here that the real power of the
compounding and exponential growth started to become visible.
By the 21st square 1 million
grains of rice are crossed and at the half way mark of 32nd square 2
billion is crossed.
But remember that the problem of the King
is not just the final number on the 64th square but the sum of all
the grains that would end up accumulating on the chessboard.
Now the number on the 33rd
square – that is the first square of the second half of the chessboard -
crosses 4 billion which alone is more than the sum of all the grains in the
first half!
The situation from then onwards got more
dire for the King with each passing square on the chessboard.
The King never realized that he had given
his word to something that he would never be able to fulfill as even today with
the modern methods of agriculture the number of existing rice grains would fail
to add up to the colossal numbers that is finally reached on the chessboard.
The progression of series in compounding is
so counter intuitive that even today if asked what you would choose if you were
offered the following two options you might choose the former over the later:
Stay tuned to the voice of an
average story storytelling chimpanzee or login at http://panarrans.blogspot.com
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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