March 10, 2018 Saturday
Bedtime Story
The Jesuit (member of Society of Jesus) and Mathematician
With the limiting function stated last
night, Bernoulli found that if he compounded an unit of investment with 100%
annual return twice a year, he got the value 2.25 and if he compounded four
times a year he got 2.4414.
Making it monthly gave him a yield of
2.613035, making it a weekly affair gave him a yield of 2.692597 and making it
a daily affair gave him a yield of 2.714567.
So you see that as the n gradually
increases, the sequence as we may call it, tends to inch towards 2.71828.
In fact, the limit that is reached when n
becomes continuous and thus very large or infinite, came to known as the number
.
It is probably the first time in the
history of human apes that the number e was defined by a limiting process.
Jacob Bernoulli at this time did not see
any connection between his result from the problem of compounding interest and
the logarithmic tables of both Napier and Oughtred.
Somewhere around 1630s in the Flemish
region of the Kingdom of Belgium there existed a priest by the name of de
Saint-Vincent.
The fact that he was both a priest and a
mathematician should not surprise us because in those days, meaning sixteenth
to eighteenth century, almost every European was not only totally dedicated to
their own church but considered it their natural calling to serve their own
version of Christianity.
Today Christianity with its hundreds of
versions and thousands of churches is the most popular and widespread world
religion but most Christians lack even the faintest idea that this happened
purely out of historical chance or accident.
One has to study history to know that each
point in history is full of quite a few possibilities if not infinite of them.
Let me quote from the chapter ‘The
Hindsight Fallacy’ of Harari’s remarkable book ‘Sapiens’ (2011) that leaves you
gasping in wonder at the breath and scale of ideas covered:
“Every point in history is a crossroads.
A single travelled road leads from the past
to the present, but myriad paths fork off into the future.
Some of these paths are wider, smoother and
better marked, and are thus more likely to be taken but sometimes history – or
the people who make history – take unexpected turns.
At the beginning of the fourth century AD,
the Roman Empire faced a wide horizon of religious possibilities.
It could have stuck to its traditional and
variegated polytheism.
But its emperor, Constantine, looking back on
a fractious century of civil war, seems to have thought that a single religion
with a clear doctrine could help unify his ethnic diverse realm.
He could have chosen any of a number of
contemporary cults to be his national faith – Manichaeism, Mithraism, the cults
of Isis or Cybele, Zoroastrianism, Judaism and even Buddhism were all available
options.”
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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