March 07, 2018 Wednesday
Bedtime Story
The first Hint of 𝓮 was in Napier's 1614 Descriptio
As I was telling last night, the number e
appeared for the first time in the early logarithmic tables of John Napier that
was published in 1614 in his work Mirifici Logarithmorum Canonis Descriptio
(Latin).
Most modern mathematicians refer to this
work simply as Napier’s Descriptio.
This work has been translated into English
and if you care to look it up it would not be too difficult to get it somewhere
on the internet.
This work is considered seminal as it
introduced to the mathematicians around the world the magic of logarithms in a
form of small booklet of tables.
This work, besides these logarithmic
tables, also had in them a manual for solving problems related to plane and
spherical triangles using logarithms.
The number e was not obviously stated but
in this booklet of tables, as an appendix was found a table of natural
logarithms of various numbers.
It was not evident to anybody then that
these tables were logarithms to the base e as it never stated explicitly.
As a matter of fact, in those days the
logarithms were not thought as the exponents to which one must raise the base
to get the required number.
This type of thinking came much later and
students are now generally taught to think of logarithm as this way though even
I personally too do not remember as having been introduced to natural logarithm
as exponent to which the base needed to be raised to get the required number.
The way I remember was that logarithmic
tables were a technique of solving complicated multiplication procedures using
only additions with the help of these tables.
This essentially meant that logarithmic was
like a manual calculator, analogous to electronic one, but only more cumbersome
and tedious.
In fact, the first question that struck me
those days was why not use a simple cheap electronic gadget to carry out the
problems instead of using these tables where one might be more vulnerable to
errors?
This essentially means that the whole
message of logarithms being a historic leap in mathematics was lost not only to
me, but I presume to nearly all the students who were around me and who I have
later came to know in life.
It is not known for certain as this
appendix to the tables was not signed by any author but it is generally
believed that this table that was listed as the appendix and had logarithms
based on the constant e was written not by Napier but the English mathematician
William Oughtred.
We had come across this gentleman long time
ago in my bedtime stories as the inventor of sliding scales to perform direct
multiplication and division in 1622 (John Napier the Scottish mathematician had
passed away in 1617).
As an aside, Oughtred had also introduced
“x” as the symbol for multiplication.
Yet, all these were indirect use or
reference to constant e with its own inventors not having precisely got the impact
of their own discoveries.
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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