March 19, 2017 Sunday
Bedtime Story
How Leibniz and Newton Were Similar and Yet Dissimilar
Newton used a lot of simple diagrams that involved curves drawn
against the x and y axes which he breaks into multiple small blocks which I
think is the origins of his method of fluxions.
This fluxion is now known as derivative.
Derivative is a fundamental tool of calculus.
It is used in the analysis of functions.
As I had described you in my previous bed time story, a function
has an input value or the argument and an output value that is called the
function value.
The derivative measures the sensitivity in the change of function
value with respect to the argument.
Even in this method of fluxions that he introduced - the novel
concept to depict the range of change, the amount of notations used is very
little.
This, in a way, makes Newton’s Principia very readable (albeit many
would call it a dry read) even though it is loaded with mathematics; the only
reason for this being that mathematics is presented to us in a very
non-mathematical form.
This non mathematical form is so because of the lack of
mathematical notations that is so scary for most of us.
Yet the story is very different when it came down to Newton’s arch
rival Leibniz.
Gottfried Wilhelm Leibniz was born in the city of Leipzig, Saxony
of the Holy Roman Empire in the year 1646.
Like his arch rival Newton, Leibniz never married and they both
never reproduced.
In fact, both these remarkable men, as far as it known, showed
very little interest in the fairer sex, which to my mind reflects their
insusceptibility to the common frailties of human apes.
Men like these can rightly object to my calling them apes as it is
these rare few whose behavior distinctly demarcates humans from their cousin
chimpanzees.
All the rest of us, to a large extent, behave like just another
primate, eating, surviving and reproducing with slight more sophistication than
a jungle chimpanzee.
Whatever may be the dispute in the Leibniz-Newton controversy over
calculus, the one thing on which there is no debate is that Leibniz in contrast
to Newton was a serious notational buff.
It was Leibniz who introduced the term dx and dy to represent
infinitely small (or infinitesimal) increments of x and y.
As far as notation is concerned, his greatest breakthrough
happened on that fateful day of November 11, 1675.
It was on this day that he wrote that that famous integral sign ∫
He did so while trying to find an area under the graph of a
function
y = f(x).
Similarly, for the inverse operation of integration, he introduced
the letter “d” from the Latin word differentia.
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.
Advertisements
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:
No comments:
Post a Comment