February 27, 2017 Monday
Bedtime Story
Arithmetic, Geometry and Logic: The Pillars of Mathematics
To my mind, much before algebra must have come logic.
As long as there were humans, there must have been arguments for
we can agree to nothing.
Disagreement is fundamentally in our nature even towards the most
common sensibilities.
In this democratic times, and even not-so democratic times, each
and individual considers his birthright to disagree.
Yet merely disagreeing and arguing is not enough.
Our ancestors long back realized that argument has to be based on
logic.
Logic is the codification or formalization of arguments.
Now that we have the three early branches of mathematics, namely
arithmetic, geometry and logic let us what kind of notations would have been
used for each.
One thing that is common to both the written language and the
mathematical notation is that both use two-dimensional strings of structures to
convey messages that cross the two dimensions both spatially and temporally.
In fact, mathematical notation can be considered a branch of
linguistics though as far as I know, no linguist has seriously taken up the
study of mathematical notation (their primary object of investigation being
languages, wither written or spoken).
As we saw in the case of the Ishango bone, the easiest way to
represent numbers is unary system.
You represent one by one stroke or one scratch and then repeat
them as many times as you wish to convey the number.
This unary system is also known as tally marking and was the
beginning of mathematical notation.
Surely it did not take a genius to construct the tally marking and
many civilizations independently of each other had figured this system out.
What happened next was more complex and far more diverse.
One way of understanding how mathematical notation evolved next is
to imagine what was the fundamental problem the humans faced once they had the
tally marks.
How to represent higher numbers?
Speaking more generally, the early societies would have wondered
how to correlate the numbers they had in their own local spoken language with
mathematical symbols.
If you see mon ami, most primitive civilization would have had
words for one, ten, twenty, hundred, thousand, ten thousand and so on.
But they would have pondered how to get them down in mathematical
symbols.
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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