Monday, February 27, 2017

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:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

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