Don’t underestimate the power of squared

Squared is just same variable multiplied twice. Rt? Think Again. This deceptively simple looking concept is very misterious and appears at places that changed course of human history forever.

Is it? Look at this equation

Aaha… the dear Pythagorus equation. Yes its well know. This is an important equation. But do you know why? Don’t tell me it helps finding length of hypotenuse in a right triangle.

This one equation brought the same impact to algebra that imaginary numbers brought to number system (curious?). For the first time, human race was able to create a circle with algebric equation. All you have to do was change the angle and you had the circle. This was so big that Geometry passed the baton to Algebra to take over the realm of Maths.

The next revolutions came with Sir Issac Newton. And what did he gave us… Calculus and equations of force and motion. The world was taken by storm and what was his equation of force?

Force = mass x velocity

And while the direction was right, it had a flaw. Mr Squared were missing. It took enormous effort and sacrifice to get it right. Blame it on Mr Newton’s aura and capability of even thinking beyond him. Whatever he said was carved on the stone. However, Mr Gottfried Leibniz, who independently worked on motion and force, and also developed Calculus parallel to Newton, had his own ideas. He proposed

Force = Mass x Velocity²    

He proposed, objects have inner energy…potential energy. Even at rest. Today we don’t think much about it but there was a huge storm in those days of 17th century. A flamboyant, independent French mathematician lady Émilie du Châtelet Franch, who was a huge fan of Neuton was couragious enough to see beyond Newton’s theories and had genuine theory in support of Velocity squared. She was pressured from all sides of the scientific community but she stood firm and pushed for validation. The experiment was finally done by Dutch scientist Willem ‘sGravesande which finally proved relation between Force and Velocity²   forever. So much for a squared. :)

Thanks to the YouTube documentary- Einstein’s Big Idea – The story behind the world’s most famous equation by Le Acharya.

Then came Mr Einstein and his famous

It changed the way we looked at Universe. This Mr Squared. But think of it, this equation was so scary in those days that Sir Einstein never got Nobel for it.

But, this topic is marked as Artificial Intelligence and Machine Learning, and all I am writing about is physics and maths. Believe me this Mr Squared is playing a crucial role in Machine Learning. Heard of Linear Regression and Least Squared

And how about Vector and Linear algebra… well we will come back to all that soon.