Monday, August 30, 2010

Even the Mona Lisa smiles behind the blackboard.

Beauty that is rare like a painting of the Mona Lisa can be found behind the blackboard, in front of a mathematics equation.
I had the “Oh my, what beauty!” experience while solving a well worn mathematics problem a new way. The problem: simultaneous equations in two or more variables.
I’m sure you do remember the age-old technique of solving simultaneous equations in two unknowns.
First, chose one of the variables as the one to exterminate. Multiply both equations, numbered of course, by suitable coefficients so that the variable that will be exterminated becomes the same in coefficients. You then subtract one from the other, giving you an equation in a unique unknown. Finally, you solve the unique unknown. Your answer for this single unknown can then be used to find the second unknown variable using one of the simultaneous equations as template.
Hmm! Very long process that!
Matrices is easier. That is where the beauty lies. Take the value of the second order determinants for the two unknowns; call this the raw determinant. For each unknown, replace the column for that unknown by the column for solution to the equations. Take the value of the determinants for each unknown whose column has been substituted. Then to get the value of that unknown, divide the value of the determinants for the substituted column by the raw determinant.
Easier. Faster. More energy efficient.
Don’t believe the above line until you get equations of more than two unknowns. I saw the Mona Lisa smiling behind the blackboard and it was a matrix blackboard with blue markers.
I’ll be taking calculus with my students tomorrow.

Saturday, August 14, 2010

The fear that is the Real Fear

Sometimes I hear the word fear and think: what does it mean to be afraid.
I see fear as being of two types:

1. Being afraid of punishment.
2. Being afraid because you regard it as a duty to do the right thing or for conscientious reasons.

I was thinking about this recently. I wonder why so many persons think people would turn to crime except for the first fear: that they might end up in jail when caught. I believe that so many persons have the second fear and the second fear should be the right kind of fear. It is a fear that is demonstrated both in private and public. The first kind, that fear is destructive; it is demonstrated only in public, in the eyes of the public while in private, this fear makes you self-destruct or destroy other persons or property.
What kind of education would make men exercise the second creative kind of fear?
Wondering. It would an exceptional kind of education. Would there be any benefits, adaptive, financial, emotional and physical exhibiting the second creative kind of fear where the world tends towards the first while manifesting tendencies of game theory? It would involve so much sacrifice but that is what is needed to build a complete individual.

Friday, August 13, 2010

The Eternal Question: who is God?

I believe God exists but how do I perceive him? The eternal question that is mind bothering and so intriguing is: how do you perceive something your senses realize, yet if your senses realize it, how come it was not perceived?
To perceive is to understand, and to realize is to know. I realize God, I know God exist but I cannot perceive, I cannot understand him. That is the most daunting frictional force that plagues and burdens me. Who knows the answer to that question; who knows who is God?
I cannot get any help from l’hôpital, newton, russel etc. not from anyone. Will I go to the grave with tears in my eyes, asking myself everyday: who is God? Why does he not allow me to know him to the fullest as I wish to.
The Infinite Eternal Question is: Qui est Dieu?
Hello Universe, who is God?

Finding contentment while searching for roots

Don’t get me wrong – I am not advocating a cure all technique. I found contentment or peace of find while looking for the roots of a quadratic equation. I’ll like to share it with you.

Suppose you are given a quadratic equation of the form: ax2 + bx + c = 0. In a given quadratic equation with double roots, α and β, one is constrained to work within the confines of given formulas like the sum of the roots and the product of the roots. Whatever other complex derivations you desire, whether in creating a new quadratic equation or playing with the roots, you must work within the confines of the sums and products.

That was what I was doing when I realized one simple truth: if I do this regularly, looking back at my resources, the sums and products of the roots, and only these, in order to create new equations or derivations, teaches me one thing: contentment. I have no other choice. I have only sums and products and no other resource to get to any other equation I desire. I have to control my desires and wishes, be satisfied with what I have before building or deriving anything new.

I wish someone else has a story to tell. Have a class on Tuesday. Been teaching my students matrices. We’ll have determinants next week.