Monday, September 27, 2010

What Pascal’s triangle taught me about life? Understand your habits

This here is Pascal’s famous triangle. By the way, Blaise Pascal was a French mathematician and philosopher.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1


Here’s how the triangle works? Each level is the power to which you want to raise a term to. Level one means raising some terms like (x + a) to power 0 which will always result in 1. Level 2 is (x + a)1 which will result in (x + a) as answer. Level 4 means (x + a)4 which results in the coefficients 1 4 6 4 1 and hence the answer x4 + 4x3a + 6x2a2 + 4xa3 + a4. This blog was not conceived to teach you Pascal’s triangle but the beauty of the triangle.

This is how it works? To get to a higher level, you need to have a knowledge of the pattern of coefficients of the level before it. This is how it helped me resolve some problems in life. To get to a higher state in life or before I start complexing my life, I need to understand the simplicities I was dealing with, otherwise, I would be lost in the maze of complexity which is our daily life. Generating a complexity from the preceding solutions involves mastering the solutions that you have been dealing with and the ability to understand the pattern for that solution whenever it arises again. I’m not talking about understanding what happened in the past in order to resolve the present. No. Pascal’s triangle is all about understanding the patterns of your past and present way of living before adding or removing one or more layers to it.

Imagine say five or three years ago. Those years ago, you must have been on a different status of life before now, maybe you progressed somewhat or it was the opposite. Did you understand the patterns in your life? Habit is something that everyone has. Did you understand what you did regularly and what made you succeed? Did you use those patterns to build upon the present or someone just gave you a lift? Understanding patterns and using them to get to where you want to can make a big difference between living a simple or complex life.

Without Pascal’s triangle, solving a problem like (x + a)6 would take me considerable time, even if I try to simplify things down to (x + a)2 three times and multiply the results. Understanding the pattern in Pascal’s triangle and building upon those patterns simplified the resolution. I found a “wow!” experience in the beauty behind the maths.

What are some scenarios that can make life complex?

1. You just got a raise in the office and your employer requires you work some extra hours? Take time to reflect on the habits or patterns in your life that made you succeed. Name that habit. Ask yourself questions just as: how would this new situation impact on my present habit of success? How would my life be if I worked the extra hours? The extra hours represent a layer of complexity to your present life. What do you need to give or take to make the extra hours conform to the present habits of success? You should never compromise on a formula for success, no matter what.

2. You discover that your source of income has been compromised. You might go financially bankrupt in the short term if things continue the way they are. What do you do? Do you allow the situation to overwhelm you and make you involve yourself in unbecoming business transactions? Donning the mantra of simplicity is what learning from Pascal’s triangle can do. Evaluate the solutions you have and the pattern of those solutions. Filter them into groups: sources that are still viable and those that will soon fall into the red. Work on the viable ones. How can you use the viable ones as a pattern to solve the problem of lost revenue? If the lost revenue cannot be recouped, then the pattern of viable sources should be what you must have in your hands before you allow the stress of the situation to overwhelm you. Evaluate your strength. In the words of Pascal’s triangle: staying at the pattern for success while scouting for solutions.

I hope you got the idea of the beauty behind Pascal’s triangle. I am presently using it to resolve some biting financial problems. You can also.

The eternal desire: Spirituality

The more one becomes mature in his development as a homo sapient animal, the more he comes to realize one difference between him and animals: the desire to worship something called God. I call it something because so many cultures and periods of history have it, they have God, but the representation is various and conflicting.
Science cannot replicate that desire, neither can the cloning laboratory produce it in us, when cloning does come commercial.
So what is this desire. Why can it not be destroyed, annihilated, suppressed? Why?

Monday, September 20, 2010

WHAT THE MATHEMATICS HAS TAUGHT ME SO FAR.

I feel awed by the beauty of maths and its insightful lessons about our daily lives and how we could live it better than I decided to share the above title in my post.
1. That to solve an chronic problem, you have to simplify your life.
When you simplify your life, you remove the layers of dirt and dense lies that you have been trying to live to justify why you cannot solve that problem.

2. Anxiety and multitasking are two twins of the same belly.
Doing maths has taught me that I should not just talk about doing one thing at a time, but that is the way of wisdom and healthiness. In our technologically driven age, multitasking tasks the resources and nerves in unknown ways that bring about uncalled for emotional friction.

3. The inbuilt desire to love solving problems.
We all claim to love solving problems. But how many persons love getting down to the dirty and cleaning the toilet when it has to be done? It is a task we prefer the maid or houseboy preoccupy himself with; yet, that is the stuff problems are made of. Problems are the dirts that clog our lifestream. Maths has helped me to see solving them as not a task but as a necessary part of life.

4. Classification of things.
Maths has taught me that the differences between things and their similarities could be the reason for my prejudices, whether hidden or expressed. Repeated filtering of objects into their similarities and differences has helped me and can also help you too to flesh out your prejudices.

5. Building the linker concept.
This is what I call the linker concept: after simplifying everything and resolving them, you eventually realize that everything and everyone is related to everyone and everything somehow. The linker concept makes me conscious of this fact. I am also conscious of the fact that nothing happens by chance; there is always a linker for anything. In maths, this concept could be called the relation or functions that connects variables.
So do you think I’d recommend a reading in maths for anyone? I would surely.
By the way, I just started teaching Advanced mathematics at a local institute in my neighborhood. Thinking of buying a digital camera so I can share the pictures. Also, I intend writing a book on how mathematics can help one when you are feeling depressed and frustrated in life. It helped me. I’d be opening a blog dedicated to my mathematical endeavors and through the blog collect ideas for the book.
Mathematics a day can keep the psychiatrist away.
Chiao.
David.

If you Believe me, I’m not going to Examine you

This blog is just a reflection of one of Francis Bacon’s words I stumbled across in one of my readings.

For as knowledges are now delivered, there is a kind of contract of
error between the deliverer and the receiver; for he that delivereth
knowledge desireth to deliver it in such a form as may be best be-
lieved, and not as may be best examined; and he that receiveth
knowledge desireth rather present satisfaction than expectant in-
quiry.
Francis Bacon

I was helping a young student solve Jamb past Questions, the one of April 2010. I made a nasty mistake on a simple multiplication. I never realized the mistake until some hours later, after the student left. As I was teaching some students a day after that on Further Mathematics, or what some call Advanced Mathematics, I nearly stumbled on making the same mistake again!
That mistake gave me a pique of conscience. I looked at the class and made them believe me that I was supposed to be their teacher but not a fumbling professor. They had to believe my capabilities and not leave the class with wry faces, wondering if their examination of my mistake would make them return to my class. I thought I should be their teacher in a formal class (this was just a tutorial class). I would have maintained a moral ground, hunched my shoulders and pronounce to all and sundry: “There will be a test tomorrow!” Yes, that fear of a test, which teachers fall to as a recourse and to threaten students would have helped me hide the mistake, keeping their young brains busy.
I smiled. I thought Francis Bacon would have been wondering what was making me smile. Yes, if I was not going to satisfy the students, I should put them on their guard, covering their arses! That is what my teachers made me believe while in my youth; that was why I took to self-study, skipping classes most times.
I didn’t have to fall to the same cycle, did I?
I’m just recovering from an unknown spiritual experience. Really think it shows the love of God in humans; may I be humble in saying myself.
It’s not every time one hears funny stories from Africa that one shivers but really there are funny stories from Africa. They really have some devious science, yet one wonders why they do not know how to apply their science?
The experience taught me some lessons:
1. Life is more precious than one can imagine it.
2. Every day is to be lived and enjoyed. Forget about tomorrow, for tomorrow have their own anxieties.
3. The failures of yesteryears should be the cause of joy for preparing successes for our tomorrows.
I just went through an awesome spiritual experience and it taught me the awesomeness of God.