## Tuesday, December 28, 2010

### STIMULATING YOUR BRAIN WITH ELECTRICITY CAN IMPROVE YOUR MATHS ABILITY?

This claim is backed up by research conducted by Dr. Alvaro Pascual-Leone at Beth Israel Deaconess Medical Center, Harvard Medical School and Universidad Autonoma de Barcelona. The original article can be found in the November 23 issue of Current Biology. His findings are paradoxical because just as I said in the preceding paragraph, for better brain performance you need a good environment, comfortable level of stress, motivation and good health, amongst other needs. But Dr. Alvaro contends that to enhance your brain performance beyond the ordinary, you should disturb the brain in a way that one part of the network, say the parietal lobes, becomes dysfunctional, while other parts of the neural network remain intact. He found out that this disruption, especially using electric current, enhances numerical ability in patients so tested.

You should not go about attaching electrical diodes above your head or exposing your skull to hot dryers the type you find in beauty salons without protection because the research is still ongoing.

You can read about it yourself, online, original article; also Scientific American has a blog on this subject.

Now, if you could do this, what is the cons of enhancing performance? There is no free lunch. What would it cost you to improve your numerical competence? As with exercises, the muscles use up energy, there are action potentials to consider in muscle contraction and relaxation and ionic interactions. What are the hidden costs of noninvasive disruptive brain stimulation? Those are questions for the future.

As they say, you cannot eat your cake and have it, but you can decide to munch your cake in bits so it’d last for days.

## Saturday, December 11, 2010

### WHAT IMPORTING TOOTHPICKS AND SIMILAR PARAPHERNALIA MIGHT INDICATE.

Maybe the feats of architectural ingenuity that one sees all over Lagos are not of our making; we are just profiting from the benefaction of some foreign construction company, like Julius Berger, to dot Broad Street with imposing skyscrapers.

With a grin, I might be accused of stupidity to say that we do not need intelligence or intelligent people in this country.

It is not an easy statement, but that is what importing toothpicks suggests. At least, chewing sticks were the playthings of our ancestors; how could we lose a micro chewing stick to foreign supply? It beats me; I am sure it would you, yourself, but if the President pronounced it to be so, then he in his wisdom knows it all along that Nigerians do not want to bother their brains any longer. So why should he bother himself?

If I am correct in my dismay, then we have collectively sold our creative and entrepreneurial inheritance to foreign imports. Creativity and entrepreneurship would surely go the way of power – into the hands of some cabal who would do anything to stifle it, even strangle it to death. Gone are the days of Industrial estates, gone are the days of assembly plants. Goodluck Jonathan has just heralded the dawn of an age where the Apapa Ports have become our industrial showpieces.

It makes me shudder.

Importing toothpicks would also cause a thinking person to conclude that Nigerians have stopped bothering themselves about solving their problems. We’d rather pay someone else some money to do the abstract problem solving. We can afford to maintain this culture of paying for solution providers from overseas but one day, the oil well will run dry. I really do foresee an apocalyptic breakdown in law and order on the streets of Lagos; an apocalypse with mayhem as its close cousin. There is no way we can beat our chest that our sovereignty can ever stand the test of nationhood. I wonder if the marionettes at Aso Rock belong to either Washington or Beijing? Either way, that is the true story and no one is ashamed or afraid to deny the truth.

Another truth, if there is anything like the truth really, is that, intelligent people in this country or people who want to lay a claim to such an exalted position, are being destroyed. Without destroying them, the culture of mental, moral, financial and inspirational dependency would be resisted. I don’t see anyone recognizing this fact in our media. Yet, this is the truth. How come no one realized importing toothpicks should be a declaration done in secrecy, without public knowledge, and not on the front pages of a national newspaper?

Those that have not been destroyed, because of the stifling climate, financially of course, have refused to express their intelligence. They’d rather shove it into some closet and work for some bank with luxurious cars as the reward for doing a work which even persons without brains can do, and do it beautifully well too.

Who is to blame then? Whose fault is it? I wish I could dig up some research about power in this country, but if you recall that the millions of generators that have become a household necessity in Nigerian homes are as a result of the fact that power will never belong to Nigerians, because the dam will never be solved, because the transformers will always fail, because their salaries are always paid even when services are not rendered, then you will understand how strong the grip on the Nigerian intellect some cabal can have to make sure creative and entrepreneurial abilities are stifled.

I keep wondering what sovereignty a country can possess if it is totally dependent on another for its existence? The speculation will never end; not until I am proved true.

## Saturday, December 4, 2010

### GOOD MATHEMATICIANS TURN OUT TO BE LEADERS

I do not know why it is so, that great men like Albert Einstein, Isaac Newton, Charles Darwin, Galileo and other notable men in the field of inventions learnt maths first before mastering their chosen fields of physics, biology and etcetera, but I have noticed that it is so.

I sometimes think that it is because maths is as old as the world itself. The Babylonians were good in maths, and I read somewhere, in a textbook while in the university, (about ten years ago), that mathematics started, modern mathematics, from Babylon. Maths, especially algebra, was a prerequisite in ancient Greece as well as Rome.

If you take a stroll along Otigba Street, Ikeja, in the hot afternoon, you will see one of the high achievements of maths and mathematical innovation on display: the computer and mobile phones. The computer industry, that started from the abacus machine, is the reason behind why men go to space today and why we can surf the Internet. It is also the reason why we can communicate today, your reading my blog on a screen, without reading it on paper and your ability to do business in any country or clime irrespective of the currency.

And talking about money, every measurement involves maths, be it in the field of social science, pure sciences or arts, you must have a knowledge of maths to do any measurement at all. I wish someone would tell me what system the Igbo were using before the decimal system came but I believe that the limitations of tallying that they must have relied upon would not involve their counting nothing much more than hundred or a so tubers of yam. Today, they can count thousands of goods on containers coming from asia; no pun intended, I am igbo myself.

So why is maths education looked down upon in this country? I really can’t answer that question. If no one thinks it’s a social problem, I think it is. We’ll never get to develop scientifically if we do not emphasis maths education in this country. By the way, University of Nigeria, Nsukka, of which I am a graduate, is a good example of the denigration of maths and mathematics education. People used to feel sorry for people in the maths and statistics department that they do not have much options in the job market. I do not think so now; but I wonder why that feeling was well imbibed in youths at that time? I wish we could invest more in maths and maths literacy, just the like that the makers of cowbell milk in Nigeria, Promasidor Nigeria Limited, are doing, sponsoring maths competition and employing them in the banking industry. Unfortunately, I couldn't find the company website on the web. It would be a helluva surprise the day I’d see a job advert that states maths is required for employment in the banking industry.

## Thursday, November 25, 2010

### WALKING ON THE TIMELINE TOWARDS A CHINESE LINGUA FRANCA?

No wonder I found myself wondering if mandarin Chinese is the next language school that will be as popular as the Alliance Française here in Lagos?

Why? Check out what this blog post numbers say: 420 milliion people in china have internet access and are available on baidu; for those who do not know, baidu is the Chinese equivalent of the search engine, Google. For a country of one to two billion, 420 million is just a scratch of the potentials, there will still be a walk towards a figure or number greater than 420 million.

Who’s not going to learn mandarin Chinese for such a huge market base? Now is the time to start. Sooner than later, Chinese language would be a necessity on the resumes of those who want to do international business.

I think I have ideas towards Chinese but that will not be so fast, maybe towards 2012 or thereabouts. By the way, do you realize that Chinese trade policy is much Africa-centric than other developed western countries?

If you want a linguistic advantage, forget learning French for now, take a course in mandarin Chinese before anything else.

## Tuesday, November 16, 2010

### ALL WORK AND NO PLAY MAKES THE BEATS UNAPPRECIATED.

It’s a pleasure to be carefree, to allow the tension flow away into the arms of some well crafted beats.

When I dance, I like dancing to the beats of the music, that is why I enjoy rap music and sentimental blues a lot. It’s been long since I listened to a track by Mary J Blige. Oh, is she heavenly. Asa also, she just has the gift.

Music is a product of maths, that I cannot deny. As I took the feet up and down, counting the beats, I thought the best musicians give one the illusion that the frequency of the beat was going to be steady and suddenly, there is a turn in the frequency, like some climax or critical point was reached. The beat changes, everyone raises their hands in the air.

Music is so beautiful. Take time and dance carefree once in a while and you’d understand why I had to write this blog. Just had to.

### THE QUESTION OF MORALITY, SCIENCE AND MY LOVE FOR MATHS.

So does science want to provide the answer?

I was reading this article:

morality: don’t be afraid – science can make us better . Although the article was interesting, I was not convinced that science is ready to take over the baton of moral leadership. Yet!

I don’t know if and when the time will come if there would be anything relevant to religion again? Science has been making so much progress in human development and evolution that sometimes one believes the fight is slowly coming the way of religion. The solutions provided by science, while mimicking creation, are so laudable, that only time will tell.

Even despite reservations about the ethics behind stem cell research, IVF and humans living outside the planet. I wonder what spirituality a homo sapiens would express living on mars for more than 365 days?

Also, there is the fear that as with the ever increasing conflicts in the theory about the origin of the earth, there surely will be conflicts in the theories science would propose in this direction. Take psychiatry and psychology for example. Those fields are replete with theories that change as the setting and rising of the sun.

Maths is part of science itself. Although I blog within the limits of high school maths, I know that there are lots of moral practices going on in the mind in solving an equation. The training behind solution finding itself can be compared to that given to a child on the ten commandments. I have observed how students react when they fail the answer to an equation. Although I cannot say there is a tinge of the conscience, yet the guilt written on their faces makes some never to come back to maths again.

Many people say maths is boring; so many say the ten commandments are boring also. Because so many persons are skeptical about these spiritual treasures do not make them so, or less important.

I rest my case on these points. I think it would be revolutionary if science finds some solutions to the moral question, then some of life’s mysterious question would be the subject of laboratory research.

## Friday, October 29, 2010

### MATHS IS NOT JUST ANOTHER ADDICTIVE RETREAT; IT IS BEAUTY.

One peculiarity about this equation, as of every other equation, is that the relational function does not take a direct one-to-one fit in the real world. I must digress, I was thinking along this lines before I heard of the death of the father of fractal geometry, Benoit Mandelbrot, who dedicated his life to searching for beauty in nature through mathematics.

Life would have been a simple beautiful equation if it follows the mathematical equations. Unfortunately, we are left with possibilities and factors and so on and so forth when we encounter the maths in the real world, especially where it comes to human relationships.

Let’s take an example of a family man. If it was easy to give one a family man and then we can interpret him as a good father or not, a good husband or not, then it would have been easy, but not so. Whatever interpretation we give to that man is dependent on whose opinion we are dependent upon. Why? Because he plays several roles in life. And so do all of us.

A family man plays the role of a husband to a woman, father to some children, breadwinner to these and to also other relations who are dependent on him, an employee or employer in a fictitious company, an in-law to an old grandpa and grandma resting their bones somewhere and all these factors have different interpretation of what he is or would have been based on how much relationship he has had with them.

He might be a good father but a bad employee; a lazy fighter but a strong talker; a good in-law but a selfish miser. Because he plays several roles, the maths from the dependent relations to his representation is not that easy. But that is why life is fun!

You think this is just another addictive retreat from the hard knocks of life, don’t you? Wait until you hear opinion on what you represent then you’d understand why the maths is not as simple as that.

### MANDELBROT, FATHER OF FRACTAL GEOMETRY DIES

THIS POST IS DEDICATED TO THE FATHER OF FRACTAL GEOMETRY.

The father of fractal geometry famous for the Mandelbrot set has died. His preoccupation in life was to search for hidden order in nature, or so to speak, the beauty in nature and its infinity.

http://www.linesandcolors.com/2006/06/08/benoit-mandelbrot/

Born 1924 and passed away recently, he was just shy of his 86th birthday.

http://blog.makezine.com/archive/2010/10/rip_benoit_mandelbrot_1924-2010.html

May his soul rest in perfect peace.

## Tuesday, October 19, 2010

### EVERYONE LIKES A LITTLE MONEY, EVEN IF IT’S SOME FORMULA.

I was thinking about money and wondering if maths ever had anything related to money? Sure it does, I bet you.

Of all the four basic qualities of money, I think the maths you get to learn or enjoy or ask someone to do for you, has just three. So I call it the quasimoney property of mathematics.

They are: 1. It can serve as a means for payment of debts. 2. It can serve as a store of value. 3. It can serve as a unit of account between mathematicians themselves.

Payment of debts: although I’d rather not recall the barter era, but sometimes we do give maths lessons to some kids in order to offset some debts, not so? Like helping out a friend in a school because you owe him some money with some hours teaching students maths? I know some courts recommend maths lectures as a form of community service for payment of reparations. So, do not despair, your maths can help you in good stead.

But that is not too strong enough to give it money status. Quasimoney, you can agree.

Store of value: The maths you learnt and was acquainted with in high school or college will never leave you; it’s some knowledge that you’ll have for the rest of your life. Recently, while teaching some students maths, I drew from my twelve years old knowledge of maths. So, never despair; whatever you have is for life.

Unit of account: this is the last of the quasimoney qualities. Every mathematician can judge his knowledge against other mathematicians and against the problems he/she is able to solve. Sometimes, this ability is written out on paper in form of certificates, degrees etc. So, whatever maths you have can be quantified and qualified.

Maths is quasimoney. Believe me, don’t throw that knowledge away, even if you just need elementary algebra for your everyday work or the ability to do fundamental calculus. It can put some money, real money, in your bank account.

## Tuesday, October 12, 2010

### TWO HIDDEN QUALITIES I DISCOVERED IN HIGH SCHOOL MATHS

I have noticed that high school students who do well in maths have two admirable qualities I cherish: obedience and loyalty.

Obedience: Maths, at the high school level, is a subject of conventions and practices. It still is in even other levels. You get to learn the formula and use that formula for every and similar problems. Sometimes, if you have to learn a proof, you don’t have to trouble your head deriving it from scratch – just follow the textbook’s method.

Ever wondered why pi is the value 3.142 when the value can run into so many decimal places? Because that is what you are told it is in high school maths. Because somebody said the angles of a triangle sum up to 180 degrees and you have to accept it like that and you accept it! You see what obedience is! High school students good in maths carry this quality into their advanced years and they get to reap a lot of benefits from it.

Loyalty: or the act of fidelity; being faithful to someone, something or what you believe in. I have also noticed that high school students who are good in maths are loyal or faithful to what they believe in. Most of them tend to be leaders in youth clubs like the Junior Engineers, Technologists and Scientists (JETS) clubs, literary societies, maths clubs etc. They carry this trait into their further years. And unfortunately, in Nigeria, where there is a lack of educational and career counseling, they tend to populate the science classes.

Maths is a subject of faithfulness. If you want to solve a simultaneous equation, you have to stick to the method which is prescribed, whether using a graph, a matrix formula or deriving it by substitution and mathematical operations. 1 plus 1 is always 2 anywhere and everywhere in the world and you don’t have to bother why it is like that because that is the way it is calculated in maths; just believe that is so.

I have learnt a lot from teaching high school students maths. Really a lot.

## Wednesday, October 6, 2010

### Out of job again.

Wish I knew how to go back to teaching. Love teaching.

I wonder how many people are out there without a job.

Right now, thinking of doing commensalism with my parents. Wish they do not notice I won’t be contributing any money to the home, just making sure I wake up late, when they are out, watch the tv, if PHCN wants me to and do some home cleaning.

It feels so bad being out of a job. And for one I love really. Teaching Further Maths.

## Monday, October 4, 2010

### A student cannot be greater than his master.

I was sleeping yesterday when, after a religious service, the thought occurred to me: a student cannot be greater than his master. Right, yeah, I do believe that. But how is that translated in the maths? I wanted to know.

I was thinking about it when the thought of sets and subsets came to mind. I thought of all the maths problems I had solved and of my maths teachers , both those loved and hated; those feared and respected. I realized one truth then: The solution space of a student, any student, is a subset of his teacher’s.

The solution space of a student cannot be greater than his master’s. A student cannot do much maths, cannot solve more advanced maths than his teachers. One would never realize it unless you take the count yourself. I’d give a reward to anyone who can prove than he can solve more complex maths than his teacher? Excepting – exceptions are always the rule in life.

Excepting:

THE STUDENT HAS TO DO A CHANGE OF PARADIGMS. I recall this term from one of Steven Corby’s books. I think it was the “Seven habits of highly successful people?” Please forgive me if I am wrong.

So, how can we do a paradigm change in solution space and maths solutions.

1. By derivation. A derivation is like a creative activity. To be able to derive a solution space different from the teacher(s)’s, the student has to be a teacher himself. A derivation is like creating a complexity out of simple objects. But although this is a paradigm change, yet there must, I say, must still be taints of the inspiration and influences of his original teachers. So, there can be no total claim that the new teacher can have a solution space greater than his own teachers, just a more complex derived space.

2. Or By intersection. While still keeping the original solution space, by intersecting with another school of thought, a school of thought with a different paradigm, he can create a new solution space that is greater than his original teacher(s)’s.

But the two options above result in complexities and complexities result in more problems to solve. What if the teacher does not succeed? Then back to the original solution space of his teacher(s) is he/she going to be going to.

You see why I have to agree with that maxim: A student cannot be greater than his teachers?

## Monday, September 27, 2010

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

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 x

^{4}+ 4x

^{3}a + 6x

^{2}a

^{2}+ 4xa

^{3}+ a

^{4}. 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

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.

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

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?

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.

## Monday, August 30, 2010

### Even the Mona Lisa smiles behind the blackboard.

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.

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## Saturday, August 14, 2010

### The fear that is the Real Fear

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.

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## Friday, August 13, 2010

### The Eternal Question: who is God?

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?

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### 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: ax^{2} + 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.

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## Wednesday, May 12, 2010

### IS THAT A MENIAL JOB OR YOU DON'T JUST LIKE YOUR SALARY TOTALS?

I was in a bank recently and the guard at the gate, a tall handsome man told us: “We are challenged right now by the generator. Could you people please wait.” I smiled. I loved the image he was throwing out. I love that word, challenge, that I replied, speaking to myself: “you better beat that challenge!” And that is the mindset I have also when I face any task I don't like. I take it as a challenge, a challenge to be faced and won.

I'd rather any job or employment I don't like the pay totals be a low paying job, rather than a menial job. Anything but the menials.

If you think the work you are doing is a menial job, then you have started on a defeatist footing. You'll never like the work and you'll never work well.

Someone who keeps gnawing hard at a menial job, although unknown to himself, believes his self-respect has been invaded somewhat. He feels abused by his employer, who might be aware or not of that situation.

A menial job puts you in an endless mindless working trap that keeps you trapped!

Rather it be a low paying job you don't like. I'll never take a menial job.

If you translate the terms for your job, no matter the tasks, as low paying, then against the menials, you are working with a positive mindset. You can still see the light at the end of the tunnel. You think of improving, of doing something or going somewhere better. Remember, you're not the only one who is poor in a world where the poor are now counted in their staggering billions. You're just a unique individual who didn't want to work at a low paying job!

By calling that job description, a low paying job you don't like, you get to keep your self-respect and your employer doesn't have that tinge of conscience of being accused in the future of abusing an employee. You might even have to ask for a raise if you think you do deserve it eventually. But make sure, my brother , that you do deserve it.

So, next time you think of your work and the job you are doing, if it does not really put so much into your pockets at the end of the month, don't ever think it's a servant's occupation you are in, just wonder why you are working at a low paying job that you don't like. And go work on it so you can get that raise!

A happy working year.

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