We all know that the shortest distance between two points is a straight line. The equation for a straight line is really simple, isn’t it? y = mx + c, where m is the gradient and c is the y-intercept of the straight line.
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.
EVERYONE LIKES A LITTLE MONEY, EVEN IF IT’S SOME FORMULA.
I know it’s a truism: everyone likes money even if some sage tells you not to be greedy for acquiring it. Money solves so many problems. Lots, I must say. Without money, we’d be doing trade by barter – one pair of your trousers for half olodo of my garri? Whoever thought of the idea of cowrie shells and money did solve mankind lots of problems.
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.
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.
TWO HIDDEN QUALITIES I DISCOVERED IN HIGH SCHOOL MATHS
Have you seen a good student in maths? Then, you’ve seen a bright, sharp eyed, well dressed and admirable personality. Indeed, students, I have noticed, who do well in maths, tend to on the average turn our with better personalities than others.
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.
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.
Out of job again.
I am out of job again. Very funny how the unemployment net keeps getting me caught. Have lost my job teaching beautiful high school student Further Maths.
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.
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.
A student cannot be greater than his master.
There is no count to the number of lessons we can learn from the simple formulas found in our maths.
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?
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?
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