Happy Birthday Évariste Galois

Happy Birthday Évariste Galois

A ‘few’ years ago, I ‘explored’ a mathematics seminar on Galois theory at university. Though they spoke English, I knew I would mostly hear mathematical Greek. But for a few Greek words that filtered into the English language, I would’ve left there grasping nothing but the atmosphere of mathematicians having high fellowship with one another; it would’ve been only an anthropological experience.

I recall Vague pictures of a four year old hand trying to span an octave while playing a piece on a piano. That was on CNN, years ago; a little maestro in the making. He made the octave in two steps, and it was beautiful. That wasn’t the ideal, or the perfect, but he went around the task excellently like children know to do well. He must have had, at the very least, a good teacher, and some motivation.

(And we praise children for their efforts, above and over the results they yield. As they grow older do we come to focus on results far above effort?)

“I had given to Moscow high school children in 1963-1964 a (half year long) course of lectures, containing the topological proof of the Abel theorem.” That was a statement by V. I. Arnold. These students, I suppose, were teenagers like Évariste when he started writing fantastic mathematical statements about our reality. A good teacher with the right perspective and proper organisation can teach some ‘high-end’ university level courses to high school kids.

High school is currently designed as a preparation and ‘selector’ for tertiary education. As currently formatted in Nigeria and many other countries, it has relatively little merit by itself. Enough university courses could be ‘downgraded’ to high school level when we think about it. Why not skip the ‘preparatory’ period, for amenable programs, and send the children straight to the degree.

If we say that high school education need not be a prerequisite for some university courses or degree programs, we mean, for example, that one could go from primary school to an MBA in six years tops. (Teeneage years better spent?) This is more easily workable if we have truly knowledgeable teachers; who can actually help the young ones learn, and who see and assert that high school students can handle more than the current standard.

Topology doesn’t sound like something that currently features in the regular high school curriculum. You’d more than likely find it at university only. But they can learn it and a few other big things earlier. It now perhaps depends on whether thats in a (direct) route to were they want to be.

Abraham Lincoln is said to have said that we’re only as happy as we want to be; it is in the same spirit to say that we’re only as knowledgeable as we want to be. But the right guidance and motivation is helpful and serves to accelerate progress. Kids would be smarter if we trained them to be smarter. (There’s a saying that an husband and wife parent a child, but the whole community raises him.)

Galois’ work in his early years are one reminder that teenagers could be trained to handle ‘much’ more than the certified curriculum designed for them. While Évariste was an outlier, that he did what he did as a teenager is telling. And there are many other examples. V. I. Arnold’s teaching Topology to high school kids says that it’s more a matter of organisation and presentation than difficultly for the age-group or grade.

Born October 25, 1811, he died about 20 years later with a legacy that was said would fill only 60 pages. For the significance of his works, Évariste Galois’ sixty pages were worth a PhD and more.

pS:
To find out more about Galois’ interesting life, visit:
www-groups.dcs.st-and.ac.uk/~history/

Advertisements

Better Clever than Brilliant

It isn’t the brilliant people that get the best results,
It’s the clever people that do.
Brilliant, is what we are;
Clever, is what we do that is wise.
But, neither, is who we are,
Even though we might be brilliant and/or clever.

If you have to choose between the two,
Choose between the two:
To be both brilliant and clever.
Neither precludes the other;
For both can be learned.

What we do can make us look brilliant, or not so;
What we do is what makes our lives.

It is the job of parents to bring their kids up into cleverness;
It is the job of ‘education’ to help make everyone cleverer;
It is the job of him who can see ‘truthly’ to follow cleverness.

Where is the place for brilliance in life?
Where is the place for brilliance, or beauty, in a ‘good’ life?

Footnote:
I hope the sense of ‘truthly’ makes sense. What ‘normal’ word could’ve been sufficient?

Thank You—March 2015

Thank you for my teachers
Those that stood out
And all the others
I had to learn from every one of them

Mr Maxwell in primary five
One big black Ghanaian
I’d top your class that year two times

Thank for the opportunity to serve
To grow these ones
It had felt like a drain once or twice
I’m sure you can guess why
For the joy I hoped for
The cross was nothing and heavy at the same time
It was the case that you helped me in it

Thank you to my students
I have loved every one of you
Imperfect though I was
I learned as we went along

Thankful that you had something for me
Grateful that I could add to you
I am the better for knowing you

Teachers honour roll:
Mr Maxwell, Mrs Ariba, Mr Eze, Mr Ibironke, Mr Kayode S.G., Engr Eziashi, Dr Anyaeji, Dr Brown …

A rehash of Beer’s law

Beer’s law (1852 by August Beer):
It relates the absorption of light to the properties of the material through which the light is traveling. (http://en.wikipedia.org/wiki/Lambert-Beer_law). That is, how well a student absorbs academic material, per topic, per time, or how much alcohol the liver will take at any specific time.

Beer Lambert Law in Solution

Beer-Lambert Law in Solution

Specifically, it is the physical law that states that the quantity of light absorbed by a substance dissolved in a non-absorbing solvent is directly proportional to the concentration of the substance and the path length of the light through the solution. (http://en.wikipedia.org/wiki/August_Beer).

Beer's Law

A is the measured absorbance (of the brain or liver etc).
ε L.mol-1.cm-1 is molar absorpitivity. The wavelength-dependent absorptivity coefficient, a function of the level/rate of understanding and comprehension, focus, attention and distraction.
l cm is path length of the sample (material),  a function of volume, presentation and pedagogy.
c mol.L-1 is solution/analyte concentration, a function of frequency and/or material concentration.

Then a saturation (can’t take this any more) point might come, or the above law break down, like when a stretched rubber (stomach or liver?) refuses to go back to its original length having been overstretched, thus distended (re: Hookes law of elasticity).

 

PS:
Reference also made to the Android app, Techcalc, by http://www.roamingsquirrel.com/calculator.html

Pictures from Wikimedia commons (File:Beer Lambert Law in Solution.jpg, File:Beer’s Law.png).