Tuesday, February 18, 2014

The Adventures of Professor Oliver and the Principle of Uniformitarianism

Professor Oliver read the student's answer. The student had not deigned to fill in any of the blanks; instead, he had opted to scrawl the phrase "THE PRESENT IS THE KEY TO THE PAST" repeatedly, haphazardly, and in big bloody letters across the page. Hnph! Professor Oliver snorted, evidently unimpressed. Nevertheless, he relented and gave the student one point for sympathy.

Saturday, February 15, 2014

Tuesday, February 11, 2014

The Adventures of Yusuf Al-Muʾtaman ibn Hud and Giovanni Ceva

Wrote the great Yusuf Al-Muʾtaman ibn Hud, the King of Zaragoza, in his magnum opus, the Kitab al-Istikmal: "... Thus, I have proven that if these three ratios on the triangle give a product of one, then these three lines in the triangle meet in a point!"

After having read this proof, the scholars in his court exclaimed: "Truly, this is an important proof! O, great King Yusuf Al-Muʾtaman ibn Hud, you are indeed called the Sage of Zaragoza; your name shall be spread far and wide, even down all the generations!"

Six hundred years later, in a dusty university room in Mantua, the Jesuit Professor Giovanni Ceva realises, with a serendipitous spark of inspiration, the same truth that had been discovered by the great Yusuf Al-Muʾtaman ibn Hud. He publishes it and we now name it Ceva's Theorem because his name is easier to pronounce.

Friday, February 07, 2014

Adventures with Brahmagupta and his Algebraic Proof

Question: Prove Brahmagupta's Formula i.e. that if a cyclic quadrilateral has sides a, b, c, d, and semi-perimeter s, then its area K is given by (...).


Professor's commentary: Everything is correct here. However, the proof is not very interesting as you have opted to prove it algebraically rather than with graphical explanation. In fact, it is really boring. In fact, my cat has just thrown up on my trousers and then died out of boredom after having read your proof. I am enraged! Zilch marks for this assignment.

Saturday, February 01, 2014

Wisdom of the Ancients

The people of the South were a great civilisation, mulled the Witchdoctor. Indeed most of us here today have our lineage going back to somewhere from the south. That was when there were more people living south of the Arctic circle than there were to the north of it. And there he collected his thoughts and nodded to himself as if making a conclusion. Yes.

Did you mean, asked the young man, that at some point, the Taimirians were not always Taimirians?

Yes, yes, said the Witchdoctor. I think if you went south from here, into the desert and just keep going south, eventually you will reach where the Chinese people used to live. Are you a Dungan, son?

Yes, replied the young man, I've been told as much by my mother.

Then you should know the Chinese. The Dungans come from there. All Dungans do. Have your parents told you that as well?

That is nonsense, scoffed the man. The Dungans have always been in Taimiria, we were never been to or lived anywhere else. That was what we were taught!

The older man smiled cryptically. Doesn't it ever trouble you that you Dungans look awfully similar to the people in Lena?

The younger man stood up, obviously displeased. If all you would do today is to heap abuse on me and my family instead of telling me something useful, I think I should go and consult some other sorcerer.

At least sit down and finish your tea before you go, you hot-blooded young man, replied the Witchdoctor soothingly. The other wizard will be telling you the same truth about the Southern peoples, if that is what you ask for. Do you know why when a boy is determined to become a Witchdoctor or Engineer or any other sort of magician, they send him somewhere far off and forget about him for twenty years? Do you know why some of us is so reluctant to speak like a normal person when asked a question? It is because that the truths are so difficult to accept by commoners like yourself that we have learned to behave this way. Are you going or not?

The young man sat down, still fuming. You're not going to expect me to believe everything you say, are you?

No, I cannot, said the Witchdoctor. You are not a wizard. The wizard truth belongs to us, is believed only by us, and only we can make good use of it. All you need to do is to enjoy the fruits of our work, but if you are curious enough to pry into them, maybe you should become a wizard yourself! 

I am a witchdoctor of this tribe. I am a wizard who can heal the sick; indeed I am trained to do so. When I was a novice, my training stint started in the college at Archangel, a city of two months' journey away in the west, perched cosily by the Little Ocean. For the first four years, each novice learns the same things. Quite a lot of it is basic, layman content, like bridge-building. Others include electric arts, biomancy and piezotics, which are not. We learned Algebra, which is a language that all novices learned to use, but no one has ever managed to learn to speak, because this language is so arcane that it is much easier written than spoken, and I think that it is only possible to write it.

And why do you use such a language, when instead you can just choose a dialect that most people speak? asked the young man.

Wisdom of the ancients, son, the Witchdoctor beamed. The Southeners know what they are doing. Algebra grants an instant path to enlightenment the way the commoner's language can never do. A wizard armed with Algebra can outperform a diligent town council in tasks such as erecting a monument or predicting the weather, even finding the best price for furs and spices in the market... that is, if the people there would be so kind to let him do it.

If there were such a tool so powerful as you say, why should you tell it to me, an outsider? Would you or any other wizard keep it to yourself, to secure yourself an advantage? The young man asked.

It is not teachable. The Witchdoctor shook his head. I have heard stories of wizards being extorted to pass on the secrets of Algebra to one of the local kings. None what they taught him could retain for any length of time; the king forgot it as soon as he woke up the next day. You could imagine his rage. Silly man, he killed them all for nothing. So I can teach you and I am quite sure it will be futile. That's unless you can understand it, but in that case, you would be a wizard now.

Seeing the incredulous look on the younger man's face, the Witchdoctor continued: The wisdom of the ancients. That, young man, was the way of world a long time ago. Everyone knew some of the wizard truths; that is to say everyone was a wizard. It was by magic that life was brought to inanimate objects that laboured away for humans, leaving them to the more savoury pleasures of life. It was by magic that the agrarians' crops could grow reliably, year after year, so that no one starved to death because of drought or disease. But alas, it was not long after when the desert came and swallowed everything, and cities were slowly abandoned as the edges of the sand seas passed over them. If you went far enough south, you can still see those empty husks of the countless great towers and bridges that belonged to the old Southerners, and you would understand that what wizards can do now is but a small sliver compared to what those people were capable of.

The young man furrowed his brows for a good while, trying to take it all in. Finally, he came to some semblance of a reckoning, and interrupted: And the desert, that was something you couldn't magick away, what with all the miracles that the ancients can pull off?

No, laughed the Witchdoctor. We couldn't magick the desert away, even the wizards who are the best in deserts. It must have been impossible to do, because not even them could do so much more than impede its advance for a short while.

The Witchdoctor leaned back in his seat and heaved a long sigh. We used to be gods! What could we not do back then? The great empires of the Russians, the Chinese, the Indians, where are they now? All dead, scattered, forgotten by their descendants (He eyeballed the young man pointedly) who huddle around a stale lake and cannot think ahead for a day beyond tomorrow...

I have no idea what they put in your heads in Archangel, but I don't believe a word that you have just said, the young man remarked. But it makes for a good story, so thank you.

The old man sat up in alarm. Are you going so soon? You would like some more of my tea; I am sure of it!

References: Taimiria (region) / Lena (region) / Archangel (city) / Dungan people