Category Archives: Math/Science

(Yet Another) Theory vs Systems Ramble

Theoretical research is like a mighty battle against a noble King. Your foe is not a ruthless warlord — he, on the other hand, is the master tactician that has seen hundreds of wars. He has a versatile and innumerable army, highly trained, unflinching and ready to make a kill when they have to.

Nevertheless, you can trust the king to not breach the rules of war. His army will take you head on, face to face, and you can count on them to fight a fair battle and not to backstab you. You can fight a fair, disciplined war, and count on your foe to do the same. You can even challenge the King to a game of chess and have the winner take the land.

However, you can’t get a mallet and bash your way through the army. There is no sidestepping and backstabbing the king. Your opponent is too good for that. To win, you have to bring in your best; bring in a clever, disciplined and dedicated fight, and hope to bring the King to your knees in the end.

Systems research is plenty different. It is like battling a ruthless werewolf. It knows no rules, other than to go for your neck. You are up against a mindless beast. Your tactics or strategies won’t help you here—only your instinct, and generous helpings of luck will. You’ll need to move fast and keep an eye behind you to survive.

However, killing the beast might be as simple as one simple, clean thrust of your sword right into it’s heart. The harder part is to survive till you get to make the swing.

The Hostel Lot Problem

I am about to join my Computer Science Master’s course in around 10 days. One of the introductory and how-to mails I received mentioned that hostel rooms are allotted by drawing lots. One of the hostels is a newly constructed block, which has slightly better rooms than the others. This situation posed an interesting problem to me: how to maximize my chances of ending up in the new hostel?

Or, phrasing in a more general way:

There are p lots, out of which q are winning lots (0 < q ≤ p). Contestants draw their lots one after the other. After drawing his lot, the contestant publicizes the lot that he has got, i.e. whether it is a winning lot or not. A lot once drawn is not returned to the box. What is the ideal time to draw your lot, so as to maximize the winning probability?

Continue reading The Hostel Lot Problem

An Extraordinary Genius

This evening, I was chatting with a good friend of mine. Not unlike usual, our topics of discussion started to take a rather interesting trajectory, spanning Nobel prize, the controversies surrounding it, Field medalists; until my friend told me about a “crackpot mathematician who developed with an ingenious method to solve differential equations”. I grew interested and wanted to know the mathematician’s name, and my friend obliged by dusting up his old textbooks. This man was Oliver Heaviside.

I fired up Wikipedia to find out more about the person – and in no time, I was stupefied by the scope and magnitude of the diverse accomplishments by this extraordinary genius. To cite the simplest example, the current formulation of Maxwell’s electromagnetic equations; as four elegant differential equations; was Heaviside’s accomplishment – which he reduced from twelve equations in twenty variables! This, coincidentally, is a single example out of his diverse fields of work ranging vector calculus, electromagnetism and electrical engineering, among others.

Oliver Heaviside is one of the most underrated scientists of all time, and probably, one of the most talented. I stand up in ovation to the extraordinary human-being, pioneer of large subsets of Mathematics and Physics as we see today.