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?

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wall-flower

Wallflower

I despise functions. Functions, social gatherings where people gather and meet each other. Functions where people walk around with fake smiles, talk to people they don’t care about, enquiring about things that they have no business knowing. Functions where fifteen people run around, ‘helping’ with errands that three people would comfortably finish. Functions where versatile ‘intellectuals’ have an opinion on everything from the political situation in the Middle-East to the quality of pepper used in the meat.

At one of these, I’m generally the wallflower.

I avoid people’s eyes as if they burn me. I’m scared of the smiles that pretend to recognise me, when I have no clue who they are. I am puzzled at the accusative looks that tell me that I am probably supposed to go help in moving a table that five people already have their hands on.

So I stand around, leaning carelessly against a wall or sitting slumped in a chair; blotting out the world around me. I stay there with eyes skidding across the horizon or staying rooted deeply on a pebble on the ground. I stay there, unobtrusively, and slowly vanish – like I am part of the furniture, like I don’t exist.
And the crowd around obliges – they move around, not noticing, like I am part of the furniture, like I don’t exist.

And I see people all around me, I can feel every one of them dearly wishing they could do the same. But a wallflower is more than they can take. So they unfold a newspaper and dig their heads into it, pretending to be engrossed. Or they pull out their cellphones and get busy tapping and swiping on them.
It’s as if everyone wishes to run away from the social commotion about them, needs an escape into their own respective secret worlds. However, the thought of being a wallflower terrifies them; the innocuous invisibility is a terrible plight in their eyes – so they shove away their phones, fold their newspapers, and start to move around; yet again, with bright smiles and outstretched arms.

And I sit there, not noticing them not noticing me as they move about. I sit there, like I’m part of the furniture, like I don’t exist.

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Obsessions

Our lives are defined by obsessions. They are always there, stippling the monotony of our lives with colours and motion.

They are there, an obsession or another; blotting out our consciousness, occupying the forefront of our realm of thoughts, at all times. A tight deadline you need to meet; the mindless game you feel the irrational need to play over and over; the train of tasks your objectivistic mind has set forth; the tormenting wait for a text message that you expect; your addiction demanding another dose of intoxicant; the face of the woman you can’t get out of your eyes—they vary in form and function, but they all manifest themselves as an inescapable, nagging presence; standing out boldly against everything else we try to indulge ourselves in. Remorseless attention-seekers, they are, begging at the loudest of their voices to be pampered, drowning out everything else.

They define, by their very existence, the sense and direction of our lives. Each day is shaped by the obsessions we choose to entertain, those we let live on, and those we try—often unsuccessfully—to stifle. Our obsessions make us who we are.

Whiteboard

For a while now, I’ve been contemplating about buying myself a whiteboard. While I was not under the illusion that a whiteboard in my room was somehow going to magically boost my creativity and productive thought; I was pretty curious, given the visual thinker that I am, what a large, solid drawing surface could do to help map my thoughts out. Thus, given that entry-level whiteboards where not prohibitively costly anyway, I decided to take a plunge and brought myself a 2’ x 3’ whiteboard and a couple or markers to test my hypotheses out.

Within three days of having the board on my wall, I find myself reeling for it quite more often than I had anticipated. First of all, the novelty of a whiteboard (I quite love the feel of the bullet-tip felt pen in the slippery surface) prompts me to write things a lot more often than I otherwise would. While watching a video-lecture, for instance, when I encounter a formula that I have a doubt about, I could pause the video and try deriving the formula myself until I’m convinced. Also given the pathetically absent-minded bloke that I am (worse, I typically go over a sum over and over wondering what’s wrong; without realizing that I’ve written 2 x 4 = 6 somewhere along the way), a whiteboard makes it easier to spot mistakes — I could just take a step back and look at the derivation, and in the second or third try, the error usually pops up to me.

Better still, I’ve started working away at problems (mostly insignificant fancies) that pop up in my mind randomly, problems which I would otherwise have put off indefinitely. With the whiteboard, I can now grab my marker when my mind starts to wonder, ‘why doesn’t anybody talk about an edge-list representation of graphs yet, where you simply store the list of edges’ ; I can instantly grab my pen and start working out the data structure and trying to build BFS and DFS algorithms on it until I’m finally convinced why it is a bad idea (there is little gain in the edge-list representation, most of the things the edge-list is good at, the adjacency list performs equally better; while the algorithms are slightly less efficient on edge-lists).

To sum things up, even though the whiteboard did not ‘magically’ boost my creativity, it did so to a non-trivial extend — mainly, it turned my otherwise lazy thought-process pro-active. I consider the whiteboard expense money well spent.

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.

The Irony of Logic

The Illusion of Black and White

Mathematical Logic is a queer field. Its ways are abstract yet rigorous, its results incredibly simple yet often surprising. It is also a much under-appreciated field – its concepts and results, besides being so fundamental to the mathematical formalism we are familiar today, is the only reason why we have computers.

Logic also is an ironic field, in fact, quite profoundly so.

Look around, look at the real world, in all it’s complexity and ambiguity; and try to frame a statement about it that is purely binary – a statement that is either True or False entirely, but never in between.

The world is not black and white. It’s really, really gray. – Joshua Topolsky

You’ll probably be surprised that you are unable to do so. The real world is never black-and-white, there is little about the world that fits an absolute “yes” or “no”.
The real world doesn’t afford the luxury of being so flawlessly deterministic. Things are often indeterminate. Physical quantities settle down at intermediate values. Things come in whole or part. It’s a whole mess of “almost”, “somewhat”, “quite” and “fairly”. Mapping this gray, gray world to an abstract, black-and-white model is seemingly a crude abstraction to make – almost shockingly so. In this regard, the entire field of Logic feels so badly grounded.

Yet here we are, with a profoundly developed field of study that frames a large bodies of our scientific studies and technological endeavors; yet is nearly diametrically opposite to what we experience in the real world. If this isn’t irony, what is!