All entries for December 2009

December 28, 2009

Popular Maths

Christmas is over, and a lot of us are presumably already enjoying our new presents. For me, no Christmas is complete without getting at least a couple of books, a present I always welcome. Lest I should sound like a total dweeb, I'd like to point out that I also wished for, and received, more standard presents. Still, a geek is a geek, and if you have followed my blog thus far -- or if you've had a peek at the 'About Me' section -- you may not be surprised to hear that I'm often given books discussing mathematical topics.

This year, however, I explicitly stated that I did not wish for any such books.

The reasons are twofold: First, it is a lot easier for me to decide which books are interesting and at the right level, and which books are too dull or too trivial. Additionally that means I can buy them second-hand, which saves money as well as paper. It is the second reason, though, that I want to focus on in this post. It may sound odd, but the majority of popular maths books that could potentially be a Christmas present, do not in fact target mathematicians like myself. Rather, they are meant to be enjoyed as gentle introductions to certain maths-related topics, to people whose main area of expertise is not maths. An appetizer, if you will. So whenever Iget one of these books, I always feel a little sad that whoever bought the book for me, did not buy it for him- or herself. 

Popular science books (books on popular science), such as Richard Dawkins' 'The Selfish Gene' and Bill Bryson's 'A Short History of Nearly Everything, are cropping up everywhere. Likewise, there are also plenty of popular maths books out there, some of which have received considerable attention and praise from the general public. Ian Stewart is worth mentioning in this context due to the popularity and success of his popular maths books, ranging from the serious, but still accessible, works ('Does God Play Dice', 'Letters to a Young Mathematician') to the more playful ones ('Professor Stewart's Cabinet of Mathematical Curiosities', 'Math Hysteria'). Then there are books which explore presents one concept in detail, but in layman terms (like 'Imagining numbers', 'Fermat's Last Theorem'), books which explore a wide range of topics on a superficial level (like "Why Do Buses Come In Threes?' or 'How to Cut A Cake'), books which give a brief introduction to maths in general ('Introduction to Mathematics'), and so on.  Not to mention the somewhat childish yet extremely enjoyable 'Murderous Maths' series. I have read many of these, and always find them agreeable to read, but when I'm confronted for the 55th time with a detailed presentation of the golden ratio, I can't help thinking: I shouldn't be the one reading this.

Stephen Hawking writes in 'A Brief History of Time':

Someone told me that each equation I included in the book would halve the sales

Most popular maths books are therefore written in an informal style and contains as few equations as possible, so as not to scare the reader. In fact, this is the main feature that distinguishes a popular maths book from a standard maths book. The author usually takes care not to lose the reader in his reasoning, and it is these clear explanations that sometimes make me realise: someone else should read this. I think this is where the problem lies. People think that any kind of maths is beyond them, and that they will never be able to understand or appreciate it. They think that what lies between the covers of those books is an inaccessible world, when in fact the content of such books is not the 'real' maths that university students are being taught, but a modified version of it, specifically designed to be understood by the non-specialist. My Algebra lecture notes are an example of a text that requires a certain degree of mathematical ability to read; 'How To Cut A Cake' isn't.

Please, come visit Mount Maths. It's a little lonely up here. But the view is incredible.

December 12, 2009

Open letter to the Vlogbrothers

Last time I wrote an open letter, it was addressed to the English people in general, and was meant more as a joke than anything else. This time, however, I have in fact written and sent a letter (that is, a short email) to John and Hank Green, and have decided to post it here as well, for your enjoyment.

A few words about the two: Hank and John Green, also known as the Vlogbrothers, are two American brothers (aged 29 and 32 respectively) who decided in 2007 to spend an entire year communicating to each other only through non-textual means. They called it the 'Brotherhood 2.0' project, and initially gave it two rules: First, any form of text-based communication, like e-mail and SMS, was forbidden. Second, every weekday one of them would post a video blog on YouTube to the other, whereupon the other would respond in a video blog the next day, and so on for an entire year. The Vlogbrothers soon gained an unexpected number of followers who were subsequently dubbed Nerdfighters, as in "someone who fights for Nerds". Although the Brotherhood 2.0 project ended the 31st December 2007, the Vlogbrothers still regularly post videos on YouTube. Recurrent themes in their vlogs include: Promoting the idea of being an intellectual (hence the 'Nerdfighter' label), donating money to charity, and adding "in your pants" to book titles for hilarious effects. The videos are often somewhat interactive, asking the viewers to help the Vlogbrothers with a search or to participate in a good cause -- like, for instance, -- and the acronym 'DFTBA' ('Don't Forget To Be Awesome') is frequently used as a reminder of the resourcefulness and creativity the YouTube followers have displayed. DFTBA has now become a popular abbreviation in the Nerdfighter community.

The email I sent to Hank and John is an example of what is known as 'constrained writing'. Constrained writing, as the name suggests, is a piece of writing like any other, but submitted to certain constraints. A classic example is George Perec's 300-word novel "La Disparition", written without ever using the letter 'E'. I will not reveal what the constraint is in my letter, but hopefully it will be obvious. Here it is:

Dear Fraternity

Title be Alexander, devoted fan. This being, Alexander delightfully followed the brothers' astonishing display 'f textless brotherhood. A double fortnights' time ('bout)  ago, Discovery Fortuitous (through bloke: Alex Day). From then, been active, darting fast through brotherhood animations. Done! From the beginning all down! Finished! Thus, became a dedicated 'Fighter.

Two brothers are -- Darn, for the best adjectives disappear from the brain. Altruistic; deep; funny; those become alluding descriptions for them, but are desperately failing to brotherhood adequately depict. For the bestselling author + ditty fabricating, treehugging brother 'Ank: durable fanfare that beautiful appraisal delivers, forever! This, both assuredly deserve!

Following things be Alexander's destined future: To buy amazing discs! Fie! the books also! Duo Fratres Triumphabunt!


The D's were a pain.

December 07, 2009

Frustration in Games

The following ideas are based on an innocent article I read years ago, but which has been stuck in my head ever since. I will be talking about games, and when I say "game", I'm referring to word as it is used in common speech. It can be solitary or involving several players; it can be a board game, a video game, a verbal game, and so on; but it must be something we play for fun, not for personal profit.

What makes a game a good game? Which aspect do all fun games have in common? What force drives our attention to the game, and keeps us motivated, addicted? I am not trying to give explanations as to why we have personal preferences, rather I want to make a conjecture about why the popular games have become so, and why many other potential ideas for games, while technically "games", would never be considered fun. So, in general, why do we like the games we play?

The answer, when you think about it, is less obvious than it would seem. Let's review some possibilities. Is it the chance that we might win, that motivates us? Partly, but consider a game where you win with absolute certainty. Surely such a game presents no interest whatsoever! The possibility of winning is naturally a crucial element in any good game, but the ability to win is, in itself, not what makes a good game. Is it the social aspect, then, the fact that it is a peaceful and relaxing way of interacting with other people? That, again, is a common trait in many games, but games like Sudoku, Crosswords or Minesweeper are also found amusing by many, and those games involve no human contact. The simple observation that it makes us forget the worries associated to our daily lives? This may very well explain why we play games in the first place, but not why certain games are generally found fun, while others have never seen the day of light.

My claim is that what keeps us attracted to certain games, is the element of frustration.

It may sound contradictory at first, but think about it. In almost every game, there is a rule which restricts you moves, blocks your play, or limits your abilities in some other way. Consider for example chess -- I will use chess as a recurring example throughout the post. Already, most of your pieces cannot move in any way they like, and to complicate things further, your most powerful pieces are initially stuck behind a row of slowly-moving pawns. The same kind of restrictive rules seem to apply to most other games I can think of: in Risk you lose men quickly, but regain them very slowly; in SET, the cards have to match in a very specific way; in Minesweeper you are only given partial information about the grid; in the well-known online Helicopter Game, green blocks constantly obstruct your way. All this contributes to the element of frustration, the feeling the game will not allow you to have things your way. And this might well be the secret little ingredient that will make you come back for more.

Now, some may argue that such restrictions are necessary, in order to make it non-trivial to win the game. But while this is true to some extent for single-player games, it does not hold when two or more people are playing against each other. Imagine a hypothetical variant of chess, in which most (if not every) piece would be allowed to move and capture like a queen. This is an "improvement" from standard chess, a removal of restrictions, but both players should still find it difficult to win, as both players will be following the new rules and thus none of the the two should have an advantage over the other. Likewise, in any other multi-player game, removal of restrictive rules should not necessarily facilitate a win. But still, what we see is that all but every multi-player game has rules that cause frustration of some kind. Not just irritation at the other players' behaviour, but also annoyance at the difficult position in which the rules themselves have put you. Who hasn't been frustrated because they were stuck in a puzzle game, or moaned at the lack of cards in your hand during a card game, or cursed at the sharp turns of a high-speed racing game -- and yet, kept playing? Regardless of what your favourite game is, chances are it has frequently caused you to feel angered, or at least slightly annoyed.

For every game there is, it is possibly to think of a less frustrating version of the same game. And still, the final product turned out to be what it is. For some reason, this unforgiving aspect of the rules makes a game more interesting, and the games with innocent and non-irritating rules, like War or Rock-Paper-Scissors, bore us quickly. There must, of course be a reason for this, and although I'm no psychologist, I think it;s safe to say that it is linked to the pleasure gained from overcoming a problem. If the game is harsh on you, you may feel a certain sense of achievement after winning, whereas if the game doesn't In a game involving multiple players there will of course always be the pleasure of having beaten the others, but an extra reward is offered for enduring, and beating, the game itself.

A final note: I'm not saying here that the more frustrating a game is, the better it is. What I mean to say, in a nutshell, is that every good game needs a certain degree of frustration incorporated in the rules. The art of making games, is finding this correct balance.

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