probability zero is not impossible, or is it

Last night at the ol' quizzor, the question arose:

Suppose identical twins marry identical twins. Will their children be identical?

the answer they were looking for was 'no'. The answer I put down was 'maybe, but it is very unlikely'. We were marked wrong - but given a bonus beer (small consolation at the time, but finishing 3 points clear at the end meant it was an ideal trade). The quizmaster's defense? 'it is no more likely than you being identical to your brother!'

In fact, it's half as likely (given that I'm male and so is my brother we've got a little extra chance built into the formulation), but both are still possible. Yes, they're unlikely: but the probability is positive.

That led me immediately to thoughts of the difference between 'probability zero' and 'impossible'. Despite what you were told in school they are not one and the same.

Choose an integer at random. Assuming you can do such a thing (not a very reasonable assumption....but whatever), the probability for a specific integer is zero. Not 'very small', but zero. So every event has probability zero - and so whatever you chose had probability zero. It was impossible, and yet it happened. How miraculous.

There are plenty of cases in mathematics where this comes up, but very few in the real (ultimately finite) world. However, too many people take this real-world intuition and drag it, kicking and screaming, into the abstract world and treat it as fact.

`Unaustralian' is unaustralian??

In an odd turn of events I found myself watching Lateline last night. Why is this odd? Because I hate so-called `serious' current affairs, and don't care to watch the schoolboy bickering of middle-aged millionaires.

But tonight it was about SPORT! So I made an exception. Specifically, it was a discussion of perhaps the biggest story in Australian sports history. Big enough that it made me care for a fleeting moment about Rugby League. Bigger in some sense than Tiger Woods, and bigger in every sense than the Starcraft Betting Scandal.

For anyone out of the loop, the Melbourne Storm was caught engaging in rampant salary cap breaches and covering it up. They were punished about as harshly as they could be, short of cutting off all the players' feet. They were stripped of two premierships, three minor premiership, and any chance of making finals this year.

The discussion was interesting and led to deeper questions: how did the NRL allow them to get away with it for 5 years? More important, were the players oblivious, or complicit?

But one thing stood out to me. A former NRL Player Warren Boland and the ABC sports dude (just made a freudian typo, and called him a `dud') Peter Wilkins - no, not the Entertainment Guru who falsely accused Jeff Goldblum of dying last year - came on to discuss it.

PETER WILKINS: Yes and there was a sad irony tonight. Just before the Footy Show on Channel 9 they're promoting the Anzac Day NRL matches involving the Melbourne Storm, they're talking about Australian values and sacrifice in this ad and then here we are with something un-Australian, something slimy, something underhand.

I got an australian value for you. PISS OFF. How tired can one sentence be? Not only does it misuse `irony' and use that old chestnut `unaustralian', but name-checks the ANZACs, the ol' diggers. Well done old man, you're officially out of touch.

Can the word `unaustralian' be used without irony? Maybe if you're talking to a 55-year-old CWA member who's too busy running her B&B to actually think for a second about what an `australian value' is, or a Young Labor/Liberals/Family First kid who's too afraid to call you out in case he ends up looking silly because nobody else has the guts, either.

Well I'm neither of those things. GRAGRARHG

One Quarter

It has been precisely (enough) three months since last I wrote here.

For all the hectic nature of the year's end and the new year's beginning, it's all so structured that it flies by and there's little room for anything but experiencing it. For those wondering, it was pretty good. Pretty standard, which means pretty great. I love Christmas.

I started playing squash once a week, and rediscovered my nontrivial anger problem. The good news is I'm better at it, and I'm able to keep it on the court. For now.

Music makes me happy (or 'time for a very conventional blog post')

I tried to count my passions the other day. They are few, and they are intense. On the other hand, they are myriad and they are shallow and transient. But a few endure, and one is music.

I love a more wide variety of music than most people. It sounds arrogant but I truly believe that. When most people say 'oh, I love all music', it comes with a caveat. 'Not that bloody rap music'. 'Not country'. 'Not dance/trance/techno/classical/jazz/gay shit'. But I love it all. Even the gay shit.

These are not my top five songs, just the first five that entered my head as I type this.

When The Saints Go Marching In - Louis Armstrong

Ok, I lie. This one probably is my favourite song ever (it helps that he describes his drummer as a 'little filipina boyyyy'). It also ties into one of my other enduring passions!

I have a huge hardon for dixieland, especially satchmo, who makes the most simple melodies so so great. Love that dude. His duets with Ella Fitzgerald are breathtaking.

Everyday I Have The Blues - John Mayer Trio


Of COURSE I got John Mayer in here. Those of you who know me (should) know he's my favourite artist. If you don't know why, then you don't know John Mayer. He fills my appetite for hardcore blues, hardcore guitar playing and seriously, seriously softcore pop. This one, from the live album 'where the light is' contains my second-favourite guitar solo of all time.

Keep an eye on his face when he plays, it's hilarious. And please ignore the terrible grammar in the title.

Little Secrets - Passion Pit


This band caters only to my love for pop. Also to my primal love for percussion mixed with high-pitched singing. That's why it succeeds: serious bass and serious treble, with a real trough in the middle. Their entire catalogue is superb (it's still small though...).

Strawberry Swing - Coldplay
http://www.youtube.com/watch?v=BYtk1Z0UUuE&feature=fvst

Embedding's disabled and I can't be arsed figuring out how to finagle it, so click the damn link already. The video's neat, but the song is neater. If you don't like Coldplay, you won't like it. But then I don't care what you think if you don't like Coldplay.

Concerto For Orchestra Movt 1, Introduzione - Bela Bartok


I know, I'm trying to make myself classy by including a classical (um...not classical!) work. But I legitimately love this song, though I don't feel equipped to describe why in any great detail. Certainly not without more time and a bit earlier in the day, perhaps.

whyyyyy

Someone recently asked me the age-old question of why the hell i do maths. Why should someone care about all of the useless crap I care about?

Do I care about it simply because it's for my qualifications? I don't think so, or I'd be doing something else. Mathematics is not something you choose to do for the glamour, power, or money.

Is it because all the people around me care about it, and I'm just mimicking them, like the new kid at school who pretends to like the same music as the cool kids and ends up loving it? Like the showbiz kid who's pushed into singing by his crazy parents and ends up needing the spotlight as much as his mum needed him to have it?

I hope not. But I can't truthfully answer this. Maybe I'm just part of a big club that happens to (barely) fund itself and make careers for its members. If it's the case, I'm not all that bothered: it's a freaking fun ass club to be in.

Is it because I was the smartest kid in the room all through primary school, and I need to hold onto that feeling? I *seriously* hope it's not that.

I hope, though, I'm in it for the fun of it. For the so-called `quest for knowledge', even if we make up the questions. The feeling you get when you beat Rubik's Cube for the first time, or solve a riddle and see how everything fits. That's mathematics. See the pattern, prove it's there. Find out why, if you can. Prove it.

If someone figures out a way to make it useful....good for them.

an early night

There is nothing for the self esteem quite
so helpful as an early night.

Though sleeping early suggests a dearth of things to do tonight,
there's nothing on this earth so right
for making one feel in control
like everything is under control
as an early night.

For in the morning you may sleep
like today's Sunday, last night a late, late Saturday night,
but upon waking look at the clock to see it's not eleven, twelve, one,
but only seven
and the day has just begun.

Writing things Down

Corrently I'm supposed to be writing a paper about matrices. Of course, writing down things that are obvious to me (only because I've been steeped in the theory for nigh on six months now) in a way that makes people gain both understanding and self-esteem (the true goal of any writer is to make the reader feel good about themself)...is not easy. Nor is it especially stimulating (with rare exceptions).

Here I sit, then, alone in my office. Type type type. Do not pity me, for it's Better Than A Real Job. It's ostensibly my dream. I suppose with every dream there comes a reality which is never the same, for when we dream we're not practising prediction but hope.

So I keep plugging away, safe in the knowledge that "I have perspective!". The mental acrobatics I perform to convince myself that I, in fact, LOVE typing and retyping this definition so that a chimpanzee could understand it, but a genius doesn't feel like I'm talking down to him. I can't please everybody, but I'm asked to. So I will just try my best, once again safe in the knowledge that in "perspective", I'm actually not that bad at it. Or rather, that I'm lucky enough to have English as my native language.

I gotta get back to work