Tuesday, 23 August 2011

Is Maths Hard?

Well, that depends on how you define hard. This article at 3 Quarks Daily talks about the fact that struggling with maths doesn't mean you're bad at it -- it means you're learning. I wholeheartedly agree with that sentiment and I wish more of my friends and classmates did too. For that matter, I wish more of my lecturers did!

The article goes on to say that anyone can appreciate the beauty of mathematics once they're past the initial hurdles. I agree more reservedly there. Perhaps everyone can appreciate maths, but that doesn't mean they will. I'm pretty sure I was the only kid in my class grinning like a fool when we proved the fundamental theorem of Calculus. Or when we started axiomatic vector analysis. Or when we did half a dozen other things that are pretty awesome, but under-appreciated.

Now I'll buy that some people can appreciate mathematics without grinning like fools; it's just not one of my particular talents. On the other hand, the fact that most of my friends gently but firmly point out that I must be crazy when I walk out of a maths lecture saying "That was awesome!"* is harder to overcome. There are a large number of people who pass courses called things like 'Advanced Calculus' quite well, but don't think that Calculus is awesome. And I don't just mean on the days when we have to integrate by parts three times, make an obscure substitution and remember the derivative of arctan(x) from eighteen months ago. Nobody I know or have heard of really likes Calculus on those days -- but hardly anybody seems to like it even on the days when we do epic proofs.

I could claim that I'm some kind of super genius wonder child, but did you notice how many times I used 'fool' up there? (There are more objective things that suggest otherwise too, but they'd be boring to go into.) I think it's far more likely to have to do with believing that maths is impossibly difficult -- or with something I haven't thought of. And so we come back to what you mean by 'hard'.

If hard means that you have to put something in to get something out, then yes, maths is hard (but so is nearly everything worthwhile, with a few notable exceptions).

If hard means that there will be struggling and use of intellectual stamina, then yes, maths is hard (but so is reading a good book).

If hard means that most people haven't managed to understand it, then yes, maths is hard (but so is, say, giving directions to my house, which most people couldn't do, although I don't find it desperately taxing).

If hard means that you'll only succeed by luck and that actually enjoying that success comes at the expense of being at all 'normal', then saying that maths is hard is nonsense.

You cannot use the first statement to prove that maths is hard, and then proceed to use the last statement to say that therefore you simply can't do it. Well, apparently you can, because people do it all the time, but it oughtn't to be possible. Maths is hard, but so are myriad other things that we learn to do and subsequently enjoy very much. Maths is fun.

Yeah, maths is fun. That seems like a good place to end. I'm not sure if this is coherent; there are so many mathematical ideas fighting for precedence in my mind that I'm not sure any of them have escaped, but at least I've tried!

Maths is fun.
*Yes, yes, I really do walk out of maths lectures saying things like that. Maths is not as horrible as people seem to think. It's kind of like art, but with less emphasis on being able to draw.
†See above re:foolishness and extrapolate to propensity for not thinking of important things as appropriate.

Monday, 22 August 2011


My Triffid and I
Er, I mean, Barberton Daisy! That doesn't have quite the same ring to it, somehow. Still, I'm very glad I have a Barberton Daisy and pretending it's a Triffid means I can be glad I have a Barberton Daisy at the same time I'm glad I have a pretend Triffid. (That kind of imaginative play is characteristic of early childhood? Really? I must be an early child then.) So it's two-for-one kind of deal.

Now I just need to apply that to the rest of life. It's quite exciting that we're writing code to model the Saturn V rockets used in the Apollo missions. Except that statement is only slightly more true than claiming I have a Triffid. Really, we're writing code that models certain aspects of the Saturn V rocket while simplifying others so that the end result is nothing like realistic. It still is an interesting project -- we really are doing rocket science -- but my Barberton daisy starts to look small and dull in comparison to a Triffid.

On the other hand, I don't really want to be handling code that's as temperamental as a Triffid, so maybe I'll stick to my little Barberton daisy project. In keeping with my early child tendencies, maybe I just need to pretend that my project report is going to my NASA supervisor. That lab report is actually a submission to Nature.

I just need to figure out why it is that I keep having to write undergrad class tests.

Sunday, 21 August 2011


"Remember the Sabbath day by keeping it holy."

So says the fourth of the ten commandments, which I rather think might be the hardest of the lot to understand. People may argue about exactly what constitutes murder, for instance, but there's widespread agreement that it would be a really bad idea for me to cut my little brother's throat, even if he is annoying. On the other hand, is it wrong to play sports matches on Sundays? To do homework? To go to work? To read anything other than the 'Sunday books' of Anne of Green Gables and the like? To skip church?

Some people will give me strong opinions on some -- or even most -- of those points, but it's difficult to find a consensus. Part of that, I think, is to do with the new covenant. Part of it is that we don't have a properly concrete understanding of what 'holy' means -- we get the general idea, but finding an actual definition that encapsulates said idea is hard. Part of it is that keeping the Sabbath holy might be even harder than figuring out what holy actually means.

My current opinion is that 'keeping holy' will look different for different people. There's probably a kind of Gaussian distribution of what's acceptable. I don't think it's great when people are so busy at work that they can't make it to church -- but maybe there are situations where the best way of giving the day to God is to go to work. I would never criticise somebody for going home after church to finish an essay due the next morning -- but I make a point of not doing that myself.

I think there's a great deal of good in my studies and the work I do for them. I also think that there's more to my life than those studies. Sundays remind me of that. When I make the rule that I don't do academic work on Sundays, I remember that. There is time to play with the kids at church, or bake for the family, or just to slow down enough to appreciate everything I have. It's not necessarily time that I think I have, but it's time that I can make. And maybe, hopefully, the more I make the time at all, the more I can make it specifically God's time.

Because it's enough of a challenge to make the time at all. Sometimes it seems like Sunday afternoon would be far better spent in getting a couple hours of work in on that tricky assignment. This semester it is oh-so-hard not to crack open my computational physics notes when I know that the lecturer of my seven forty-five Monday morning class loves spot tests. I don't think opening the file would be wrong in itself, but trying to reclaim the time that God has told me to put aside would be wrong. It's a kind of sacrifice. The first fruits of my week are going to God, not to my comp. phys. lecturer.

That's what it means for me. Maybe it would be different for everyone else. Maybe it's just where I am right now. It does make me realise, though, that something I'm tempted to dismiss as impractical is actually just hard. (It's hard for me, at least.) It makes me wonder what else we dismiss as impractical because we don't want to do it, rather than because it can't be done.

It makes me wonder how much we're missing.

Monday, 08 August 2011

Freewriting: Real Life

Because I can.

Because I'm not going to blog at all if I make too many rules.

Because real life doesn't come in chapters and stanzas, however much we may mould it into them.

It's people wanting me to explain the homework from courses I've never heard of. It's about planning to spend a morning doing computer science, but leaving your flash drive at home and arguing about CSS and open source software in the labs instead. It's about being thrilled that the Pottermore beta has opened, but too busy writing Mathematica code to keep up with all the excitement.

It's about wanting to study at Cambridge, but being afraid of moving halfway across the city. It's about being soon-to-move-out, but not changing your own light bulbs. It's about joyful abundance and mountains of homework being almost the same thing. It's about adoring mathematical physics in the same breath you call it an oxymoron, because no physicist can be mathematical.

And then it's about wondering if you really mean what you just said. About thinking that some physicists might be able to do maths and that enough homework to keep you busy might not quitebe mountains. About thinking you hold the world in the palm of your hand and that you'll never achieve anything; about confronting the impossible, the paradoxical, the unthinkable.

It's about something more real than our fragile, finite brains can dream up.