The Scotsman explains “Why 47+16+2 > 65 could be Salmond’s favourite sum”. Shouldn’t that be 47 + 16 + 2 = 65? (You don’t need to be an economist to work this out.)
Archive: mathematics
Is handwriting really needed any more? Kids around the world are forgetting how to handwrite — because all of the writing we do is on the computer. It’s a familiar story. Every time we went back to school after the long summer break, my friends and I would all comment that the most difficult thing was getting used to writing again. “I haven’t had to write anything for about two months!” So every year our handwriting would get a little bit worse.
That wasn’t just because we were using computers all the time. It was just that there really isn’t much need to write at all is there? The only thing I can think of is letter writing. But how often do you do that? Once a year, if that? Maybe, back in the day, people wrote letters to each other. Nowadays people keep in touch by IM or text message. Or, if you’re really old-fashioned, by email. No need to lift a pen.
It’s sensible for me just to avoid writing altogether because my handwriting is a complete mess, and it has been probably since I started secondary school. My lowercase letters are all over the place. If I’m not careful, my ‘b’ looks like an ‘S’, my ‘a’ and ‘o’ both look like an ‘e’, my ‘i’ looks like an ‘l’, my ‘g’ looks like a ‘y’, ‘m’ looks like an ‘n’. And ‘v’ and ‘u’ look exactly the same.
The article says, “Teenagers are still experimenting with their handwriting and trying out new things”. The shocking thing is, I’m not a teenager, and I’m still experimenting with my handwriting. I could cope with all of the other things because I could understand myself what I was writing. But when my ‘v’ and ‘u’ began to look the same I had to take action. In the past couple of months I’ve actually added on a tail to my ‘u’. I never used to add tails because I thought they were a waste of time. Now they are how I tell a ‘u’ (or a ‘U’) from a ‘v’ (or ‘V’).
It became necessary because a lot of the equations I have to use at university involve a u or a v — often in the same place, meaning subtly different things. But I can’t be confusing them or I will get myself… well, confused. At the same time I’m coping with how to write Greek letters. Before it was just π in maths and the occasional μ in physics.
Now, in economics, I have to grapple regularly with Σ, θ, δ, γ, α and the dreaded σ. When you’re struggling with the Latin alphabet, the last thing you want to do is work out how to write a σ (my ‘σ’ actually looks like ‘δ’!).
Whenever I have to handwrite a note or something, I always write it in all capitals. Not print, though, because I am such a lazy bastard that I can’t even be bothered to write neatly in block capitals. My capitals used to be neat — when I was in primary school. But when my lowercase letters became illegible and I moved on to using capitals instead — well, of course my capitals became illegible as well. Nevertheless, it is the least-worst option. Although I always have to apologise and explain that I’m not shouting!
I don’t have a signature either. Well I do, but it’s basically just a scrawl. I’ve tried practicing writing my name, but I think I am actually physically incapable of doing it. It looks kind of like “D____ Sl_____”. Distinctive, in a way, but it’s just a scrawl. Some people are genuinely shocked by my signature.
Despite my uneasy relationship with handwriting, I find it absolutely fascinating. It’s interesting to note how different people can take such radically different approaches to writing the same symbols. My friend and I had a discussion about somebody else. I just said, “I like her ‘a’s.” My friend thought I was using some kind of secret man-code euphemism. But no. I genuinely like her lowercase ‘a’.
Maybe that’s why I don’t have a girlfriend.
If you’ve ever wondered why more and more pupils are passing exams, yet the British public remains as boneheaded as ever, you need look no further than this report.
Too many schools are “teaching to the test” in mathematics, stifling genuinely stimulating thinking about the subject, a report suggests.
The report is wrong. In actual fact, every school “teaches to the test” in every subject. There is no genuinely stimulating thinking about any subject going on in schools. That is the inevitable consequence of having exams.
I am going to use the example of one subject here, but you could talk about all of them. Looking back at school, none of us learned any physics. We were all taught how to pass a physics exam. And when you’re being just about constantly tested from the start of school to the end that can take up a lot of time. It took up so much time that there wasn’t any time to actually learn physics. All our effort was geared towards passing the exam at the expense of actually learning something.
I’m not complaining. As I said, it’s inevitable when all that matters is not what you learn but the grade that’s printed on a piece of paper. As a result, pupils only want to pass the exams and teachers only want the pupils to pass the exams. It is not at all unusual for a pupil (or a student at university) to ask, “Do we need to know this for the exam?” And it’s not unusual for a teacher to say, “You don’t need to know why this is the case. You just need to remember it for the exam.” You can’t blame pupils or teachers for that.
It might not be such a problem if there was only the summer exam to worry about, but some wise guy invented the Unit Assessment, which are spread out across the entire year. And then there are prelims. The whole school year is geared up towards these peaks of activity and there is no time to worry about anything else.
It’s not just about drumming home the parts of a subject that are in the curriculum. There is the dark art of question spotting. At my school the Modern Studies department seemed particularly fond of this, but they all did it. Teachers study past papers and try to find patterns. They’ll work out which questions are most likely to be asked. If a question wasn’t asked last year but has been asked on a few previous occasions, the question is likely to come up again. Questions that were asked last year are unlikely to come up this year unless they are asked every year. And so on. This is the stuff we were taught at school!
And then there are appeals. Never mind if you mess up the final exam — we have enough prelims and coursework to appeal for an increased grade! My old school is number one in the country for appeals. It made 800 appeals for Standard Grades and Highers in two years. I had my Computing Higher grade raised from a C to an A, even though I underperformed in Computing all year and I can’t remember ever getting an A in any Computing exam.
But until some really clever person can devise a way of proving that people have learned a lot about a subject without having to examine them, this sort of business is inevitable.
My dad is disappointed in me. He tries to restrain it, but every so often he lets it come out. He thinks I shouldn’t have chosen to do Economics at University. “It’s not a real science,” he says. He is a chemist, you see. Sometimes I find it difficult to disagree with him, although I don’t think that it makes economics worthless at all. I hated chemistry at school anyway. Besides, my mum warned me not to do a science at university because according to her it’s almost impossible to get a job. What do I do with parents like this?
Anyway, that throny issue as to whether or not economics is a science is something that Greg Mankiw has got his teeth into on his blog.
In my opinion there are a few barriers to economics being a science (so far). One of the things my dad says is that because the behaviour of humans is “random” (his word), you cannot possibly make any serious predictions. Perhaps so. It does get tiring after a while to see economic models assuming “rationality”. Every human becomes the robotic Homo economicus (there was a post about this yesterday at The Fluffy Economist).
Nevertheless, many economic theories do appear to hold true in real life. I should have asked my dad, “When the price of a good goes up, is it really a ‘random’ occurance if the demand for that good goes down?” Yet even such simple concepts which even non-economists would recognise almost as facts of life are not without their problems.
I was discussing economics with a friend on my way back home from our exam yesterday, and I mentioned that my biggest personal gripe with the economics I have learned at university and that I read in the textbooks is all of the maths involved. The movement towards a more maths-based approach was an attempt by the discipline of economics as a whole to gain more credibility; to look more like a real science and not one of those wooly humanities subjects.
But I think I would take a lot of economics much more seriously if it stopped trying to sum up human behaviour in an abstract equation. It is a square peg in a round hole, in my view. By coming out with such an approach that gives you such precision makes it look like economics is promising the moon on a stick when it evidently cannot bring you it. Maybe this is just my personal aversion to maths coming out though. 
Another huge barrier to economics being seen as a science is that it is so closely related to politics. To make a comment about economics is to make a comment about politics. And as we all know, making a comment about politics makes you ten instant friends and a hundred instant enemies. Even if many economists can agree on something (which isn’t often, but hey), many non-economists almost certainly will not. Immigration is a good example (and I’ll probably have a post on that tomorrow — I bet you can’t wait!).
As one anonymous commenter on Mankiw’s blog said, “One hardly hears of Republican chemical theories and Leftwing chemistry.” Is it any coincidence that, for the man on the street at least, one of the most controversial scientific theories today is that of evolution? The scientific community may be pretty well united in its support of the theory of evolution, but because creationism / Intelligent Design and evolution has become such a politicised issue, the theory of evolution has become questionable in the eyes of the general public.
This is a rare, freak event: a biology theory has become politicised, and therefore questioned. Economics is not so lucky: every economic theory is politicised from the word go, and is therefore questioned.
Here is some better news for economics though. Economics is still an extraordinarily young science. While people have been pondering about mathematics, biology, physics and chemistry for thousands of years, modern political economy is said to have begun with Adam Smith just a couple of hundred years ago.
If we go back to when chemistry was that old, we would probably find four elements: earth, fire, water, air. So perhaps we shouldn’t be too critical if economics still seems a bit unsteady on its feet, and we should instead make do with what we’ve got.
Apparently Edinburgh University is bucking the trend, and admissions for its maths courses are up. I was there for one lecture in first year, and it was certainly quite busy (although not nearly as busy as Politics).
Yup, last year I almost took Maths as my outside subject, but just one lecture was enough for me to realise that it was far too difficult for me. This is despite the fact that my original idea was to do Maths and Statistics or something along those lines at university. I had wanted to take Advanced Higher Maths in sixth year at high school, but not enough other people wanted to do it (they only needed seven!). So I had to take a year off without thinking about any maths. It was enough to practically knock it all out of my system entirely. Now I can’t imagine why I ever thought Maths and Stats would be a good idea?!
So guess what I took in sixth year instead of Maths? Economics. And I found it pretty interesting. In fact, my friend who also took Economics and I both found it incredibly refreshing, because it was a subject that seemed to actually mean something outside the classroom. It was something that we could go home and think about and say, ‘yes, I see that happening in real life.’ Goodness knows what crap I was learning in Maths or Physics and at the time, but I certainly didn’t seem important, and I can’t remember most of it now.
(I can remember that s = ut + ½at², but only because when I got some plants for my bedroom, for some reason that I still don’t understand today, my mother was eager for me to name them. So I called them all stupid names to take the piss. ‘s = ut + ½at²’ died quite quickly.)
So after the success of Higher Economics I decided to take Economics (along with Politics) at University as well. Imagine my shock when I ended up having to know calculus inside out! Sometimes I think I almost might as well have pulled a subject out of a hat. Now I wish I took Meteorology instead. I think I’ve been interested in weather all my life, except for those couple of weeks when the Ucas form was in my possession. But the grass is always greener, huh? Who knows what I’d be saying if I actually did do Meteorology…
It’s not that I dislike Economics or anything. Infact I think it’s very interesting. But I find it difficult to be fully convinced by everything that we’re taught, and I do find it the subject difficult as well, which isn’t a help. Nevertheless, I’m quite determined to see Economics through because I feel deep down that it is somehow a better subject than Politics.
I’ve mentioned six or seven subjects so far, and I’ve been somewhat agnostic about all of them for at least part of my life. But sitting here today I feel that so much of what happens in life is down to pure luck, so I guess I should just take what I’m given and be happy with it.
In the past, though, it was a different matter. I think I should tread carefully here, because I got a bit of criticism when I gave up piano lessons. Some people thought that I should have appreciated that I had talent, and that it was a bit selfish of me to just reject it when so many people would give their right arm to be able to play the piano (they obviously haven’t thought about how they would actually play the piano once they had lost said arm). But then again I did get criticised by somebody else who said that I should have quit earlier because I wasn’t interested in it. You can’t win, can you?
Anyway, there are two subjects that everybody thought I was good at in school: English and Computing. But I just have to say no no no.
I have no idea why people thought I was good at English. I hated English with a passion, but for some reason double English was always the most fun subject in fifth year because it was also the one where we were allowed to skive. I can’t remember what we were supposed to be doing, but we weren’t doing it and it must have been something where having loud, jovial conversations and pissing ourselves laughing wouldn’t arouse the teacher’s suspicions.
The only good marks I got in English were for speaking. I don’t know what it was, but something always seemed to click when I had to make a speech about something in front of the whole class. Unfortunately, it was never so when I had to write something. Ironic, given that I now spend so much of my spare time writing for fun. Anyway, I hated writing — especially stories, because I have all the imagination of a sieve (I’m equally bad at similes).
And I know you’re not supposed to admit this if you want people to think you’re really smart or whatever, but I almost never read books for pleasure, and I certainly don’t read novels. In fact, all forms of fiction (films, dramas, plays, whatever) need to be bloody amazing to grab my attention. Don’t ask me why, but I just find it all boring.
Which brings me on to Computing. Zzzzz. Apparently if you do Computing you’re going to make loads of money, but who gives a stuff about that if you’ve got to spend your whole life doing boring shit like programming. Unlike with English, I actually was good at Computing, but I simply could not see myself spending my whole life doing that sort of thing.
Third year, when you start Standard Grades, is when the really boring shit starts. I was sitting at the computer during a lesson, and just as I was actually thinking how incredibly dull programming was, my Computing teacher came up to me wielding a piece of paper with a note scrawled on it: “fourth year and talented third year only”. I was one of those third years singled out. My teacher wanted me to enter this annual programming competition which I think a lot of people actually take quite seriously.
“Errrrrr, I don’t really like competitions,” was my lame excuse.
“But you like programming,” came my teacher’s reply.
AAARGH.
This is nice. I’ve been wanting to get some of those things off my chest for ages! I guess I’ve come to the conclusion that there is no point in finding a dream subject or career. They are all pretty shit, the grass is always greener, and so on. So there’s not much point in worrying about it by, for instance, writing an oversized blog post about it…
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