The first was that growing up in Australia in the 1970s made it tough to see the relevance of learning French or German.
The second, I've now realised, was much, much more significant. In short, I don't think the same way language teachers think.
I've discovered now that I really love languages. What's more, I seem to have a knack for picking up enough to understand and be understood. Travelling for work I've managed to pick up enough conversational Danish, Swedish, French, Spanish, German, Bulgarian and Arabic to be really, really useful. Useful, that is, provided the other person tries to be cooperative.
So why wasn't this noticed when I was at school? The answer seems to be that the teachers didn't find out that I don't think the way they do, and I don't learn the way they do. Maybe they cared, maybe they didn't. Maybe they couldn't conceive of someone thinking in ways other than the way they thought.
Whatever the reason, I now have a way to learn the essentials in a new language really, really quickly and efficiently. It's not a magic formula. Just as there is no royal road to arithmetic, there is no royal road to languages. You have to put in the time and effort, just as when you learn to juggle. My method is given on the page about Learning Languages. If it helps you, please, let me know. I only wish I'd known it in school when my mind was faster, and emptier.
In the meantime, let me tell you about a really weird thing that happened to me. I was on the Holyhead train coming back from giving a juggling talk. I had just bought a sandwich and coffee and was about to go, when a young lady asked for a soup. Now, what I heard was "Una sopa, por favor," which struck me as being slightly odd, especially when the attendant replied in Welsh.
It turned out that the request had been in Welsh, and yet I had clearly heard the Spanish. I think. And no, they don't sound at all alike.
I'm confused ...
2006/07/12 If it ain't Baroque ...We went to a concert in Chester last night, performed by Red Priest. Extraordinary. They not only played the music, but they brought to life the story behind the pieces. They were ably assisted by having chosen pieces that attempted to tell specific stories - namely Vivaldi's "Four Seasons" and other pieces with seasonal themes - but the presentation was staggering.
There's a review on the Red Priest page.
It took a while for the audience to get warmed up, but they soon started joining in. Kraig Thornber as the Alderman was impressive, as indeed he had been in the production of Sugar, a musical loosely (actually quite closely!) based on the film "Some Like It Hot", which we saw a few weeks ago. Kraig tap-danced, played drums, trombone and the fool, and yet it was playing to a house that was only half full. Or half empty.
Why is it that superb productions, amazing productions or brilliant performances are so often undervalued or ignored? Why does marketing have such a sway over the success or failure of technical innovation?
How can marketing make a technically inferior product more successful? How can we educate people into making informed choices, rather than simply doing what the marketing people convince them?
information - a small fact."
Please note that, despite this most common usage, analysis shows that "factoid" should mean something that appears to be, but is not necessarily, a fact. Compare with "humanoid", which means something that takes the appearance of, but is not necessarily, a human.
I know I'm fighting a losing battle on this, and that grammatical and linguistic drift will overwhelm me in a sea of inconsistencies and lost opportunities, but as Sky Masterson says to Nathan Detroit in "Guys and Dolls", "You can fight it Nathan, you can fight it."
Of course, as my wife points out, he turns out to be wrong ...
As a warm up exercise I worked out that the orbital period at the Earth's surface would be 42 minutes, and mentioned to my wife that this was satisfying as it matched my memories from long ago. She immediately leaped up and dashed from the room, which I confess surprised me a little, this not being her usual reaction.
She then returned with our copy of the Complete Works of Shakespeare, and quoted:
I'll put a girdle round about the earth In forty minutes.
Stated by Puck, in Midsummer Night's Dream, Act II, scene 1.
Also, spot the (not so) deliberate mistake ...
Pure Mathematics is incredibly important as the foundations of so many other subjects, but not every student will go on to be a mathematician. Why should they study mathematics? Why should they learn about calculus, theorems, proofs, and algebra?
Go and talk to any high-level athlete today and you will find that as a part of their training they "do weights". They don't want to be weight-lifters, but without exception they will do weight-training as a part of their overall program. This is because weight-training builds strength and stamina for the body as a whole. This is then augmented by sport specific training.
Mathematics is like weight-training for the mind. You may not want to be a mathematician, but studying mathematics builds your ability to analyse situations, think abstractly and solve problems. It enhances your critical thinking so you can find weaknesses and strengths in arguments.
It's not the mathematics that's useful, it's the style of thought and techniques of analysis that are being trained and exercised, and that will be useful in almost everything you ever do.
It has been said that the internet, and the World Wide Web in particular is a great leveller, a great equaliser. It gives pretty much anyone the ability to publish on a world-readable medium what ever they want to say. They can make available their photographs, their diary, pages about their cats, houses, genealogy, hobbies, etc. All this is very well, and it certainly lets people with minority interests find each other, but what have we really learned?
Well, firstly, not everyone has a computer, not everyone has 'net access, but I guess that doesn't really matter because the only ones who miss out aren't very important. After all, they obviously don't have money.
Secondly, we've found that those who care only about money will exploit any opportunity and really, really, really don't care about anyone else. But that's part of the definition of only caring about money I guess.
But really, what we've discovered upon giving everyone who matters the ability to publish, is that most of them don't have anything interesting to say.
And yes, that probably almost certainly includes me.
But to someone who has done research in mathematics this is something of a tragedy. It means that when I talk about beauty and elegance in mathematics it more often than not draws sniggers or expressions of disbelief, pure and simple. And saying that you like mathematics is akin to admitting something mildly obscene.
But what I mean by mathematics is not tables, arithmetic, long division or adding huge columns of figures.
So what is it?
Ah, good question.
Mathematics, like science, starts with a question, an itch that needs scratching. Like science, it proceeds by looking at the question from every direction, and gathering as much information about it as possible. Like science, it tries to find order in the chaos, patterns in the data. If patterns are found, they are used to predict what new data should be gathered, and goes to see if it works. If so, the pattern gains credence. If not, we start again with the new knowledge.
That's basically the idea in science. We then use our patterns, which we call "theories", to help explain existing data, and to predict new data. Good theories make accurate predictions, and sometimes theories can be regarded as "good enough" when they work reliably in everyday circumstances.
But what about mathematics?
In mathematics we go a stage further and try to prove that the pattern is always true. We can't do this with real world things. We can't prove that the sun will rise tomorrow, although it seems a pretty good working hypothesis. But when we take a step back and deal with more abstract objects then proof becomes possible.
It's the job of mathematicians to prove that things are true, because Patterns Fail.
Examples to follow.
So what happens in zero gravity?
Be careful! The steady state solution is easy to find, but is it stable? Maybe the steady state solution is not what happens in practice. If not, what does happen, and how can you tell?
This is repeated on the Challenge Question page, where you can find several other, equally awkward questions.
We'll see how long it lasts. ...
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