Sep 16, 2009 •
Here's a lovely quote that students will empathize with:
"A recent study on the use of vectors by introductory physics students summarized the conclusions in two words: "vector avoidance". This state of mind tends to propagate through the physics curriculum. In some 25 years of graduate physics teaching, I have noted that perhaps a third of the students seem incapable of reasoning with vectors as abstract elements of a linear space...I have come to regard this concept of a vector as a kind of conceptual virus, because it impedes development of a more general and powerful concept of a vector..."
David Hestenes, Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics. Reference made to E. Redish and G. Shama, AAPT Announcer vol 27, p98 (1997)
Sep 14, 2009 •
Photo from NASA
Have a look at the latest pictures from the upgraded Hubble Space telescope. I particularly like this one. The universe really is a huge place. If we look carefully enough, maybe we'll even find a solution to the All Black lineout.
Sep 11, 2009 •
OK, following from my ability to break web-applications (it's not the first time I've done it - a couple of years ago I managed to break one of our staff-only applications on our website - about 30 seconds later I got a call saying "we don't know what you've done but you weren't supposed to be able to do it...") you may be wondering what has the log of -1 to do with my blog, apart from both having the letters 'log' in them?
Sep 10, 2009 •
Well, what do you know? I write an entry about complex numbers and the next thing that happens is my blog editor breaks down and I get an error message "cannot take the log of -1 at lib/MT/Template/ContextHandlers.pm line 2032". Our nice support people have fixed it now, so hopefully I am readable again.
For those of you that don't see the mathematical irony, the log of -1 is a complex number. (Logs tell you what power to raise 10 to in order to get your number; so log 1000 is 3, log 100 is 2, log 10 is 1, log 1 is zero, log 0.1 is -1 etc etc, but there is no real log of -1. Logs of negative numbers are complex.)
Sep 09, 2009 •
Sometimes the divide between physics and mathematics is a thin one. Particularly between theoretical physics (which is what I do most of) and mathematics. The difference is that physicists have to keep one foot loosely planted in reality. It's true that sometimes it just the tip of a little toe that's behind the reality-line, but look hard enough and you'll find realism in all that a physicist does.
Sep 08, 2009 •
Well, what does one expect living in Waikato? Four days of gorgeous spring weather in a row is a bit much to ask for.
So the fog was back this morning, and with it the idiot car drivers who don't put their lights on. Why? Do they want to die? A white car with no lights in fog is really hard to see. White is the worst colour of all; the water droplets in the air scatter the sunlight so much that the environment appears uniformly lit from all directions, and a white surface just reflects that illumination, meaning it appears at exactly the same luminance (brightness) as its environment. Grey viewed against the same tone of grey. Not easy to spot without lights. Dark cars are a little better; they appear darker than the grey environment and are so a bit easier to see. But lights help so much. Switch them on.
Sep 06, 2009 •
Recently I was asked by a scientific journal to review an article that had been sent to them. This is pretty standard procedure for journals, and every scientist will know what I am talking about. For those non-scientists, peer review is a way of ensuring (or rather, trying to ensure) quality in scientific publication. If someone writes an article and submits it to a scientific journal, the editors will send it to people reasonable competent in the field for them to comment on. For example, is the subject matter appropriate for the journal? is the method sound? are the results believable? are the conclusions backed up by the results? etc etc.
Sep 03, 2009 •
We've had our dishwasher for a couple of years, acquiring it after the one we inherited with the house went out with a bang (and shot sparks the entire length of the kitchen.) It's a nice dishwasher - that is, it washes dishes nicely, but it's got an annoying habit that I have just experienced for about the zillionth time. If I've got the kitchen sink full of water, and the dishwasher reaches a stage in its cycle where it pumps its water out, it pops the plug out of the sink and I lose my water. (The old dishwasher did this occasionally - the new one does it every time.)
Sep 01, 2009 •
I was reading in the New Zealand Herald at the weekend about a curious problem relating to electric cars. But it's not a technological problem - it's one of language.
My car runs on petrol. It's fuel economy is pretty easy to measure. Start with a full tank, take a note of the odometer, run it until the gauge gets low, fill it with fuel, noting carefully how much goes in, take another note of the odometer, and then divide your kilometres by number of litres for kilometres per litre, or divide your litres by your kilometres and multiply by 100 to get litres per hundred kilometres. (Or work out miles per gallon if that's what you want.)