Jim Choate wrote: > > On Thu, 25 Apr 2002, Ken Brown wrote: > > > One of the classic examples of what is now called "chaos" (a word that I > > don't like in this context). The exact trajectory taken by simple models > > Uhuh... > > > of predator-prey systems is often very sensitively dependent on initial > > conditions. Of course in real life these things are stochastic anyway > > Then I take it you don't like 'stochastic' since they really mean the same > thing in this context.
Same as what? "Stochastic" certainly doesn't mean the same thing as "chaotic" in this context, so I assume you didn't mean that. [...] > > so the variables in your model should actually be probability > > distributions, which makes the sums much harder and leads to > > considerable handwaving. > > unpredictabilty <> hand waving. What I meant was that many biologists, even people who teach biology, don't have the maths to describe the models in detail. So the books and lectures tend to handwaving. The mutual incomprehension between maths & biology can get extreme at times. And even if they did their students, or the readers of their books, certainly don't. I have been present at a practical class when a student complained to the lecturer that he had promised that there would be "no mathematics" on this course. She was moaning about something simple to do with exponentials - the sort of algebra they tried to teach us at the age of 12 or 13. From the lecturer's point of view it *wasn't* mathematics, it was just general knowledge, the sort of thing he'd expect any reasonably educated person to know about, or at least able to pick up quickly. As the course was about (amongst other things) enzyme reaction kinetics it is a bit hard to understand how anyone could imagine getting though it without at least that level of maths. Possibly a worse problem in UK education than in most other countries. We encourage extreme early specialisation. In our schools you can drop mathematics at 15 or 16 if you want, even if you later go on to study science subjects at university. Well, you'd have trouble getting on to a physics or engineering course, but you could do biology. The most advanced maths I did in what you would call high school was very introductory calculus - simple differentiation mostly. Also the briefest introduction to integration. We weren't expected to be able to do it, just know what it was, only a couple of hour's teaching. And that was an /optional/ course, I could have got away without it. Not a mention of matrices, nothing even approaching statistics, probability, number theory, none of what they then called "modern maths" (anything which mentioned sets or topology), no algebra more advanced than the quadratic equation formula (which we were expected to be able to use, but not derive or prove). And I was someone on a science track (Biology, Chemistry, Physics) at a selective school that specialised in science. My undergraduate courses included pick-ups on statistics and probability, without which it would be impossible to take Biology, but that was all. Then these biologists who are semi-literate in maths become graduate students and, need to do some modelling, and meet up with mathematicians or physicists who may not have studied any biology since the age of 13. Of course all these folk did science at school - they probably have never had any serious language or history teaching at all. It is compulsory in British schools to do at least one modern language, usually French for some reason, but only between the ages of 12 and 16, and it is usually badly taught. In my experience most people who go on to do science simply fail the class - they make you go to it, but you don't have to pass to get onto other courses. There is no requirement to "graduate" in classes you don't intend to continue with, so loads of kids don't. The same works the other way even more strongly. Most people studying arts or humanities at university will never have passed a science exam or maths exam in their lives, and will have dropped or failed most of the subjects *before* GCSE. I think the US equivalent to that would be leaving a junior high school to go to a senior high school. They are exams you take at 15 or 16, and most of the brighter kids only attempt the ones that they intend to continue later. Of course the other side of the coin is that what we call "6th form" education, 16-18, is, in sciences at any rate, the equivalent of the first year of University in other countries. So the system is good at producing very knowledgeable people, very young. One of the reasons that British research is significantly more productive than French or German. By the time the French or German advanced student catches up with their British counterpart in knowledge of their specialised subject they are probably in their late 20s. I didn't intend to write this rant... don't get me onto school sport Ken
