Thursday, March 01, 2007
It has raineth
Garden now as wet as I have seen it for some years. Pond overflowing down the hill. It might be fine today but we had some more good rain yesterday - complete with thunder, lightening and two rainbows (at the same time that is).
Discovered that a new evergreen clematis growing in the our back hedge is more or less destroying my part of the hedge so am cutting it back hard. Probably the entirely wrong time of year. Funny how one struggles to grow the things in one part of the domain and struggle to keep them at bay in others. Clematis full of dead twigs which have fallen off a tree just the other side of the hedge, following the regularly anti-social bonfires far too close to both hedge and tree. BH had one go at bellowing at the culprit; seemingly without effect.
First celandine is now out. No signs of anything eating them.
Sodoku more or less on the back burner at the moment. Having got as far as the wrong solution yesterday, the first attempt for some weeks. On the other hand an interesting rat puzzle. You have a square compartment and a rat at each inside corner. The rats are trained on the word of command to chase after the one in front. How far does each rat run before it catches up with the one in front? Playing with nested rotating squares inside the first square, I decide that the answer is 1, where 1 is the length of the side of the original square. After a bit more work - say half an hour - I get a non liner differance equation which describes the behaviour of the approximating squares. I am then completely stuck. No idea how to solve the equation and proving that the thing converges, let alone converges to the right answer as one decreases the amount of rotation at each step, is well beyond my fading powers. On the other hand, half an hour in Excel VB computes the rotating squares. The first approximation is a number a little above 1. As the amount of rotation per step decreases (making the approximation better one hopes) the approximation steadily decreases to something just below 1, then starts climbing again, this time looking to converge to 1 from below. Reasonably complex behaviour which does not encourage me to think that I am going prove convergance.
Now which is the better way to do this? When I was small and the computation involved was unavailable - at least in schools - no question but that you had to solve a problem like this algebraically - and theoretically correctly - with no approximations. But given the likelihood of making algebraic mistakes, is the theoretic answer better than the computed one? Could one persuade young people of the merit of sweating through the algebra when Excel is available?
But then again, maybe I have missed some far simpler way to do this!
I learn from TB that the 'Daily Mail' is having a go at immigrants from Eastern Europe. First line of attack is the rate that these people (presumably mostly young and single) are gobbling up our infrastructure services and resources. Second line of attack is the way they are depressing wages. So an electrician earning perhaps £400 a week for the last few years is now getting pushed down well below that. With unfortunate effect on his mortgage repayments, agreed on the basis of the £400. Now while this is a bit of a problem, ironic that the complaint should come from this thunderer for the merits of market forces. And the evils of workforces - like those in France - not fully exposed to the chill winds of competition in level playing fields.
My take is two-fold. On the one hand, I think that these people are largely doing jobs that native Brits don't want. And on the other, with places like China making trillions of consumables on the cheap, we are living beyond our means. We are paying ourselves too much. Sooner or later there is going to be a nasty adjustment.
Steady trickle of senior moments. Some the entirely ordinary sort. Some more complicated, as when I got into a complete muddle - after the event that is - as to whether I had turned right at some traffic lights at Cheam village just as they were turning against me or just as they were turning for me. No safety issue though - lower level processing was in charge of making the actual turn, and not cycling under a bus, whatever higher order processing might or might not have thought about the lights.
And one virtual senior moment. That is to say, I was not fully awake but dreaming about putting a date in my diary. And as I finished writing it in, I realised that I had included the full date in the written entry - completely superfluous in a diary which presumably had printed dates and days of the week ready made. All without properly waking up. Maybe I will start dreaming about putting the frozen peas in the washing machine rather than the freezer.
Discovered that a new evergreen clematis growing in the our back hedge is more or less destroying my part of the hedge so am cutting it back hard. Probably the entirely wrong time of year. Funny how one struggles to grow the things in one part of the domain and struggle to keep them at bay in others. Clematis full of dead twigs which have fallen off a tree just the other side of the hedge, following the regularly anti-social bonfires far too close to both hedge and tree. BH had one go at bellowing at the culprit; seemingly without effect.
First celandine is now out. No signs of anything eating them.
Sodoku more or less on the back burner at the moment. Having got as far as the wrong solution yesterday, the first attempt for some weeks. On the other hand an interesting rat puzzle. You have a square compartment and a rat at each inside corner. The rats are trained on the word of command to chase after the one in front. How far does each rat run before it catches up with the one in front? Playing with nested rotating squares inside the first square, I decide that the answer is 1, where 1 is the length of the side of the original square. After a bit more work - say half an hour - I get a non liner differance equation which describes the behaviour of the approximating squares. I am then completely stuck. No idea how to solve the equation and proving that the thing converges, let alone converges to the right answer as one decreases the amount of rotation at each step, is well beyond my fading powers. On the other hand, half an hour in Excel VB computes the rotating squares. The first approximation is a number a little above 1. As the amount of rotation per step decreases (making the approximation better one hopes) the approximation steadily decreases to something just below 1, then starts climbing again, this time looking to converge to 1 from below. Reasonably complex behaviour which does not encourage me to think that I am going prove convergance.
Now which is the better way to do this? When I was small and the computation involved was unavailable - at least in schools - no question but that you had to solve a problem like this algebraically - and theoretically correctly - with no approximations. But given the likelihood of making algebraic mistakes, is the theoretic answer better than the computed one? Could one persuade young people of the merit of sweating through the algebra when Excel is available?
But then again, maybe I have missed some far simpler way to do this!
I learn from TB that the 'Daily Mail' is having a go at immigrants from Eastern Europe. First line of attack is the rate that these people (presumably mostly young and single) are gobbling up our infrastructure services and resources. Second line of attack is the way they are depressing wages. So an electrician earning perhaps £400 a week for the last few years is now getting pushed down well below that. With unfortunate effect on his mortgage repayments, agreed on the basis of the £400. Now while this is a bit of a problem, ironic that the complaint should come from this thunderer for the merits of market forces. And the evils of workforces - like those in France - not fully exposed to the chill winds of competition in level playing fields.
My take is two-fold. On the one hand, I think that these people are largely doing jobs that native Brits don't want. And on the other, with places like China making trillions of consumables on the cheap, we are living beyond our means. We are paying ourselves too much. Sooner or later there is going to be a nasty adjustment.
Steady trickle of senior moments. Some the entirely ordinary sort. Some more complicated, as when I got into a complete muddle - after the event that is - as to whether I had turned right at some traffic lights at Cheam village just as they were turning against me or just as they were turning for me. No safety issue though - lower level processing was in charge of making the actual turn, and not cycling under a bus, whatever higher order processing might or might not have thought about the lights.
And one virtual senior moment. That is to say, I was not fully awake but dreaming about putting a date in my diary. And as I finished writing it in, I realised that I had included the full date in the written entry - completely superfluous in a diary which presumably had printed dates and days of the week ready made. All without properly waking up. Maybe I will start dreaming about putting the frozen peas in the washing machine rather than the freezer.
# posted by Jim @ 7:19 AM 
