Friday, 26 September 2014

Stay in or drive

When faced with a difficult hypothesis in maths or physics there's a long tradition of simply turning it on its head, assuming the opposite, and then seeing what happens. For example, Galileo used the idea of dropping different sized cannonballs off the Leaning Tower of Pisa to illustrate his hypothesis that all objects, no matter what their mass, fall at the same rate. With the equipment available at the time this would actually have been a very difficult experiment to do  - analogous to the tightest off side decision a referee's assistant has ever had to make - and subject to far too much human error. In reality, he did do practical timing experiments but these were made on balls rolling down slopes (to slow everything down) and he measured the different distances traveled in equal times by using bells that could be positioned at different points along the track. By adjusting their positions he could make them sound at equal musical intervals and then work out how they were speeding up. 

But, the real experiment was carried out in his head. Suppose, he thought, large bodies really did accelerate faster than small ones. If you made a combined body made of a small one attached to a large one with a piece of string and then dropped it, the large body would be held back by the smaller body and hence the combined body - which is even larger than the large body - would fall slower than the large body by itself. This contradicts the original assumption and thereby proves it wrong.

A similar trick is often played in maths. For example the proof that the square root of 2 is an irrational number - cannot be expressed as the ratio of two whole numbers (e.g. p/q) - involves the assumption that it can followed by a little bit of algebra which ends up contradicting the assumption. This sort of argument is given the glorious name of "reductio ad absurdam".

So, you'll have to forgive me for shifting this idea to a completely different context. 

Recent survey work carried out by Sport England and published by Public Health England suggests that in North Yorkshire only 25% of those aged 40 to 79 year take the minimum recommended amount of physical activity. Since this amounts to just 150 minutes a week (half an hour a day on five days out of seven) of the sort of exercise that tickles up your heart rate or makes you aware of having to breathe, instead of trying to think why the vast majority are so inactive I wondered what I'd have to do to join them in their inactivity.

I live in a small town (60,000 people in winter about 100,000 in the summer) about 15 minutes walk from the town centre. 3 or 4 times a week, I'll walk into town, or across to the other side and almost everyday I'll cycle for half an hour or so on my way to pick up heavy shopping or attend meetings. In addition, I frequently head off for an hour or so into the local countryside. So, as you can see, even without the recreational trips into the countryside, let alone my habits of running up stairs, sawing timber, mowing the grass or clipping the hedges - all by hand - I'd have trouble making the cut.

I could, of course, stay in and simply fail to get the things that need doing done - which wouldn't please the rest of my household - or do them by walking so slowly so that I don't raise my heart rate. You've seen this sort of walking. For men it usually involves thrusting your hands in your trouser pockets and then swinging from the hips. Unfortunately slow walking, which in days long past I'd be forced to practice on demonstrations, makes my lower back hurt. Or I could walk slowly to the bus stop and then take the short bus ride into town; though that would demand enormous patience to stop myself from simply walking off. So, there's probably no practical alternative but to pick up those car keys, take the car and drive.

Oh, and is that the dog asking for a walk....

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