Exponential decay

Saturday 24 August 2019

“What’s wrong? Is there something you want to talk about?”

Clara had a look on her face that I have come to recognise. We had just returned from an overnight trip to Sussex for my birthday and she looked concerned.

There was silence for a while. She seemed reluctant to speak but eventually came out with it.

“It’s your driving. You were driving too fast and there were two or three times…”

I interrupted with the typical male response.

“There’s nothing worse than a passenger seat driver. I wasn’t driving too fast. Maybe just over the speed limit, but not by much.”

But then I reflected on it for a minute and put my ego to one side.

"Actually, you're right," I continued. "I'm not safe any longer. At least not on long journeys."

We were only talking about a 1 hour 40 minute drive, but in that time I’d had to stop twice because I had been feeling pretty out of it. Tired and dizzy, I even had a brief nap at a service station. At times I had been driving in a bit of a daze, too fast and with slow reactions.

“From now on, I won’t drive for more than an hour,” I concluded. “Next time we go on a similar journey, either you can drive or we can take the train.”

Currently on a 3 year medical review licence (see previous post cleared to drive), I am legally allowed to drive only until the spring, after which I need to apply to renew my licence. I’m confident it will get extended, but I need to stay safe and that means limiting my time behind the wheel. I’m pleased that I got a couple of driving holidays, in the US and Canada, completed in the last two years, because I don’t think I could manage them now.

I expect that in another two years’ time I will again still be driving but perhaps even shorter distances – maybe I’ll be capping myself at 30 minutes by then. It’s a similar story with other activities, for example running. A year ago I was regularly running 5K. Now I still run once or twice a week but 3K seems to be the comfortable limit.

So I can still do many things, just less and less of them each year. In mathematical terms, this is called exponential decay. It’s the same concept as a half-life. For example, I reckon the distance I can drive and the distance I can run both have a half-life of about 2 years. This means that in 2019 I can do roughly half of what I could do in 2017, like running 3K instead of 6K.

Projecting forwards, I can expect to still be running in 2021, but perhaps only for a mile (1.6K) or thereabouts. Possibly I have got this wrong and the half-life is more like 3 years, meaning I can still run a mile in 2022.

At least, that’s my hypothesis. The term exponential decay sounds bad but, if my hypothesis is correct, this is actually a very good thing. I will still be active for quite a few years yet, just limited in how much I can do.

And with the running, because my mileage is so low and ever-diminishing, I probably never need to buy a pair of running shoes again…

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