Time

The concept of ‘time’ is rather slippery; there is only the ‘now’, but we know there has been a ‘past’ and we expect that there will be a ‘future’. It’s a bit like drifting downstream in a boat, looking at the banks; we can’t row back upstream, nor can we row faster downstream.

Mechanical clocks used to show the local time, the time where they were. This didn’t matter that much originally, but the development of the railway and the telegraph lead to changes. There were two clock faces on the railway station in Basel, Switzerland; one showed Basel time, and the other showed the time in adjacent Germany — only a matter of a few minutes difference, but not identical.

Time was initially standardised in individual countries, the railways ran to it, but it was a while before there was international cooperation with the establishment of time zones, and the international date line. Of course, there was considerable national rivalry over this; but with the adoption of the Greenwich Meridian for ships’ charts, the same meridian was used as the basis for time. The French were not amused by this.

You might well wonder where the idea of having 60 minutes in the hour and 60 seconds in the minute came from; it doesn’t seem very logical. Why not a decimal system? The Babylonians didn’t used a decimal system, one with a base of 10, they used a system with a base of 60. Pragmatically, 60 can be divided by far more integers than 10 — by three and four for starters — and the Babylonians were very good at sums. And we’re talking around 5000 years ago. Another little echo from the very distant past.

If time only exists in the ‘now’, Newton and Leibnitz took this quite literally, and talked of ‘instantaneous’ events and changes, from which they developed their versions of the calculus. The two methods are similar, and while Newton and Leibnitz argued over who was the first to discover calculus, Leibnitz’s notation is the one we use today. If you never did calculus at school don’t be alarmed; I’m not going to describe it in any detail. You won’t have learnt, I’m quite sure, that calculus was regarded with suspicion for quite a while after it became public knowledge; it was seen as mathematical prestidigitation — chicanery almost — and as not very ‘pure’.

You might remember that differentiation is about finding tangents to curves, or acceleration, and that integration is about the area under a curve between two points on it. You might recall that there was a strange symbol to represent integration, looking something like this:

∫

Did you know that it is the long form of the letter ’s’ ? It stands for summa — adding all the bits up under the curve. You’ve probably seen the long ’s’ in old books or reproductions of them, though often an ‘f’ is used instead. The best modern version I’ve found is ‘ſ’  (in a different font). It doesn’t have the cross-stroke of the ‘f’.