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Bus Lessons in Maths

Author: Brian Robertson
Year: Future

We start at the most basic level. Some would not call it maths, maybe just arithmetic. But small juniors love it.

'Come to the window, can you spot a bus?'

Statistically, success is likely. During the daytime peak, 24 buses an hour pass the window, 12 in one direction, 12 in the other.

'I wonder how many buses you can count.'

'One...two...six...three...nine...seven...' might come the youthful reply.

'Well done!'

And so the mathematical development could go on. Maybe a more taxing task for the older ones would be to log the number of buses each hour and draw a bar chart or a line graph showing the variation throughout the day. Let’s have an exciting day with maths.

'Why are we wasting our time counting?' they might reply. 'If you just get hold of the timetable, the data is already there.' Point taken.

We could still enthuse the little ones.

'I know, let’s count the number of passengers on each bus.'

With double-deckers flashing past with anything up to 70 or 100 passengers, the office-workers in one direction, the students in another, counting is well nigh impossible. There our maths lessons could rest.

Until now. Change is afoot and it started about a week ago. We didn’t have the lessons organised but it’s too late for the small youth to participate in any case. They were always much-loved visitors but they are not part of this household. Lockdown has begun.

But should this data really be the raw material of a maths lesson for the young?

It took a few days until our first realisation that the buses were getting quiet. Soon we could easily count the number of travellers, spaced out as they were. More lately though, the questions were 'Are there any passengers on the bus? I can’t see them. Where are they sitting?'.

The buses charged past and, over the days, that did not slacken. Now, though, a Sunday Service. How should we modify the graphs? The buses are still there. The passengers are not. The bus company will have the data.

Would the number of passengers be following a linear decline? An exponential decline? It is interesting to ponder how even a linear decline would approach the x-axis as it tends towards zero. Should the bus driver count as a passenger or is it only when the bus no longer runs that the curve will finally hit zero? But we’re drifting into maths again. No pupils, so no lessons.

Let’s get a mirror. The graph may trundle along the x-axis for a time but the mirror will show us the curve rising as, in its time, it fell. A return to normal. Maths lessons can resume…except they can’t.

A Critical Services timetable has dispensed with an entire route and, instead of 24, there are now 4 buses an hour. We long for the pupils’ return, There is so much to catch up on without maths but everything’s all now timetabled by the Lockdown Route Map. Whether a map can timetable or not is immaterial. Things are changing. As the first visit is made, the non-mathematical phrase 'Nicola says...', uttered by the little ones, resolves any lingering doubt about how things should be done.

And the rising graph will never mirror its fall. Working from home, remote tuition and fewer journeys for pleasure, will all make it distinctly unsymmetrical, in no way resembling a potential well or even an upside-down sombrero. A mathematical challenge, but only one of many that exist in more serious places – the modelling, the predictions, the spikes, the clusters and the waves.

And the future? The political decisions involve the most difficult calculations of all and they’re not even mathematical. Let’s hope the little ones learn for when their time comes.