The Mathematician’s Tale

Tales from End to End
The Mathematician’s Tale

by Roger Eckersley

There was a tap on the window last night – the carrier pigeon had arrived. I let him in and read the note strapped to its leg. ‘Dad’, it said, ‘I need your help. My abacus has broke and I’ve been looking all over the place for a new battery; but I can’t find one for love nor money!’ What could I say?

John with his Abacus
John with his Abacus

Apparently my Mum and Dad had been arguing (well, they’d say ‘discussing’) which of them would be expending the most energy on their mammoth walk and so they asked me, as a thoroughly respectable, reliable and trustworthy son, to be an Honest Broker and to adjudicate for them. So I thought I’d give it a go, and try very hard to avoid the accusation that all Mathematics is merely ‘Lies, damned lies and statistics’. After all, Logic is closely allied to Mathematics.

First, I thought, let’s consider how far they are actually walking. I’m using imperial units because both my parents are getting on a bit now and they’re not use to new-fangled things like metric.

The total distance to be covered on the route that they are taking is 1,280 miles. In ‘old money’ that means (1280 x 1760 x 3 x 12) inches. Now at a slow walking pace, Dad’s average pace length is 30 inches while Mum’s is only 24 inches.

So for the whole walk Dad will take
((1280 x 1760 x 3 x 12) divided by 30) = 2,410,496 paces

On the other hand, my Mum will take
((1280 x 1760 x 3 x 12) divided by 24) = 3,013,120 paces

Roger Eckersley
Roger Eckersley

If you can believe this logic, then my Mum is going to walk a lot more and expend much more energy than my Dad.

However, there are other things to consider. Heart rate is one factor. Dad’s got a slow heart beat with a resting pulse rate of 52 beats per minute. That’s what you might expect from a runner – he’s been running for over 50 years now and cardio-vascular exercise like this builds up strong heart muscles. Mum’s comparable pulse rate is 64 beats a minute. This means she is healthy and fit but playing tennis doesn’t build up the heart in the same way that running does. Anyway, what it means is that Mum’s heart is beating (64 – 52) = 12 times more every minute that they are walking LEJOG. Excluding Sundays and other rest days, they plan to be walking for 111 days.

This means that Mum’s heart will be beating
12 x 60 (mins in an hour) x 24 (hours in a day) x 111 (days) =
1,918,080 times more than Dad’s.

Again, if you follow this line of argument, Mum is going to be working much harder than Dad.

Then there’s the small matter of how much rest and recuperation they are liable to get during the course of the walk. On average, my Dad needs about 9 hours sleep every 24 hours – he is able to make up for night-time losses by snoozing off any time he chooses during the day. He claims his power-napping follows in the noble tradition of Sir Winston Churchill. Mum, on the other hand, only needs a total of about 6 hours. So you could say that this 3 to 2 ratio means Mum is getting far less time to recover from the ardours of long-distance walking. If they walk for the full 111 days, Mum will be getting
(3 x 111) = 333 hours less sleep than Dad – that sounds a lot less sleep to me.

Is there anything I can say in my Dad’s favour? Well, perhaps one thing. It’s hard to quantify but my Dad will almost certainly be expending far more energy talking to every Tom, Dick and Harry they meet along the way. Despite being married to a Yorkshire lass, living in York since they got married and loving the Yorkshire countryside, at heart my Dad’s still proud of his Merseyside roots. He’s got some Irish blood in him, as well as a touch of the blarney and if he gets half a chance to tell you how you can buy one of his Christian Aid Walking books, you’ll never stop him. Dads; what are they like!

Roger, our elder son, and his wife Karen are both teachers, enthusiastic cyclists and keen walkers.