Counting gaps in space and time is often confusing

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

03 March 2024

After a long dispute about the boundary between their parcels of land, two neighbours finally settled on a straight line running for 30 metres. They also agreed to split the cost of building materials on 50:50 basis. The fencing posts were to be placed at 3m-intervals. Therefore, they worked out that they needed 10 poles (30m divided by 3m). So, each person bought 5 poles and the work started.

Towards the completion of fixing the poles, the workers reported that one pole was lacking. A new dispute erupted with each neighbour blaming the other of short-changing – buying four poles instead of five!

A re-count of the poles and re-measurement of their spacing was done and it turned out that 10 poles were not enough to complete the job. The reason is that, dividing the length of boundary (30m) by the distance between poles (3m), the number (10) of spaces; not the number of poles.

One more pole was needed at the end to hold the last space of the fence. That is, they should have bought 11 poles; not 10. This kind of mistake is quite common especially when counting time intervals.

Suppose a doctor gives you four tablets with instructions to take one every hour; if you start at 12pm, when will you finish taking the medication? It is very tempting to simply add 4 hours to 12pm and say 4pm. But that would be wrong! Count them and see…

This is the kind of mis-counting we did and ended up celebrating the golden jubilee of our country one year late (in the 51st year instead of the 50th)! But, if it is any consolation, we are not alone in making this mistake. The town of Wemding in Bavaria, Southern Germany, was founded in the year 793AD. As part of celebrating the 1,200th anniversary in 1993, a local artist came up with a brilliant idea of a simple structure that would take another 1,200 years to complete.

It is a pyramid made with 120 concrete blocks stacked up at the rate of one every ten years. The first one was placed in 1993, the next one in 2003 and so on. So far, there are four blocks in place. But there is a problem: If the four blocks have counted 30 years (1993 to 2023), how many years will the 120 blocks count? The answer is not 1,200 as intended by the artist! Count the years and see.