The Power of Observation - the pill counter example
If you have ever worked in a pharmacy, you will recognise the ubiquitous triangular pill counter (fig. 1). Ever wondered how the row of numbers was derived?
fig. 1
The row of numbers looks something like this:
fig. 2
So if you have 7 rows of tablets, the number of tablets you would have counted is 28 and so on. The question of how these numbers were derived exercised my curiosity recently. I wanted to develop a mathematical model for working out these numbers. The process I went through highlighted some profound issues relating to the power of observation.
…
An approach to solving the problem [Model 1]:
What seemed obvious to me initially, was that the number of tablets in the row of numbers will only work when the tablets being counted are round, forming a triangle of tablet which is equilateral (having all sides of equal length)-fig. 1. The model should therefore look something like this:
No. of tablets = (Area of the equilateral triangle formed by tablets - Sum of the areas of the inter-tablet spaces) / Area of a single tablet - fig. 3
Simple? Not really (see box 1 below).
| box 1 |
 |
This way of solving a problem makes the idiomatic expression about a sledgehammer and a nut very apt.
Another approach - Observation [Model 2]!
Observing the way the tablets are arranged in the triangle provide a better insight. Provided the tablets are round and the triangle equalateral, a pattern seem to emerge:
1st row = 1 tablet
2nd row = 2 tablets
3rd row = 3 tablets
4th row = 4 tablets…etc
No. of tablets = sum of the tablets in each row
therefore, if there are 5 rows, then
No. of tablets = 1 + 2 + 3 + 4 + 5 = 15
for y = number of rows;
No. of tablets = 1 + 2 + 3 + 4 +….+ y
This is a classic triangle sequence which is well known to mathematicians and can be represented as:
This approch to solving a problem reminded me of the article by John C. Harrison - The Power of Observation in which he described an encounter with Frijof Capra, the author of The Tao of Physics (Flamingo)
Capra was quoted to have said
"We arrived at those advanced concepts (about the picture of the universe) through careful scientific reasoning. The Chinese got there by simply observing".
Whilst the two models described above will eventually provide identical answers to the problem, model 2 is clearly a more desirable model, especially if like me, you are time poor. Observation may prove to be the key for improving efficiency and productivity.
Harrison wrote: ‘…all personal changes begins with observation….the challenge, then, is to learn to obeserve objectively’.
Objective observation defines Iforg®’s approach to all our projects and we expect to make efficiency and productivity savings as a result.
- 88Jwd
(1 votes, average: 3 out of 5)
Loading …