I think that every number has its own personality. Maybe not a very strong one but at least a little bit of one. What focused my attention on 5 is the idea of the Five Whys. I first learned about them in a book by Peter Stenge on systems analysis, an underappreciated subject in my opinion. I'm a system, so is my neighborhood, so is a flock of geese or a site of mold on bread. Sometimes, helpful things are noticed about any collection of interrelated parts.
The five whys is much like the little child's practice of repeatedly asking "Why?" As part of studying a system, especially in trying to get to the root of a problem, one asks "why is this problem occurring?" and asks why about the answer and so on, for a total of 5 times. It can throw surprising light on one's knowledge and understanding of something.
Of course, 5 is the number of fingers we have which leads to 10 for both hands and is probably why our usual numbering system is based on 10 even though we use a binary system based on 2 much of the time, in our computers and electronics, and one based on 16 in them, too.
Since five is a smallish number in the scope of things, it doesn't have lots of power and grandeur like a million or a trillion. It can still be surprising as an exponent, though. 2 to the 5th power = 32. So, if you halve something and halve the parts and do that for a total of 5 cuts, you reduce the original to pieces that are one 32nd of the originals.
Similarly, while 5 is not large enough for a very good sample for most purposes, having taken 5 separate samples of something can be enough to get a good idea of a result.
Finally, I have always been interested in repeated trys at something. Trying to do something with a low chance of success is hard, since we fail many times and that is discouraging. Sure, with better training and good analysis of the problem, we may increase the probability of success but even if we can't, even if the same small probability continues to hold, repeated tries may lead to success.
In the table below, the probability of success, p, is in the first column and the column for 1 or more successes gives the chance of having at least one success in 5 separate tries. To the right, is a more complete listing for 5 separate tries, using only the chance of success of 1 in ten.
| p | q | all fail | 1+ success | tries | P(fail) | P(some success) | ||
0.1 | 0.9 | 0.59049 | 0.41 | 1 | 0.9 | 0.1 | ||
0.2 | 0.8 | 0.32768 | 0.67 | 2 | 0.81 | 0.19 | ||
0.3 | 0.7 | 0.16807 | 0.83 | 3 | 0.729 | 0.271 | ||
0.4 | 0.6 | 0.07776 | 0.92 | 4 | 0.6561 | 0.3439 | ||
0.5 | 0.5 | 0.03125 | 0.97 | 5 | 0.59049 | 0.40951 | ||
0.6 | 0.4 | 0.01024 | 0.99 | |||||
0.7 | 0.3 | 0.00243 | nearly 1.00 | |||||
0.8 | 0.2 | 0.00032 | nearly 1.00 | |||||
0.9 | 0.1 | 0.00001 | nearly 1.00 |
--
Bill
Main blog: Fear, Fun and Filoz
Main web site: Kirbyvariety
