20 07 2010

At the algebraic level, you can check your answer by substituting in your numerical answer for the unknown, and then finding out whether the left and the right side are equal, as initially proposed.

There are other, simpler examples of this process. Times tables. 4 x 8 is 32. How can you tell? Well:

1. it sounds right :)

2. 4 x 10 is 40, so two fours less than this is 32

3. count up in eights: 8, 16, 24, 32… the fourth item is 32

4. count up in fours: 4, 8, 12, 16, 20, 24, 28, 32… the eighth item is 32

Two different ways of getting the same answer suggests you’ve got the right answer. Like the general rule of thumb that if you find a fact in two “independent” sources, they greatly increase the chance of them being right.

This should be provable simply with Bayes’ Theorem.

One instance, me thinking there is another side to maths, simply makes it peculiar or unique. Two instances, and we have some validity, and so on. The jump from one to two is huge. This goes for a lot things. 2020worldpeace springs to mind…