## Tuesday, July 5, 2011

### ECE

I was reading this math post. It is about puzzles and one simple method of solving most math puzzles- thinking of an extreme example. What he means is that you can assume some extreme values for the variables involved, and deduce the answer by logic. (I like the puzzles listed as well!)

Admittedly, this is a very useful method. Especially in your competitive objective type exam scenario (Though for this scenario, I personally think "Inky Pinky Ponky" is undoubtedly the method of preference!)

Few things I want to highlight though. One- You should think of the 'right' extreme example. Some extreme examples might not lead you to any conclusion at all! I remember how, in schools, teachers used to start explaining proofs by saying "draw perpendicular AD to BC" or "AM to NP" or some such thing. And immediately I would think how was I supposed to  know which perpendicular to draw? Later on I realized that if you understand geometry well enough, actually rephrase- if you know well enough to think from a geometrical angle (Pun unintended!) you will know exactly which perpendicular to draw. But point remains that you need to choose the "right" perpendicular (Oh! Again, pun unintended!) In the same way, one does not always know which extreme example to choose. And if you don't choose the right one, you might end up a) getting a long and roundabout proof or b) not proving anything at all!

Anyway, why I brought this up here is that this method is not only useful for mathematical problems. I find it a good tool to understand human behavior. For eg: When someone says I value money but I value family more, one easy way to verify it is to ask the question- "if you had to give up all your money so you could retain your family would you do that?" or something of that sort. Basically pick an extreme scenario and check your statement. In fact, this method helps even if you are simply trying to understand your own selves.

Anyway, I have used this method before, and though not mine, I thought someone should give a name for it. "Extreme Case Evaluation" sounds OK by me. Maybe I should publish a paper on it someday...

P.S: I hope people found out why the title is ECE... Ya ya, I know I am wicked .. :P