Thursday, April 19, 2007

The bookstore problem

You are in a bookstore with the intention (and resources) to buy ONE book, and all the books are wrapped in plastic. Is there a way other than judging a book by its cover?

And what if you find the covers of more than one book interesting? How do you judge different books based on the cover?

One would think that based on apriori knowledge/information/wisdom you buy a book which had the most interesting cover. But what if AFTER buyin the book, you happen to read the preface of another book... And now THAT book ALSO seems interesting...

Is that a start of something?

Saturday, April 14, 2007

The ice-cream problem

I go to an ice-cream parlor. I haven't tasted an ice-cream earlier, but 'heard' that it tastes delicious.

There are 27 varieties. I have to make a choice between these flavors. I choose a flavor.. educted guess, I would think. I like the ice-cream. It's not AS good as I had heard, but it's good.

I presume that I had not made the BEST decision about the flavor. But now I have more knowledge (Experience) and hence, the next decision wil be better. And next time, I summon the courage to make a choice of another flavor. A more educated guess, again I think.

And I like this flavor much more... But then, the mind is not happy. It wants to 'explore' further.
And it has seen the pattern - more educated the guess, the greater chance of the flavor being tastier.

So, next time I go to the ice cream parlor, I choose ANOTHER flavor. It's delicious. It's as good as it can get. I think it can't get better. But the weak mind tempted... to make the next guess... to explore a vertex on the next level of the traversal..

I do that. And this time, I also gets toppings... peanuts, oreo cookies etc. Now the ice-cream is thoroughly tasty. I am GLAD I took the step.

But there are questions:-

1. There is a modification to the problem. Once I choose another flavor, the previous flavors are discarded for good, and I cant get back to them. Under such circumstances, when should I stop exploration?
Should I stop when I find a GOOD flavor, even though there are chances that I might find a better flavor in the next step of exploration? (It is MY belief that the next educated guess will be better... but that need not be true).

2. Was the last ice-cream better because of the toppings? Or was it inherently good?

3. There are ice-cream flavors that are reallly popular (recommended). Am I biased towards those?

There are so many subtleties that are not captured in this analogy, although they can be.

Anyway, my roomie suggests a similar story - about a shishya (student) and his guru. THe guru asks the shishya to go to the forest and pick up the tallest branch, on the condition that e cannot pick up a brach on his way back.

Well... this is easy to solve... coz one can keep hold of the tallest branch SO FAR, and then discard it when a taller branch is seen. (FInd the max number in an array algorithm).

But this solution UNFORTUNATELY does not hold for all situations!

Friday, April 13, 2007

The bike-path Teaches

I enjoy enjoying the scene around me when I bike.
I like to leave the clutched handle and free my clenched fists.

If I am biking up-slope, I can never leave my hands.

If I am biking on level ground. I can somehow manage to leave my hands ... but my eye is tied to the path and I cannot look around.

If I am going down-hill at a steep gradient, I can leave the hands. But again, I have to be cautious. One small mistake can cause me to topple and ruin the whole ride.

However, if I find a down-hill path with a gradual descent, I can continue peddling and watch around and ENJOY, without any effort or fear of falling.

The aim is to find that path... THAT balance where one is not struggling and there is no inertia... where one is enjoying the journey without concentrating too much on the journey... without any strain of intense effort, or fear of 'toppling' over.

That's what an ideal income should be!