Thinking about thinking

Hey ya,

There is/was a Hindi Writer , Mr Vidya Niwas Mishra, who writes to strike the deep roots of blind faith and the thinking of the so called , high class society. In my school days , I came across one of his passage which concludes with a famous poet's line, "कभी आती थी हाले दिल पे हंसी , अब किसी बात पे नहीं आती ". I remembered this quote recently while in discussion with my friend Sam.
Some times life plays with you such games that you are gripped over by OCD :) .
Anyways with out discussing much on this I will share some good experiences here,

1. I have made a promise to continue french course to somebody , now if I don't do that , it will cost me a lunch at five star hotel, so going forward, will actively work on it.
2 .. guess what ? Murphy's law experimented in my life for some 3 odd cases and i can say it holds true :D.
3. Clash of the Titans is worth watchable once, i liked background score of this movie.


Thinking about thinking, not like the paper of Widrow while contributing LMS algorithm I am thinking about how thinking changes over the period of time in a well cultured mind. They become possessive for their comfort. Even though life is uncertain and they should believe more on values which they are going to deliver to upcoming generation than the comfort. You must be thinking what the hell I am talking about :) so I leave it here and give an exercise for curious minds, don't think too much for my last statement,


Do we have an "intuitive" proof for the following statement,
Given a,b,c positive integers, a/(b+c)+b/(c+a)+c/(a+b) is always greater than or equal to 1.5

PS: It's a famous Math Olympiad problem, but remember I am asking for an intuitive solution.

Update :
Yes, it can be solved trivially by considering (a+b), (b+c) and (c+a) as another 3 independent variables, but my question is how do we get that intuition :) Anyways... wait for my next post in next month.