Dienstag, 3. Juli 2012

Mathematical proof- grass is greener on other side

Two envelops' paradox...


The basic setup: You are given two indistinguishable envelopes, each of which contains a positive sum of money. One envelope contains twice as much as the other. You may pick one envelope and keep whatever amount it contains. You pick one envelope at random but before you open it you are offered the possibility to take the other envelope instead.[3]
The switching argument: Now suppose you reason as follows:
  1. I denote by A the amount in my selected envelope.
  2. The probability that A is the smaller amount is 1/2, and that it is the larger amount is also 1/2.
  3. The other envelope may contain either 2A or A/2.
  4. If A is the smaller amount, then the other envelope contains 2A.
  5. If A is the larger amount, then the other envelope contains A/2.
  6. Thus the other envelope contains 2A with probability 1/2 and A/2 with probability 1/2.
  7. So the expected value of the money in the other envelope is

    {1 \over 2} (2A) + {1 \over 2} \left({A \over 2}\right) = {5 \over 4}A
  8. This is greater than A, so I gain on average by swapping. i.e grass is greener...further...
  9. After the switch, I can denote that content by B and reason in exactly the same manner as above.
  10. I will conclude that the most rational thing to do is to swap back again.
  11. To be rational, I will thus end up swapping envelopes indefinitely.
  12. As it seems more rational to open just any envelope than to swap indefinitely, we have a contradiction.

Donnerstag, 28. Juni 2012

MMT

Somehow agree to Modern Monetary Theory... http://pragcap.com/understand-the-modern-monetary-system/understanding-modern-monetary-system

The moot point is clear division of goals between government and central banks...where central banks ought to have a single goal of inflation control, government should work towards increasing economic efficiency, increasing employment etc...hope indian government does understand this.

Samstag, 19. Mai 2012

Chelsea vs Bayern Muenchen 2012


Just saw the match between Chelsea vs Bayern Muenchen, Champions League Final 2012.

http://www.youtube.com/watch?v=l2G6NueO0k8&feature=related

Throughout match Chelsea remained underdog but had the last laugh......guess, that the diversity they had paid handsomely. BM on the other hand are seemed uniform, disciplined and virtuous (seemingly), but the difference they lacked proved decisive. 

Freitag, 24. Juni 2011

Change, change and change

So the prophesies of certainly, theoretically future has been belied again. GS predicted BRIC after china had silently risen already...it lasted for few years when Next 11 came. Now another twist. When obituaries for Europe was being written, it is emerging more of a solid block. So the customary power is back. And eternally optimistic Indians will be dis-heartened after reading this.

So this leaves the world in contrasting 3 blocks: US, Europe and China. Capitalistic (still), socialist and neo-communist. It is the game of Keynes, free market and state control...new theories are being tested. Hopefully the 2nd wins.

Meanwhile, it also means that big money-makers, in absence of new productivity, can manufacture money by increasing its speed (currency). No wonder we are living in so fast forward yet decadent world.

Montag, 15. Februar 2010

Euro-Neti Neti

Neti, neti: in Sanskrit- neither this nor this(that)....logic of negations to arrive at something conclusive.

Never was it truer than concurrent developments. Example, Eurozone. At the time of its inception, it was held as the paramount of ideals. And now serious threats have emerged on account of member's indiscipline (Greece default, France's regular 8% of budget deficit instead of norm 4%), criticism of loss to members over free monetary policy (no one country can devalue the currency if need be) etc etc.

The question about Greece is not Greece alone (it accounts for only 4% of whole euro economy), but who next. Already term PIIGS is coined: Portugal, Ireland, Italy, Greece and Spain. It would probably take just one member country to walk away and the whole of 10 years experiment will wash away.

Should likes of UK(though it is not doing good either) and Sweden be happy that they didn't relinquish their currencies or Turkey should have Schadenfreude that luckily it was barred to join Eurozone itself.

Dienstag, 29. Dezember 2009

Reading God's Mind

So after all theory and conceptual possibilities, scientists are doing what they do best.......confirming it by experiment.

Only it takes 20 years and nearly 10 billion dollars to set-up the most advanced experiment ever conceived via Large Hadron Collider..

Least we expect is the confirmation of Higgs particle, any journey beyond quark begins from.

Beyond this will be revealation on Dark matter, extra dimensions, string theory (which one out of theoretical million postulates) etc etc. All this with 1.0×10-9 grams of H2 at near absolute zero temperature.

Will they generate black hole, will it consume us..though scientists are unanimous in opinions against it, it will still be better to die wiser....