സോപ്പുകുമിള ജീവിതം

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അന്നു വൈകുന്നേരം ഞാന്‍ പതിവിലും നേരത്തെ ശംഖുമുഖം ബീച്ചിലേക്ക് പോയി. ഏകദേശം അഞ്ചു മണിയോടെ ബീച്ചിലെത്തി. അവിടെ പതിവു കാഴ്ച്ചകള്‍ എന്നെ കാത്തിരിപ്പുണ്ടായിരുന്നു –  പട്ടം വില്പ്പനകാരന്‍, ഐസ്ക്രീം കച്ചവടക്കാര്‍, സഞ്ചരിക്കുന്ന ഗായകന്‍, പിന്നെ സോപ്പുകുമിളക്കാരന്‍. അല്പം വെയില്‍ ഉണ്ടായിരുന്നു. എന്നിട്ടും എനിക്കും മുമ്പേ കുറെ പേര്‍ അവിടെ എത്തിയിരിക്കുന്നു.

എന്‍റെ ശ്രദ്ധ സോപ്പുകുമിളക്കാരനിലേക്കായി. അയാള്‍ക്ക്‌ ഏതാണ്ട് പതിനെട്ടു വയസ്സ് പ്രായം തോന്നും. അയാളുടെ കൈയില്‍ ഒരു കുഴലുണ്ട്. അതിന്റെ അറ്റത്തില്‍ വളഞ്ഞ ഒരു വയറും. കുഴലിനുള്ളില്‍ സോപ്പുവെള്ളമാണ്. ആ വയര്‍ കുഴലില്‍ മുക്കി എടുത്തു കാറ്റത്ത്‌ വീശുമ്പോള്‍ കുമിളകള്‍ അങ്ങനെ വരവായി. കുമിളകള്‍ കാണാന്‍ നല്ല ഭംഗിയാണ്. അയാളുടെ അടുത്ത് കുട്ടികള്‍ എത്തുമ്പോള്‍ അയാള്‍ അവരുടെ നേര്‍ക്ക്‌ കുമിളകള്‍ പറത്തി വിടും. അത് കണ്ടു കുട്ടികള്‍ സോപ്പുകുമിളക്കുഴല്‍ വാങ്ങാന്‍ നിര്‍ബന്ധം പിടിക്കും. അതാണ്‌ അയാളുടെ ബിസിനസ്‌ ട്രിക്ക്.

മൊത്തം അയാളുടെ കൈയില്‍ നാല്പതു കുഴലുകള്‍ കാണും. കൂടെ പത്തു ഗിറ്റാറും. ഇരുട്ടായാല്‍ പിന്നെ കുമിളകള്‍ക്ക് ഡിമാണ്ട് ഇല്ല. അപ്പോഴും വല്ലതും വില്‍ക്കെണ്ടേ?

ഒരു അഞ്ചേമുക്കാല്‍ ആയപ്പോള്‍ അവിടേക്ക് ഒരു കൂട്ടം പെണ്‍ കുട്ടികള്‍ എത്തി. ഏതാണ്ട് ബി ടെക് പ്രായം. അവര്‍ അഞ്ചു പേരുണ്ടായിരുന്നു. ഇത് പതിവിലും അല്പം വേറിട്ട ഒരു കാഴ്ചയായിരുന്നു. സാധാരണ ഫാമിലി ആയിട്ടാണ് ആള്‍ക്കാര്‍ വരിക. അല്ലെങ്കില്‍‍ പയ്യന്മാര്‍ ആയിരിക്കും വരിക. പെണ്‍കുട്ടികള്‍ ഇങ്ങനെ കൂട്ടത്തോടെ വരുന്നത് ഞാന്‍ ആദ്യമായിട്ടാണ് കാണുന്നത്. എന്‍റെ ശ്രദ്ധ അവരിലേക്കായി. അവരില്‍ രണ്ടും പേര്‍ പാന്റും ടോപ്പുമാണ് ഇട്ടിരിക്കുന്നത്. ബാക്കിയുള്ളവര്‍ ചുരിദാറും. ഒരാള്‍ പാന്‍റ്സ് അല്പം കേറ്റിയിട്ടിട്ടുണ്ട്. അവളുടെ ഭംഗിയുള്ള പാദസരം നന്നായി കാണുന്നു.

പെട്ടെന്ന് അവരുടെ നേര്‍ക്ക്‌ കുറെ കുമിളകള്‍ കാറ്റില്‍ വന്നെത്തി. പതിവിലുമധികം കുമിളകള്‍. ഞാന്‍ സോപ്പുകുമിളക്കാരനെ നോക്കി. അയാള്‍ ഒരു ചെറു പുഞ്ചിരിയോടെ ആ പെണ്‍കുട്ടികളെ നോക്കുകയായിരുന്നു. പെണ്‍കുട്ടികള്‍ ആകട്ടെ കുമിളകള്‍ പൊട്ടിക്കുന്ന തിരക്കിലായിരുന്നു. അവര്‍ അയാളെ ശ്രദ്ധിച്ചോ എന്തോ. അപ്പോള്‍ അവിടെ വീശിയടിച്ച കാറ്റ് ആ കുമിള വില്പനക്കാരനെ ഒന്ന് തോട്ട് തലോടിപ്പോയി. ആ ഒരു നിമിഷത്തിനു ശേഷം അയാള്‍ തന്‍റെ പതിവു വ്യാപാരത്തില്‍ എര്‍പെട്ടു. ഞാനാകട്ടെ ആ പെണ്‍കുട്ടികളെ നോക്കിയിരിപ്പായി..

Consider a discrete Markov source, {\mathscr{X} \ = \ X_i\}_{i=1}^{\infty}} ona finite alphabet set. Let the initial distribution be {Q} and the transition probability for the {n^{th}} step be {P_n}. When can we say that {\mathscr{X}} is stationary?
Clearly, the source has to be time invariant and thefore we need {P_n = P, \forall n}. For {\mathscr{X}} to be stationary, we need
\displaystyle f(X_1) = f(X_2) = \ \ldots \ f(X_n)
etc, where {f()} is the distribution. But {f(X_n) = QP^n}. Thus {Q = QP} guarantees that all {X_n}‘s have the same distribution. Now, consider, say, {f(X_1;X_2;X_3)} and {f(X_2;X_3;X_4)}.
\displaystyle f(X_1;X_2;X_3) = f(X_1)f(X_2/X_1)f(X_3/X_2).
\displaystyle f(X_2;X_3;X_4) = f(X_2)f(X_3/X_2)f(X_4/X_3).
It is clear that for the two joint distributions to be equal, {f(X_1) = f(X_2)} is enough and therefore {Q = QP} is sufficient.

The centenary celebrations of the Indian Institute of Science concluded this week. The centenary year saw many events- the centenary conference attended by Kalam, Dr Sam Pitroda’s speech, the centenary marathon run and a concluding ceremony precided over by the President Smt Prathibha Patil. To mark the end of the celebrations there was a violin concert by Shree Ganesh and Kumaresh. What should I say about the concert! Before the concert one of my friends asked me about the artists to which I replied, “Attend the whole concert. Your will remember your life as before the concert and after.”

The concert was in a big special Pandal made at the Gymkhana grounds. For once there was no issue of no-seats-to-late-comers in IISc :). The acoustics was good. Accompanying the violinists were Phalgun and Krishnan on Mrudangam and Ghatam. They started with a short piece in Sahaana. It set the mood for the moment. It was followed by Mayamaalavagowla – their own composition called Ragapravaha – and then a Varnam in Kannada. Then they played Reethigowla, one of my favourite raagas. Later they played one more of their composition, in Naasika Bhooshani, followed by a sudden spurt of Kadhanakuthoohala. What then started as an RTP in Naatabhairavi later turned to a wonderful Raagamaalika. And then the percussion duet. At the time of vote of thanks the speaker did not resort to any cliches and the whole audience gave a standing ovation to the artists.

Ganesh and Kumaresh performed in my native place when I was ten. After that, I had to wait for another 11 years to listen to their next concert. They have been my favourites. Though I expected them to play some of their fusion compositions, they completely enthralled the audience just with carnatic classical.

Let there be more centenary celebrations. Why can’t time run faster !

One of my profs made the following remark in the class:

“I hate late comers. They think that they can come a few minutes late and still follow the class. But then by induction they can skip the whole class.”

Clearly his reasoning has a mistake. The induction proof wont go through that ‘N’ for which he erases the black board !

My analysis professor mentioned the following comment made by Rudin : The whole of analysis is all about finding out when two operations commute ! (I could not find the source)

If one goes through the whole of Rudin’s books on Analysis – Principles of mathematical analysis and Real and Complex analysis – one finds only only two figures: The McGraw Hill logo on the front cover and the TMH logo on the back cover ! (Well Apostols book, for example, has more figures)
Mentioning to the fact that a random walk in one or two dimensions is recurrent but a three dimensional random walk is not, the great Kakutani made the following remark :
“A drunk man will find his way home, but a drunk bird may get lost forever.”

The great Prof. Varadhan made a visit to the IISc on Febrary 13th. He gave a lecture at the IISc faculty hall on entropy and large deviations. The following example was interesting.

Consider a bug with limited energy trapped in the valley of a steep peak. It tries to scale the peak and reach the other side. Evey time it fails, it falls to the bottom of the valley. It changes its strategy and starts all over again. After a very large number of attempts, it succeeds and reaches the peak. As it goes down the other side, an observer on the other valley sees the bug coming down. He becomes curious, goes to the top of the peak and looks below to see how steep was the bug’s scale.

A bug scaling a peak

Now, having seen the bug, what can he conclude about the strategy adopted by the bug? Prof Varadhan made the following comment. The observer can surely conclude that the bug would have adopted the most efficient strategy. That has to be the case because as the number of iterations becomes very large, the probability of success is dominated by that of the best strategy and if a success ocurs it must come from the best strategy.

In about 1902 a person named Sri Sivaprakasam Pillai met Sri Ramana Maharshi at the Virupaksha cave in Thiruvannamalai and posed his doubts on self realisation. His questions and Ramana Maharshi’s answers (about 28 in number) have been published as the book ‘Who Am I ‘ . These questions and their answers can be read here. I would like to highlight below one question which explains how to practice self inquiry. It may be used as a method to channelize ones thoughts. Here is a photo of Ramana in his young age.

ramana

Qn: What is the means for constantly holding on to the thought Who am I ?

Ans: When other thoughts arise, one should not pursue them, but should inquire: ‘To whom do they arise?’ It does not matter how many thoughts arise. As each thought arises, one should inquire with diligence, “To whom has this thought arisen?”. The answer that would emerge would be “To me”. Thereupon if one inquires “Who am I?”, the mind will go back to its source; and the thought that arose will become quiescent. With repeated practice in this manner, the mind will develop the skill to stay in its source. When the mind that is subtle goes out through the brain and the sense-organs, the gross names and forms appear; when it stays in the heart, the names and forms disappear. Not letting the mind go out, but retaining it in the Heart is what is called “inwardness” (antar-mukha). Letting the mind go out of the Heart is known as “externalisation” (bahir-mukha). Thus, when the mind stays in the Heart, the ‘I’ which is the source of all thoughts will go, and the Self which ever exists will shine. Whatever one does, one should do without the egoity “I”. If one acts in that way, all will appear as of the nature of Siva (God).

Let us consider the following problem which is a popular example in game theory.

A mother wants to divide a cake between her two children. To make both of them happy she has to ensure that each one gets an equal share. That is she has to cut the cake into two equal halves. But the problems is that the cake does not have a regular shape. Hence what is equal to her eyes may not be equal to the eyes of her children. The consequences of an unequal division are imaginable. So how can she make both her kids happy?

The solution is to ask one of the kids to cut the cake into two and the other to choose the piece. It can be verified that this solves the problem. The interesting thing about the solution is that the mother was able to satisfy both the kids even without knowing what will make them happy.

Now if the mother has N kids what will she do?

What will happen if some kids form a collusion and try to get a bigger share for them ?