Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!”
This is typically how Analogies work. I want to explain some concept to someone, say A->B (A implies B). After a while, I find that the logical relationship between A and B is quite difficult to get across. I then resort to an analogy, say X->Y (X implies Y). I pick this analogy from everyday life so that the logical relationship between X and Y are evident, if not obvious. Then, with some conviction, I claim that as X->Y is so obviously true, A->B must also be true. The unsuspecting listener vaguely gets A->B, but looking at how strongly X->Y holds, she is convinced that A->B must hold as well.
The catch is that whether A==X and B==Y is never touched upon, let alone proved.
Let me give an analogy to explain this – (grimace)
Say my aunt wants to prove it to me that a guru is required to navigate the path to enlightenment, she first tries to convince me by using just their merits and interactions. I am hardly convinced, and thats when she resorts to an everyday analogy. We all know how a little curd is necessary and sufficient to ferment a whole vessel of milk into curd. Similarly, a guru is necessary and sufficient to get you across the sea of ignorance into nirvana. I am now thinking – Oh! Where do I find my own guru?
See the catch? Who is to ever suspect that my aunt never touched upon the similarity between the situations? Did she prove that a guru equals a tea spoon of curd? Or that I am a vessel of milk? Or that enlightenment is a vessel of curd that I am interested in, etc.
Informal reasoning of this sort has had me always suspecting every analogy that anyone throws at me to make me see their points. I grimace every time I do it myself. This had led me to believe that there are some severe restrictions when it comes to proving something to someone.
As I lamented about this with the vaakpatu (vaachaLi?) Nisrani Ramchandra, he told me that Nyaya says that there are four odd sources of knowledge.
– Pratyaksha (Perception)
– Anumana (Inference and Contrapositive)
– Upamana (Analogy)
– Aptavakya (Testimony)
If A->B was obvious by perception, there would be no need for a proof. If whenever A were present, B were seen (inference); if whenever B were not present, A would not be present (contrapositive) – QED. We have already covered Analogy. And of course, if some one whom I consider wise, someone whom I trust, were to tell me that A indeed implies B, I would just believe it. That would be Aptavakya.
I also want to add two more such concepts.
Proof by Contradiction: When you see that everything else is eliminated, whatever is left, however counter-intuitive, must be true. (Sherlock Holmes would’ve smiled)
Proof by Enlightenment: When you know that ‘it’ is true. You just know it. No proof is ever required.
I wonder what formal logic theory says about these techniques. I have seen various mathematical proofs which use these notions formally, but when it comes to social sciences, or philosophical reasoning, I feel the void. Many a time, I have felt this desperate craving to have things formal, so that the wheel of thought need not be reinvented during each dialogue. Sigh.
Finally, in spite of so much thought about logic, conviction, proofs, etc., there is this feeling that everything comes down to faith/belief/trust; Or so I believe.
I, like most others, did not have a choice when I first chose a religion to follow. I was….er….born into one. After spending quite a while seeing it being practiced, practicing some of it myself, defending subtle nuances in quasi-intellectual arguments with friends, thinking about it for quite a while, I gave up on conventional religion. This decision was driven by conscious rational thought and emotionally charged events.
From the outside, this gave me a chance to look at religion as a concept. I respect conventional religion for its ability to give solace to helpless minds. There have been times when I wished I could enjoy religious comfort. I am amazed at how religious thoughts have united various peoples across time. One’s belief in religion constitues a big amount of one’s identity.
Of course, the importance of religion could be accepted if religion were to be defined by its followers as “code of conduct in ALL aspects of life.” I am sure most religions define codes of conduct for most aspects of life. Rules and consequences of (not) following them are written down with great clarity. “Popularly understood religions” have unambiguous rules and even more unambiguous consequences. This is what makes them popular I suppose.
However, to understand the “whys”, the “how exactlys”, the “what ifs”, and other questions, deeper thought and more importantly, deeper study into religion is required. This, unfortunately, takes a lifetime. The irony of the situation is that religion tells us how to live, and its takes a lifetime to understand one religion. So, what is the way out?
It is evident that we have been leading lives. Without much problem, that too. Codes of conduct have been easy to follow. We do not break legal rules in most situations. People, mostly, are fair to others. So, why this fuss about religion?
This is because people mostly lead double lives. The life of day to day actions, intuitively selfish decision making, profit maximizing, etc. The other life of love, fear, insecurity, emotional traumas, indecisions, ego, inner-conflicts, peace-seeking, theorizing, etc. Of course, these two lives are closely intertwined, and with some people, are not separable at all. Religion, at some level, helps the latter life, and brings the two together.
Out of all the knowledge I had acquired over the years I have been thinking, and the built-up emotional reserve that had some thoughts of its own, I had come to the conclusion that I could formulate my own religion. Of course, an informally specified religion will have its own pitfalls during testing times, and mine was no different. Formally specifying religious tenets proved to be extremely hard. Achieving completeness seems intractable, if not undecidable.
So, currently, I am thinking about respecting centuries of distilled wisdom. The best approximation seems to be Hinduism, as it seems more liberal than other choices. Approaching a religion with absolutely no pre-conceived thoughts seems to be impossible. But I am giving it a try, and lets see where it leads me.
On an aside, I think that human thought has not been able to generate really significant movements for the last so many centuries because I do not see any new religion that has been developed. Have we really advanced in terms of thought and its corresponding conviction? Einstein supposedly believed that God is a “natural order of things.” He could have made a religion out of it. Formulated a set of principles, etc. But I guess he didn’t fully get it to make it into a full fledged religion.
While browsing through someone‘s website, I came across this thought provoking take on nostalgia –
“I’ve always viewed nostalgia as a heresy, but it becomes increasingly harder to fight it off as one grows older. Perhaps it is part of the mechanism we use to cope with regret: when enough patina accumulates, mistakes can be viewed as formative experiences, and switch from being sources of regret to being key moments that contributed to the development of one’s present self. Viewed in that light, nostalgia is a form of self-deception, which doesn’t make it any easier to accept.”
I pondered over it for a while: in the abstract, through the light of my own experiences, my own ideas on it. I conclude (at least for now) that for me, nostalgia is prevalent, but not important/controlling/mood-altering. As I write this, a nagging doubt that nostalgia is indeed mood altering, though not controlling, is creeping in. Why do I say this? As my mood….
I lost a few “instense-nostalgia-triggers” with my wallet a few days back. The first thought was of sadness at loosing these nostalgia-triggers. And now, I can think of the sadness these triggers themselves used to bring about each time by making me take nostalgic trips down memory lane. Now, as I think of the lost triggers, I am struck that I now have memories of my memories. Time to move on.
H. W. Longfellow thought that Nostalgia is a feeling of sadness and longing that is not akin to pain, and resembles sorrow only as the mist resembles the rain. Poetic eh?
Here is my interpretation of one of Samba’s various bursts of inspiration. An abstract idea whose viability, logistics, implementation etc. need to be worked out.
We know that a lot of effort goes into the preparation for these competitive exams; out of which only the top 2% or so make it in to IITs, IIMs etc. Out of say every 100 candidates that takes each exam, 2 of them actually make it in, and so, in some sense, their efforts are not wasted. And I will assume that around 40 of them just took it up as a part of their regular path, and weren’t really serious about them. These numbers can be inaccurate; but bear with me.
The real wasted effort lies in those 50 of them, who actually put in a lot of effort, and out of them, there are at least 10 of them who almost as good as the 2 of them that get in, but just cannot make it in because the number of seats are limited. Now, the question is: can this effort be harnessed to do something good? something profitable? Can the exam structure or the interview structure be changed to do this?
One concrete implementation of this idea. The top few percentile people from CAT are called in for a GD/PI stage, where they are put against each other, and are evaluated for managerial potential, stress, ability to think on their feet etc. One idea is to divide them into chunks, and assign them to random villages in the rural heartland of India. Their job is to stay in these villages for a week (along with an official from the IIMs), and involve themselves in some constructive activity. Call this a real case study as opposed to the arm-chair variety that gets done right now.
This suggestion is not all that preposterous for few reasons
– Candidates are quite serious about their admissions and an IIM admit is a great incentive.
– Its more realistic than an arm-chair case study because real results can be evaluated giving better candidates to these institutes.
– The candidates are smart and some real work that might be useful to these villages can be carried out.
– As CAT filtering has already been carried out, we have a more manageable number of people.
Of course, all these details, and the basic idea itself are up for debate, and thats why the posting 🙂 The rationale behind this thinking is to somehow harness the efforts and the incentives that are a part of this big circus.
Any ideas? problems? possibilities?
Are there enough people in this world for all the tasks that are around? I mean, is the load distributed properly? are there enough complexity theorists? enough newsreaders? enough teachers? enough sportsmen? enough truck drivers? enough glassblowers?
Is it balanced? or are we fooling ourselves that things are in equilibrium? Lemme tell you why this equilibrium is floating in my head now. I was pondering about the so called “micro” and “macro” level interests of any person. At least me. At a micro level, I am working on web-search, or in a more general sense, concerned about computer science. At a macro level, I feel for India, Indian politics, socialism, economics, historical injustice, hunger, etc. Though my macro level interests are viable career options, I just dont take them for various reasons. Now, I somewhere, deep down, subconsciously, desperately hope that human equilibrium exists and all those areas of work that I am not involved in, but are important to me, are being taken care of; by professionals, by passionate people, by zealots, by selfless volunteers etc. And my working on search engines will somehow help them do their job better. Some theory guy proving approximation lower bounds for some O.R scheduling problem will save some money in some facotry line up which will be given as bonus. Some IAS officer streamlining infrastructure efforts might get me from KanjurMarg to Mulund in time for a movie.
Anyways, as I am writing this, I feel quite stupid, but the equilibrium thought did come to my mind and was quite futile in convincing me that what I am doing currently is worthwhile…