Wednesday, September 26, 2007

On Theism and Proofs

Someone needs a course in binary logic and proof theory.

It all sounds so wonderful. I do not believe that god does not exist. I just don't believe that god exists. I am all rational, but also do not have any burdens of proof. Act of faith vs rationality, and all that. Amazing, right?

Wrong. Let this be cleared once and for all. All scientific/logical theories are by definition only explanations/observations of the truth and not the truth themselves (the map is not the territory and all that jazz). Thus, the statement that "Gravity exists" is logically the same as "I believe that gravity exists". The reasons for your beliefs and your ability to justify them will qualify the strength of this belief. Hence, a rational person will have no qualms stating that "gravity exists" but will need to qualify his belief in god by saying that "I believe that god exists". "Belief" is a qualifier to the strength and justification of your theory - it doesn't change your assertion of the truth value of your theory. Knowledge is only a representation of the truth, not the truth itself.

Hence, I believe that god does not exist and I do not believe that god exists are logically one and the same. Any attempts to try to prove otherwise miss the important distinction between the truth and the representation. What is wrong with these modern day atheists? Don't they even have the balls to say "God is dead, and has always been" (or something like that)? Come on people, you have Richard Dawkins as your intellectual fountainhead. Show some bloody guts.

There are exactly three major logical positions to take w.r.t the existence of god. "I believe that god exists", "I don't know and the world will in all probability never know", and "I believe that god doesn't exist". (Actually there are four - one can always say "I don't bloody care".) There can be variants within these major positions, but to try and get out of committing yourself to one of them broadly is just intellectual dishonesty.

If all you want to talk about is the burden of proof, here's how you frame it - proofs are either constructive or by contradiction, but can never be by assumption. A positive assertion ("God exists") will typically need to have a constructive proof or a strong reductio ad absurdum. As long as you can thrash the positive proof, it will be considered a good enough negative proof. An example of this is the god of the gaps rebuttal given by atheists.

When it comes to God, or the final explanation, the absence of evidence is pretty much the evidence of absence, irrespective of what Carl Sagan says in the preface to A Brief History of Time. All we need to remember is that the evidence need not necessarily be a positive empirical observation. Counterfactual reasoning is often the only way of determining causuality.

Tuesday, September 18, 2007

Of inductive logic, perceptions, and natural languages

He reads this and hates all men. Frivolous as it seems, I am tempted to ask, why not just Pakistani men?

The problem is, of course, central to all of inductive reasoning. How strong is the inductive link in your generalization? The solutions are very context-specific. And the interpretation of context is very experience-specific. One of the main irritants with life is that statistical inference is not readily obtainable. Hence, one's experience becomes one's truth. And we all have different versions of the truth - each one, a priori, as true as the others. Post-modernism suddenly seems attractive.

Given the sentence "Rand is popular in the girls' hostels", how do you interpret it? Does the speaker want to suggest that Rand is more popular than unpopular in the girls' hostels? Or does he want to say that Rand is more popular in the girls' hostels than in the boys' hostels.

Mathematically, let's define a threshold of popularity, say x% readership, and denote the reader base of Rand (expressed as a percentage) among hostelite girls as P(h-girls), among hostelite boys as P(h-boys), and among non-hostelite girls as P(nh-girls). What does the speaker want to say by "Rand is popular in the girls' hostels" ?

A) P(h-girls) > X : Rand is popular on an absolute scale, the dictator's interpretation)
B) P(h-girls) > P(h-boys) : Rand is more popular among hostelite girls than among among hostelite boys
C) P(h-girls) > P(nh-girls) : rand is more popular among hostelite girls than among non-hostelite girls.

The above question is not rhetoric - all readers are encouraged to answer A, B or C in the comments, along with reasons if they have any. The results, as we shall see in the next post, will probably have some insight for Statistical Natural Language Processing, which, incidentally, is roughly the field I worked on in my undergraduate final year project.

p.s. : Of course I was kidding about postmodernism. It's a pile of garbage, worth only our collective contempt and ridicule.

Friday, September 14, 2007

The value of a socio-economic argument

is exactly equal to the value of the way in which it has been presented. Ravikiran says here that " this kind of fisking, where you quote the article and try to rebut it point by point. The problem with doing this is that there is a high risk of missing the overall point the article is making " is "unfair".

Right. So can I now write an article that goes something like this -

1. Remove poverty : ( some illogical substantiation about how it can be removed)
2. Solve the Kasmir issue : (some more illogical substantiation about how it can be solved)
3. India has to win the cricket world cup (no substantiation, the passion will suffice)
4. World Peace ( no substantiation, a flying kiss should be enough)

and claim that my article was great and those who rebut my substantiation point by point are missing the 'overall point' and being patently unfair?

Socio-economic arguments are not independent of the people who make them and the way in which they have been made. They are unlike the laws of physics, which are true, quite literally, even in vacuum and do not need human observation to be true.

One day, psychology and the cognitive sciences may just provide THE definitive theory(ies) of human behaviour and interaction - a few theoretical attempts have already been made, most notably by Friedrich Hayek who proposed the connectionist hypothesis of cognitive science. Until then, we will just have to consider each theory case by case, assumption by assumption, and implication by implication. The worth of every argument, every article on the society and economics, then, is simply the way in which it has been substantiated, point by point, by the author. One does not have the liberty of saying 'you may be right in your rebuttal you're missing my overall point'. The overall point is nothing but the sum total of all the substantive points, and if each one of them has been attacked, the overall point has been attacked as well. Anyone who wishes to make only the overall point should go easy on the not-so-solid substantiation.

p.s : I find it quite amusing that the one who was criticized is a lot more appreciative of the point by point analysis than the zealous defender. May be he is just modest.

Wednesday, September 12, 2007

Personal Notes - I and II

1 - People in my institute, when they prepare for an economics exam, read Pindyck and Rubinfeld. I, on the other hand, indulge in this. I am so bloody screwed.

2- One needs to measure one's tone. There's only so much egotistic vitriol that one can justify to oneself. Every once in while, something will happen that will raise guilt pangs about having spoken/written in a certain way.

Thursday, September 06, 2007

Choice and Specialization in schools, contd.

Reference : We're fisking this article

Context : We've already seen why the economic logic is rather contrived.

Now, we move on to the empirical. Witness this paragraph.

Now comes the other reason why I think children should be allowed to settle into subjects and activities that they are good at. We often ask each other why there is such a weak correlation between those who top the board exams and those who actually succeed in life. Most of us have also gone through the almost mandatory shock of being told at a school reunion that the class duffer is now a famous doctor or a CEO. My friend Avinash was a known troublemaker in school. Later, he struggled through junior college before dropping out. He is today one of the most successful photographers in the Hindi film industry.

The old technique of singular anecdote as evidence. Actually, sir, we don't ask why there is a weak correlation between those who top board exams and those who succeed later in life because in our experience, there is a rather strong correlation between those who top board exams and those who later succeed in life, assuming that we're both measuring the same parameters of success - money, power and prestige (in any order that you want it). You see, if someone tops board exams, it implies certain things. One, that she is no stranger to hard work. Two, that she probably managers her time well. Three, that she has learnt and has imbibed atleast something from her formal education. All three will go a long long way in ensuring success as we perceive it publicly. The class duffer will not really become a famous doctor. To do that, he will have to get into a decent medical college. To secure this admission, he would have to either maximise performance in the board exams, or maximise performance in an entrance test. To do either one of those two things, he can't really afford to be the class duffer. Top notch CEOs will typically come from one of the better B-schools. To get into one of these schools, one has to maintain good academic performance throughout. It is reasonable to assume that many of my batchmates here at IIM-A will go on to occupy several top positions in firms around the world - very successful by the public defintion of the word (which is what we're discussing anyway). If he took a look at the number of board toppers/school toppers in this place, Mr Rajadhyaksha would have had to eat his words. If your class duffer made it conventionally big, I would have to conclude that you did not have a good idea of what the word 'duffer' means when you were in school.

And as for the photographer friend, what kind of evidence is that? What formal education system at the school level will ever be able to measure how talented a student is at photgraphy? How many students even develop an interest in photography when they are in school? How will a student figure out in school itself that he/she has a comparative advantage in photography? Photography workshops are definitely organised in the bigger cities and lots of people enrol and learn from them - why at school? What would be the curriculum of a 'photography' subject at school? What would be the evaluation system? Sachin Tendulkar failed at his 10th standard board exams. Are we to conclude that the Indian education sytem needs a dose of Ricardo and 'comparative advantage'?

Then, there are the practical issues involved. Mr Rajadhyaksha has argued for choice and specialization. More choice is a better scenario than less choice - this is almost a truism. But how does one provide more choice in subjects at school? By offering electives. A school will then need to have teachers, infratsructure, pedagogy etc. for each of the electives that it offers. How many schools, even well-heeled ones, will be able to manage to find and/or fnance these resources? At the 12th boards level, that much hated government body called CBSE actually offers 600+ subjects, and allows a student to choose a combination of any 5. Most schools still teach only 5-7 and have well defined science, commerce and arts streams. If you blame the education 'system', you're basically ignoring the prevalent constraints of a non-ideal reality.

Of course, Mr Rajadhyaksha realizes the absurdity of a school education that is very specialized from the very begining. Witness this

So, does this mean that our children should be allowed to do just as they please? That would be another extreme. Clearly, we send them to school to develop certain basic language and numeric skills. That (to draw yet another analogy from economics) is the basic infrastructure that the school system must provide so that students can make the most of life’s opportunities, just as public provision of good roads or legal protection is a building block of economic success.

and this

Given the basic intellectual infrastructure of the three Rs—reading, writing and arithtmetic—our children should be allowed to seek their comparative advantage.

The 3R funda is one of most shallow and outdated formulations to ever grip academic imagination. First, is it really three R's? Is it possible that someone who is taught how to read will eventually not figure out how to write? In my book, numerical and verbal skills are just 2 dimensions, not 3. Second, I am completely convinced that a fixation with these two dimensions of human intelligence has stunted development along a very important third one. There's a reason why an aptitude for mechanics does not translate into a natural flair for mechanical engineering, and that reason is a little something called the ability to think in three dimensions. I would argue that developing a basic level of capability or familiarity in 3-D thought, through some courses in the visual arts, is just as important to this "basic intellectual infrastructure".

More importantly, by saying 'arithmetic' do we mean to say that the other mathematics taught in school till the compulsory (10th standard) level is not essential? Can a "basic intellectual infrastructure" be devoid of the knowlegde of parallel lines, circles, triangles, spheres, cylinders and cones? (Digression - I also believe that an understanding of mathematics and logic through set theory is actually the most essential of all basic intellectual infrastrutures. This claim shall be justified in the promised post on propositional logic). I doubt if anyone has ever been able to justify this particular choice of the level of granularity for essential education. Does arithmetic include or exclude the concept of exponentiation and compounding? Is it truly not essential to know and understand a baisc minimum level of science, history and geography? 3Rs is, in my opinion, a convenient rationalization - what it says is a truism and what it doesn't say is truly important. A soundbyte is not an argument.

Lastly, we move to the social and the philosophical. What is the purpose of education and an education sytem, especially at a level as fundamental as school? The problem with trying to define a 'comparative advantage' for students at the school level become clear when we see that we often lament the lack of a liberal arts education for our engineers in India. Essentially, what we are saying is that tangibly and intangibly, it pays off to be well rounded in life. Of course, one cannot be a generalist throughout one's life and needs to start focusing after a particular time. If 18 is seen as the normally accepted age of adulthood, 18 seems to be about right for taking such a decision. If we encourage our children to specialize in school, Mr Rajadhyaksha's daughter may just be happier, but given the current trends in the country, I foresee a much larger cross section of parents pushing their children to concentrate only on physics, chemistry and mathematics right from the age of 10 (or whatever is the age that Mr Rajadhyaksha feels is right to begin specializing). This system will end up producing scores of JEE stud, intellectual dwarf type students who were never given the chance to realise their actual aptitudes and interests because the system encouraged specialization and market demand started ruling their lives much before it does now.

Inspite of the arguments presented in the article being wrong or underdeveloped on almost all counts, why is it that one still feels that Mr Rajadhyaksha's daughter should not have to worry about flunking her arts exam? The problem is the fact that school is unable to think beyond the control mechanism of pass/fail to encourage interest and competence in art. The problem is the school's presumption that it will be able to judge artistic performance through a limited time examination. The problem is not the concept, but the failure to look beyond conventional pedagogy. All this indicates design inertia. Inertia of design is not a flaw of philosophy.

Wednesday, September 05, 2007

The Trouble with Economics

Is that too many people misuse its theories. Actually, that's the trouble with people and their habit to pass off overly stretched analogies as arguments. However, 'the trouble with people' is a little too cynical for my tastes. Misanthropy is best left to Nilu and the dictator. (I'm repaying your link love in kind, dictator). Hence, the title of the post.

So why do I say this? Exhibit 1. Niranjan Rajadhyaksha argues that school children should have more choice and specialization in the subjects that they study. He brings in David Ricardo and the theory of comparative advantage in the picture. He draws his conclusions by presenting an analogy with the situation his daughter faces at school.Why is this analysis and analogy flawed? Many reasons - economic, empirical, educational, practical and philosophical. Let's deal with the flaw in the economic logic of the argument in this post.

What does the theory of comparative advantage say? Essentially, that firms/countries should focus on what they do best. The classic example that Ricardo considered is that of the trade of cloth and wine between England and Portugal. England produces cloth more efficiently than wine and Portugal produces wine more efficiently than cloth. Also, Portugal produces both the products more efficiently than England. The result from the analysis is that Portugal should produce enough wine to meet both countries' demands and no cloth at all and England should produce cloth for both countries's demands, but no wine at all. It is a very strong argument in support of free trade and specialization. Mr Rajadhyaksha argues that similarly, his daughter, who his apparently not too keen on art, should not be made to study art as a compulsory subject and should instead be allowed to specialize - possibly to leverage her comparative advantage. (some B-school jargon was bound to creep in).

Ricardo's theory is one of the most insightful in the entire field of classical and neoclassical microeconomics but it makes certain assumptions, namely

1) There is free trade of goods (explicit)
2) There is no trade of labour or capital, i.e factor inputs (explicit)
3) The demand for the traded products is reasonably similar (implicit, because what is actually being measured is the opportunity cost)

Here, the 'good' that his daughter will specialise in is a certain level of competence in a field or a subject. It is thus safe to assume that the free trade assumption holds true. However, the second and the third assumptions are not true. The factor inputs in this case are aptitude and capital (the investment into the education to gain these skills) and on the individual level, capital can easily be traded. The situation will hence move towards absolute advantage. The product that her daughter, or anybody for that matter, will get in return for their skills is money. Money has a high demand almost universally. The same is not true for the product traded in return - i.e skills.

Mr Rajadhyaksha is fortunate that his daughter has a disliking for the visual arts and a preference for the more conventional subjects. What if it was the other way round? What if, in addition, Mr Rajadhyasha belonged to a less privileged socio-economic segment. The economy places a high premium on numerical and verbal skills and lesser on the visual arts. It then makes more sense for his daughter to focus on math and science rather than pursuing the visual arts, even though her 'comparative advantage' lies in the visual arts. If you are a better artist as well as a better computer engineer than I am (absolute advantage), in the given economic environment it makes more economic sense for you to become a computer engineer even though you are a better artist than you are a computer engineer (comparative advantage). In terms of economic opportunity cost, the area in which you have a 'comparative advantage' may be very different from the area in which you have a comparative avantage in terms of pure aptitude or skills. The unnecesary introduction of Ricardo shows a failure to 'think it through' at best, and shallow intellectual show-offism at worst.

With reference to the misuse of economic theories, everyone would do well to remember what a cetain Mr Neelakantan Rajaraman once said - and I quote him verbatim - "Economics is the result of the human condition, not the other way round." Instead of superficial impositions of economic theories by presuming their a priori correctness in all situations, one must strive to fully analyse the actual situation and see if it has any implications on the nuances and assumptions of the theory itself. At the very least, one must strive to avoid this tendency to name-drop when one writes. Ricardo may have been right Mr Rajadyaksha, but if you ignore the foundations on which his theory is built, you may turn out to be absolutely wrong. And you will not fool us simply because because you mention Ricardo.

For the other reasons detailing why that article says too little too callously , readers must wait with bated breath for the next post.

Monday, September 03, 2007

Of Readers and Apologies

Dear regular readers,

Sincerest apologies for the prolonged gap. As soon as time permits (which means after the end terms), you shall be treated to a series of discourses on randomness, probability, determinism, propositional logic, free will, quantum mechanics, Advaita Vedanta, and theism and atheism. Until then, do hang on.

Dear new reader from math department at TIFR,

You click on my blog so often that my stat counter is pushed up by a large number everyday, even though the blog has seen deplorably low activity in the recent past. This is most fascinating. If it's not too much of a problem, please identify yourself. Do I know you by any chance?