Environmentally friendly cows!

Once you start hearing papers say such things, you know something is seriously wrong. The motivation behind such a statement is that apparently cows belch too much, and their burps contain methane and this is a very potent greenhouse gas, and therefore we must breed new cows which burp less, so that they don’t contribute to climate change!

I have been trying to wrap my head around the concept of an environmentally friendly cow for almost a day now, just not happening. Maybe scientists nowadays are too advanced for us mere mortals to understand. But wait, just due to their sheer numbers, termites probably emit more methane than cows overall. Therefore, we must also try and breed new termites, and ban people from keeping termite farms. While we are at it, we should also breed new set of humans who do not eat junk food (especially peanuts!), since that is a huge cause for methane emissions as well. Looking at what junk gets done in the name of science these days, funding should not be too much of a problem.

Why is it that cows, that have peacefully belched their way through a couple of million years without causing too much climate change suddenly the enemy ? Obviously, the problem is not with the cows themselves, but the rate at which beef is being consumed makes their number quite formidable. So what is the answer to this ? according to the previous link, control the number of people, so that they can eat lesser number of cows!! Beef is not the staple food in most countries, and the population increase happens in classes which cannot normally afford too much beef, so wonder who is eating such a large amount of it.

This insane and ludicrous issue brings to the fore the contradictions of a civilization that cannot accept that its way of life is completely off track. It wants to keep thinking that the way it has progressed is viable, and only few minor issues arise that can be solved by ’scientific innovation’. This blame-the-cow attitude has been with us for a long time: blame the poor, blame the corporation, blame the Muslim – as long as we are not blamed. Wonder when people will grow up!

Math: The geometry of Matrices

Was attending a workshop on Linear Algebra, and one of the lectures was by Dr. C. R. Pradeep. It was supposed to be on positive-definite matrices (whatever that might be!), but finding that no one really understood what a matrix was or stood for, it became a geometry class, to everyone’s benefit.

The standard way to look at a matrix is that is a set of numbers arranged in some order in between some brackets, and that they can be added with some effort and are multiplied in a completely obscure manner. This much one learns by the time one leaves Pre-University, and this does not help one bit in appreciating the whats and the whys behind the whole thing.

The best way to start off is with an example. Consider a general vector multiplying a matrix:

If we take the general vector to be some point on the plane, then note that every point on the right hand side of the above equation has its x-coordinate equal to its y-coordinate. Therefore, if we think of this matrix as a machine that takes in all vectors in the plane and spits out some other vectors also in the plane, then things begin to look very nice.

This is because, if we start feeding this machine all the points on the plane, what we will get as a result is all the points whose coordinates are equal. From elementary geometry, this is a line passing through the origin at an angle of 45 degrees to both the coordinate axes:

How is it managing to do this ? Consider two special cases: and . These are the well known unit vectors on the plane, representing the y axis and the x axis respectively. Substituting these values in the equation, we see that they both are sent to the same point! Therefore, this matrix is collapsing the plane onto a single line, very much like closing a Chinese hand held paper fan. We can write any point on the plane in terms of the unit vectors, and similarly, we can write any point on the line using both the columns of the matrix. In this case they are the same, so it is a trivial relationship. But in general, the columns of the matrix are such that any point at the output can be written uniquely in terms of them.

Therefore, this matrix seems to be taking as its input a 2 dimensional ’space’, i.e, the entire plane and giving back a 1 dimensional ’space’ – a line through the origin. Another interesting thing to note is that both the points and both end up in the same point . This means given a point , we would not know which point on the plane it corresponds to, i.e, the inverse is not well-defined.  (In fact, given any point at the output there are an (uncountably) infinite number of points which could have produced that) When we say that a matrix is singular or non-invertible, this is what we mean. We normally check this by finding the determinant of the matrix (which is zero in the singular case), but this normally does not appeal much to intuition.

To generalise this, any matrix that takes a higher dimensional space to a lower dimensional space is not invertible. The natural next question to ask is that if a matrix maintains the dimension of the output space equal to the input, is it invertible ? This can in fact be proved to be true, and this can be taken as a simple interpretation of the Rank-Nullity Theorem.

Going back to our example, what if the point/vector at the input was already on the line ? For example, the point would end up at , which is the same as . This is consistent with out Chinese fan approach, the line in the middle of the fan does not really move when it is closed (It does not get elongated either, but that is a special case of this). In Linear Algebra terminology, such points/vectors are called eigenvectors, and the value by which they are multiplied is called the eigenvalues of the matrix. In the general case, the axes do not collapse into each other, but maintain some angle between them. Even then, there will be some set of points/vectors which do not move, and these are called the eigenvectors.

Almost all the basic concepts of Linear algebra can be interpreted in this geometric manner. The heart of this whole discussion is the concept of linear transformations, which are represented by matrices for convenience and analysis.

Linear Algebra is an interesting subject, and on this is built almost all of engineering!!

Location shift

As a compensation for writing ridiculously bad exams like GATE, will be moving to the Centre for Atmospheric and Oceanic Sciences (ominously called CAOS!) in the Indian Institute of  Science, Bangalore. One hopes Bangalore is far more tolerable inside one of its greenest areas. The next couple of months will be spent preparing for another interview in the same department for another program, so expect fundas from fluid mechanics and miscellaneous boring things to dominate this space.

Society and Ecology – courtship and conflict

The variety of disciplines and specializations that have proliferated sometimes hinders larger understanding of any phenomenon, especially one that involves anything more than (an arbitrarily selected number!) 3 variables of different types. Then someone comes along and sees things happening that cannot be explained through any existing theory, and hence we have ‘inter-disciplinary’ studies. So, we can have, for example, economics, mathematical economics, ecological mathematical economics and so on, as long as we are comfortable with unwieldy (but cool sounding!) names.

So is the study of relationships between collections of humans and collections of everything else, living and non-living. Sometimes called human geography or social ecology, the main aim is the same: to study how man and nature are intertwined in a circle of courtship and conflict. The separation of man from nature itself is quite arbitrary, and has roots in religion rather than in any sensible thinking. Study of people interacting with each other, which is commonly studied under the banners of economics, sociology and anthropology (and all combinations of the three) has very rarely touched upon our interactions with plants, animals, trees, mountains and rivers, assuming a mutual independence between the material and social worlds (which is again quite arbitrary).

This separation of man from nature is extremely well reflected in products of present culture like TV series and novels. Take for example, the latest hit shows (which I religiously follow) in the US, House M.D. and Heroes. The absence of nature from the studio sets unless it is absolutely required (i.e, it is an outdoor shot) is quite remarkable. This is even more so in our very own Saas-Bahu soaps, which don’t seem to be shot outside a single set. New generation ‘Multiplex movies’ by film makers like Rahul Bose also show how little nature has a role to play in the lives of residents in metropolises. Traditional movies aimed for the less cultured masses still have a role for nature in them, since their audiences may still interact with it on a daily basis.

Take another example of the latest NDTV campaign to spread environmental awareness. As usual, NDTV got a lot of celebrities to support their campaign. A sampling of their comments leads to interesting conclusions : They articulate their concerns in abstract terms like climate change, aesthetics (beautiful/green city = good), energy. The only true down-to-earth concern is that of dwindling water supply, since that is what each and every city dweller is really constrained of. Citizens of the city have really very little understanding of what it means to be part of an ecosystem that does not contain only asphalt and concrete, and typical gathering grounds for them like malls, movie theatres, pubs, nightclubs are indicative of this epistemic void.

But we seem to have evolved to also like being among living beings which do not wear spaghetti tops or rippling abs, and hence the urbanite’s courtship with nature. Nature is an abstract entity that manifests itself in regular trips to National sanctuaries and mountain treks. Not something one needs for daily life (Spencer’s Daily is there for such things), but something that has some nebulous link to our aesthetic and moral sense.

This understanding is quite inaccurate and unfortunate, since it hides from us our means of sustenance. This is where the conflict between different people and people and animals arises. The environmental movements in India started mainly because of these conflicts between man-man and man-beast for natural resources (Chipko Andolan, Narmada Bachao), whereas those in the West derive from the urbanite view of Nature. In fact, the first few to articulate environmental concerns in Europe were artists and poets.

The bitter irony of the matter is that the same people who seem to court nature with their concern towards it are locked in a huge conflict with other people over the same nature, albeit unwittingly. The conflict has been ‘outsourced’ to their creations, the State and the Corporation, and so they can feel purged of moral obligation by buying village handicrafts and tie-dye clothes. Does our obligation stop here ? Are there ways by which one can indulge in ‘high’ culture and still live in harmony with other people and animals?

As always, the questions are easy to ask, the answers may not follow as easily.

Review: A Pedagogue’s Romance by Krishna Kumar

Contrast between the Ideal and the Real

This book is a collection of the author’s short essays and deals with a wide range of topics, ranging from spitting and its implications to selection of ‘talented’ students for special attention to concern about lack of understanding of adolescent development in the Indian context to concern about elimination of Nature and Handicrafts from schools.

Anyone with an interest to work with children and would like to understand what one is getting into rather than jump right in and wreak unintended havoc (like yours truly) must give this book a shot. Not only does the author try to discuss the various reasons why education in India has become a new means of social exclusion, like the caste system, but also what can be done to make it better, and what should be the ultimate goal of an education.

Even though the themes are varied, all of them have a strong connection running through them: As the author puts it (paraphrased) :

Education is reflection in the process of relating (to one’s environment, society, etc )

Reflection, in the sense of leisured observation and understanding. Most of the author’s analyses use this as the analytical looking glass to view the system by, and obviously it fails miserably to live upto such an ideal. He discusses many problems which make education such a difficult system to reform like lack of social status for teachers, competitive and narrowly focused, results-oriented pedagogy and the social scenario within which a school is embedded. He also deals with gender issues and induction of everyday life into schooling.

He deplores a system which is so mixed up as to require a separate ‘value education’ or ‘moral education’ class. Another major issue, that of a scientifically based caste system which is being set up due to our primary schooling system, which eliminates almost 80% of children by class 10 takes up quite a bit of his time.

Culturally and linguistically relevant education is also something that he stresses and having handicrafts as a core curricular activity to both learn the value of manual labor and save the varied heritage of India which is fast disappearing.

Definitely worth anyone’s money.