Spherical Cows and Geometry

The first part of the name comes from the famous book on Environmental problem solving called Consider a spherical cow by John Harte. According to the book, the title comes from a joke within the environmental science community about a group of scientists who are approached by a farmer to ask why his cow was producing less milk. After large amounts of deliberation, the scientists call the farmer and start explaining : “Consider a spherical cow….”

The title is to reinforce the fact that certain problems cannot be solved exactly, and idealizations need to be made so that the solution is computable. In fact, the book (just started reading it!) has quite a few problems which do not expect answers exact to the 100th decimal point but an answer in the orders of magnitude is sufficient, i.e, $41,041$ can be written as $10^4$. If one begins to wonder what kind of quackery this fellow preaches, consider the first problem statement that he puts forward: Calculate the number of cobblers in the US! no other info, one has to make amazing assumptions and only then even start to solve the problem. This, for me, is to drive in home the fact that solving problems in as large and complex a system as the environment is simply too hard to do precisely as a watchmaker might like to. One has to rely on intuition and great deal of ‘common sense’ to go ahead without being bogged down by the finer details. It is uncertainties like this which are really making a debate of global warming possible. People who say that humans are putting too much crap into the atmosphere, are ‘reasonably certain’ that humans will destroy the planet. Sceptics say that there is evidence to show that global warming and cooling cycles have always been happening, and this is not too great a cause for concern. The debate, however, seems to be converging in the favor of the ‘we are suicidal ‘ camp, due to more and more data pointing to the adverse effects of anthropogenic intervention in the global climate system.

Thus, until one gets more data, one guesses, and more data only refines the guess to a state where we can be ‘reasonably confident’ (or ‘quite sure’, especially when giving lectures or talking to mediapersons ;). This is where the role of geometry comes in, hidden sometimes in algebra, but ever-present in any situation which calls for a guess. One of the fundamental beliefs of the natural sciences is that nature follows a pattern, and that can be discovered and propounded as laws. Therefore, given a set of data or readings regarding any phenomenon, they would try and see if they can fit some known functions (or shapes, to the mathematically challenged), which can help them find intermediate values, and also help predict future outcomes. If the model (that is what fitting a function would be called) is bad, chuck and find another more suitable function, and hopefully get more readings to confirm their hypothesis. Thus, if anyone hears a scientist talking about ‘exponentially increasing population’ or ‘linearly changing system’, you can be sure that the above is what they have probably done.

Polynomials, exponentials, sines, cosines, are among the darlings of the geometric modelling community, and you will be hearing more about them here, hopefully with as little math and as many pretty curves as possible :)