Monday, 27 June 2016

A math lesson for disability rights 

I want to give a sermon on the two ways - one good, and one not-so-good - of doing something on a large scale (from the pulpit of a mathematician to `social justice' ministries). So I request your forbearance while I start with a little high school mathematics.

Write C(n,r) for the number of teams of r players that can be made from a population of size n, where r is a whole number no larger than another whole number n. There is a scary/ugly formula which counts this number. For example, C(8,3) is the ratio (8x7x6x5x4x3x2x1)/[(3x2x1)(5x4x3x2x1)]; in general if we write n! (read n factorial) for (nx(n-1)x(n-2)x...x3x2x1), then C(n,r)=(n!)/[(r!){(n-r)!}].) Coming up with clever and elegant ways of solving such potentially horrendous`counting problems' is the delightful area of combinatorics.

Let me begin by discussing the equation:  C(n,r)xr = nxC(n-1,r-1). The right way of seeing this equation is as follows. (and the inelegant way is to use the formula with `factorials' discussed above.) Imagine that the task in hand is to see how many ways there are of choosing a team of r players out of a population of n, and select a captain to lead that team. There are (at least) two ways of finding the answer: on the one hand, you can first pick the team (in one of C(n,r) possible ways), and after that, pick one of the r players of the team you have chosen as captain, hence arriving at C(n,r)r as the desired answer; on the other hand, you can choose one of the n people in the land as captain and then choose the remaining (r-1) players from the available (n-1) people to find that the answer is also given by nC(n-1, r-1). Legend  has it that the English (and the Indians) opted for  the second method of choosing their team, while the Australians adopted the `more democratic' first way of choosing their team.

While I am at it, let me cite one more lesson I have learnt from mathematics. There is a tradition of holding an International Congress of Mathematicians once every four years. For example, ICM 2010 was held in Hyderabad, India. Even then, appropriate committees met to decide on the venue (Seaoul, Korea) for the next ICM from among the cities wsho had `bid' for the honour, and the compositions of all the various working committees decided on by the current committee which comprised only of mathematicians and not a single political appointee - and the new committees started having meetings soon in order to draw up an agenda of tasks to be completed before the next ICM, and a time-line for what tasks must be completed by when.

Now for Indian reality. India periodically reconstitutes her Ministry of Social Justice and Empowerment (MSJE) to look into the tasks to be performed for the betterment of her citizens who have disabilities of some sort. A novel way that our Governmant hs arrived at to handle all such problems is to rename ministries and draw up a pretentious list of tasks. And they keep having their meetings without broad-based consultations or doing their homework first. Let me give a few brilliant decisions taken by our Govt:

(i) They flagged off an `accessible model train' which a wheelchair could not enter.

(ii) They are thinking of a bullet train from Mumbai to Ahmedabad. when there are no elevators in normal train stations.

(iii) The MSJE was suddenly renamed (with a Hindi name) because our brilliant Prime Minister decided that it was better to call a PwD Divyang (a person endowed with with divinity) - how else will they have special abilities to do all they do?

(iv) I have written in the past about our horrific experience with the lack of accesssability of the Chennai Metro.

(v) Disability Activists all around the world have been chanting the slogan `Nothing for us without us'. We have been shouting ourselves hoarse with `No to Divyang' and `Nothing for us without us'; but our relevant ministry is either hearing impaired Divyang or wilfully chooses not to listen!

Now you see why I hate the British thinking which first chooses a captain and then asks him to choose his team!