An intersection of mathematics and politics

The past Saturdays I have been volunteering as a Maths tutor for the Upstart Youth Development Project. As far as many of my beloved learners were concerned, Maths wouldn’t reside in a planet designated for languages. Maths would reside in a different and very distant planet with a hard to pronounce name— I would imagine, to banish it properly from the memories of people.

I found this disappointing but not entirely unexpected. So, in a slightly determined fashion, I decided one of my key priorities will be to help the learners locate Maths within the language planet. And, of course, allow them to gradually come to terms with the fact that another planet for Maths is as non-existent as Pluto.

In pursuit of this priority, I found myself in an unusually happy space where my politics intersected with Maths. We were discussing functions, which naturally one can’t discuss without establishing an understanding of relations: for a function is but a special relation. Different examples were given to describe multiple everyday relations. Most of these examples were not very exciting until we explored a relationship between Dr. Jacob Zuma and Mr. Mbogeni Ngema. Both men are polygamists and whether or not they have gone on record as pro-patriarchy is detail we suspend. I asked my beloved learners whether a polygamous relationship qualified as a function.

First, there was a reasonable pause in the classroom, as the learners work out whether such a relation qualified as a one-to-many or many-to-one relation. Then, we proceeded to do the obvious, represent the relation on the board, like as shown below:


Almost feverish with excitement, I realised that we had proven mathematically that polygamous relationships are not functional. And, of course, I used the moment productively. I brought into the discussion the idea of “contexts” as sensitively as I could, to explain why the two relational sets may not be swapped around. I argued (without using the term patriarchy) that the instinct to put the male set before the female set defines a very particular context to understanding polygamy as a cultural practice; a context in which a man is defined, for example, as the head of the family—ergo not an equal partner to a woman. I stressed that their instinct was tied to that context, as such, swapping of the sets will lead to a contradiction.

These are high school learners who are familiar with topics like ratios; so it really wasn’t difficult to leverage on this familiarity to cement my point. I simply reminded them that in ratios, the ratio of males to females in the classroom is different from that of females to males —a fact that has been drilled into them by their teachers and one I may need to revisit later with them.

With my learners reasonably convinced that the sets could not be swapped, the conclusion stood: polygamy, expressed in English, is not functional despite what the patriarchs may think!

I remain delighted by the conclusion. In entering what I regard as my political space, I managed to communicate, in subtle ways, how concepts are incrementally developed in Maths such that it eventually becomes possible to bring the idea of contexts to answering questions. I also found the language to communicate the embedded ethics in Maths. As a result, I was even able to dutifully explain the rationale I (and many other beautifully minded Mathematicians) use in marking:

You present me with just an answer and no work (or context to appreciate your thought process)…I will give partial marks on paper but I will certainly give full marks in my heart. Not in my (beautiful) mind but in my heart because that will be a loving act of instilling the value of labouring for your rewards.

This Saturday I will be playing around with the idea of restricting the domain of functions, I hope the idea of contexts will become even much more clearer. In the meantime, I am just looking forward to finding more “inspired” examples that may be useful in concretising concepts and the view of Maths as a language of variables, sets, functions, etc.

Vuka and Spruce up the Language!

Vuka, awake! A season of rebirth or new beginnings has arrived. For many people, including myself, it is a season for de-cluttering our emotional, intellectual and physical environment. A season in which we are inspired by nature itself to create space for new ideas, people and things.

As we de-clutter, we ask ourselves a number of critical and reflective questions to rid ourselves and our environment of certain things, while we keep or protect those things that we cherish. The question is: do we ever remember to ask questions that may allow us to value language in the context of our environment? I don’t just mean in terms of using language to send positive vibes in our environment; I mean in terms of truly reclaiming ourselves, and connecting deeply to our environment and heritage!

Indeed, I am well aware of the increasing and commendable efforts by many countries and individuals to protect their environment and heritage. But when it comes to dealing with language, I feel the spirit of lumping together the protection of the environment and heritage is lost.

Otherwise put, although language is central to heritage, I think we have done a poor job in framing its importance within the context of the environment and its protection. As such, I think people still have difficultly in seeing the extend of the overlap between issues of the environment and that of heritage (cultural or otherwise). They fail to see the embeddedness of issues of heritage within the broad set of issues of the environment. Mathematically speaking, they fail to conceptualise heritage issues as but a proper subset of environment issues.

In my mind, without this conceptualisation, being connected to the broad vision of the country, continent or planet would remain a challenge. At the moment, though saving the rhino is as important as saving my Sesotho language, I sometimes forget this truth. While this is an embarrassing admission to make, with the arrival of spring, I hope to wake up permanently from a slumber that sometimes denies me of this truth.

Happy spring to all. May the beauty brought by the season inspire us to spruce up our views on language … to see beyond its functional use … and be moved to find ways in which we (re)enchant its use to (re)connect to the richness of our heritage and the environment as whole!

My Love for Mathematics

For a few years now, I have had a question that I could not quite answer. The question is: “why do people hate mathematics?” Perhaps hate is a strong word but even when I tone the question down by using the word ‘like’ I still cannot find an answer that satisfies me.

Today being world maths day, I shall ignore the urge to find an answer. Instead, I shall attempt to answer the inverse of the question, which is: “why do I love mathematics”?

I suppose my love emanated from the realisation that mathematics is but a language backed with the ‘power’ of logic. From this realisation, I fell in love and I have almost always managed to view mathematics as nothing but a tool to explore the unknown without worrying about the uncertainties. For example, in aspiring to run a business of my own in the near future, I am aware that I will be faced with multiple uncertainties. Should these uncertainties deter me? Perhaps! But since I believe the key to success lies in the ability to formulate a sound (logical) strategy, I know that my focus should not really be on the uncertainties. The challenge therefore, is how do I start to build a sound strategy? For me, as you would expect, my answer, courage and inspiration come from the world of mathematics in the form of a simple productivity formula shown below.

    \[ productivity =\frac{output}{input} \]


Using the above formula and a simple mathematical analysis, one can deduce that productivity and hence profitability will be high if:

  • Fewer or less resources are used to yield an output i.e. input < output
  • There is more output than input i.e. output >input

From the two above-mentioned facts, it follows then that I can easily develop a strategy that always strives to lower the inputs and increase the outputs – or at the very least make them equal! This will therefore result in success since the strategy itself will be developed with the sole purpose of offering me the highest probability of a successful outcome.

With the strategy, my exuberance or enthusiasm and my mathematical background that has equipped me with the ability to reason logically, what are the odds that I would fail? Quite frankly, I don’t know! But the point I am trying to make is: I love mathematics because it provides me with the understanding that many things in life are relative just by simply knowing that 1+1 is not necessarily 2! I am thus able to dream for I know success itself is relative… Happy maths day to all!

PS: I also love mathematics because it helps me spell out my name to people: MATHEmatics without the ‘matics’ ;-)!