The Beauty of Mathematics

Bethechange – wym091708

The Beauty of Mathematics

When I was in school, mathematics or maths as we usually shorten the word, was one of my most challenging subjects. I was an average performer, neither failing nor passing with flying colours right across the curriculum. But I was sure of a spinning head each time I was faced with those quadratic equations, geometrical drawings and so on. Each time that happened, which was almost always, I convinced myself that once this ordeal was over, I would stay as far away from the subject as Mars is from Earth. But many years later I realised how the phenomenon was an integral part of everyday life just like the air we breathe, the sunlight that helps us see all those beautiful things, the water we run for when we are thirsty, and so forth.

Every day without exception we talk and do mathematics. We tell the time – in minutes, hours, days, weeks, months, years. We count money, whatever currency we use, sometimes in billions and trillions. We tell the distance between places, and the speed of travel. We tell ages of items, animals and people, and sing about them at birthday parties, wishing them many more even when they have had more than enough. We tell durations between points in time. We tell sizes of vessels and pieces of land, weights and prices of food items; we watch our weights with hawkish eyes, and we take our meds in such quantities so many times a day. Every day is maths day; it makes life so easy and we all love it. Or perhaps, love it or hate it, we are completely dependent on it to addiction.

In the world of work, many tasks, even the simplest ones, involve mathematics. Garment construction requires complex mathematical calculations and geometrical projections to produce a certain size garment that fits a particular body structure whatever its shape or size. Everyone has a size, from pencil slim to fully full figure. Farming involves matching the hectarage with the amount of seed, fertilizer, water and labour. Even the depth of ploughing and planting depending on the soil and seed type, moisture content, and so on. Preparing a commercial meal requires exact calculations of inputs and ingredients. And organising an event involves grappling with timeframes, number of participants, amount of supplies required and processes involved. Naturally, rocket science and such other fields are on the other extreme, feats of human ingenuity impossible without the fullest measures of mathematical diet.

Mathematics stays in our faces so much that in some respects we have come to take it for granted. That’s how things are, we ‘whisper’ to our internal selves. In many situations and for many of us, it stays behind the scenes such that on average we do not notice it and therefore might not appreciate it. The tall building from which we work. The roads along which we travel – whether they are ‘simply’ wide and straight or they are narrow and curvy, whether they fly over or ‘fly’ under, they always do so in accordance with mathematical principles. The vehicles that we drive or ride in – whether they are little minis, bullet trains or Concorde planes. Even the ‘simple’ bicycle! The ‘houses’ we live in – whether it’s a thatch hut, a tin shack or a brick-under-tile mansion. The electricity that lights our homes, offices and streets and drives out gadgets. And the gadgets that we use every day – phones, kitchen utensils, computers. The list is endless. All works of mathematics. Human beings have indeed mastered the subject!

But perhaps the greatest work of mathematics of all is creation, performed by the most masterful mathematician of all, the creator him/herself. The wonder of the solar system – the huge masses of matter, that we call planets, suspended in nothing and ever going round and round, and around and around, nonstop at a fixed distance from each other and from the centre. How the earth, for example, is calculated to travel at a certain speed along a certain track in a certain direction and to start all over again at the same spot at the same time every time to effect a year, and to change its tilt at certain points in time every time during its round trip to effect seasons, while at the same time all the time going around at a certain speed to effect day and night. And on it and within it abundant life of various forms, each with various distinguishing characteristics and behaviour, all going on at the same time all the time, and all carefully calculated to complement each other to achieve some equilibrium, most of it invisible to the naked eye.

Within each life form, how it begins, develops and ends. In human beings for example, how the conception project is timed to proceed at a certain pace, all the supplies being brought together in right quantities at the right time to produce a fully formed human being who is ready to eject by a certain time, and to achieve more developmental milestones at specified time points throughout its life time. And in plant life how a maize plant, for example, knows when it’s time to tassel regardless of its height depending on its life circumstances, and to produce the right quantity of seed within its capacity to carry.

Looking at these phenomena, you begin to suspect that there are layers in this mathematics, however it’s called in all those many languages there are in this world. In a lay person’s terms, you could say that there is consumer mathematics, for those who are there simply to benefit from the works of mathematics done by others, usually without even thinking about it in those terms. Then there is interpretational mathematics, for those with enough grey matter to understand and explain the underlying calculations, to see the undergirding connections. Then there is the engineering (not the simple university engineering) mathematics which involves laying those girders that bring about the phenomena that we experience. This is possibly where the DNAs in biological sciences come in. And perhaps finally there is enabling mathematics that built into those girders the mathematical properties to behave that way. In our youthful geography years we used to say the higher you go the cooler it becomes. Similarly the higher you go, or is it the deeper you go, in this mathematical conundrum, the fewer the minds, down to one, the ultimate mathematician (for lack of a better word).

Therein lies the beauty of mathematics. It shapes our lives so much, permeating every nook of it. Yet it is so difficult that it is no field for mere mortals to comprehend let alone manipulate or implement. In fact it is bigger than life itself. No wonder why my head – this little head of mine – used to spin at the sight of it, and (forgivably) still does so with aplomb. But thanks to my newly ‘discovered’ gradations of it, after so many years of pointing a deprecating finger at myself, I now know where I belong. I can freely enjoy the benefits of it all I want without having to flog myself dead for having been so chicken hearted all those many years ago.

Samuel Maruta, August 2017

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Troubling Memories

Bethechange – wym081708

Troubling Memories

One of these days I took a trip down memory lane. Naturally of course this was not the first time to go there, but this time it was special; it got me thinking. After a few kilometres down the lane I found the going getting tough and tougher before I recoiled at what I saw, jolting back to the present, with a twinkle in my eyes. A near miss, hmm! Memory lane can be this decorated boulevard with a lot of nice scenes to imbibe. But it can also resemble walking barefoot on spikes. Ironically whether or, it can turn out to be a no go area. Memories can be troubling regardless of whether they are about something pleasant or painful.

Good memories are like a pleasant dream. One day a friend was having a nice dream that was in keeping with his real life dreams. Then he heard someone calling his name and when he tried to answer back, he woke up. When he realised that it was all a dream, he was deeply disappointed. He immediately went back to sleep hoping that the dream would come back and repeat itself or continue from where he had left off, to no avail. So is it with memories. However pleasant the event recollected might have been, it never comes back, much to one’s disappointment. That is why you sometimes see someone looking fixated at a picture, or whatever it is that triggers the recollection, then after a while, a click of the tongue, a head shake, a deep sigh, a low murmur, or combinations thereof. Neither can it be recreated exactly however one may try. It all remains a piece of memory which fades and blurs as the years go by.

Painful memories are naturally troubling. They are like a bad dream, but worse, because it is one that one cannot wake from, particularly if the pain was one of our own making – you’ll continue to blame yourself forever. One day during my childhood my colleagues and I were driving our cattle home from the mountains after quite an eventful day. The sun was already down and we were certain to reach home well after dark. We had started the drive home late because we had lost some of the cattle while we were playing hide and seek among the boulders and bushes, and we had to recover the lost cattle at all cost for fear of the wrath of our parents back home. Soon the owls were hooting from high up the tall trees, peering down at us with their piercingly sharp night-vision eyes while we were timidly trotting behind and beside the cattle making sure none remained behind nor strayed away. Fortunately the owls could not be more than mere spectators or cheerleaders although they sent cold chills down our little spines and our small hearts throbbing faster.

However real danger came from the forest floor, behind the boulders and bushes. For no sooner had we adapted to the hooting of the owls than our ears were greeted by the howling of hyenas which seemed not very far behind us. We tried to drive the cattle faster, but soon the hyenas were upon us. The whole bush behind us seemed in motion as a whole pack of the hyenas surged forward, laughing menacingly in the process, perhaps a way of communicating their game plan with each other. Somehow instinctively we knew that they were more interested in the cattle than in us, but we could be targeted since they saw us as a hindrance to their meal. So, panic stricken, we spontaneously decided to abandon ship, running in all directions, each one for himself, fear shooting through the roofs of our heads. In the confusion meanwhile the cattle, also sensing danger, went galloping, cows mooing for their calves, all adding to the commotion. In that whirlwind of fear, desperation and anticipation, one big hyena charged at me in a giant leap for my small neck, its powerful jaws wide open, and its long fangs menacing in their whiteness. Instinctively I opened my throat and let out the scream of my life calling my mother who my mind knew was far out of ear shot. It was utter desperation.

Before I let out a second, I felt an elbow jab in my back and heard a frightened voice calling. At first it felt like the hyena’s bite and the voice like its laughter as if to say ‘I’ve got you!’. I came to with the mother of all screams well formed and ready to jet out of my mouth, and rivers of tears cascading down my cheeks. It was nothing but a horrible dream. What a relief! I scrambled for thought, my little heart pounding its way out of my small chest, my little eyeballs standing an inch in front of my face, my… I was a mess. Indeed some of our bad choices land us in a mess, making a visit back there a trip to the jaws of a hungry hyena.

One particularly troubling memory derives from an opportunity lost to make amends with someone for a hurt done to them whether by commission or by omission, and whether they were aware of it or not. Quite often we feel bad for having done something wrong to someone, whether it was deliberate or by mistake, or for not having done some good for someone. When that happens, usually we feel the urge to rectify the situation, make up for any loss or injury incurred by the other, or at least apologise for the wrong done, or make up later for the opportunity missed previously. Unfortunately this is not always possible, for one or a combination of many reasons. One is for self-preservation where you don’t want to expose yourself for having harboured such ill intentions, and even carried them out. You would rather maintain your silence, preferring to dies with the secret, therefore maintain the statusquo and keep the peace between you and them, and your image intact. Another is because you don’t have the material wherewithal to compensate for the damage done. So, although your heart may want to own up and make up, your pocket cannot, so you keep your silence about it while burning inside, rather than stir a hornet’s nest without a remedy. Perhaps the worst case scenario is where regardless of your good intentions and material ability to make amends, or your courage to let the secret out, you simply can’t, because the person is late. For the rest of your life you will continue to char in your own fat.

Pleasant or painful, a memory can be troubling if there is no one to share it with. It’s like carrying a burden alone. They say a burden shared is a burden halved. So with no one to share it with, reliving a memory can be really troubling. Lack of someone to share a memory with is usually because there is no one around who is privy to the events of the memory. One is that there was no one else when the event happened, so the exact details and the specific emotions it triggered then were experienced by you alone. However much you may try to explain them to someone else, it is always reported speech. The speaker is and will always be in his/her own space, alone. Another could be that the only other person present then was on the other side of the fence – either the victim or the perpetrator of the proceedings of the event. So the speaker is and will, similarly, always be in his/her own space, alone on this side of the fence. Perhaps the saddest and most poignant of them all is that those who were there together with the speaker are all late. Death is one phenomenon that transforms one’s circumstances. Our physical environments – the hills in our village, the buildings in town, our neighbourhood streets – generally remain unchanged over a period of time. What changes is how we relate to them, which is influenced by our memories of our experiences there, which in turn are linked to who we built those memories with. If those people are no longer there, the place assumes new characteristics; it is no longer the same. This usually happens the older you get, as your pyramid of contemporaries ever tapers off towards the summit. No wonder why the most common prayer among the very old is to die, to join their colleagues on the other side.

We are where we are because of where we have been, good or bad. Where we are determines where we will be. And when we get there, looking back on here can be a daunting task, whether or not we are in a good space, and whether we like it or not. It’s all part of the equation of this life. How I wish I could choose to go or not, where to, how and who with or without!

Samuel Maruta, August 2017

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This Is Where I Belong

Bethechange – wym041707 

This Is Where I Belong

One English proverb says ‘If wishes were horses beggars would ride’. At the time the proverb was coined, horses were perhaps the fastest or most reliable means of transport. Beggars as some of the poorest people in society did not have the horses, nor ready access to them. Yet given the nature of their profession and the sparse population at the time, they needed to travel long distances to earn a living. As a result, tired of walking yet with more distances to cover, they usually found themselves wishing they could get to such and such a place but without much effect.

Today the proverb still holds true in many if not all facets of life. We often find ourselves wishing we had certain things, could do certain things or could be in a certain place or country other than where we are. Sometimes we wish we had done certain things in a certain way, that we would be in a certain situation or be a completely different person, all of it much better than who we are currently or the situation we are in at the moment. Often you hear people crying in prayer: ‘Why me, oh Lord!’, kind of wishing to exchange their circumstances with someone else.

Perhaps the most recurring wish is to go back in time and change the course of one’s life. This often derives from the belief that the current situation of one’s life could have been better had it not been for some specific event in the past. So you often hear people say: ‘Dai udiki hwaidzokerwa’ (If only I could go back to being a child again). This hypothesis takes a very concrete shape in one’s mind if there are comparable cases. For example one always makes reference to his/her age-mates, childhood colleagues or former school mates. It is not uncommon to hear someone say: ‘Vamwe vangu vaamberi’ (My colleagues/ age mates are now way ahead). It is especially poignant if someone who missed the cut at ‘O’ Level or some level else winds up ‘ahead’ of you. My nephew often recounts his personal story where while he was at university in 2008 he was borrowing food money from his former classmate who had dropped off at ‘O’ Level having not obtained enough or the right passes to proceed to ‘A’ Level. Many people are aware how during the height of our economic crisis in 2007-8 professionals were left stuck at the starting blocks of informal deals by those with less bookish education.

It is true that there are so many arisings in one’s life that can cause it to change course significantly, whether for better or for worse, depending on their point of incidence. In childhood, the most debilitating arising is the change in family circumstances. This could be loss of the family’s breadwinner or his/her earning capacity. While the long term effects are not completely predictable, the most immediate is a negative impact on one’s chances of an education. One may end up changing schools, or dropping out, at least for a period of time. In youth and early adulthood years, unwanted pregnancies and early marriage are some of the arisings that can derail a course of life, especially for girl children. Suddenly a child becomes a parent, or is saddled with husband or wife duties and responsibilities. You hear those around you say, hopefully in encouragement: ‘Ah, watokura; ndiko kukura kwacho’ (Well, you are an adult now; that’s what it means to be an adult). At any point in time there are always dangers to our physical and mental wellbeing. A debilitating injury can drastically change the course of one’s life, sometimes even that of those around you.  And always lurking in the shadows around us are risks associated with decisions that we take. A wrong turn here or a right turn at the wrong time there makes a huge difference.

Yet some observers may see this ‘derailment’ from one’s desired course of life not as such but as part of the natural scheme of things. They urge us to accept whatever life throws at us, arguing that whatever happens was meant to happen to someone at some point in time and that it only so happens that you or me are that person at this point in time. Those of a Christian persuasion usually, after a bucketful of grumblings and wishes about the misfortune, end up saying: ‘Mwari haakupi mutoro wausingakwanisi kutakura’ (God will not give you a burden he knows you cannot carry). My mother would say (may her soul rest in peace): ‘Zviwira vanhu. Waida kuti zviitirwe ani?’ (It is part and parcel of this life. Who did you want that to happen to [other than yourself]?). You could take these utterances as consolation or coping strategies, but there are truths in them – those mishaps are part of the deal of life, one we enter into by ‘agreeing’ to be born.

While the immediate impact of these derailments is undeniable, it is difficult to prove beyond reasonable doubt that one’s situation would have been better in the long run. If my life had not taken the turn it took some forty years ago, for example, I cannot say with all certainty that I would have been better off today. Maybe I would not be here today. I know a sad story of a colleague who ‘beat’ someone, adjudged to be more deserving at the time, to an opportunity because of connections who was befallen by a misfortune soon after. A riddle is often told that if a group of people were to take off their lives, put them down in a designated place like shoes at the entrance to a place of worship, and asked one after another to take a life they preferred, everyone would take back his/her original life. A related English proverb says something like the grass is greener across the river… until you get there.

On several occasions I have wracked my brain revisiting all the mistakes I have made in my life. Believe you me, I have made more than my fair share of them, both by omission and by commission.  I also relive the opportunities I missed, condemning the fool in me for missing such glaring chances, like a striker in the game of football scooping the ball off the goal line instead of just tapping it in for a goal. All the time convincing myself that I would be elsewhere much better, physically and socially, were it not for those failings, mistakes and misfortunes. However a faint inner voice always makes a point of reminding me that over that same period riddled with those errors and misfortunes, I scored some successes and exploited some opportunities that fell my way more or less like manna from heaven. Counting my blessings, you would say.

At the end of an exhausting reflection process, putting both pros and cons of my life on a scale of justice and cross-examining them with all the interrogative venom in my arsenal, I invariably come to the conclusion that right here where I am is where I belong. And that I am happy to be here. A beggar unknowingly wishing to get to where he/she already is!

Samuel Maruta, July 2017

What kind of a grandfather are you?

Yesterday evening one of my children had their first child. They sent me through whatsapp a picture of themself holding the new born baby in their arms, and the words: Tatoti mauya Mwoyo (we have already welcomed Mwoyondizvo). Mwoyondizvo is our praise word, being of the Rozvi clan, Dhewa Bvumavaranda; some go as far as saying ‘varidzi venyika’ (owners of the land) perhaps deriving from the historical Changamire Dombo fame. So, this little one is standing on the shoulders of giants.

This morning I shared the good news with my neighbours. When they asked me whether it was male or female, a boy or a girl, I told them that I did not ask that of my child in question, which was true; I did not ask the question. When I received the news, I convinced myself that it was neither here nor there whether it was a boy or a girl. I was just happy for myself, for them and for everyone in the circle. Because a child is a child, so my inner self said.

The neighbours went on to ask why I had not asked the question, I said to them ‘what does it matter whether it is a boy or a girl, does it diminish the fact of the baby and does it make me any less or more happy whether it is either or’. Of course there was no answer to that, for my happiness was mine, not theirs. Instead the response came in form of another question, a shocker at that, especially given the disgusted ‘perplexion’ on the face of the asker: What kind of a grandfather are you who does not ask if it’s a girl or a boy? Externally I laughed it off, putting up a brave face, while my mind scrambled for a response. It came up with something like ‘Well, this one!’ kind of pointing to myself, but there was no time for my mouth to form it. They were all laughing, and other scenes took over the stage.

Traditionally people value male children more than female ones. The rationale used to be that the male children would perpetuate the clan while female ones would only add value to other clans by marriage. This view was held most strongly by male members of the clan. Those men with many boy children would pride themselves for their ‘impressive’ achievements, while those without or with only a few would just lick their wounds.

I think my father was one of the victims of these wounds. On quite a few occasions when I was young he would remark, with a sigh after some rumination, and a facial expression exuding with wishful admiration: Nhingi uya une magomana mhani, xa! (That so-and-so has these big gangling boys!). Of course there is no way I can recreate those moments for you given my limited vocabulary. But the picture of his typical posture whenever he said this, his facial expression and the sound of his voice are all clear in my mind as I write this; it’s like he is right in front of me and saying those exact same words in the exact same way over and over again. And I a little boy, not privy to his inner world and limited of life experience, sat there busy picturing what his mind’s gangling big boys were like, often picturing one of the local boys I knew.

It’s not like he himself did not have boys. At least I was there. But in hindsight I think the issue had to do with comparison with his brothers or some colleagues, or with the age and proportion of his boy children to his girl children. For at the end of his fathering stint stretching over some thirty years, he had a balanced team of seven a side. Not a bad return, a passerby would say. Unfortunately the team was led by two girls, followed by two boys (my big brother and I), then three girls, some sputtering down the line before it was tailed by two boys, all in single file. Definitely not a good showing at a time when ‘gangling big boys’ were in ‘demand’.

Well, I don’t think they are in demand any more. Today’s society is a far cry from what it was when my father was on the trail. While biologically it is still possible that male children help to perpetuate the clan in a patriarchal society such as ours, I wonder if people still place a premium on that. I think people are now more concerned about their quality of life. On average, people now work with target numbers. If by the time the score is reached it’s a one-sided team, so be it. There now seems to be a high degree of acceptance for girl children if not a shift in preference. Female children are rising in value to the family more than male children, not because of the over-the-top lobola that some opportunistic if not out-of-sync parents charge their in-laws for ‘taking’ their beloved daughters on whose education they spent a fortune, but because of what they do for their parents.

Recently one of my other neighbours said girl children are more preferable these days because they take care of their parents better than boy children. They went on to explain how boy children go for good, sometimes waste themselves away and never look back to their parents. They rounded off their theory with ‘but the girl child never forgets, however wayward she might be’. And the other day I found myself co-walking with two strangers who seemed to corroborate that theory, going as far as to give percentages of probability to support the theory. If these sentiments are anything to go by, there seems to be a shift from focus on clan perpetuation to considerations of security in economic hardships, old age or infirmity. Thus the new trend seems to be that instead of worrying about what will happen to my name after I am gone, I would rather focus on what happens to me while I am still here. Whether or not this is statistically the case on the ground is a matter for social scientists.

I do not know if my neighbours had any preference on the sex of my grandchild, or if they thought I had any preference. But the question of the sex of the child is one that is often if not always asked upon receipt of such news. Because of that, they are forgiven for instinctively quizzing me about my credentials as a grandfather just for not asking the question that they and many other people take for granted. Unfortunately thanks to their otherwise good-natured selves I remain saddled with a tricky question whose slippery answer defies all my ‘unteething’ grandfather faculties to fathom.

Enhance Your Literary Authorship Credentials… Become A Published Essayist!

You might be a renowned academic, celebrated novelist, poet or playwright, or prominent journalist, but if you are not a published essayist… here is an opportunity for you to become one, and add to your otherwise impressive literary authorship credentials. Even if you are all or none of the above, this is for you too.

Word Craft Global is organising a seminar on the Zimbabwean Essay in English for Friday 6 October 2017 in Harare, Zimbabwe. Essays can be on any subject – people, places, objects, fauna, flora, events, processes, issues and/or various combinations thereof. Authors will present their essays for discussion and critique in a panel discussion format. Essays so presented will be considered for publication in book form as a collection of essays.

To present your essay at the seminar, send in a brief summary by 1 July and the full essay by 1 September. The summary should be 50-100 words long and the essay 1500-2000 words long. Do not be left behind… Come with us on this exciting journey! And please do share with colleagues and friends.

For more information or assistance in this endeavour, please feel free to email us at acadtechzw@gmail.com or call/whatsapp us at +263 772 349 407.

Writing to the Top

At a higher level of cognitive functioning, strategies of thinking and strategies of writing are so enmeshed that each one is severely limited without the other. No wonder why society values those that do both best.

Experts in the field talk of writing to learn and writing to communicate as simultaneous processes. As I am writing this piece and struggling to express myself I am not only clarifying my existing knowledge and understanding of the subject but also extending them. In the end there will (hopefully) be something on paper and I will have more knowledge of it than when I started, something that would not have happened if I had not taken to paper on the subject.

Of the two processes of writing and thinking, one is more accessible to manipulation by the individual concerned than the other. It’s like one is the inner room and the other the outer room in a house with many rooms; to get to the one you must pass through the other. Thus to improve one’s thinking capacity, one’s ability to think critically and productively on a given subject in a given unit of time, one must improve one’s writing ability.

Perhaps no wonder why, everything else being equal, those peoples that acquired and perfected the art and science of writing first, better and faster than the others developed socially and technologically first, better and faster than those others. That is why those nations that place a premium on teaching writing fair better in all critical spheres of human endeavour than the others. That is why organisations that write better perform better. At the individual level, that is why success in life – regardless of one’s walk of life or field of endeavour but especially in academia, the workplace and the professions – generally associates with ability to put one’s ideas down on paper, to express oneself effectively in writing. Birds of a feather, one might say!

Unfortunately some people in the sciences, particularly high school and undergraduate students, might be tempted to think that there is no need for them to learn to write well. To think that writing is for those in the arts, for poets, novelists and so forth; that mastery of mathematical equations or scientific formulae is all they need. The idealism of youth, you’ld say. So too with those at the bottom of their employment pile; they might be tempted to busk in the false comfort that writing is not for them but for their supervisors, managers and directors. In both cases, they are very right if they want to remain at the entry levels of their professions and become everybody’s doormat. But very wrong if they want to rise to the top of the monkey hill, to be the top dog, to be lion king. You have to write your way up there!

So, go on writing. Or start writing. Or start learning to write.