Mathematics lectures revisited – thanks to Oxymoron

-Bernard Fernandes

A few days back a post on the Facebook home page caught my attention. It read: “STC ad at the airport: Riyadh di Janeiro.” Below that was a tongue-in-cheek comment by my friend: ‘Oxymoron of the year’.  Through a remarkable coincidence, a list of oxymorons followed on my mobile. The sms read: Clearly misunderstood, Exact estimate, small crowd, act naturally, found missing.

Set me thinking. Why not some oxymorons in Mathematics – after all, it is a subject I love!  Unlike the English language, Mathematics is not spoilt for choice in the oxymoron domain. Here are a few after having scraped the barrel:

Sitting in the classrooms of the haloed precincts of the Nowrosjee Wadia College, Pune attending Mathematics lectures is a vivid recollection. In my time, Nowrosjee Wadia College was renowned and the most sought after college for a degree in Mathematics – it had the names of some top class Mathematics professors: Mugad, Rao, Andar…to name a few. However learning Abstract Algebra was not simple. And the terms used therein were far removed from reality – as the topic suggests!  Take for instance, ‘delta neighbourhood of a point p’. It is a concept pivotal to the topic on limits – and thereafter to related topics of Calculus that begin to spiral out of control! To make it practical, it is the set of points in the vicinity (neighbours!) of p; and applying it to ‘limits’, a point from this set ‘tends to’ p when the distance gets extra small on either side of the point, but has not reached p.  (Brushing up the memory of our Lonavlites: Chug…chug…chug…the train is approaching Lonavla station, but has not reached the station! Sigh!) So simple… Or, is it?

Let’s go easy on the mind now!  One pair of adjacent angles that add up to 180 degrees forms a linear pair; and an angle of 180 degrees is a straight angle. And what about a Null set? It’s a fully empty set.  Talk fractions – and operations on them – and our ‘borderliners’ get the jitters.  Mathematicians speak of a fraction as a part of a whole (part). ¾ is three parts of the four parts that make the whole. Ever heard of a constant variable?  It is a variable whose value cannot be changed once it has been assigned a value.  Equations of motion are the examples that come to mind in this regard.

Statistics, a branch of Mathematics, has come to stay, and this part of Mathematics is finding its way into the syllabus of the lower classes as well.  It tells us about the raw data that is arranged in a random order, and if you wish to interpret/classify it further you have to rearrange it in an ascending or descending order.  Speaking about order and a definite pattern, we arrive at sequences.  Da Vinci code gives you the Fibonacci sequence: 1 - 1 - 2 - 3 - 5 - 8 - 13 - 21 ....  The simplest to understand is of course the AP (Arithmetic Progression) that has a common difference between two successive terms.

Now then?!

Here comes another Dominic Savio…and another…

-         Bernard Fernandes

Dominic Savio, the little angel saint in the Oratory of Don Bosco, is remembered the world over on 6^th May.  However, in India, this feast is celebrated on 6^th July, to give an opportunity to our school going students to get to know and imitate their role model a little better.  Dominic Savio was not a born saint. He was a young boy like any youngster with dreams and aspirations, with his strengths and shortcomings.  It is said that he was overenthusiastic about his sanctity – at times he would give in to self-flagellation. At such moments Don Bosco would intervene through a word in the ear: “Dominic, remember ordinary things in an extraordinary way!”  And Dominic Savio did not disappoint Don Bosco.  He embraced sanctity with alacrity. He began to enjoy life to the full – he played, prayed, loved, forgave. He stood up to his beliefs – did not mind the blows and insults, if that meant bringing a struggling soul closer to God.  He eschewed violence and negativity, and prevented others from doing so. Very soon, he was taking giant strides towards holiness.  However, God thought otherwise.  He called Dominc Savio to himself at a tender age of fourteen; not before Dominic had exerted a tremendous influence over his companions and friends through his sanctity and cheerfulness.

Dominic Savio died in 1857, and 155 years later, his legacy lives on.  He lives on in the youngsters who are resolute in their commitments, in the young who show a heart to be kind, generous and forgiving, in trailblazers who wish to make a difference, and in young minds desirous of knowledge of God and His works.

A few recent happenings to substantiate this:  Young Dinesh Gowda from Nalasopara fought taunts to pass SSC with distinction (TOI, dated 24^th June 2012). He lost his father at six and mother at 11.  His elder sister eloped, leaving him to fend for himself. No relatives cared to take responsibility for him. He stayed with a benefactor ‘uncle’. While the school of Infant Jesus took care of his fees, uniform and other expenses, the teachers chipped in with food. Dinesh did not let his benefactors down and (without any coaching classes) topped his school this year with 93%! He goes on to say, “Hurdles have only made my resolve to study stronger and I will be successful one day.”

Pinky Karmakar, 17, a young class X girl from Assam, helps run a Unicef sports programme in her school, besides teaching adults, including her mother who works as a tea plucker. (TOI, 24^th June 2012).  After her classes, she speaks to parents about the importance of fitness for children’s development.  She was selected to represent India at the Olympic torch relay in London on 28^th June. She hopes her London visit will help garner support to restart a night school which shut down a decade ago.

It was a wet rainy day on 4^th July. Our school children were enjoying their short recess – the rains had kept them indoors. Every nook and corner of the school building was utilized for play and recreation.  One of our physically handicapped students – we have a couple of them – from Std. VI, Vikas,  was edging his way back to the class room on the slippery corridor.  Vikas’ young classmate who was enjoying his moments of play and fun, on noticing Vikas, stopped in his tracks, held him by his hand, and gently escorted Vikas to his classroom.  Now that is concern and sensitivity. I was touched.  After all, it takes small acts from us to be noble and gentle. 

As he lay dying, Dominic Savio’s last words to his father were: “Good bye, Dad, good bye….Oh what wonderful things I see!” A life well lived surely merits ‘wonderful’ things from God.  Is this gift not ours for the asking?

Of fighters and sword ‘tales’

- Bernard Fernandes

The topic suggests a combat- however it’s not.  It’s rather about a passionate hobby.  It got started as a therapy, and is turning out to be a happy addiction. Diabetes, unacceptable levels of cholesterol, and an investigation of sorts brought me inadvertently to the doorstep of a relaxing and engaging past time. Thus opened the floodgates of knowledge of a different kind – fish tanks and their inhabitants!

The first fish tank arrived from distant Naigaum – our Salesian school out there was generous to part with the extra five footer tank that they had.  In came the tiny guppies and the mighty sharks, small mollies and swordtails, together with the exotic flower horns (florans, in India) and parrot fish. Aerators, filters, sand, colorful pebbles and shells, shrubs and plants, all found their way to the aquarium. Children flocked to it, visitors admired it, I loved it.  Smaller fish tanks were now a part of my room and office décor, and soon, another bigger fish tank followed in the school.  The fish (in all sizes and colors) kept coming – cichlids, angels, tetras, discus, piranhas, arowana, black ghosts, platys, oscars, red caps, gold fish, turtles, cat fish, suckers, silver dollars and gourami.

A closer observation, and you get the amazing behavioral patterns of the fish. I learnt that smaller guppies are a ready meal for the bigger grown up gold fish and turtles; cichlids, parrot fish and sharks can coexist; flower horns are to be kept in isolation, oscars are social as long as they are young; and angel fish are no angels! Fighters – so named, because they fight with their kind, to the extent of tearing the fins, and even killing the other – are no fighters in a tank of discus, angels, red caps and gold fish.  Sadly, they are the attacked. 

The male fighters have decorated fins – in fact that’s what makes them so attractive.  The female fighters – and that’s true for the majority of fish – come a distant second with a shorten fin and duller colors. And I wonder why! What caught my eye was the manner in which the fighters breed.  The mating season and after, has all the ingredients of an intriguing courtship: the bubble nest prepared by the male fighter, the embrace, the scooping of eggs from the bottom of the tank to a meticulous placement in the bubble nest by the male, and then the sole concern for the care and the breeding of the eggs and the fry by the possessive male, is a lesson in upbringing and ‘baby’ care. Why we have so many cases of foeticide (female?) and abandonment of infants in bins!

The swordtails and the guppies have it in them to ‘be fruitful and multiply’, albeit in a unique way.  The female swordtail can produce more than one batch of fry in a span of 2-3 months (without the presence of the male to mate for the second or the third reproduction cycle!). This is because the female can store enough sperm to fertilize six batches inside her body! Mind boggling! As of now, I have got two batches of fry by the same female swordtail in the absence of a male partner.

There you are…quite some facts through observation. It’s not even a year, and nature has thought me this much.  Never dreamt that I would put my hands to such an engaging and absorbing activity, and enjoy some peace of mind that comes along with it!  For all of you out there, it is not important that you go out and buy a fish tank – I confess it’s a difficult and ‘messy’ stuff – or go scouting to some far off places for some exotic fish.  Rather, stop running – some lessons from ‘The monk who sold his Ferrari’ here? – and stop to enjoy the wonderful nature around you before nature stops in its tracks and find you gone!