Geometry
(A broad short story)
(The scholar’s headache: “…what then is the relation between Geometry and the laws of nature?”
--- The physical nature of the universe: J W N Sullivan)
It was before two months. The intermediate exams were nearing. ‘A’ was counting heads with his friend ‘C’, standing at the crossroads. Both of them are not studying well, probably both of them will fail. ‘A’ said, “ I really feel so bad. Math is somehow manageable, but in English – even a zero is enough. ‘C’ said, “ you can at least hope for a zero. I won’t even get a negative mark. If I fail, I won’t be able to study more- you well know. All the hopes plans - everything will finish. I don’t know what course life will take. I will lose myself amidst the crowd, probably. Maybe you will also forget me. Friends, all those who will be lucky enough to be successful in life will forget that there was a person called ‘C’—very natural. “In this large world”- what was that poem we read for our matriculation?”
“ I am a ve got everything. Had we realized it before the terminals we would have got a few more marks. We’ve got, still we haven’t.” ‘C’ said “ Water water everywhere, not a drop to drink --”. Just then the accident occurred. Walking with a kid in half pants –
“What’s that? Is that a Mekhela Sador1?”
‘A’ shouted-“ A sail, a sail.”
“Never seen the face before. Wow! Where was this thing all these days in this area? Does she study a lot? Got specs at such a young age!” Both the friends do not like red clothes, but today the blouse really looked quite good! The plaits were moving as if-as if…leave it- why does one need a simile?
‘C’ asked, “ Know her?”
‘A’ said nothing. ‘A’ had all his looks and attention centered on the moving specs-- with the hidden naughtiness in the face. The speed of the red blouse slowed down for a moment, as if a beacon came out from the inside of the specs and abruptly and suddenly stopped. The half pants and the Mekhela Sador disappeared at the end of the road- the specs had to cautiously look back towards the traffic. ‘C’ coughed meaningfully. ‘A’ was serious. ‘C’ showed serious. That was the ‘prelude’ or in ‘C’s words ‘the beginning’, another repetition of the same age-old story. Right at 10 to 10 ‘B’ goes to school; she has come here recently, she will appear the matriculation, along with her little sister and a few girls from her neighbourhood. Right at that time, keeping the whole world aside, and ‘A’ and ‘C’ always come out to the mouth of the road. From there you can clearly see ‘B’’s place. Both of them wait restlessly. At the corner-more conveniently – there is a tea stall, which they use as their observation point. They sit and take two single teas and wait restlessly. ‘A’ keeps on talking about ‘B’, ‘C’ listens silently. At first ‘C’ gave his friend a few words of advice and reason, but gradually he became silent. After the tedious waiting finally the gate at ‘B’’s place opens, ‘C’ becomes conscious, ‘A’ sets his hair, running his fingers across the hair. Talking to her friends ‘B’ smiles near the tea stall, ‘A’’s heart beats faster, a look comes from ‘B’ for ‘C’. And ‘C’?
At ten ‘B’ goes to school, 4o’clock she returns home. The hands of the clock form two right angles. As days pass by the two friends give more attention to their attires and no attention to their studies. ‘A’ perspires while waiting for ‘B’ in the sun. ‘C’ also perspires just as the Satan suffers along with the sinner. ‘A’ suffered from pneumonia also, as he drenched himself in rain while waiting for ‘B’. Need less to mention the corollary that the stall also had to suffer loss for a few days.
The same looks, the same smile. It looked very mechanical to ‘A’. The restlessness increased for contact, he almost crazy for something positive. “ Shall I write a letter?” ‘A’ sought advice. “Be patient”—said ‘C’ who used to support written correspondence. ‘A’ was surprised.
From ‘A’’s place to ‘C’’s place it is a long straight line. From ‘C’’s to ‘B’’s place it is a longer straight line, from ‘B’ to ‘A’ it is the largest. ABC forms a triangle. Of course there are a few short cuts of a few lanes. But ‘A’ does not use the AC path to go to ‘C”s place, he uses the ABC path, ‘C’ does the same. If the BC side of the triangle ABC is extended, at the point ‘D” there is a college. Earlier they would reach the college at the right time. But now even the use of the BCD straight line somehow makes them late. The attendance percentage decreases.
“Now I know that Euclidean geometry is wrong.” ‘C’ says, “Einstein is right, when he says that the minimum distance between two points is not the length of the straight line that connects the points—“
Why not--- ‘A’ smiles knowing the reason.
School was closed. ‘B’ does not come out much, parents also are very strict. ‘A’ and ‘C’ face difficulty.
‘C’ said once—‘B’ has gone to her uncle’s place with her mother. They will return after a few weeks. No point for us to go that way. ‘A’’s face becomes dark.
‘A’ passed a few days restlessly. He knows ‘C’ wont be wrong. Yet he went on the AB line once or twice. Great Expectations! But ‘B’ was nowhere to be seen. Even ‘C’ was missing—he was not there at home also.
Suddenly once walking I on the AC line, in the tea stall—‘A’ saw ‘C’ sitting there. ‘A’ grew a suspicion. He watched carefully. At the slit of the curtain of one of the windows of ‘B’’s place—‘A’ could not believe his eyes…
The dramatic instinct in the two friends wakes up.
‘A’: “ Is this your friendship? You fraud!”
‘C’: (Hiding the guilty feelings)—“What is my fault? I am just a puppet controlled by the powers of an invisible hand.”
‘A’ (with hatred):“Don’t you feel ashamed?”
‘C’ (softly, being defensive): Just think we are such old friends. Can I do it myself? You have misunderstood me.
‘A’ (ruling out the “substitute proof” of the theorem put forward by ‘C’): well, then today onwards ‘A’ and ‘C’ are not friends, but competitors.
Both of them stared at each other for some time. Thus on a fine morning, in a nameless tea stall, a new eternal triangle ABC was created.
The latter story is the eternal story of competition. Both of them drew lines of violence, hatred and anger to each other—to the internal point, the mid point. As if from the three height of the triangle they drew lines to the opposite side of the triangle. The bisectors. The bisectors of a triangle meet at a single point. That point is called the center of gravity.
* * *
‘A’ was very depressed. The grief of separating with friend, to, which new regrets are added. Even ‘B’ has become silent, indifferent; those sweet words, the pretty smile, even the nice look are all there—still “as if something is not there—as if she is doing the things habitually.
Negligence? ‘C’’s effects on her? Flirting?
One day ‘E’ came out smiling from ‘B’’s place, along with ‘B’. ‘A’ saw it. Even ‘C’ saw and understood.
The triangle turned into a rectangle. ‘A’ showed sullen resentment. ‘C’ felt like punching ‘E’ on his face. Needless to say, with the help of the Natural Laws ‘E’ understood that ‘A’ and ‘C’’s searching eyes were on him. But ‘C’ was unmoved. He is a jolly guy, smokes all the time, good at studies (he could not top in chemistry only for four marks, in the last exam). ‘E’ left both of them dazed. ‘E’ told both of them everything very plainly.
“ I know, you are annoyed with me. But believe me I am not an obstacle on your way.
Yes ‘E’ can be believed. He ahs got a simple heart, he is straight forward, truthful, just like his figure—slim with no breath and circumference, only height—a straight line. “ I don’t deny,” ‘E’ said smiling, “once I really loved ‘B’. But ‘B’ rejected me. I have taken it easily—just as I took the incident of not being the topper in chemistry. I hate jealousy. Hope you won’t be jealous of me too. The relation between ‘B’ and me is just of friends now… I request you – because you’ll mind me giving you advice—withdraw from this game.”
“Why?”
“Because, you won’t be able to know her. A woman’s heart is unexplainable, complicated is the female character. “Deva na jananti…(is the Sanskrit right? I always failed in Sanskrit at school.)—
Smoking a cigarette ‘E’ tried to explain (both of them assumed that amidst all these ridicule of ‘E’ there is a hidden pitiful smile for both of them) that a girl’s mind is too complicated. Not a straight line—but circular, round. Whenever it comes to a round it is always complicated—it becomes clear when we think about money—does not it? In the circle we can see many faces in different points—a mother’s, a sister’s, a wife’s—but in the heart there’s only one—
“There’s no such rule,” ‘A’ said with anger, and with suppressed jealousy ‘C’ asked—“Who is that lucky fellow?”
The danger of the lucky one is arriving—‘E’ knew. ‘E’ said—who the lucky one is he does not know exactly, maybe ‘P’ or ‘G’, and he does not claim that it is free from error, but experience says, just like a theorem of geometry, it is not non admittable. ‘A’ and ‘C’ will be surprised to learn that not only to them, or to ‘E’, but ‘B’ smiled to many others also—the same pretty smile—and the stupid were charmed by her—thought she is in love with them. No, no, no need to be furious, it is the nature of ‘B’, she has no bad intention. Just as she smiles at a flower, she smiles (with much pain ‘E’ found this comparison) at you and me, maybe she becomes partial for a day or two—only that.
“ That is another theory; it is about the circumference of the circle. The center is still mysterious. And that special point which is related to the heart can be touched by only one person—“
‘E’ enjoyed his own humour (?) and finished the cigarette and lit a new one. Both of them remained unanswered—because they found nothing that ‘E’ has said could be opposed. Its true. From an external point numerous tangents can be drawn to a circle, but a particular point has only one tangent. That is a proven fact—(Euclid III.18)
“Leave it. It’s not your fault. The fault is with your age. Don’t be serious. Whoever has become serious—is dead. Take it easy. Do you know that ‘R’ spoiled his career for ‘B’? A few more are yet to be disappointed with the problems of caste, creed and income. After rejected by ‘B’, you might not know that ‘M’ only writes poems now a days. ‘K’ roams around like a lunatic. Moreover—“
The rectangle gradually transformed into a polygon. “ I came to know that you have sent letters to ‘B’. ‘B’ herself has told me. I mean—you know. She found it very funny. ‘E’ tried to make the situation light--, “ No point of running for her, she is will-o-wisp. Neither ghost nor God, just gas: mere marsh gas, CH4…
‘E’ smiled. Suddenly ‘A’ discovered faintly that the smile is very superficial. As if a secret is left behind the smile, ‘C’ said slowly—“Brother ‘A’! Forgive me. Let us be friends again.” ‘A’ replied sarcastically, in the same dramatic manner, “ Friends? Impossible ‘C’, in the game of fate, we have chosen different orbits. We started our journey at the same way—but today we are moving parallely towards the same goal. Parallel lines. Is it possible to meet?
‘A’’s words sounded too dramatic. ‘C’ remained silent.
After quite some time ‘A’ became soft and said—“ Maybe you wont get ‘B’, maybe even I wont get ‘B’. Yet”—without finishing the matter ‘A’ again brought back the rough nature. ‘C’ was stunned after listening to his friend. He clearly saw ‘A’, ‘C’, ‘M’ and ‘K’ are orbiting around the point ‘B’ keeping it as the center, the center of all the hopes and aspirations is always out of reach. Yet like fools ‘A’, ‘C’, ‘M’ and ‘K’ will revolve in their own orbits, they will debate, think—it is impossible to meet.
‘A’ stood creating a right angle on the ground. ‘E’ smoked cigarettes leaning at 450 on the door.
‘C’ burst out crying.
* * *
After a few days the results were out. ‘A’ and ‘C’ both failed, it seemed that their probable future had its last act finished. ‘E’ also failed. Everybody was surprised. After getting the news ’E’ disappeared to somewhere. As the train crossed the distant signal that evening, it stopped and returned to the station carrying a beheaded corpse. Gradually people gathered at the station, the news spread at the speed of light. One or two said—never thought that ‘E’ could be so cowardice, shame; just because he failed in a silly exam…
After roaming around aimlessly for many nights in front of that tea stall, suddenly ‘A’ and ‘C’ met. Like the other days both tried to cross each other silently, but suddenly an unknown powerful force stopped both. For about five minutes both of them said nothing.
‘A’ said first—
“ See, how ‘E’ bluffed the whole world?”
“Yeah. Everybody will think that he killed himself because he failed. Intelligent guy.”
“Whereas, he said to us ‘Take it easy’, is it an easy thing?”
Unconsciously both of them stretched their hands. Both held each other’s hands emotionally…
(It is not impossible for parallel straight lines to meet, it seems Einstein has proven it.)
* * *
…. Afterwards, on a rainy day in the month of Shravana ‘B’ was married to ‘F’. The polygon broke down. Both ‘A’ and ‘C’ desired to see the photograph of the spec laded round beautiful face with the approximately trapezium shaped healthy handsome face—but they left the desire unfulfilled, months after days and years after months passed by. After the funeral of all bright hopes and aspirations both of them are white collared clerks. Married, blessed with children. ‘C’’s wife ‘C/’ is fight prone; she is length and width but no circumference. ‘A’’s wife ‘A/’ is ever ill not circumference less as ‘C/’ is. ‘C/’’s geometric name is area and ‘A/’’s is volume. ‘A’ is really a volume: voluminous.
Both cherish the past sometimes—“Never forget the
past”—they remember reading the poem. ‘B’’s children might have grown
– ‘A’ says humourously—may be like their parents they might be creating
a new triangle with an unnamed heart in an unknown place. ‘C’ smiles and
says—may be it is the rule. We have also proven it. Atra idang upapadyam—
A concept comes, establishes itself for a day or two, and then goes away. The forefathers were proven wrong by Newton; Newton is proven wrong by the 20th century. After Euclid-Descartes-Pythagoras, Reemun and Einstein. Shaking the base of the Euclidean geometry of the flat world, leaning on the____ geometry Einstein says—straight line is a great myth… maybe Einstein will also be wrong one day. There is no consistency; nothing can be the last word, no theorem is the ultimate truth--- one thing is certain, and rest all lies, that time flies…
‘A’ thinks himself: Yet in our flat world, the reenactment of the same eternity takes place; with the same rules of geometry the little grandson makes grandpa’s triangle. In the universe the planets and the moons create geometry, the petals of the flower matches its tune with the Cartesian geometry, jeans says with amusement—God is a brilliant mathematician. After the days work, at night ‘A’ goes to ‘C’s place to play cards. Not by the ABC path, but by the AC line, hurriedly. The he doesn’t remember it though ‘A’ knows—(Euclid I.20) – the sum of the length of any two sides of the triangle is greater than the length of the third side. *
* The beginning is heard from a friend-- maybe some old source (?).