“Why? There just is.”
Stiffly, he stands, opens a drawer and takes out a piece of chalk, then to her baffled expression, passes it to the girl. He gestures her across the room to a table where among papers and paraphernalia, sits a globe of the world. He spins it experimentally.
“Very well Jenny. Let us take what you know and apply it.” He gestures her to the globe. “Carefully, you will chalk a triangle onto the surface here. Any triangle, you choose, but keep the sides as straight as you can to create a true triangle.”
Perplexed and frowning, she picks up a straight edge and chalks a triangle, joining a couple of random points on the equator with the North Pole. As she does so, the tip of her tongue protruding as she works to keep the lines straight, Mr Kalkowski takes a protractor from another drawer, then passes it to her.
“Now measure the angles.”
She measures, mutters to herself, then frowns. She measures again.
“What is your answer?”
“About two hundred and fifty. It’s hard to be exact with it not being flat.”
“Of course. And what do you make of that?”
She surveys her handiwork. “Um…. Those two angles have to be ninety degrees each because they’re drawn straight up from the equator to the pole, so the angle at the pole has got to be extra…. so…. The answer can’t be a hundred and eighty. It always has to be more.”
“Quite so. And perfectly deduced I might add. There Jenny is the difference between scholarship and education. The scholar may know many things, a great list of the knowledge of the world of humanity. You knew that there are one hundred and eighty degrees in a triangle, but when faced with the reality, you arrived at a correct answer.”
“A correct answer?”
He continues “This is an illustration of the difference between Euclidean geometry and non-Euclidean. I was being unfair in my original question because I knew you would assume a flat surface. This is what you were taught when you were at school.”
“Does it matter?”
He huffs. “It certainly matters if you are trying to navigate a globe rather than a flat Earth. In fact, it was from these sorts of discrepancies that Columbus knew he was trying to sail around a sphere. However.…” He sniffs. “…. Columbus also tampered with the figures, for political reasons, and produced an incorrect answer for the size of the globe. It enabled him to obtain the funding to launch his expedition. In fact, it was known in Greek times that the world was spherical and they had a very good approximation of the size….”
Jenny stares at him. “Mr Kalkowski, why are we talking about geometry?”
His eyes slide to hers and his lips curve to a small smile. “Always the right question, eh Jenny?”
He reaches for his pipe and tobacco pouch.
Jenny watches him, this ritual of his she has seen so many times. And she knows this is her teacher’s way of filling the space while he finds his words.
She seats herself again, and she waits.
And as blue smoke curls from the pipe, he joins her and sits also, the tobacco a glowing ember as he draws.
“Why are we talking about geometry? I was trying Jenny, to create…. Let us call it a parable. You knew the answer to the question. And the answer was correct, for a given situation, a given paradigm. Change the paradigm and the answer can be entirely different.”
She stirs, beginning to understand. He continues. “For you, the old paradigm was childhood, a belief that this was the place you should be. That a simple life as a wife, perhaps a mother in this simple place, would suffice you. Now you know this is not true. You have a new paradigm. New answers. A new way of seeing the world.”
He takes the pipe from his mouth, looking at it for a moment. “It is a bad habit, I know. The doctor tells me I should not do it, but at my time of life…. I have seen and experienced, I think, everything I have wished for.”
He points the pipe at her, punctuating his words with the movement. “Jenny, your life is ahead of you. You say you believe you should leave. I believe you are correct.”
She holds up her hands, palms to heaven. “What should I do? I don’t know….”
The old man puffs a curling ring of smoke. It spins, a writhing vortex in the air, then disperses. “The Greek philosopher Plutarch said that the mind is not a vessel to be filled but a fire to be kindled. Here, Jenny, you have learned. You have been taught. But when you are truly educated, you learn to think.”
“You still think I should go to university?”
“It is what I have always believed Jenny. It was not my place to interfere when you decided to marry Chad, but now….”
Thoughtful, she pours another cup of tea, tilts the pot to her mentor. He nods, and she pours a second cup.
“How would I do it?”
“I retained all the forms and other information from when you were first going to apply. You have only to use them.”
“You didn’t throw them away?”
His eyes crinkle. “No, I did not.”
Her eyes fall on the cake again. It’s awfully good. Mrs Collier bakes wonderful lemon drizzle cake. She cuts another thin slice for herself, then another for Mr Kalkowski.
“It’s awfully expensive. How would I raise the money?”
“Perhaps you will have to work for a while, save for the fees. I have a little money, Jenny. I am happy to contribute.”
She shakes her head. “No!” Her refusal is violent.
She blushes, moderating her tone. “No, I’m sorry. I didn’t mean to be rude. But I’ve lived on charity long enough….”
“This is not charity, Jenny. Merely…. a gift between friends.”
Stubbornly, she looks away. He sits forward, tilts up her chin with a finger, angling her face to his. “Jenny, I have no family. No children.” He gestures around the room, his hand trailing smoke as he does so. “I have all I need here, and I am an old man. Let me do this for you. Yes, no?”
Still she hesitates. “Let us say instead then,” he continues, “that it is a loan. You will pay me back when you are able…. Please, Jenny. Let me do this. Let me help.”
And finally, she nods, her smile slight.
“Good,” he says. “It is not much I fear and will by no means be enough. But it will be a start. If nothing else, it will help you eat and live while you find your feet in the outside world.”
Her eyes flood again. “I don’t want to say goodbye, Mr Kalkowski.”
“I am sure you will come to see me, to visit. Perhaps when you have reached your university. You will come back and give me your news. In the meanwhile, you can write to me. I would enjoy reading your letters.”
“I’ll do that, I promise. I’ll come to see you again before I go.”
“You do that Jenny.”
*****
James
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