“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….”
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
think I
believed Jenny. It was not my place to interfere when you decided to marry
the pot to her mentor.
would I
all the forms and other information from when you
throw
crinkle. “No, I did
eyes fall on the cake again. It’s awfully good. Mrs Collier bakes wonderful lemon drizzle cake. She cuts another thin slice for herself,
expensive. How would I raise
save for the fees. I have a little money, Jenny. I
her head. “No!” Her refusal is
moderating her tone. “No, I’m sorry. I didn’t mean to be rude. But
not charity, Jenny. Merely…. a gift
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
“that it is a loan. You will pay me back when you are able…. Please, Jenny. Let me
nods, her smile
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
eyes flood again. “I don’t want to say
reached your university. You will come back and give me your news. In the meanwhile, you
I promise. I’ll come to see you again
“You do that Jenny.”
*****
James
detests the work on accountancy. She doesn’t have to do a lot of it, but Richard’s right. If she wants to make any headway
…. and she does….
got to learn at least
necessary evil, but sometimes the medicine doesn’t come sugared and
a good couple of hours, sitting on the
my great
on the couch, working through the text Richard gave her,
she know she’s
tapping her fingers as
book in one hand, but if he’s reading it, I’ll plait fog. Every thirty seconds, his eyes slide down to the red-haired beauty next
Perfect….
She sighs….
is
concentration
to notice me,
crinkle then slide down. “Charlotte, how about
abandoned. Her head tipping back to look up at him.
towards me. “I believe your Master is trying to
against him
rise, crossing the room to stand over her, looking down.
I don’t hear the words, but her breath catches and her pupils expand. Whatever he said, my cock approves the result, jolting to life and making my trousers