I adore paradoxes. I collect them, think about them, try to invent new ones. I have loved paradoxes ever since I saw a reproduction of M.C. Escher's 'Waterfall' in a children's book when I was young. Discovering Zeno was, for me, a major revelation. The following story is based on my third favourite paradox, often attributed to Betrand Russell though probably it was not devised by him. For many years I confused the spelling of antimony the element with the spelling of antinomy the mutual incompatibility of two laws.
Friday, 30 May 2014
Travels with my Antinomy (2014)
There is no absolute truth. Or is there? I went travelling with my knapsack and curiosity over a range of mountains far from home. I was looking for a village I had once been told about, a village where I might find something I had lost that was neither my senses nor my virginity. It was a long way, but ways are longer often than this one, so complain I did not.
At last, when the sun was setting beautifully in the west, where always it sets, at least to my knowledge, I saw the village spread below me. It was tinted rose and purple at that hour and I hurried down the slope towards it. There was a solitary tavern with an oaken door that yielded to my knocking. I asked for a room for the night and was given the attic.
After resting for a short time, I went down to where there was a blaze and mugs of cider available for me to slake my thirst. And while engaged in the arts of stretching my legs afore the flames and sharpening my innards on the brew, I asked the barman, who seemed an agreeable fellow, if there were any other men hereabouts who had a beard just like mine.
“Not only not like yours, but not like anyone else’s.”
“There are no beards here?”
“Every man in this village, Señor, is clean shaven.”
“You have a very busy barber.”
“Ah, the barber shaves only the men who do not shave themselves. That is the law among us who dwell here.”
“And no man ever neglects to shave or be shaved?”
“That is correct, Señor.”
Then I knew I was in the village I was seeking, the village where all men are smooth cheeked and either shave themselves or are shaved by the barber. So I tugged at my beard, the beard of a wanderer, and I sipped my cider and felt the warmth radiate outward from my body toward the fire, as if two different kinds of heat were about to meet and mingle.
“In that case,” I said lightly, “who shaves the barber?”
“Shaves the barber, Señor!”
“Yes indeed. Who?”
The barman sighed and tapped his nose; but it was mercifully clear he did not yet regard me as a troublemaker, merely as a stranger, an ordinary man who had finally asked the awkward but inevitable question he had been expecting for years, if not decades. He poured a mug of cider for himself and he shrugged and then he came over and sat next to me.
“The barber has two choices, Señor. He can shave himself or he can go to the barber to be shaved. There is only one barber in the village, so if he decides to visit the barber he will visit himself. In other words, he really has one choice and it is not even a choice. He must shave himself. But by tradition he shaves only the men who do not shave themselves.”
“So he cannot shave himself?”
“As you say, Señor. But he cannot grow a beard because there are only clean shaven men dwelling in this village.”
“That is the paradox,” I replied. “I had it once upon a time but I lost it in my youth. Now I have found it again.”
“What will you do with it, now you have it?”
“Take it with me when I leave.”
“But we need it, Señor; it is the only one we have. This is the village with only one barber, who is male, and who shaves all those, and only those, who do not shave themselves. If you take the paradox with you, what will we have left? And he is a very heavy man, too heavy for you to lift. I also believe he will fight back and perhaps slash open your throat.”
“My presence here spoils the paradox anyway.”
He gazed at my beard a long time.
“Yes, Señor, I suppose it does. But if you are gone in the morning, it will be repaired. The paradox will thus only be suspended for one night. And in fact you cannot take the paradox away with you, because while you are here there is no paradox. The paradox only works if every man in the village is clean shaven and you most definitely are not that.”
This was true. I realised that I had been questing for a rainbow or horizon, something that would move further away and out of reach the nearer I got to it. I understood that this was a logical consequence of my situation and that only one of two courses of action would help. I would either have to shave myself or else go to the barber to be shaved. So I said:
“May I borrow a razor from you tonight?”
“You may not, Señor.”
“Then I will have to visit the barber tomorrow morning.”
The barman lowered his head.
I finished my cider and went up to my room. There was a desk in a corner of the attic and a chair. I did not feel sleepy and so I decided to update my travel journal. I opened my knapsack and took it out, together with my quill and bottle of ink, which I arranged neatly on the desk. I heard footsteps outside and I went to the little window and peered cautiously out.
The barman was hurrying down the street in the moonlight. I guessed that he was going to rouse the barber and tell him to hide when I called round to see him in the morning. I would not easily get a shave here; but if I did manage to, I would certainly not be permitted to take the barber back with me. I would have to remain here, a prisoner, imbibing cider.
Shaking my head ruefully, because that is my favourite way of shaking it among the several methods I am aware of, I sat down and opened my journal to a new page. Then I dipped my quill into the ink and began writing. I told of my trek over the mountains and how I... but no, those were not the words that now lay on the page before me. I blinked at them.
My blinking was so rapid and my eyelashes are so long that the ink dried more quickly than it would have done had another man penned those words. It appeared that I had written an account of how to tend horses in a stable. Had the rigours and stresses of my journey muddled my brains? I began again on a clean page but once again the words tricked me.
Now I had written about gathering windfall apples in the orchards on the edge of the village. I tried a third time. Now my account told of milking goats on the slopes where the wild flowers grew.
A fourth and fifth time, a sixth time, seventh, eighth...
It was peculiar and unnerving.
At last, in agitation, I got up and paced the room, creaking warped boards with muddy boots. I paused only at the window and looked out again. The moon was still shining brightly and I could see the whole village. In every house just one window was illuminated and it always belonged to the highest room of that house. They were lit by lamps like mine.
And men were behind each one of those windows; and some of these men were sitting at desks of their own, writing in journals identical to mine; but most of them simply stood there, faces pressed to the glass, and gazed in my direction and grinned when they saw me looking back. And then I realised that I was part of another paradox, one related to the first.
There is a village with just one professional scribe, who is bearded, and in this village every man keeps a careful account of the day’s events, and does this by doing one of two things. Either he writes his own journal or the scribe writes it on his behalf. The scribe writes only the journals of the men who do not write their own. Who writes the scribe’s journal?
I knew that if I took my journal with me when I left, as I was planning to do, I would free the paradox from this prison. It would be my companion on all my future travels, like a woman but easier to read, to flick through, to replace or forget; not at all like a woman really. I blew out the lamp and went to bed and I dreamed only once of a looming shiny blade.