The Fifth Proposition; or, The Bridge of Asses. A Love Story by Euclid.

“I glanced over it,” said he. “Honestly, I cannot congratulate you upon it. Detection is, or ought to be, an exact science and should be treated in the same cold and unemotional manner. You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love-story or an elopement into the fifth proposition of Euclid.”

The Sign of the Four.

Let ABC be a love triangle having the side AB equally strong as the side AC; and let the unlived lives BD, CE be prolonged in a straight line with AB, AC.

I say that the agony of ABC is equal to the agony of ACB, and the anticipation of CBD to the anticipation of BCE.

Let a point F be made at random against BD; from AE the greater let AG be cut off at AF the lesser’s level; and let the straight lines FC, GB be joined at cross-purposes.

Then, since AF is no better than AG and AB than AC, the two sides FA, AC are just as bad as the two sides GA, AB, respectively.

Therefore the base FC is as committed as the base GB, and the triangle AFC is a lot like the triangle AGB, and the remaining answers will sound just like the remaining excuses and explanations, namely those which are all alike; that is, the angle ACF sounds just like the angle ABG, and the angle AFC acts like the angle AGB, and since the whole AF is just a whole other AG, and in this AB can be hard to tell from AC, the prospects of BF are the same as the prospects of CG.

But FC also proved as reliable as GB; therefore the two sides BF, FC, give nothing to choose between with the two sides CG, GB respectively; and the corner BFC is as close as the corner CGB; while at BC they all want the same thing; therefore the triangle BFC is also as acceptable as the triangle CGB, and the remaining anxieties will be equal to the remaining uncertainties respectively, namely those which the equal sides inspire; therefore FBC angles the same way as GCB, and BCF’s angle is the same as CBG’s.

Accordingly, since the whole angle ABG was proved as equivocal as the angle ACF, and in this the angle CBG is as confining as the angle BCF, the remaining angle ABG is the same from all angles as ACB; and they are, at base, still the triangle ABC.

But the angle FBC was proved at cross-purposes with angle CGB; and they are both asses.

Therefore: no to both.



It is doubtful to call anything human instinctual. Drives are not instincts; drives compel thought, but instinct supplants it. Instinct is something in the individual that is not of the individual. We can see real instinct in our pets: when the dog swings a toy high into the air as if to snap its neck, or when the cat, after the instinctive pounce or chase, sits in front of the crippled mouse or overturned cockroach in a confusion obvious even across species (we are all mammals here).

We must distinguish drive from instinct. Sexual behavior is the most obvious hold that evolution has on us. With secondhand guilt, even the irreligious talk of this hold as if, because we are animals at all, we are only animals. But what we consider an overthrowing storm would be judged, by other animals, gripped by estrus, to be no more than a gentle, steering breeze. In the way of nature what could be sillier than an animal which, when strength and spring are come, must be taught how to reproduce? For human beings instinct is unequal even to the original operation of life.

There is of course some instinctual flotsam on the unconscious: hitting with the heel of the hand, for example, or not rolling over a pet, or a baby, in your sleep. But we are too willing to consider behaviors instinctual which are only unavoidable; territoriality, for example. It is a necessity in all modes of life, one which if not learned from instinct is still enforced later as a hard lesson. Boundaries will always be encroached on, even the skin; and those whose only boundaries are for their vitals and victuals will find their lives and livelihoods in constant danger. Artificial boundaries remove the fight from the vulnerable center, as clothing wears or tears in place of skin.

We are animals, made of the same stuff as other animals; but we are not like other animals. Even without assuming a creator, we can see that the changes we make in raw materials by way of art or technology, to make them speak or show or do, are the same kind of changes that made animals into human beings. There is no line in us with instinct to one side and self on the other. What we do is what we are. Human consciousness is not a kind of animal nature; it is map and image and story of that nature.

Eating School

I came without a journey to an ideal city. It had been built, I observed, during the Renaissance; but time and romantic patination and eruptive modernity had softened its rigid geometries. Still every path through that city was like a strain of music; a harmony of architecture, geomancy, statuary, mural, ironwork and garden.

After some time wandering and admiring, I found on sitting that I was tired and hungry; so I went in search in food. In the first restaurant I came to, I saw people sitting, each alone, eating from bowls of porridge, pablum, and gruel, with glasses of a gray drink at their elbows. Health food, I thought, and looked farther; but all the restaurants were like that one.

I resolved to do as the people of the ideal city did. I sat and ordered, with an encompassing gesture, “Whatever they’re having.” Sitting among them, I could see from their hunched postures and pinched faces that they took no pleasure in their food.

The porridge had the consistency of diluted cottage cheese, and tasted of dish soap. The gray drink tasted of chalk. I asked the man at the next table: “Where can I find some real food? Maybe a hamburger?”

He laughed at me. He whispered something to the next table. I looked away, but I could still see them in reflection: they were laughing at me. A third, with his head thrown back and nose in the air, aped the act of cutting meat, reducing the others to near-hysteria.

I swept my food from the table, laid down paper in payment, and left the restaurant. Someone ran up behind me and tapped me on the back. When I turned, there stood a well-suited man with a bright chain of office around his neck. “I am the Mayor,” he said. “I want to apologize to you. I know that our city has a food problem. We’ve made attempts at establishing serious restaurants, but we can’t seem to keep up the patronage. But I don’t want foreigners to take home the impression that nothing is being done. In fact, we’ve just completed a major renovation of the Eating School. Would you permit me to give you a tour of the new facilities, and tell you about our programs?”

“Of course. I would be honored.”

The city was so sensibly laid out I was not sure that we had left before we arrived. There was a long wall, and a broad gate, over which appeared in lettering worthy of Trajan’s column:


“Why is it behind a gate?” I asked.

“People pay for their children to come here and have their palates trained,” said the Mayor. “How could the Eating School support itself if anyone could wander in and eat there?”

“They could pay for what they ate,” I said.

“Don’t be silly,” said the Mayor. “Good food is wasted on those not trained to appreciate it. And if we made it available to everyone, they would use up the supply. There’d be nothing left for real eaters. The Eating School is for those who live to eat, not those who eat to live.”

By this time we had been heard, and the gate was open for us. We entered onto an long avenue, where gracious brick buildings ran to either side of us, and we and they alike were shaded by the trees. Young people, from children to late teenagers, milled or ambled, or sat and talked on the spacious grass.

“I don’t see anyone eating,” I said, “or smell any food.”

“Eat outside!” The Mayor shook his head. “Where any passing smell could distort the olfactory experience? Or let the smells of food just drift around to clash with each other? You’re joking, sir.”

“The smell of food raises the appetite.”

“Now I see,” said the Mayor. “You think that just because we’re out of the way, we’re yokels. I’ll have you know that we begin training in appetite suppression on the very first day of school. We may not be New York or London or Paris, I grant you that, but that doesn’t mean we just gorge ourselves whenever our stomachs start rumbling. Just look over there. That’s our graduate cafeteria – the largest in the world. The chefs there can re-constitute samples of any dish known to man, from the cuisine of any country or ethnicity. Or look over there! That’s world’s largest walk-in freezer. Frozen samples of every fruit, vegetable, livestock meat, game meat, fish, grain – anything you could get anywhere from hunting, fishing, gathering, agriculture or aquaculture. I did my doctoral research there on calamari.”

“You like calamari?” I asked.

“Like!” He laughed. “As if I made a meal of a squid. I’ll have you know, sir, that I’ve sampled calamari on four separate occasions, under controlled conditions and with fully provenanced ingredients. I’ve written twelve research papers on calamari. I have, in fact, conclusively proven that it tastes nothing like chicken.”

“I believe you.”

“And look over there. There is our finest accomplishment – the Adult Eating School. Classes day and night. In a year, sir, only a year, we can take a common hardtongue – forgive my language – and teach him to distinguish at first taste between seven different grains, twelve different spices, and six kinds of meat. We hope to be able to offer sour training by the end of the year – it’s a question of keeping up the lemon supply.”

“Where do they eat? The adults you train? Your graduates?”

“Many of our finest eaters return as instructors. We also have a certain number of positions open for visiting eaters – and there are fellowships in the Eating Institute. Institute fellows are entitled to three meals a day with no charge and no teaching duties. And we have outreach programs, which make high-quality sandwiches available from roving kitchens.”

“I would like to eat something. Is there somewhere here I can get real food?”

“Of course. Here, come with me, we’ll register you.” We walked into a low building full of computers and unsmiling people, all behind a counter. The Mayor leaned meaningfully on the counter and talked to one of them in a soft voice. He returned smiling. “I threw my weight around. I can get you in for the faculty gumbo.”

“Can you show me the way?”

“I’ll send someone to show you on Tuesday.”

“That’s three days from now!”

The Mayor nodded. “I was afraid I wouldn’t be able to get you in this month.”

I told the flabbergasted Mayor that I had lost my appetite, and took the short walk out of the ideal city.

Young and Old

Even on common ground, even when there is much to be said, when the old and the young talk together it is always somehow unsatisfactory. It is not that the young ask stupid questions; not that the old are preoccupied; not that the young are clever, but the old are knowledgeable; not that the young are forward, but the old are wary. These are only obstacles, and obstacles can be overcome. But as one is young and the other is old, each wants from the other what they cannot have.

The young want the wisdom of the old without understanding what they ask for. Death is coming – even the young know this. Even the young are broken to the awareness of death when first something they love dies. What the old know that the young are free of is how short and how wasteful life is before death: that no matter how narrow the range of your possibilities, even in the longest life there is not enough time to fulfill them. You must choose. You must live by glimpses and intimations and barren plans. The old are generally kind enough not to pass on this poison wisdom before its time; and if they said what they knew they would not be believed.

The young do not get what they want from the old; the old do not get what they want from the young. They want to get to know a person while they are new, while they are strong and armored with laughter; but their efforts are frustrated.

What the old forget is what it is like not to know who or what you are. To be young is only to be indignant that, not having asked to be born, so much is expected of you in return. Who you are, who you will be, is arrived at, not received from nature or from nurture, for then like causes would yield like people – but viewed exactly and patiently, no two people are really alike. You cannot win the hope of a place in the world to pursue, or the having of a place to defend. They must in some sense be given to you. Until then, the self remains unsettled.

You must know yourself before others can know you. All we know of one another is what we sympathize with; and what is obvious enough in another to share in, is only what they have first distinguished for themselves. It is not that you can pass on your self-knowledge; as your face is different to the mirror, to the camera, and to the world, it is different to everyone in the world. But only stupidity is unselfconscious. You must know yourself: if you do not know yourself rightly, you have a false idea of yourself. If you then try to be understood – or even to be recognized – you seem either a fool, or a mass of affectations; and if you do not try, you confuse or mislead. This ends badly: at best in disappointment, at worst in unintended betrayal.

Age is a double tragedy. Age not only ruins us, it isolates us. We reflect – “If I knew then what I know now…” But we cannot even teach what we have learned to the present, let alone the past. And youth is a double farce: we do not know what we are doing; we do not even know who is doing it.

And in between – what is in between? Who can mediate? Nothing is in between. There are no mediators. Youth bears us up until the moment it lets us fall. Age descends the moment youth departs. One evening we go to sleep not yet knowing who we are; the next morning we wake up strangers to ourselves.