Summer Solstice Part 6

"You have a point, mapmaker. Well then, reverse the case. We Phoenicians needed dreams, and we produced them. We have established trading outposts at the limits of the known world. We have sailed through the Pillars of Hercules to the Tin Islands. We have circ.u.mnavigated Africa. We have traded in the Black Sea. Our s.h.i.+ps rule the Western Mediterranean, and business on great waters has made us rich. And all because we had a vision. We still have it, and with it, we shall beat the Romans."

"Peace, gentlemen," said Ptolemy. Wars and rumors of war made him uneasy. "Let us talk of other things. Eratosthenes, how go the angles?"

"Today, my lord Ptolemy, the day of the summer solstice, I measured the angle of the sun at high noon. I found it to be seven degrees and ten minutes."

The Second Ptolemy smiled graciously, yet warily, and with a warning in his eyes. "And pray what is the significance of seven degrees and-what was it-?"

"Ten minutes, my lord. Significance?" The geometer eyed the Greek pharaoh carefully. "To determine the significance, we may need the a.s.sistance of the priests"-he bowed gravely to Hor-ent-yotf and Rabbi Ben Shem-"and the historians"-a bow to Cleon, the Homeric exegesist-"and perhaps to other philosophers, living and dead."

Claudius Pulcher had meanwhile returned from the credentia with a wine refill. "Aside from all this a.s.sistance, real or threatened," he grumped, "can anyone tell me the significance of seven degrees and ten minutes?"

"By itself, nothing," volunteered Hamilcar Barca. "However, taken with certain other measurements, it could give you the size and shape of the Earth." He said to the librarian: "Am I right?"

Eratosthenes sighed, and glanced at Ptolemy from the corner of his eye.

"Oh, go ahead," said the pharaoh wearily. (And oh, to be on that barge!)

The Greek shrugged. "At Syene, where the finest red granite is quarried, a tall pole casts no shadow at noon on the day of the summer solstice, and the sun s.h.i.+nes directly into the wells. This is so because Syene lies almost directly on the Tropic of Cancer. Also, Alexandria lies almost due north of Syene, at a distance of 5,000 stadia. Now seven degrees and ten minutes is about 1/50 of a full circle, so 5,000 is 1/50 of a full circle on the Earth. Thus we multiply 5,000 by 50, and we get 250,000 stadia as the circ.u.mference of the Earth."

"One moment," interposed Ptolemy. "You say 5,000 stadia. How did you measure that?"

"From cadasters-registers of land surveys for tax purposes, made by the Second Rameses, over a thousand years ago. The exact dimensions of the nomes are given. It's a matter of simple addition, from Syene to the sea, with certain adjustments."

The Roman frowned. "I still don't see. What's a 'stadia,' anyhow?"

Hamilcar Barca smiled. "The singular is stadion. A bit over eight stadia to your Roman mile. Using your units, General, the world is a sphere about 30,000 miles in circ.u.mference."

"Ridiculous," breathed Pulcher. "It can't possibly be that big."

"This is entirely unofficial," interposed Ptolemy hastily. "The Great House takes no position..."

Rabbi Ben Shem smiled uneasily. "Dear Eratosthenes... the Earth cannot be a sphere. Our Holy Scriptures state, 'the four corners of the Earth.' "

"I think we may be overlooking the obvious," said Hor-ent-yotf. "Our esteemed geometer a.s.sumes the sun is so far away that its rays, as received here, are parallel. The a.s.sumption is totally unwarranted, as I shall show. There are other, much more reasonable conditions that will give the same data." He pulled a piece of papyrus from his linens and inspected it. "If the sun is 40,000 stadia distant, it will give your same shadow angle of about seven degrees here at Alexandria, will it not, Eratosthenes?"

The mathematician smiled. "Quite so-a.s.suming the Earth is flat."

"As is indeed the case," said the Roman amba.s.sador.

Hamilcar Barca shook his head. "Like the Greeks, we Carthaginians are a seafaring people. On sh.o.r.e, when we watch a s.h.i.+p come in, we see first the tip of the mast, then the sails, then the bow. That means to us that the Earth is a great ball, and that the s.h.i.+p comes up into view over the curvature. It is the same at sea. For example, my trireme arrived here at night. We came in. guided by the great Pharos light tower. At first, our man at mast-top could not see the light at all. And then, suddenly, 'Light ho!' and there it was, just over the belly of the sea."

There was a moment's silence, broken by Ptolemy. His voice was strained. "This is a very interesting discussion; yet I do not feel that we can ignore a thousand years of research and thought that have gone into the problem. Certainly the ancient authorities leave no doubt on the question. Homer said the Earth was a flat disc, bounded by the River Ocea.n.u.s. A decade before the battle of Marathon, Hecataeus announced the same fact."

"One moment, your majesty," said Hamilcar Barca. "Your own Aristotle believed the Earth to be a sphere because of the round shadow on the moon, during lunar eclipse."

Ptolemy shrugged. "Homer's disc, head-on, would cast a round shadow."

"My lords," said Rabbi Ben Shem harshly, "/ make no attempt to define or deal with impiety. Certainly Greek history provides ample precedent. I have read widely in your Library, Eratosthenes, and I can cite your own laws and applicable cases. Your Anaxagorus propounded a heliocentric system, and wrote that the sun was a big blazing ball, bigger even than the Peloponnesus. He was condemned to prison for his impiety. Pericles was barely able to save his life. Aristarchus also proposed a heliocentric cosmos, and was accused of impiety. Alcibiades was recalled from the Syracuse campaign to face charges of impiety to Hermes: whereupon Athens lost the war. Socrates was executed for impiety. Protagoras confessed agnosticism and fled Athens with a price on his head."

Ptolemy rubbed his chin. "I, for one, believe Homer, who declared the Earth to be flat, with its omphalos-navel-at Delphi. A sphere seems quite impossible. People at the antipodes would walk with their heads hanging down. Trees would grow downward. Rain would fall up. These things cannot be." He fixed a grim eye on Eratosthenes. "The G.o.ds gave us a flat world, my young friend. Adjust your numbers to fit the facts, not the other way around." And so having delivered his views, and having thus dried his throat, he and Pauni left the group in search of the wine table.

"Well, then, man of the Library," said Ben Shem, with just a hint of triumph, "you will of course recant?"

Eratosthenes found his body turning, not to face the rabbi, but instead to Hor-ent-yotf. It was to the priest of the hawk-G.o.d that he gave his answer: "No! I do not recant. I do not retract. It is as I said." The hawk-priest stared at him without the slightest expression.

"Oh!" said Ben Shem. "You claim the Earth is a sphere?"

"Yes."

"And it circles the sun?"

"Did I say that? If I didn't, I meant to."

"Aiee!" shrieked the rabbi. "Heresy, heresy compounded!" He pulled at his beard, and a few hairs tore loose.

"Sorry," said the Greek apologetically. "I didn't know you'd take it this way."

The priest stumbled away, muttering.

Khor shot a thought into the geometer's mind: "Science is a very upsetting subject around here."

"Yes."

Hamilcar Barca broke in. "May I ask a question about your 5,000-stadia measure to Syene?"

"Of course."

"Does that include a rake-off by your local priests? Say, one-sixth?"

"How do you mean?"

"Well, suppose the true measurement is actually 4,285 stadia. Do the priests add one-sixth, or 715, for their share of the grain crops?"

"Yes." It was Hor-ent-yotf who answered. They all looked around at him. "From the time of Menes," said the priest, "the first pharaoh, who united upper and lower Egypt, the temples have taken one-sixth of the crops. We do this painlessly, by telling the farmer his plot is one-sixth larger than it really is."

Eratosthenes was embarra.s.sed. "I am caught in a gross error. The circ.u.mference is then 4,285 times 50, not 5,000 times 50. More accurately, the circ.u.mference is"-he thought a moment-"214,250 stadia, or about 26,000 Roman miles."

"The one-sixth difference is not significant," said Hor-ent-yotf. "The crux of the matter is, you have attempted to heresy of the gravest order." He signaled to Ne-tiy. She glanced once at Eratosthenes, then followed the hawk-priest away from the group.

"Watch him," warned Khor. "I see into his mind. He has condemned you, and he means to kill you."

The geodesist shrugged. "It had to come."

"Shouldn't you leave now?"

"Why delay the confrontation? It might as well be here. Regardless of what happens to me, Ne-tiy can drive you back to your s.h.i.+p."

"I wasn't thinking of that. When the time comes, I can manage by myself."