+Linkica+ the newcomer said when he saw that he was not alone.
+Dehan+
They paddled near each other for a few moments, observing the customary period of silence in case either of them did not wish to converse at this time. They remained close by.
+The sun appears to have moved down toward the water+ Dehan said, squinting up at it.
+Yes. It won't be long before we must find another beach until it returns. I worked the figures out from observations once. This planet has a period of rotation of six thousand, four hundred thirty time units. The day is three thousand, two hundred fifteen long. Although it is too cold to swim in the early morning+
+You are a man of science?+
Dehan knew that the other must be of some high standing or he would not have used this Door. The ocean of Ytong was here to be enjoyed by anyone, but Doornumbers were exchanged only among people of the same levels of attainment. Somewhere on this beach was a child's Door. Perhaps a madman's Door; he neither knew nor cared.
+I am a phylogeneticist+
Dehan nodded unknowingly and splashed water onto his head. Another long word. Another speciality. There must be thousands, perhaps millions of them. +I am a historicollator+
+How interesting. I have always wanted to meet one+
Dehan closed both his eyes in the expression that meant humorous disbelief. +Can it be true? I have never met anyone other than another historicollator whoever heard of the speciality+
The other man rubbed his hairless scalp, now reddening under the sun, and smiled.
+I can pretend no great breadth of knowledge. I must admit that I searched the word out as a reference. In relation to my own work of course… +
At the mention of his work he suffered a natural embarrassment and Dehan sank beneath the water and swam in a circle to lessen it. There are certain things that are never discussed while bathing. +I should like to close my pores+ he said upon surfacing again. +And you?+
+A fine suggestion+ They waded ashore and quickly put on their robes.
+I have recently visited a frigidarium that is very unusual+ Linkica said hopefully, volunteering the information to excise the memory of his recent breach of conduct. He spoke the code number aloud, his fingers unconsciously tapping out the combinations of numerals in the air.
+I do not know it. I will be pleased to follow you+ Happier now Linkica moved quickly to the Door and activated it. Dehan stepped through behind him and his body recoiled as the subzero air and swirling snow struck at him, gasping at the sudden shock. They appeared to be on an icy ridge that fell away into snow-clouded nothingness on both sides. Ahead, barely visible through the pelting flakes, were two other Doors set into the cliff face. Linkica had to shout into Dehan's ear to be heard.
+When it is not snowing one can see impossibly far in this direction. Mountains, valleys, snowcap, terribly impressive+
+I shall… remember+ Dehan stammered through numb lips.
They shuffled across the slippery ice surface, following the groove worn by other footsteps, sharply aware that only a single waist-high bar on either side stood between them and plummeting destruction. Gratefully they passed through the Door and into a robing room and each took a cubicle. Dehan sent his soiled robe through a small Door back to his own quarters, then dried and put on a one-use lounge suit from the dispenser. His skin tingled and he felt wonderful. That was certainly a fine frigidarium. He would try it again, hopefully on a clear day.
Linkica was waiting for him at a table by the immense window. The light of twin moons flooded the valley outside, filling it with infinite shades of gray and black where hills, jungle, and river met and merged. Dehan knew this place, built into a high hillside of some tropical world. They nodded, ordered drinks, then sipped at them when they appeared on the table.
+What is your work?+ Dehan asked. +Phylogen- something you said+
+Phylogeneticist. I attempt to trace the origin of different species, ancestorship, relationships. Most useful in stockbreeding, food plants, that sort of thing+
Dehan nodded although he had no idea of what the man was talking about. Encouraged, Linkica went on.
+Some time ago I was consulted about a gene-linked human disease. I traced its origin and found the correction that must be made. Because of this I became most interested in mankind, this most unusual of all animals, and I began to trace our history. In some ways, one might say, there is a slight resemblance between my small labors and your great work. Are you working well of late?+
Dehan nodded and smiled. The man was goodmannered after all. One never discussed one's own work in detail until all present had mentioned theirs.
+I have done with the Elstaran. A tedious task, a portion of history that was singularly dull as human history goes, and entirely too long for its own worth. A dozen suns, twenty or so planets, now thankfully gone by courtesy of a fortuitous supernova. I reduced over nine hundred volumes to a single volume, losing nothing of value in so doing+
+Admirable. How we do need your sort of talent to pare the long ribbon of history to manageable units. We would drown in the superfluous were it not for you. I can state this truthfully, for in my own research I have realized for the first time the incredible length of the history of our species. Would you say millions of time units?+
+More. More+ Dehan spoke the words slowly, with deep feeling.
+That it could be so. I do believe it+ Linkica bowed his head beneath the weight of the thought. +A moment for beauty, if you will. Sunrise is near and the sky changes+
They watched silently for a brief time. The sky was lightening with a tropical swiftness. Mist rose from the trees and river and the first muted pink brought color to the grays, touching the swirls and pools with an invisible brush. It was entrancing and they opened themselves to appreciate it.
+I have uncovered strange curious quaint and mystifying facts along this endless trail of progress+ Linkica said. +Have you ever considered why we count from a twelve-digit base?+
+Mathematically it is the best. There are but eleven digits and the zero to remember. Yet still capable of infinite amplitude. Divisible as well by one, two, three, four, and six. A fine base+
+That is all?+
+That is enough+
+Have you never considered that at some time, in the dawn of our race, we must have first started to count and in our simplicity used our fingers as a basic system+ He spread his hands on the table and looked at his dozen fingers. +Could that not be possible?+
+Possible. But just a theory. You might just as well say that if we had had five fingers on each hand we would have used ten as a base+
Linkica's face went white in an instant and he lifted his glass and drained it quickly. Control returned.
+An interesting number. Did you pick it by chance? Or has there been a system of mathematics using base ten in the same manner that computers use base two?+
+I do not remember. But we can find out easily enough+
Dehan strolled across the room to the computer outlet that graced all public places. He was experienced, greatly experienced, at ruthlessly tracking down the most stubbornly hidden facts, and this was simplicity itself in comparison. At all times he knew the right questions to ask. His fingers moved on the control squares constantly, changing the displays at almost the very instant they appeared. Through the local computer to the infinite computer, linked through transmatter connections to all the memory units in the galaxy, to mathematics and history and ever deeper. He returned quickly to the table and sipped his drink.