During a very long journey through space light waves, on the other hand, are “shaken up” and the light quanta lose part of their energy. This phenomenon has now been studied — the red waves may also be fatigued “old” waves of ordinary light. Even light waves that penetrate everywhere “grow old” from their journey over tremendous distances. What hope had man of overcoming such distances unless he attack gravitation itself by means of its opposite, following Renn Bose’s calculations?

His anxiety was fading away! He was doing the right thing by carrying out the unprecedented experiment!

Mven Mass, as usual, went out on the observatory veran-dah and began walking swiftly up and down. The distant galaxies still shone in his tired eyes, galaxies that sent waves of red light to Earth like signals calling for help, like appeals to the all-conquering thought of man. Mven Mass laughed softly and confidently. These red rays would become as familiar to man as those at the Fete of the Flaming Bowls that had wrapped Chara Nandi’s body in the red light of life — Chara, who had appeared to him unexpectedly as the copper daughter of Epsilon Tucanae, the girl of his impossible dreams.

And he would direct Renn Bose’s vector precisely at Epsilon Tucanae, not merely in the hope of seeing that wonderful world, but also in honour of her, of its terrestrial representative!

CHAPTER NINE

A THIRD CYCLE SCHOOL

Third Cycle School No. 410 was situated in Southern Ireland. Broad fields, vineyards and oak groves ran down the slopes of the green hills to the very sea. Veda Kong and Evda Nahl arrived when the children were still in class; they walked along a corridor running round class- rooms on the perimeter of a circular building. The day was dull with a drizzle of rain so that all classes were being held indoors instead of out in the open as was more usual.

Veda Kong felt like a schoolgirl again as she crept up to listen at the entrances to the classrooms which, as in the majority of schools, were without doors and shut off by overlapping projecting walls. Evda Nahl joined in the game and the two women peeped into class after class in an attempt to find Evda’s daughter and remain unnoticed themselves.

In the first classroom they saw a drawing in blue chalk covering the whole length of one wall: it showed a vector that was encircled by a spiral unfolding along it. Two sections of the spiral were encircled by transverse ellipses in which a system of rectangular coordinates was inscribed.

“Bipolar mathematics[21]!” exclaimed Veda in mock horror.

“This is something more than that! Wait a minute!” said Evda.

“Now that we know something about the shadow functions of the cochlear[22], or spiral progressive movement, that occurs along the vector,” — the elderly teacher with deep-set, blazing eyes, thickened one of the lines with his chalk — ’’we are close to understanding the repagular calculus. The name of the calculus comes from the ancient Latin word ‘repagulum,’ a barrier or obstacle, and it is the transition from one quality to another, seen in a two-sided aspect.” The teacher pointed to an extensive ellipse across the spiral. “In other words, it is the mathematical analysis of mutually transitional phenomena….”

Veda Kong disappeared behind the outjutting wall, pulling her companion after her.

“That’s something new! It’s from that branch of mathematics Renn Bose was talking to us about down on the seashore.”

“The school always gives its pupils the newest of everything and discards whatever is outworn. If new generations repeat old conceptions how can we expect to ensure rapid progress? As it is, a terrible amount of time elapses before a child takes its place in the relay race of knowledge. It takes dozens of years for a child to become fully educated and ready to undertake gigantic tasks. This pulsation of the generations, where you take one step forward and nine-tenths backward — backward while the next shift in the relay is learning — is that most difficult of all biological laws for man, the law of death and renascence. Much of what we learned in mathematics, physics and biology is already out of date. Your history is different, it grows old more slowly because it is very old itself.”

They glanced into another room. The schoolmistress, Standing with her back to them, and the interested children, did not notice them. The attentive faces of the pupils — they were young men and women seventeen years of age, in the higher classes of the Third Cycle School — and their burning cheeks told how thrilled they were with the lesson.

“We, the human race, have passed through many trials,” the voice of the teacher resounded with her excitement, “and the most important thing in your school history is the study of the historic mistakes made by man and their consequences. We have passed through the stage of the unbearable complication of life and things used by man and have arrived at extreme simplicity. The complication of life led dialectically to the simplification of spiritual culture. There must not be any unnecessary thing to tie man up, his experiences and perceptions are finer when he leads a simple life. Everything relating to everyday life is studied by the best brains as befits important scientific problems. We have followed the general line of development of the animal kingdom which was directed towards the liberation of attention by making movements automatic and developing reflexes in the work of the nervous system. The automation of the productive forces of society created an analogous reflex system of control in production economy and released many people for what is now man’s chief occupation — scientific research. Nature has provided us with a big brain capable of scientific inquiry although at first it was only used to search for food and investigate its edibility.”

“Very good!” whispered Evda Nahl and at that moment noticed her daughter. The girl did not suspect anything and sat staring in contemplation at the corrugated glass that prevented the pupils from seeing what was going on outside the classroom.

Veda Kong was curious to compare her with her mother. They had the same long straight hair, the daughter’s plaited with a blue thread and tied up in two big loops. Both had the same oval face, narrow at the chin and somewhat babyish from the too high forehead and the high cheekbones protruding below the temples. A snow-white sweater of artificial wool stressed the dark paleness of the girl’s skin and the acute blackness of her eyes, eyebrows and eyelashes. A necklace of red coral harmonized with the girl’s unquestionably original appearance.

Evda’s daughter, like all other pupils, wore wide shorts, hers differing only in a red fringe that was stitched into the seams.

“An American Indian ornament,” whispered Evda Nahl in answer to her friend’s inquiring glance.

Evda and Veda just had time to step back into the corridor when the teacher left the room followed by several pupils, Evda’s daughter amongst them. The girl stopped suddenly in her tracks as she noticed her mother, her pride and an example to be followed. Although Evda did not know it, there was a circle of her admirers in the school, youngsters who had decided to take the same road in life as she had taken.

“Mother!” whispered the girl, casting a shy glance at her mother’s companion and clinging to Evda.

The teacher stopped and then came over to them, giving them a nod of greeting.

“I must inform the school council,” she said, disregarding Evda’s gesture of protest, “we must gain something from your visit.”