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The theory of interpenetrating spaces had been worked out long before this experiment. This theory regarded the world as a perhaps infinite aggregate of interpenetrating spaces with quite various physical properties. It was this difference in properties that permitted spaces to coexist physically, with no noticeable interaction with each other. It was an abstract theory, and had not led to experimentally verifiable concrete equations. However, it followed from the theory that various forms of matter possess differing abilities to penetrate from one space into a neighboring one. It was proven as well that the penetration pro-cedes the more easily the greater the energy concentration. The concentration of the energy of the electromagnetic field was enormous in the experiment with the spacecraft. This led to the proposal that the energy “leakage” could be explained as an energy transfer from our space to some neighboring space. There were few data, but the idea was so attractive that it immediately found adherents in the Institute.

Experimental work on the theory of interpenetrating spaces had been undertaken by members of the Department of the Physics of Discrete Space. They immediately turned away from the cumbersome, dangerous, and not very precise experiments connected with the swallowing up and excretion of enormous energies. Anyhow, such experiments left open the question of unknown fields. Consequently it was planned to carry out research on spatial penetrability on the most varied fields: gravitational, electromagnetic, nuclear. But the trump card and main hope was the brilliant idea of one of the members who had noticed a remarkable similarity between the psychodynamic field of the human brain and the hypothetical “linkage field,” whose general mathematical description had been established by the theory of interpenetrating spaces at a time when researchers in psychodynamics had not yet even possessed a mathematical apparatus. The hypothetical “linkage field” was a field which, according to the theory, had the maximum ability to penetrate from one space into the next. Sufficiently accurate artificial receivers for the “psychodynamic field” (and accordingly also for the “linkage field”) did not exist, and so it was up to the espers.

There were ten billion people on the Planet, and a total of one hundred twenty-two registered espers. The espers read thoughts. The mystery of this unusual ability was still apparently very far from solution. It was clear only that the espers were surprisingly sensitive to the psychodynamic radiation of the human brain and that this sensitivity was innate. Some espers could detect and decipher the thoughts of a person thousands upon thousands of kilometers away. Some received psychodynamic signals only over a distance of a few paces. The parapsychologists argued over whether the espers were the first signs heralding the appearance on the evolutionary ladder of a new kind of human being, or whether this was simply an atavism, the remnant of a mysterious sixth sense that had once helped our ancestors to orient themselves in the dense primeval forest. The more powerful espers worked in the long-distance communication stations, augmenting the usual radio link with distant expeditions. Many espers worked as doctors. And many worked in fields unrelated to thought-reading.

However that might be, the workers of the Institute for the Physics of Space hoped that the espers would be able to simply “hear” the linkage field. This would be remarkable confirmation of the theory of interpenetrating spaces. The best espers on the Planet had gathered at Kotlin Island at the invitation of the Institute. The plan of the experiment was simple. If a linkage field between neighboring spaces existed, then, according to the theory, it should be very similar to the psychodynamic field of a human brain and should accordingly be picked up by the espers. If an esper were isolated in a special chamber shielded from the outside world (including human thoughts) by a thick layer of mesomatter, then there would be left in that room only the gravitational field of the Earth, which made no difference to the psychodynamic field, and the hypothetical linkage field coming from the neighboring spaces. Of course, such an experimental arrangement was far from ideal. Only a positive result would be decisive. A negative result indicated nothing—it neither confirmed nor rejected the theory. But so far it was the only chance. The espers were stimulated with neutrino radiation, which increased the sensitivity of the brain; were placed in the chambers; and were left to “listen.”

Peters and Kochin walked unhurriedly down the main street of the science town. The morning was foggy and grayish. The sun had not yet risen, but far, far ahead the gridded towers of the energy receivers reflected a pink light at an enormous height. Peters walked with his hands clasped behind his back, and sang in an undertone a ditty in English about “Johnny coming down to Highlow, poor old man.” Kochin, with a look of independence, walked alongside and tried not to think about anything. Near one of the cottages Peters suddenly ceased singing and stopped. “We have to wait,” he said.

“Why?” asked Kochin.

“Sieverson is asking me to wait up.” Peters nodded in the direction of the cottage. “He’s putting on his overcoat.”

One-two-three / Pioneers are we, Kochin thought. Two espers—that’s twice as… five times five is eleven—or something like that. “Is Sieverson really by himself? Doesn’t he have a guide?”

“Five times five is twenty-five,” Peters said querulously. “And I don’t know why Sieverson wasn’t assigned a guide.”

Sieverson appeared at the door of the cottage. “Don’t swear, young man,” he said to Kochin sternly. “When we were your age we were more polite.”

“Now, now, Sieverson old chap,” said Peters. “You yourself know you don’t think that—Thank you, I slept very well. And you know, I dreamed about beavers. And that my Harry had come back from Venus.”

Sieverson came down to the sidewalk and took Peters’s arm. “Let’s go,” he said. “Beavers—I’ve felt like a beaver myself these past few days. You, at least, have dreams, but I-did I tell you that I’ve just had a granddaughter born, Peters?… Oh, I did tell you. Well, I can’t see her even in a dream, because I haven’t seen her even once in real life. And I feel ashamed, Peters. To spend my old age on nonsense like this… Of course it’s nonsense—don’t you contradict me.”

Kochin trudged behind the pair of venerable espers and repeated to himself, The integral from zero to infinity of e to the minus-x-squared power, radical pi over two… A circle is a geometric locus of points equidistant…

Old Sieverson grumbled, “I’m a doctor, and in my village I know everyone unto the seventh generation backward and forward, and everyone knows me. I’ve listened to people’s thoughts all my life. Every day I’ve been able to be of help to someone because I heard his thoughts. Now I’m ashamed and stifled. Ashamed and stifled from sitting in total loneliness in these stupid casemates and listening to—what?—the whisperings of ghosts! The whisperings of imaginary spirits springing from someone’s delirious imagination! Don’t you contradict me, Peters! I’m twice as old as you!”

The unwritten code of the espers forbade them to converse mentally in the presence of a non-esper. Kochin was a non-esper, and he was present. He repeated to himself, The mathematical expectation of a sum of random quantities is equal to the sum of their mathematical expectations… Or to put it another way… uh, the sum of their mathematical expectations… mathematical expectations…

“They drag us away from our regular work,” Sieverson continued grumbling. “They drive us into this gray fog. Don’t argue, Peters, they do drive us! They drove me! I couldn’t refuse when they asked me, but nothing prevents me from looking upon this request as an attack on my person… Don’t argue, Peters, I’m older than you! Never in my life have I had cause to regret being an esper… Oh, you have had cause? Well, that’s your business. Of course beavers don’t need an esper, But people, sick and suffering people, they need—”