MATHEMATICS The synthesis of the calculus of n-variables and of n-dimensional geometry is the basis of what Seldon once called “my little algebra of humanity”…
Consider a room!
The location of the room is not in question at the moment. It is merely sufficient to say that in that room, more than anywhere, the Second Foundation existed.
It was a room which, through the centuries, had been the abode of pure science – yet it had none of the gadgets with which, through millennia of association, science has come to be considered equivalent. It was a science, instead, which dealt with mathematical concepts only, in a manner similar to the speculation of ancient, ancient races in the primitive, prehistoric days before technology had come to be; before Man had spread beyond a single, now-unknown world.
For one thing, there was in that room – protected by a mental science as yet unassailable by the combined physical might of the rest of the Galaxy – the Prime Radiant, which held in its vitals the Seldon Plan – complete.
For another, there was a man, too, in that room – The First Speaker.
He was the twelfth in the line of chief guardians of the Plan, and his title bore no deeper significance than the fact that at the gatherings of the leaders of the Second Foundation, he spoke first.
His predecessor had beaten the Mule, but the wreckage of that gigantic struggle still littered the path of the Plan- For twenty-five years, he, and his administration, had been trying to force a Galaxy of stubborn and stupid human beings back to the path-It was a terrible task.
The First Speaker looked up at the opening door. Even while, in the loneliness of the room, he considered his quarter century of effort, which now so slowly and inevitably approached its climax; even while he had been so engaged, his mind had been considering the newcomer with a gentle expectation. A youth, a student, one of those who might take over, eventually.
The young man stood uncertainly at the door, so that the First Speaker had to walk to him and lead him in, with a friendly hand upon the shoulder.
The Student smiled shyly, and the First Speaker responded by saying, “First, I must tell you why you are here.”
They faced each other now, across the desk. Neither was speaking in any way that could be recognized as such by any man in the Galaxy who was not himself a member of the Second Foundation.
Speech, originally, was the device whereby Man learned, imperfectly, to transmit the thoughts and emotions of his mind. By setting up arbitrary sounds and combinations of sounds to represent certain mental nuances, be developed a method of communication – but one which in its clumsiness and thick-thumbed inadequacy degenerated all the delicacy of the mind into gross and guttural signaling.
Down – down – the results can be followed; and all the suffering that humanity ever knew can be traced to the one fact that no man in the history of the Galaxy, until Hari Seldon, and very few men thereafter, could really understand one another. Every human being lived behind an impenetrable wall of choking mist within which no other but he existed. Occasionally there were the dim signals from deep within the cavern in which another man was located-so that each might grope toward the other. Yet because they did not know one another, and could not understand one another, and dared not trust one another, and felt from infancy the terrors and insecurity of that ultimate isolation – there was the hunted fear of man for man, the savage rapacity of man toward man.
Feet, for tens of thousands of years, had clogged and shuffled in the mud – and held down the minds which, for an equal time, had been fit for the companionship of the stars.
Grimly, Man had instinctively sought to circumvent the prison bars of ordinary speech. Semantics, symbolic logic, psychoanalysis – they had all been devices whereby speech could either be refined or by-passed.
Psychohistory had been the development of mental science, the final mathematicization thereof, rather, which had finally succeeded. Through the development of the mathematics necessary to understand the facts of neural physiology and the electrochemistry of the nervous system, which themselves had to be, had to be, traced down to nuclear forces, it first became possible to truly develop psychology. And through the generalization of psychological knowledge from the individual to the group, sociology was also mathematicized.
The larger groups; the billions that occupied planets; the trillions that occupied Sectors; the quadrillions that occupied the whole Galaxy, became, not simply human beings, but gigantic forces amenable to statistical treatment – so that to Hari Seldon, the future became clear and inevitable, and the Plan could be set up.
The same basic developments of mental science that had brought about the development of the Seldon Plan, thus made it also unnecessary for the First Speaker to use words in addressing the Student.
Every reaction to a stimulus, however slight, was completely indicative of all the trifling changes, of all the flickering currents that went on in another’s mind. The First Speaker could not sense the emotional content of the Student’s instinctively, as the Mule would have been able to do – since the Mule was a mutant with powers not ever likely to become completely comprehensible to any ordinary man, even a Second Foundationer – rather he deduced them, as the result of intensive training.
Since, however, it is inherently impossible in a society based on speech to indicate truly the method of communication of Second Foundationers among themselves, the whole matter will be hereafter ignored. The First Speaker will be represented as speaking in ordinary fashion, and if the translation is not always entirely valid, it is at least the best that can be done under the circumstances.
It will be pretended therefore, that the First Speaker did actually say, “First, I must tell you why you are here,” instead of smiling just so and lifting a finger exactly thus.
The First Speaker said, “You have studied mental science hard and well for most of your life. You have absorbed all your teachers could give you. It is time for you and a few others like yourself to begin your apprenticeship for Speakerhood.”
Agitation from the other side of the desk.
“No – now you must take this phlegmatically. You had hoped you would qualify. You had feared you would not. Actually, both hope and fear are weaknesses. You knew you would qualify and you hesitate to admit the fact because such knowledge might stamp you as cocksure and therefore unfit. Nonsense! The most hopelessly stupid man is he who is not aware that he is wise. It is part of your qualification that you knew you would qualify.”
Relaxation on the other side of the desk.
“Exactly. Now you feel better and your guard is down. You are fitter to concentrate and fitter to understand. Remember, to be truly effective, it is not necessary to hold the mind under a tight, controlling barrier which to the intelligent probe is as informative as a naked mentality. Rather, one should cultivate an innocence, an awareness of self, and an unself-consciousness of self which leaves one nothing to hide. My mind is open to you. Let this be so for both of us.”
He went on. “It is not an easy thing to be a Speaker. It is not an easy thing to be a Psychohistorian in the first place; and not even the best Psychohistorian need necessarily qualify to be a Speaker. There is a distinction here. A Speaker must not only be aware of the mathematical intricacies of the Seldon Plan; he must have a sympathy for it and for its ends. He must love the Plan; to him it must be life and breath. More than that it must even be as a living friend.
“Do you know what this is?”
The First Speaker’s hand hovered gently over the black, shining cube in the middle of the desk. It was featureless.
“No, Speaker, I do not.”
“You have heard of the Prime Radiant?”
“This?” – Astonishment.
“You expected something more noble and awe-inspiring? Well, that is natural. It was created in the days of the Empire, by men of Seldon’s time. For nearly four hundred years, it has served our needs perfectly, without requiring repairs or adjustment. And fortunately so, since none of the Second Foundation is qualified to handle it in any technical fashion.” He smiled gently. “Those of the First Foundation might be able to duplicate this, but they must never know, of course.”
He depressed a lever on his side of the desk and the room was in darkness. But only for a moment, since with a gradually livening flush, the two long walls of the room glowed to life. First, a pearly white, unrelieved, then a trace of faint darkness here and there, and finally, the fine neatly printed equations in black, with an occasional red hairline that wavered through the darker forest like a staggering rillet.
“Come, my boy, step here before the wall. You will not cast a shadow. This light does not radiate from the Radiant in an ordinary manner. To tell you the truth, I do not know even faintly by what medium this effect is produced, but you will not cast a shadow. I know that.”
They stood together in the light. Each wall was thirty feet long, and ten high. The writing was small and covered every inch.
“This is not the whole Plan,” said the First Speaker. “To get it all upon both walls, the individual equations would have to be reduced to microscopic size – but that is not necessary. What you now see represents the main portions of the Plan till now. You have learned about this, have you not?”
“Yes, Speaker, I have.”
“Do you recognize any portion.”
A slow silence. The student pointed a finger and as he did so, the line of equations marched down the wall, until the single series of functions he had thought of – one could scarcely consider the quick, generalized gesture of the finger to have been sufficiently precise – was at eye-level.
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