There is, of course, provision for consultation of the record by the usual scheme of indexing. If the user wishes to consult a certain book, he taps its code on the keyboard, and the title page of the book promptly appears before him, projected onto one of his viewing positions.

A mathematician is not a man who can readily manipulate figures; often he cannot. He is not even a man who can readily perform the transformation of equations by the use of calculus. He is primarily an individual who is skilled in the use of symbolic logic on a high plane, and especially he is a man of intuitive judgment in the choice of the manipulative processes he employs.

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If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability. The abacus, with its beads strung on parallel wires, led the Arabs to positional numeration and the concept of zero many centuries before the rest of the world; and it was a useful tool — so useful that it still exists.

Babbage, even with remarkably generous support for his time, could not produce his great arithmetical machine. His idea was sound enough, but construction and maintenance costs were then too heavy. Had a Pharaoh been given detailed and explicit designs of an automobile, and had he understood them completely, it would have taxed the resources of his kingdom to have fashioned the thousands of parts for a single car, and that car would have broken down on the first trip to Giza.

The impulses which flow in the arm nerves of a typist convey to her fingers the translated information which reaches her eye or ear, in order that the fingers may be caused to strike the proper keys. Might not these currents be intercepted, either in the original form in which information is conveyed to the brain, or in the marvelously metamorphosed form in which they then proceed to the hand?

Much needs to occur, however, between the collection of data and observations, the extraction of parallel material from the existing record, and the final insertion of new material into the general body of the common record. For mature thought there is no mechanical substitute. But creative thought and essentially repetitive thought are very different things. For the latter there are, and may be, powerful mechanical aids.

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The responsibility for the creation of new scientific knowledge — and for most of its application — rests on that small body of men and women who understand the fundamental laws of nature and are skilled in the techniques of scientific research. We shall have rapid or slow advance on any scientific frontier depending on the number of highly qualified and trained scientists exploring it.

Improvement in the teaching of science is imperative; for students of latent scientific ability are particularly vulnerable to high school teaching which fails to awaken interest or to provide adequate instruction.

A spider web of metal, sealed in a thin glass container, a wire heated to brilliant glow, in short, the thermionic tube of radio sets, is made by the hundred million, tossed about in packages, plugged into sockets — and it works! Its gossamer parts, the precise location and alignment involved in its construction, would have occupied a master craftsman of the guild for months; now it is built for thirty cents. The world has arrived at an age of cheap complex devices of great reliability; and something is bound to come of it.

In order for great progress to be made on methods and weapons of war, there has to be a system of close joint effort of military and civilian men, especially engineers. The civilians must have independence and the opportunity to explore the bizarre; it is not enough that they be the engineers of contractors to the armed forces. Above all, there must be mutual respect and reliance. This must be present whenever we have to fight again.

In these days, when there is a tendency to specialize so closely, it is well for us to be reminded that the possibilities of being at once broad and deep did not pass with Leonardo Da Vinci or even Benjamin Franklin. Men of our profession - we teachers - are bound to be impressed by the tendency of youths of strikingly capable minds to become interested in one small corner of science and uninterested in the rest of the world ... It is unfortunate when a brilliant and creative mind insists upon living in a modern monastic cell.

There is another form of selection best illustrated by the automatic telephone exchange. You dial a number and the machine selects and connects just one of a million possible stations. It does not run over them all. It pays attention only to a class given by a first digit, and so on; and thus proceeds rapidly and almost unerringly to the selected station.

We puzzle as to whether the universe is bounded or extends forever; whether, indeed, it may only be one universe among many. We speculate as to whether our universe began in a vast explosion, whether it pulsates between utter compression and wide diffusion, whether it is self-renewing and thus unchanged forever. And we are humble. But science teaches more than this. It continually reminds us that we are still ignorant and there is much to learn. Time and space are interconnected in strange ways; there is no absolute simultaneity. Within the atom occur phenomena concerning which visualization is futile, to which common sense, the guidance from our everyday experience, has no application, which yield to studies by equations that have no meaning except that they work. Mass and energy transform one into another, Gravitation, the solid rock on which Newton built, may be merely a property of the geometry of the cosmos. Life, as its details unfold before us, becomes ever more intricate, emphasizing more and more our wonder that its marvelous functioning could have been produced by chance and time. The human mind, merely in its chemical and physical aspects, takes on new inspiring attributes. And what is the conclusion? He who follows science blindly, and who follows it alone, comes to a barrier beyond which he cannot see. He who would tell us with the authority of scholarship a complete story of why we exist, of our mission here, has a duty to speak convincingly in a world where men increasingly think for themselves. Exhortation needs to be revised, not to weaken its power, but to increase it, for men who are no longer in the third century. As this occurs, and on the essential and central core of faith, science will of necessity be silent. But its silence will be the silence of humility, not the silence of disdain. A belief may be larger than a fact. A faith that is overdefined is the very faith most likely to prove inadequate to the great moments of life.