... finding that in [the Moon] there is a provision of light and heat; also in appearance, a soil proper for habitation fully as good as ours, if not perhaps better who can say that it is not extremely probable, nay beyond doubt, that there must be inhabitants on the Moon of some kind or other?

… There can be no doubt about faith and not reason being the ultima ratio. Even Euclid, who has laid himself as little open to the charge of credulity as any writer who ever lived, cannot get beyond this. He has no demonstrable first premise. He requires postulates and axioms which transcend demonstration, and without which he can do nothing. His superstructure indeed is demonstration, but his ground his faith. Nor again can he get further than telling a man he is a fool if he persists in differing from him. He says “which is absurd,” and declines to discuss the matter further. Faith and authority, therefore, prove to be as necessary for him as for anyone else.

...That day in the account of creation, or those days that are numbers according to its recurrence, are beyond the experience and knowledge of us mortal earthbound men. And if we are able to make any effort towards an understanding of those days, we ought not to rush forward with an ill considered opinion, as if no other reasonable and plausible interpretation could be offered.

“Expect surprises!” should be the watchword of all scientists who try to look beyond the fashions of the day.

[1665-08-31] Up, and after putting several things in order to my removal to Woolwich, the plague having a great increase this week beyond all expectation, of almost 2000 - making the general Bill 7000, odd 100 and the plague above 6000 .... Thus this month ends, with great sadness upon the public through the greateness of the plague, everywhere through the Kingdom almost. Every day sadder and sadder news of its increase. In the City died this week 7496; and all of them, 6102 of the plague. But it is feared that the true number of the dead this week is near 10000 - partly from the poor that cannot be taken notice of through the greatness of the number, and partly from the Quakers and others that will not have any bell ring for them. As to myself, I am very well; only, in fear of the plague, and as much of an Ague, by being forced to go early and late to Woolwich, and my family to lie there continually.

[Beyond natural history] Other biological sciences take up the study at other levels of organization: dissecting the individual into organs and tissues and seeing how these work together, as in physiology; reaching down still further to the level of cells, as in cytology; and reaching the final biological level with the study of living molecules and their interactions, as in biochemistry. No one of these levels can be considered as more important than any other.

[In the beginning, before creation] There was neither Aught nor Naught, no air nor sky beyond. …
[There was only]
A self-supporting mass beneath, and energy above.
Who knows, who ever told, from whence this vast creation rose?
No gods had yet been born—who then can e’er the truth disclose?

[Man] … his origin, his growth, his hopes and fears, his loves and his beliefs are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling can preserve an individual life beyond the grave; that all the labour of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the debris of a universe in ruins…

[P]olitical and social and scientific values … should be correlated in some relation of movement that could be expressed in mathematics, nor did one care in the least that all the world said it could not be done, or that one knew not enough mathematics even to figure a formula beyond the schoolboy s=(1/2)gt². If Kepler and Newton could take liberties with the sun and moon, an obscure person ... could take liberties with Congress, and venture to multiply its attraction into the square of its time. He had only to find a value, even infinitesimal, for its attraction.

[The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.

[When I was a child] I grew up in Brooklyn, New York, and I was a street kid. … [T]here was one aspect of that environment that, for some reason, struck me as different, and that was the stars. … I could tell they were lights in the sky, but that wasn’t an explanation. I mean, what were they? Little electric bulbs on long black wires, so you couldn’t see what they were held up by? What were they? … My mother said to me, "Look, we’ve just got you a library card … get out a book and find the answer.” … It was in there. It was stunning. The answer was that the Sun was a star, except very far away. … The dazzling idea of a universe vast beyond imagining swept over me. … I sensed awe.

[Recalling Professor Ira Remsen's remarks (1895) to a group of his graduate students about to go out with their degrees into the world beyond the university:]
He talked to us for an hour on what was ahead of us; cautioned us against giving up the desire to push ahead by continued study and work. He warned us against allowing our present accomplishments to be the high spot in our lives. He urged us not to wait for a brilliant idea before beginning independent research, and emphasized the fact the Lavoisier's first contribution to chemistry was the analysis of a sample of gypsum. He told us that the fields in which the great masters had worked were still fruitful; the ground had only been scratched and the gleaner could be sure of ample reward.

Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.

Homo hominem arreptum a tellure, et utcunque exigua impulsum vi, vel uno etiam oris flatu impetitum, ab hominum omnium commercio in infinitum expelleret, nunquam per totam aeternitatem rediturum.
Were it not for gravity one man might hurl another by a puff of his breath into the depths of space, beyond recall for all eternity.

Ita est … rerum natura, post omnia oceanus, post oceanum nihil.
Thus is nature, Beyond all things is the ocean, beyond the ocean nothing.

L'imagination au contraire qui tend à nous porter continuellement au-delà du vrai, l'amour-propre et la confiance en nous-mêmes, qu'il sait si bien nous inspirer, nous sollicitent à tirer des conséquences qui ne dérivent pas immédiatement des faits.
Imagination, on the contrary, which is ever wandering beyond the bounds of truth, joined to self-love and that self-confidence we are so apt to indulge, prompt us to draw conclusions which are not immediately derived from facts.

2³⁰(2³¹-1) ... is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for; as they are merely curious without being useful, it is not likely that any person will attempt to find a number beyond it.

A mind exclusively bent upon the idea of utility necessarily narrows the range of the imagination. For it is the imagination which pictures to the inner eye of the investigator the indefinitely extending sphere of the possible,—that region of hypothesis and explanation, of underlying cause and controlling law. The area of suggestion and experiment is thus pushed beyond the actual field of vision.

A science is any discipline in which the fool of this generation can go beyond the point reached by the genius of the last generation.

A troubling question for those of us committed to the widest application of intelligence in the study and solution of the problems of men is whether a general understanding of the social sciences will be possible much longer. Many significant areas of these disciplines have already been removed by the advances of the past two decades beyond the reach of anyone who does not know mathematics; and the man of letters is increasingly finding, to his dismay, that the study of mankind proper is passing from his hands to those of technicians and specialists. The aesthetic effect is admittedly bad: we have given up the belletristic “essay on man” for the barbarisms of a technical vocabulary, or at best the forbidding elegance of mathematical syntax.

A world of facts lies outside and beyond the world of words.

After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.

Alas, your dear friend and servant is totally blind. Henceforth this heaven, this universe, which by wonderful observations I had enlarged by a hundred and a thousand times beyond the conception of former ages, is shrunk for me into the narrow space which I myself fill in it. So it pleases God; it shall therefore please me also.

Alexander the king of the Macedonians, began like a wretch to learn geometry, that he might know how little the earth was, whereof he had possessed very little. Thus, I say, like a wretch for this, because he was to understand that he did bear a false surname. For who can be great in so small a thing? Those things that were delivered were subtile, and to be learned by diligent attention: not which that mad man could perceive, who sent his thoughts beyond the ocean sea. Teach me, saith he, easy things. To whom his master said: These things be the same, and alike difficult unto all. Think thou that the nature of things saith this. These things whereof thou complainest, they are the same unto all: more easy things can be given unto none; but whosoever will, shall make those things more easy unto himself. How? With uprightness of mind.

All fossil anthropoids found hitherto have been known only from mandibular or maxillary fragments, so far as crania are concerned, and so the general appearance of the types they represented had been unknown; consequently, a condition of affairs where virtually the whole face and lower jaw, replete with teeth, together with the major portion of the brain pattern, have been preserved, constitutes a specimen of unusual value in fossil anthropoid discovery. Here, as in Homo rhodesiensis, Southern Africa has provided documents of higher primate evolution that are amongst the most complete extant. Apart from this evidential completeness, the specimen is of importance because it exhibits an extinct race of apes intermediate between living anthropoids and man ... Whether our present fossil is to be correlated with the discoveries made in India is not yet apparent; that question can only be solved by a careful comparison of the permanent molar teeth from both localities. It is obvious, meanwhile, that it represents a fossil group distinctly advanced beyond living anthropoids in those two dominantly human characters of facial and dental recession on one hand, and improved quality of the brain on the other. Unlike Pithecanthropus, it does not represent an ape-like man, a caricature of precocious hominid failure, but a creature well advanced beyond modern anthropoids in just those characters, facial and cerebral, which are to be anticipated in an extinct link between man and his simian ancestor. At the same time, it is equally evident that a creature with anthropoid brain capacity and lacking the distinctive, localised temporal expansions which appear to be concomitant with and necessary to articulate man, is no true man. It is therefore logically regarded as a man-like ape. I propose tentatively, then, that a new family of Homo-simidæ be created for the reception of the group of individuals which it represents, and that the first known species of the group be designated Australopithecus africanus, in commemoration, first, of the extreme southern and unexpected horizon of its discovery, and secondly, of the continent in which so many new and important discoveries connected with the early history of man have recently been made, thus vindicating the Darwinian claim that Africa would prove to be the cradle of mankind.

All men hate the wretched; how, then, must I be hated, who am miserable beyond all living things! Yet you, my creator, detest and spurn me, thy creature, to whom thou are bound by ties only dissoluble by the annihilation of one of us.

All progress is based upon a universal innate desire of every organism to live beyond its means.

All that Anatomie can doe is only to shew us the gross and sensible parts of the body, or the vapid and dead juices all which, after the most diligent search, will be noe more able to direct a physician how to cure a disease than how to make a man; for to remedy the defects of a part whose organicall constitution and that texture whereby it operates, he cannot possibly know, is alike hard, as to make a part which he knows not how is made. Now it is certaine and beyond controversy that nature performs all her operations on the body by parts so minute and insensible that I thinke noe body will ever hope or pretend, even by the assistance of glasses or any other intervention, to come to a sight of them, and to tell us what organicall texture or what kinde offerment (for whether it be done by one or both of these ways is yet a question and like to be soe always notwithstanding all the endeavours of the most accurate dissections) separate any part of the juices in any of the viscera, or tell us of what liquors the particles of these juices are, or if this could be donne (which it is never like to be) would it at all contribute to the cure of the diseases of those very parts which we so perfectly knew.

All the species recognized by Botanists came forth from the Almighty Creator’s hand, and the number of these is now and always will be exactly the same, while every day new and different florists’ species arise from the true species so-called by Botanists, and when they have arisen they finally revert to the original forms. Accordingly to the former have been assigned by Nature fixed limits, beyond which they cannot go: while the latter display without end the infinite sport of Nature.

Although we are mere sojourners on the surface of the planet, chained to a mere point in space, enduring but for a moment of time, the human mind is not only enabled to number worlds beyond the unassisted ken of mortal eye, but to trace the events of indefinite ages before the creation of our race, and is not even withheld from penetrating into the dark secrets of the ocean, or the interior of the solid globe; free, like the spirit which the poet described as animating the universe.

America has never been united by blood or birth or soil. We are bound by ideals that move us beyond our backgrounds, lift us above our interests and teach us what it means to be citizens. Every child must be taught these principles. Every citizen must uphold them. And every immigrant, by embracing these ideals, makes our country more, not less, American.

And beyond our galaxy are other galaxies, in the universe all told at least a hundred billion, each containing a hundred billion stars. Do these figures mean anything to you?

And do you know what “the world” is to me? Shall I show it to you in my mirror? This world: a monster of energy, without beginning, without end; a firm, iron magnitude of force that does not grow bigger or smaller, that does not expend itself but only transforms itself; as a whole, of unalterable size, a household without expenses or losses, but likewise without increase or income; enclosed by “nothingness”' as by a boundary; not by something blurry or wasted, not something endlessly extended, but set in a definite space as a definite force, and not a space that might be “empty” here or there, but rather as force throughout, as a play of forces and waves of forces, at the same time one and many, increasing here and at the same time decreasing there; a sea of forces flowing and rushing together, eternally changing, eternally flooding back, with tremendous years of recurrence, with an ebb and a flood of its forms; out of the simplest forms striving toward the most complex, out of the stillest, most rigid, coldest forms toward the hottest, most turbulent, most self-contradictory, and then again returning home to the simple out of this abundance, out of the play of contradictions back to the joy of concord, still affirming itself in this uniformity of its courses and its years, blessing itself as that which must return eternally, as a becoming that knows no satiety, no disgust, no weariness: this, my Dionysian world of the eternally self-creating, the eternally self-destroying, this mystery world of the twofold voluptuous delight, my “beyond good and evil,” without goal, unless the joy of the circle itself is a goal; without will, unless a ring feels good will toward itself-do you want a name for this world? A solution for all its riddles? A light for you, too, you best-concealed, strongest, most intrepid, most midnightly men?—This world is the will to power—and nothing besides! And you yourselves are also this will to power—and nothing besides!

And this grey spirit yearning in desire, To follow knowledge like a sinking star, beyond the utmost bound of human thought.

Antiqua consuetudo difficulter relinquitur: & ultra proprium videre nemo libenter ducitur.
Old habits are hard to break: and no one is easily led beyond his own point of view.

Any conception which is definitely and completely determined by means of a finite number of specifications, say by assigning a finite number of elements, is a mathematical conception. Mathematics has for its function to develop the consequences involved in the definition of a group of mathematical conceptions. Interdependence and mutual logical consistency among the members of the group are postulated, otherwise the group would either have to be treated as several distinct groups, or would lie beyond the sphere of mathematics.

Any one who is practically acquainted with scientific work is aware that those who refuse to go beyond fact, rarely get as far as fact.

Art arises in those strange complexities of action that are called human beings. It is a kind of human behavior. As such it is not magic, except as human beings are magical. Nor is it concerned in absolutes, eternities, “forms,” beyond those that may reside in the context of the human being and be subject to his vicissitudes. Art is not an inner state of consciousness, whatever that may mean. Neither is it essentially a supreme form of communication. Art is human behavior, and its values are contained in human behavior.

As regards railways, it is certain that nothing is so profitable, because nothing is so cheaply transported, as passenger traffic. Goods traffic, of whatsoever description, must be more or less costly. Every article conveyed by railway requires handling and conveyance beyond the limit of the railway stations; but passengers take care of themselves, and find their own way.

As the human fetus develops, its changing form seems to retrace the whole of human evolution from the time we were cosmic dust to the time we were single-celled organisms in the primordial sea to the time we were four-legged, land-dwelling reptiles and beyond, to our current status as large­brained, bipedal mammals. Thus, humans seem to be the sum total of experience since the beginning of the cosmos.

As we look ahead through the vista of science with its tremendous possibilities for progress in peacetime, let us not feel that we are looking beyond the horizon of hope. The outlook is not discouraging, for there is no limit to man’s ingenuity and no end to the opportunities for progress.

Astronomers and physicists, dealing habitually with objects and quantities far beyond the reach of the senses, even with the aid of the most powerful aids that ingenuity has been able to devise, tend almost inevitably to fall into the ways of thinking of men dealing with objects and quantities that do not exist at all, e.g., theologians and metaphysicians. Thus their speculations tend almost inevitably to depart from the field of true science, which is that of precise observation, and to become mere soaring in the empyrean. The process works backward, too. That is to say, their reports of what they pretend actually to see are often very unreliable. It is thus no wonder that, of all men of science, they are the most given to flirting with theology. Nor is it remarkable that, in the popular belief, most astronomers end by losing their minds.

At first he who invented any art that went beyond the common perceptions of man was naturally admired by men, not only because there was something useful in the inventions, but because he was thought wise and superior to the rest. But as more arts were invented, and some were directed to the necessities of life, others to its recreation, the inventors of the latter were always regarded as wiser than the inventors of the former, because their branches of knowledge did not aim at utility.

At the present time there exist problems beyond our ability to solve, not because of theoretical difficulties, but because of insufficient means of mechanical computation.

Beyond a critical point within a finite space, freedom diminishes as numbers increase. ...The human question is not how many can possibly survive within the system, but what kind of existence is possible for those who do survive.

Beyond lonely Pluto, dark and shadowless, lies the glittering realm of interstellar space, the silent ocean that rolls on and on, past stars and galaxies alike, to the ends of the Universe. What do men know of this vast infinity, this shoreless ocean? Is it hostile or friendly–or merely indifferent?

Beyond these are other suns, giving light and life to systems, not a thousand, or two thousand merely, but multiplied without end, and ranged all around us, at immense distances from each other, attended by ten thousand times ten thousand worlds, all in rapid motion; yet calm, regular and harmonious—all space seems to be illuminated, and every particle of light a world. ... all this vast assemblages of suns and worlds may bear no greater proportion to what lies beyond the utmost boundaries of human vision, than a drop of water to the ocean.

But beyond the bright searchlights of science,
Out of sight of the windows of sense,
Old riddles still bid us defiance,
Old questions of Why and of Whence.

But if we are to control evolution we shall have to find out how to influence gene reproduction in a definite direction, just as organic chemists nowadays work for definite ends. Such a possibility is at present entirely beyond our grasp, but a century hence it may not be so.

But that which will excite the greatest astonishment by far, and which indeed especially moved me to call the attention of all astronomers and philosophers, is this: namely, that I have observed four planets, neither known nor observed by any one of the astronomers before my time, which have their orbits round a certain bright star [Jupiter], one of those previously known, like Venus or Mercury round the sun, and are sometimes in front of it, sometimes behind it, though they never depart from it beyond certain limits. All of which facts were discovered and observed a few days ago by the help of a telescope devised by me, through God’s grace first enlightening my mind.

But the best demonstration by far is experience, if it go not beyond the actual experiment.

But the nature of our civilized minds is so detached from the senses, even in the vulgar, by abstractions corresponding to all the abstract terms our languages abound in, and so refined by the art of writing, and as it were spiritualized by the use of numbers, because even the vulgar know how to count and reckon, that it is naturally beyond our power to form the vast image of this mistress called ‘Sympathetic Nature.’

But when science, passing beyond its own limits, assumes to take the place of theology, and sets up its own conception of the order of Nature as a sufficient account of its cause, it is invading a province of thought to which it has no claim, and not unreasonably provokes the hostility of its best friends.

By death the moon was gathered in Long ago, ah long ago;
Yet still the silver corpse must spin
And with another's light must glow.
Her frozen mountains must forget
Their primal hot volcanic breath,
Doomed to revolve for ages yet,
Void amphitheatres of death.
And all about the cosmic sky,
The black that lies beyond our blue,
Dead stars innumerable lie,
And stars of red and angry hue
Not dead but doomed to die.

By explanation the scientist understands nothing except the reduction to the least and simplest basic laws possible, beyond which he cannot go, but must plainly demand them; from them however he deduces the phenomena absolutely completely as necessary.

By research in pure science I mean research made without any idea of application to industrial matters but solely with the view of extending our knowledge of the Laws of Nature. I will give just one example of the ‘utility’ of this kind of research, one that has been brought into great prominence by the War—I mean the use of X-rays in surgery. Now, not to speak of what is beyond money value, the saving of pain, or, it may be, the life of the wounded, and of bitter grief to those who loved them, the benefit which the state has derived from the restoration of so many to life and limb, able to render services which would otherwise have been lost, is almost incalculable. Now, how was this method discovered? It was not the result of a research in applied science starting to find an improved method of locating bullet wounds. This might have led to improved probes, but we cannot imagine it leading to the discovery of X-rays. No, this method is due to an investigation in pure science, made with the object of discovering what is the nature of Electricity. The experiments which led to this discovery seemed to be as remote from ‘humanistic interest’ —to use a much misappropriated word—as anything that could well be imagined. The apparatus consisted of glass vessels from which the last drops of air had been sucked, and which emitted a weird greenish light when stimulated by formidable looking instruments called induction coils. Near by, perhaps, were great coils of wire and iron built up into electro-magnets. I know well the impression it made on the average spectator, for I have been occupied in experiments of this kind nearly all my life, notwithstanding the advice, given in perfect good faith, by non-scientific visitors to the laboratory, to put that aside and spend my time on something useful.

Chemistry as a science is still in its infancy. I hold to my view because there is still so much beyond our understanding even in the simplest systems the chemist has cared to deal with.

Climbing is all about freedom, the freedom to go beyond all the rules and take a chance, to experience something new, to gain insight into human nature.

Come, my friends,
’Tis not too late to seek a newer world.
Push off, and sitting well in order smite
The sounding furrows; for my purpose holds
To sail beyond the sunset, and the baths
Of all the western stars, until I die.

Computers are incredibly fast, accurate and stupid. Human beings are incredibly slow, inaccurate and brilliant. Together they are powerful beyond imagination.

Concerning the alchemist, Mamugnano, no one harbors doubts any longer about his daily experiments in changing quicksilver into gold. It was realized that his craft did not go beyond one pound of quicksilver… . Thus the belief is now held that his allegations to produce a number of millions have been a great fraud.

Consciousness is not sharply defined, but fades into sub-consciousness; and beyond that we must postulate something indefinite but yet continuous with our mental nature. This I take it be the world-stuff.

Crowds of silent voices whisper in our ears, transforming the nature of what we see and hear. Some are those of childhood authorities and heroes; others come from family and peers. The strangest emerge from beyond the grave.

Data isn't information. ... Information, unlike data, is useful. While there’s a gulf between data and information, there’s a wide ocean between information and knowledge. What turns the gears in our brains isn't information, but ideas, inventions, and inspiration. Knowledge—not information—implies understanding. And beyond knowledge lies what we should be seeking: wisdom.

Decades spent in contact with science and its vehicles have directed my mind and senses to areas beyond their reach. I now see scientific accomplishments as a path, not an end; a path leading to and disappearing in mystery. Science, in fact, forms many paths branching from the trunk of human progress; and on every periphery they end in the miraculous. Following these paths far enough, one must eventually conclude that science itself is a miracle—like the awareness of man arising from and then disappearing in the apparent nothingness of space. Rather than nullifying religion and proving that “God is dead,” science enhances spiritual values by revealing the magnitudes and minitudes—from cosmos to atom—through which man extends and of which he is composed.

Despite the continuing expansion or even explosion of information, there will forever be limits beyond which the devices of science cannot lead a man.

Do not great Bodies conserve their heat the longest, their parts heating one another, and may not great dense and fix'd Bodies, when heated beyond a certain degree, emit Light so copiously, as by the Emission and Re-action of its Light, and the Reflexions and Refractions of its Rays within its Pores to grow still hotter, till it comes to a certain period of heat, such as is that of the Sun?

Does it not seem as if Algebra had attained to the dignity of a fine art, in which the workman has a free hand to develop his conceptions, as in a musical theme or a subject for a painting? It has reached a point where every properly developed algebraical composition, like a skillful landscape, is expected to suggest the notion of an infinite distance lying beyond the limits of the canvas.

Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence? No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility.

Dr. Walter Baade of Mount Wilson Observatory facetiously accused the present generation of Milky Way astronomers of not having looked sufficiently far beyond our “local swimming hole”.

During my pre-college years I went on many trips with my father into the oil fields to visit their operations. … I puttered around the machine, electronics, and automobile shops while he carried on his business. Both of my parents are inveterate do-it-yourselfers, almost no task being beneath their dignity or beyond their ingenuity. Having picked up a keen interest in electronics from my father, I used to fix radios and later television sets for fun and spending money. I built my own hi-fi set and enjoyed helping friends with their amateur radio transmitters, but lost interest as soon as they worked.

Each human life is unique, born of a miracle that reaches beyond laboratory science.

Education, then, beyond all other devices of human origin, is the great equalizer of the conditions of men–the balance-wheel of the social machinery.

Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.

Ever since celestial mechanics in the skillful hands of Leverrier and Adams led to the world-amazed discovery of Neptune, a belief has existed begotten of that success that still other planets lay beyond, only waiting to be found.

Every new theory as it arises believes in the flush of youth that it has the long sought goal; it sees no limits to its applicability, and believes that at last it is the fortunate theory to achieve the 'right' answer. This was true of electron theory—perhaps some readers will remember a book called The Electrical Theory of the Universe by de Tunzelman. It is true of general relativity theory with its belief that we can formulate a mathematical scheme that will extrapolate to all past and future time and the unfathomed depths of space. It has been true of wave mechanics, with its first enthusiastic claim a brief ten years ago that no problem had successfully resisted its attack provided the attack was properly made, and now the disillusionment of age when confronted by the problems of the proton and the neutron. When will we learn that logic, mathematics, physical theory, are all only inventions for formulating in compact and manageable form what we already know, like all inventions do not achieve complete success in accomplishing what they were designed to do, much less complete success in fields beyond the scope of the original design, and that our only justification for hoping to penetrate at all into the unknown with these inventions is our past experience that sometimes we have been fortunate enough to be able to push on a short distance by acquired momentum.

Everything material which is the subject of knowledge has number, order, or position; and these are her first outlines for a sketch of the universe. If our feeble hands cannot follow out the details, still her part has been drawn with an unerring pen, and her work cannot be gainsaid. So wide is the range of mathematical sciences, so indefinitely may it extend beyond our actual powers of manipulation that at some moments we are inclined to fall down with even more than reverence before her majestic presence. But so strictly limited are her promises and powers, about so much that we might wish to know does she offer no information whatever, that at other moments we are fain to call her results but a vain thing, and to reject them as a stone where we had asked for bread. If one aspect of the subject encourages our hopes, so does the other tend to chasten our desires, and he is perhaps the wisest, and in the long run the happiest, among his fellows, who has learned not only this science, but also the larger lesson which it directly teaches, namely, to temper our aspirations to that which is possible, to moderate our desires to that which is attainable, to restrict our hopes to that of which accomplishment, if not immediately practicable, is at least distinctly within the range of conception.

Evolution: At the Mind's Cinema
I turn the handle and the story starts:
Reel after reel is all astronomy,
Till life, enkindled in a niche of sky,
Leaps on the stage to play a million parts.
Life leaves the slime and through all ocean darts;
She conquers earth, and raises wings to fly;
Then spirit blooms, and learns how not to die,-
Nesting beyond the grave in others' hearts.
I turn the handle: other men like me
Have made the film: and now I sit and look
In quiet, privileged like Divinity
To read the roaring world as in a book.
If this thy past, where shall they future climb,
O Spirit, built of Elements and Time?

Extrasensory perception is a scientifically inept term. By suggesting that forms of human perception exist beyond the senses, it prejudges the question.

Faith is a knowledge within the heart, beyond the reach of proof.

For many of us, water simply flows from a faucet, and we think little about it beyond this point of contact. We have lost a sense of respect for the wild river, for the complex workings of a wetland, for the intricate web of life that water supports.

For strictly scientific or technological purposes all this is irrelevant. On a pragmatic view, as on a religious view, theory and concepts are held in faith. On the pragmatic view the only thing that matters is that the theory is efficacious, that it “works” and that the necessary preliminaries and side issues do not cost too much in time and effort. Beyond that, theory and concepts go to constitute a language in which the scientistic matters at issue can be formulated and discussed.

FORTRAN —’the infantile disorder’—, by now nearly 20 years old, is hopelessly inadequate for whatever computer application you have in mind today: it is now too clumsy, too risky, and too expensive to use. PL/I —’the fatal disease’— belongs more to the problem set than to the solution set. It is practically impossible to teach good programming to students that have had a prior exposure to BASIC: as potential programmers they are mentally mutilated beyond hope of regeneration. The use of COBOL cripples the mind; its teaching should, therefore, be regarded as a criminal offence. APL is a mistake, carried through to perfection. It is the language of the future for the programming techniques of the past: it creates a new generation of coding bums.

Fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have [played] … an historical role … in the development of pure mathematics. A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th. Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton. Modern mathematics began with Cantor’s set theory and Peano’s space-filling curve. Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. These new structures were regarded … as “pathological,” .… as a “gallery of monsters,” akin to the cubist paintings and atonal music that were upsetting established standards of taste in the arts at about the same time. The mathematicians who created the monsters regarded them as important in showing that the world of pure mathematics contains a richness of possibilities going far beyond the simple structures that they saw in Nature. Twentieth-century mathematics flowered in the belief that it had transcended completely the limitations imposed by its natural origins.
Now, as Mandelbrot points out, … Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.

God does not die on the day when we cease to believe in a personal deity, but we die on the day when our lives cease to be illumined by the steady radiance, renewed daily, of a wonder, the source of which is beyond all reason.

Goethe said that he who cannot draw on 3,000 years of learning is living hand to mouth. It could just as well be said that individuals who do tap deeply into this rich cultural legacy are wealthy indeed. Yet the paradox is that much of this wisdom is buried in a sea of lesser books or like lost treasure beneath an ocean of online ignorance and trivia. That doesn’t mean that with a little bit of diligence you can’t tap into it. Yet many people, perhaps most, never take advantage of all this human experience. They aren’t obtaining knowledge beyond what they need to know for work or to get by. As a result, their view of our amazing world is diminished and their lives greatly circumscribed.

He [Lord Bacon] appears to have been utterly ignorant of the discoveries which had just been made by Kepler’s calculations … he does not say a word about Napier’s Logarithms, which had been published only nine years before and reprinted more than once in the interval. He complained that no considerable advance had been made in Geometry beyond Euclid, without taking any notice of what had been done by Archimedes and Apollonius. He saw the importance of determining accurately the specific gravities of different substances, and himself attempted to form a table of them by a rude process of his own, without knowing of the more scientific though still imperfect methods previously employed by Archimedes, Ghetaldus and Porta. He speaks of the εὕρηκα of Archimedes in a manner which implies that he did not clearly appreciate either the problem to be solved or the principles upon which the solution depended. In reviewing the progress of Mechanics, he makes no mention either of Archimedes, or Stevinus, Galileo, Guldinus, or Ghetaldus. He makes no allusion to the theory of Equilibrium. He observes that a ball of one pound weight will fall nearly as fast through the air as a ball of two, without alluding to the theory of acceleration of falling bodies, which had been made known by Galileo more than thirty years before. He proposed an inquiry with regard to the lever,—namely, whether in a balance with arms of different length but equal weight the distance from the fulcrum has any effect upon the inclination—though the theory of the lever was as well understood in his own time as it is now. … He speaks of the poles of the earth as fixed, in a manner which seems to imply that he was not acquainted with the precession of the equinoxes; and in another place, of the north pole being above and the south pole below, as a reason why in our hemisphere the north winds predominate over the south.

Hitherto, no rival hypothesis has been proposed as a substitute for the doctrine of transmutation; for 'independent creation,' as it is often termed, or the direct intervention of the Supreme Cause, must simply be considered as an avowal that we deem the question to lie beyond the domain of science.

How have people come to be taken in by The Phenomenon of Man? Just as compulsory primary education created a market catered for by cheap dailies and weeklies, so the spread of secondary and latterly of tertiary education has created a large population of people, often with well-developed literary and scholarly tastes who have been educated far beyond their capacity to undertake analytical thought … [The Phenomenon of Man] is written in an all but totally unintelligible style, and this is construed as prima-facie evidence of profundity.

However high we climb in the pursuit of knowledge we shall still see heights above us, and the more we extend our view, the more conscious we shall be of the immensity which lies beyond.

I always rejoice to hear of your being still employed in experimental researches into nature, and of the success you meet with. The rapid progress true science now makes, occasions my regretting sometimes that I was born so soon: it is impossible to imagine the height to which may be carried, in a thousand years, the power of man over matter; we may perhaps learn to deprive large masses of their gravity, and give them absolute levity for the sake of easy transport. Agriculture may diminish its labour and double its produce; all diseases may by sure means be prevented or cured (not excepting even that of old age), and our lives lengthened at pleasure even beyond the antediluvian standard. Oh! that moral science were in as fair a way of improvement; that men would cease to be wolves to one another; and that human beings would at length learn what they now improperly call humanity!

I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them upon the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge—knowledge mingled with ignorance, producing doubt.

I am not unmindful of the journalist’s quip that yesterday’s paper wraps today’s garbage. I am also not unmindful of the outrages visited upon our forests to publish redundant and incoherent collections of essays; for, like Dr. Seuss’ Lorax, I like to think that I speak for the trees. Beyond vanity, my only excuses for a collection of these essays lie in the observation that many people like (and as many people despise) them, and that they seem to cohere about a common theme–Darwin’s evolutionary perspective as an antidote to our cosmic arrogance.

I am not, personally, a believer or a religious man in any sense of institutional commitment or practice. But I have a great respect for religion, and the subject has always fascinated me, beyond almost all others (with a few exceptions, like evolution and paleontology).

I ask any one who has adopted the calling of an engineer, how much time he lost when he left school, because he had to devote himself to pursuits which were absolutely novel and strange, and of which he had not obtained the remotest conception from his instructors? He had to familiarize himself with ideas of the course and powers of Nature, to which his attention had never been directed during his school-life, and to learn, for the first time, that a world of facts lies outside and beyond the world of words.

I believe television is going to be the test of the modern world, and that in this new opportunity to see beyond the range of our vision we shall discover either a new and unbearable disturbance of the general peace or a saving radiance in the sky. We shall stand or fall by television—of that I am quite sure

I cannot conceive of a God who rewards and punishes his creatures, or has a will of the type of which we are conscious in ourselves. An individual who should survive his physical death is also beyond my comprehension, nor do I wish it otherwise; such notions are for the fears or absurd egoism of feeble souls.

I consider [H. G. Wells], as a purely imaginative writer, to be deserving of very high praise, but our methods are entirely different. I have always made a point in my romances of basing my so-called inventions upon a groundwork of actual fact, and of using in their construction methods and materials which are not entirely without the pale of contemporary engineering skill and knowledge. ... The creations of Mr. Wells, on the other hand, belong unreservedly to an age and degree of scientific knowledge far removed from the present, though I will not say entirely beyond the limits of the possible.

I definitely deny that any pathological process, i.e. any life-process taking place under unfavourable circumstances, is able to call forth qualitatively new formations lying beyond the customary range of forms characteristic of the species. All pathological formations are either degenerations, transformations, or repetitions of typical physiological structures.

I do not … reject the use of statistics in medicine, but I condemn not trying to get beyond them and believing in statistics as the foundation of medical science. … Statistics … apply only to cases in which the cause of the facts observed is still [uncertain or] indeterminate. … There will always be some indeterminism … in all the sciences, and more in medicine than in any other. But man’s intellectual conquest consists in lessening and driving back indeterminism in proportion as he gains ground for determinism by the help of the experimental method..

I do not want to write beyond this point, because those days when I studied relentlessly are nostalgic to me; and on the other hand, I am sad when I think how I have become increasingly preoccupied with matters other than study.

I had a feeling once about Mathematics—that I saw it all. Depth beyond depth was revealed to me—the Byss and Abyss. I saw—as one might see the transit of Venus or even the Lord Mayor’s Show—a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.

I have tried to read philosophers of all ages and have found many illuminating ideas but no steady progress toward deeper knowledge and understanding. Science, however, gives me the feeling of steady progress: I am convinced that theoretical physics is actual philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics), and it has taught us new methods of thinking (complementarity) which are applicable far beyond physics.

I hear beyond the range of sound,
I see beyond the range of sight,
New earths and skies and seas around,
And in my day the sun doth pale his light.

I like the scientific spirit—the holding off, the being sure but not too sure, the willingness to surrender ideas when the evidence is against them: this is ultimately fine—it always keeps the way beyond open.

I need scarcely say that the beginning and maintenance of life on earth is absolutely and infinitely beyond the range of sound speculation in dynamical science.

I see nothing wrong ethically with the idea of correcting single gene defects [through genetic engineering]. But I am concerned about any other kind of intervention, for anything else would be an experiment, [which would] impose our will on future generations [and take unreasonable chances] with their welfare ... [Thus] such intervention is beyond the scope of consideration.

I suspect there could be life and intelligence out there in forms that we can't conceive. And there could, of course, be forms of intelligence beyond human capacity—beyond as much as we are beyond a chimpanzee.

I traveled among unknown men,
In lands beyond the sea;
Nor England! did I know till then
What love I bore to thee.

I will insist particularly upon the following fact, which seems to me quite important and beyond the phenomena which one could expect to observe: The same [double sulfate of uranium and potassium] crystalline crusts, arranged the same way [as reported to the French academy on 24 Feb 1896] with respect to the photographic plates, in the same conditions and through the same screens, but sheltered from the excitation of incident rays and kept in darkness, still produce the same photographic images … [when kept from 26 Feb 1896] in the darkness of a bureau drawer. … I developed the photographic plates on the 1st of March, expecting to find the images very weak. Instead the silhouettes appeared with great intensity.
It is important to observe that it appears this phenomenon must not be attributed to the luminous radiation emitted by phosphorescence … One hypothesis which presents itself to the mind naturally enough would be to suppose that these rays, whose effects have a great similarity to the effects produced by the rays studied by M. Lenard and M. Röntgen, are invisible rays …
[Having eliminated phosphorescence as a cause, he has further revealed the effect of the as yet unknown radioactivity.]

If I choose to impose individual blame for all past social ills, there will be no one left to like in some of the most fascinating periods of our history. For example ... if I place every Victorian anti-Semite beyond the pale of my attention, my compass of available music and literature will be pitifully small. Though I hold no shred of sympathy for active persecution, I cannot excoriate individuals who acquiesced passively in a standard societal judgment. Rail instead against the judgment, and try to understand what motivates men of decent will.

If I had been taught from my youth all the truths of which I have since sought out demonstrations, and had thus learned them without labour, I should never, perhaps, have known any beyond these; at least, I should never have acquired the habit and the facility which I think I possess in always discovering new truths in proportion as I give myself to the search.

If the finding of Coines, Medals, Urnes, and other Monuments of famous Persons, or Towns, or Utensils, be admitted for unquestionable Proofs, that such Persons or things have, in former Times, had a being, certainly those Petrifactions may be allowed to be of equal Validity and Evidence, that there have been formerly such Vegetables or Animals. These are truly Authentick Antiquity not to be counterfeited, the Stamps, and Impressions, and Characters of Nature that are beyond the Reach and Power of Humane Wit and Invention, and are true universal Characters legible to all rational Men.

If the Humours of the Eye by old Age decay, so as by shrinking to make the Cornea and Coat of the Crystalline Humour grow flatter than before, the Light will not be refracted enough, and for want of a sufficient Refraction will not converge to the bottom of the Eye but to some place beyond it, and by consequence paint in the bottom of the Eye a confused Picture, and according to the Indistinctuess of this Picture the Object will appear confused. This is the reason of the decay of sight in old Men, and shews why their Sight is mended by Spectacles. For those Convex glasses supply the defect of plumpness in the Eye, and by increasing the Refraction make the rays converge sooner, so as to convene distinctly at the bottom of the Eye if the Glass have a due degree of convexity. And the contrary happens in short-sighted Men whose Eyes are too plump. For the Refraction being now too great, the Rays converge and convene in the Eyes before they come at the bottom; and therefore the Picture made in the bottom and the Vision caused thereby will not be distinct, unless the Object be brought so near the Eye as that the place where the converging Rays convene may be removed to the bottom, or that the plumpness of the Eye be taken off and the Refractions diminished by a Concave-glass of a due degree of Concavity, or lastly that by Age the Eye grow flatter till it come to a due Figure: For short-sighted Men see remote Objects best in Old Age, and therefore they are accounted to have the most lasting Eyes.

If we imagine an observer to approach our planet from outer space, and, pushing aside the belts of red-brown clouds which obscure our atmosphere, to gaze for a whole day on the surface of the earth as it rotates beneath him, the feature, beyond all others most likely to arrest his attention would be the wedge-like outlines of the continents as they narrow away to the South.

If you ask a person, “What were you thinking?” you may get an answer that is richer and more revealing of the human condition than any stream of thoughts a novelist could invent. I try to see through people’s faces into their minds and listen through their words into their lives, and what I find there is beyond imagining.

Imagine a school-boy who has outgrown his clothes. Imagine the repairs made on the vestments where the enlarged frame had burst the narrow limits of the enclosure. Imagine the additions made where the projecting limbs had fairly and far emerged beyond the confines of the garment. Imagine the boy still growing, and the clothes, mended allover, now more than ever in want of mending—such is chemistry, and such is nomenclature.

In all works on Natural History, we constantly find details of the marvellous adaptation of animals to their food, their habits, and the localities in which they are found. But naturalists are now beginning to look beyond this, and to see that there must be some other principle regulating the infinitely varied forms of animal life. It must strike every one, that the numbers of birds and insects of different groups having scarcely any resemblance to each other, which yet feed on the same food and inhabit the same localities, cannot have been so differently constructed and adorned for that purpose alone. Thus the goat-suckers, the swallows, the tyrant fly-catchers, and the jacamars, all use the same kind ‘Of food, and procure it in the same manner: they all capture insects on the wing, yet how entirely different is the structure and the whole appearance of these birds!