...the scientific cast of mind examines the world critically, as if many alternative worlds might exist, as if other things might be here which are not. Then we are forced to ask why what we see is present and not something else. Why are the Sun and moon and the planets spheres? Why not pyramids, or cubes, or dodecahedra? Why not irregular, jumbly shapes? Why so symmetrical, worlds? If you spend any time spinning hypotheses, checking to see whether they make sense, whether they conform to what else we know. Thinking of tests you can pose to substantiate or deflate hypotheses, you will find yourself doing science.

[Archimedes] is said to have requested his friends and relations that when he was dead, they would place over his tomb a sphere containing a cylinder, inscribing it with the ratio which the containing solid bears to the contained.

[There was] in some of the intellectual leaders a great aspiration to demonstrate that the universe ran like a piece of clock-work, but this was was itself initially a religious aspiration. It was felt that there would be something defective in Creation itself—something not quite worthy of God—unless the whole system of the universe could be shown to be interlocking, so that it carried the pattern of reasonableness and orderliness. Kepler, inaugurating the scientist’s quest for a mechanistic universe in the seventeenth century, is significant here—his mysticism, his music of the spheres, his rational deity demand a system which has the beauty of a piece of mathematics.

Bernard: Oh, you’re going to zap me with penicillin and pesticides. Spare me that and I’ll spare you the bomb and aerosols. But don’t confuse progress with perfectibility. A great poet is always timely. A great philosopher is an urgent need. There’s no rush for Isaac Newton. We were quite happy with Aristotle’s cosmos. Personally, I preferred it. Fifty-five crystal spheres geared to God’s crankshaft is my idea of a satisfying universe. I can’t think of anything more trivial than the speed of light. Quarks, quasars—big bangs, black holes—who [cares]? How did you people con us out of all that status? All that money? And why are you so pleased with yourselves?
Chloe: Are you against penicillin, Bernard?
Bernard: Don’t feed the animals.

Copernicus, who rightly did condemn
This eldest systeme, form’d a wiser scheme;
In which he leaves the Sun at Rest, and rolls
The Orb Terrestial on its proper Poles;
Which makes the Night and Day by this Career,
And by its slow and crooked Course the Year.
The famous Dane, who oft the Modern guides,
To Earth and Sun their Provinces divides:
The Earth’s Rotation makes the Night and Day,
The Sun revolving through th’ Eccliptic Way
Effects the various seasons of the Year,
Which in their Turn for happy Ends appear.
This Scheme or that, which pleases best, embrace,
Still we the Fountain of their Motion trace.
Kepler asserts these Wonders may be done
By the Magnetic Vertue of the Sun,
Which he, to gain his End, thinks fit to place
Full in the Center of that mighty Space,
Which does the Spheres, where Planets roll, include,
And leaves him with Attractive Force endu’d.
The Sun, thus seated, by Mechanic Laws,
The Earth, and every distant Planet draws;
By which Attraction all the Planets found
Within his reach, are turn'd in Ether round.

A conflict arises when a religious community insists on the absolute truthfulness of all statements recorded in the Bible. This means an intervention on the part of religion into the sphere of science; this is where the struggle of the Church against the doctrines of Galileo and Darwin belongs. On the other hand, representatives of science have often made an attempt to arrive at fundamental judgments with respect to values and ends on the basis of scientific method, and in this way have set themselves in opposition to religion. These conflicts have all sprung from fatal errors.

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 thing is either alive or it isn’t; there is nothing that is almost alive. There is but the remotest possibility of the origin of life by spontaneous generation, and every likelihood that Arrhenius is right when he dares to claim that life is a cosmic phenomenon, something that drifts between the spheres, like light, and like light transiently descends upon those fit to receive it.

After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formerly used, if some assumptions (which are called axioms) were granted me. They follow in this order.
There is no one center of all the celestial circles or spheres.
The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere.
All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe.
The ratio of the earth’s distance from the sun to the height of the firmament is so much smaller than the ratio of the earth’s radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.
Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth’s motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.
What appears to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion.
The apparent retrograde and direct motion of the planets arises not from their motion but from the earth’s. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.

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.

All religions, arts and sciences are branches of the same tree. All these aspirations are directed toward ennobling man’s life, lifting it from the sphere of mere physical existence and leading the individual towards freedom.

Also the earth is not spherical, as some have said, although it tends toward sphericity, for the shape of the universe is limited in its parts as well as its movement… . The movement which is more perfect than others is, therefore, circular, and the corporeal form which is the most perfect is the sphere.

And we daily in our experiments electrise bodies plus or minus, as we think proper. [These terms we may use till your Philosophers give us better.] To electrise plus or minus, no more needs to be known than this, that the parts of the Tube or Sphere, that are rubb’d, do, in the Instant of Friction, attract the Electrical Fire, and therefore take it from the Thin rubbing; the same parts immediately, as the Friction upon them ceases, are disposed to give the fire they have received, to any Body that has less.

Anthropology has been compared to a great region, marked out indeed as within the sphere of influence of science, but unsettled and for the most part unsubdued. Like all such hinterland sciences, it is a happy hunting-ground for adventurers.

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.

Archimedes [indicates] that there can be no true levelling by means of water, because he holds that water has not a level surface, but is of a spherical form, having its centre at the centre of the earth.

Aristotle ... imputed this symphony of the heavens ... this music of the spheres to Pythagorus. ... But Pythagoras alone of mortals is said to have heard this harmony ... If our hearts were as pure, as chaste, as snowy as Pythagoras' was, our ears would resound and be filled with that supremely lovely music of the wheeling stars.

As a little boy, I showed an abnormal aptitude for mathematics this gift played a horrible part in tussles with quinsy or scarlet fever, when I felt enormous spheres and huge numbers swell relentlessly in my aching brain.

Astronomy was not studied by Kepler, Galileo, or Newton for the practical applications which might result from it, but to enlarge the bounds of knowledge, to furnish new objects of thought and contemplation in regard to the universe of which we form a part; yet how remarkable the influence which this science, apparently so far removed from the sphere of our material interests, has exerted on the destinies of the world!

Between the lowest and the highest degree of spiritual and corporal perfection, there is an almost infinite number of intermediate degrees. The succession of degrees comprises the Universal Chain. It unites all beings, ties together all worlds, embraces all the spheres. One SINGLE BEING is outside this chain, and this is HE who made it.

Dr. M.L. von Franz has explained the circle (or sphere) as a symbol of Self. It expresses the totality of the psyche in all its aspects, including the relationship between man and the whole of nature. It always points to the single most vital aspect of life, its ultimate wholeness.

Even though the realms of religion and science in themselves are clearly marked off from each other, nevertheless there exist between the two strong reciprocal relationships and dependencies. Though religion may be that which determines the goal, it has, nevertheless, learned from science, in the broadest sense, what means will contribute to the attainment of the goals it has set up. But science can only be created by those who are thoroughly imbued with the aspiration toward truth and understanding. This source of feeling, however, springs from the sphere of religion. To this there also belongs the faith in the possibility that the regulations valid for the world of existence are rational, that is, comprehensible to reason. I cannot conceive of a genuine scientist without that profound faith. The situation may be expressed by an image: science without religion is lame, religion without science is blind.

Every serious scientific worker is painfully conscious of this involuntary relegation to an ever-narrowing sphere of knowledge, which threatens to deprive the investigator of his broad horizon and degrades him to the level of a mechanic.

FAUSTUS: How many heavens or spheres are there?
MEPHASTOPHILIS: Nine: the seven planets, the firmament, and the empyreal heaven.
FAUSTUS: But is there not coelum igneum, et crystallinum?
MEPH.: No Faustus, they be but fables.
FAUSTUS: Resolve me then in this one question: Why are not conjunctions, oppositions, aspects, eclipses all at one time, but in some years we have more, in some less?
MEPH.: Per inaequalem motum respectu totius.
FAUSTUS: Well, I am answered. Now tell me who made the world.
MEPH.: I will not.
FAUSTUS: Sweet Mephastophilis, tell me.
MEPH.: Move me not, Faustus.
FAUSTUS: Villain, have I not bound thee to tell me any thing?
MEPH.: Ay, that is not against our kingdom.
This is. Thou are damn'd, think thou of hell.
FAUSTUS: Think, Faustus, upon God that made the world!
MEPH.: Remember this.

Following the example of Archimedes who wished his tomb decorated with his most beautiful discovery in geometry and ordered it inscribed with a cylinder circumscribed by a sphere, James Bernoulli requested that his tomb be inscribed with his logarithmic spiral together with the words, “Eadem mutata resurgo,” a happy allusion to the hope of the Christians, which is in a way symbolized by the properties of that curve.

From man or angel the great Architect did wisely to conceal, and not divulge his secrets to be scanned by them who ought rather admire; or if they list to try conjecture, he his fabric of the heavens left to their disputes, perhaps to move his laughter at their quaint opinions wide hereafter, when they come to model heaven calculate the stars, how they will wield the mighty frame, how build, unbuild, contrive to save appearances, how gird the sphere with centric and eccentric scribbled o’er, and epicycle, orb in orb.

From the rocket we can see the huge sphere of the planet in one or another phase of the Moon. We can see how the sphere rotates, and how within a few hours it shows all its sides successively ... and we shall observe various points on the surface of the Earth for several minutes and from different sides very closely. This picture is so majestic, attractive and infinitely varied that I wish with all my soul that you and I could see it. (1911)

Gaia is a thin spherical shell of matter that surrounds the incandescent interior; it begins where the crustal rocks meet the magma of the Earth’s hot interior, about 100 miles below the surface, and proceeds another 100 miles outwards through the ocean and air to the even hotter thermosphere at the edge of space. It includes the biosphere and is a dynamic physiological system that has kept our planet fit for life for over three billion years. I call Gaia a physiological system because it appears to have the unconscious goal of regulating the climate and the chemistry at a comfortable state for life. Its goals are not set points but adjustable for whatever is the current environment and adaptable to whatever forms of life it carries.

Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.

How can a man sit down and quietly pare his nails, while the earth goes gyrating ahead amid such a din of sphere music, whirling him along about her axis some twenty-four thousand miles between sun and sun, but mainly in a circle some two millions of miles actual progress? And then such a hurly-burly on the surface …. Can man do less than get up and shake himself?

I am quite aware that we have just now lightheartedly expelled in imagination many excellent men who are largely, perhaps chiefly, responsible for the buildings of the temple of science; and in many cases our angel would find it a pretty ticklish job to decide. But of one thing I feel sure: if the types we have just expelled were the only types there were, the temple would never have come to be, any more than a forest can grow which consists of nothing but creepers. For these people any sphere of human activity will do, if it comes to a point; whether they become engineers, officers, tradesmen, or scientists depends on circumstances.

I can well appreciate, Holy Father, that as soon as certain people realise that in these books which I have written about the Revolutions of the spheres of the universe I attribute certain motions to the globe of the Earth, they will at once clamour for me to be hooted off the stage with such an opinion.

I have accumulated a wealth of knowledge in innumerable spheres and enjoyed it as an always ready instrument for exercising the mind and penetrating further and further. Best of all, mine has been a life of loving and being loved. What a tragedy that all this will disappear with the used-up body!

I saw Eternity the other night,
Like a great Ring of pure and endless light,
All calm, as it was bright;
And round beneath it,
Time, in hours, days, years,
Driv’n by the spheres
Like a vast shadow mov’d; in which the world
And all her train were hurl’d.

I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Saturn and Jupiter by their attractive powers, have a considerable influence upon its motion in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipse, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Cœlestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first compleat and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the Great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.

I therefore took this opportunity and also began to consider the possibility that the Earth moved. Although it seemed an absurd opinion, nevertheless, because I knew that others before me had been granted the liberty of imagining whatever circles they wished to represent the phenomena of the stars, I thought that I likewise would readily be allowed to test whether, by assuming some motion of the Earth's, more dependable representations than theirs could be found for the revolutions of the heavenly spheres.

I would by all means have men beware, lest Æsop’s pretty fable of the fly that sate [sic] on the pole of a chariot at the Olympic races and said, “What a dust do I raise,” be verified in them. For so it is that some small observation, and that disturbed sometimes by the instrument, sometimes by the eye, sometimes by the calculation, and which may be owing to some real change in the heaven, raises new heavens and new spheres and circles.

If we peep into Dom Claude’s cell, we are introduced to a typical alchemist’s laboratory—a gloomy, dimly-lighted place, full of strange vessels, and furnaces, and melting-pots, spheres, and portions of skeletons hanging from the ceiling; the floor littered with stone bottles, pans, charcoal, aludels, and alembics, great parchment books covered with hieroglyphics; the bellows with its motto Spira, Spera; the hour-glass, the astrolabe, and over all cobwebs, and dust, and ashes. The walls covered with various aphorisms of the brotherhood; legends and memorials in many tongues; passages from the Smaragdine Table of Hermes Trismegistus; and looming out from all in great capitals, ’ANAΓKH.

In all speculations on the origin, or agents that have produced the changes on this globe, it is probable that we ought to keep within the boundaries of the probable effects resulting from the regular operations of the great laws of nature which our experience and observation have brought within the sphere of our knowledge. When we overleap those limits, and suppose a total change in nature's laws, we embark on the sea of uncertainty, where one conjecture is perhaps as probable as another; for none of them can have any support, or derive any authority from the practical facts wherewith our experience has brought us acquainted.

In all spheres of science, art, skill, and handicraft it is never doubted that, in order to master them, a considerable amount of trouble must be spent in learning and in being trained. As regards philosophy, on the contrary, there seems still an assumption prevalent that, though every one with eyes and fingers is not on that account in a position to make shoes if he only has leather and a last, yet everybody understands how to philosophize straight away, and pass judgment on philosophy, simply because he possesses the criterion for doing so in his natural reason.

In science, as in art, and, as I believe, in every other sphere of human activity, there may be wisdom in a multitude of counsellors, but it is only in one or two of them. And in scientific inquiry, at any rate, it is to that one or two that we must look for light and guidance.

In science, each of us knows that what he has accomplished will be antiquated in ten, twenty, fifty years. That is the fate to which science is subjected; it is the very meaning of scientific work, to which it is devoted in a quite specific sense, as compared with other spheres of culture for which in general the same holds. Every scientific “fulfilment” raises new “questions”; it asks to be “surpassed” and outdated. Whoever wishes to serve science has to resign himself to this fact. Scientific works certainly can last as “gratifications” because of their artistic quality, or they may remain important as a means of training. Yet they will be surpassed scientifically—let that be repeated—for it is our common fate and, more our common goal. We cannot work without hoping that others will advance further than we have. In principle, this progress goes on ad infinitum.

In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Bionomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.

In the beginning there was an explosion. Not an explosion like those familiar on earth, starting from a definite center and spreading out to engulf more and more of the circumambient air, but an explosion which occurred simultaneously everywhere, filling all space from the beginning, with every particle of matter rushing apart from every other particle. ‘All space’ in this context may mean either all of an infinite universe, or all of a finite universe which curves back on itself like the surface of a sphere. Neither possibility is easy to comprehend, but this will not get in our way; it matters hardly at all in the early universe whether space is finite or infinite. At about one-hundredth of a second, the earliest time about which we can speak with any confidence, the temperature of the universe was about a hundred thousand million (10¹¹) degrees Centigrade. This is much hotter than in the center of even the hottest star, so hot, in fact, that none of the components of ordinary matter, molecules, or atoms, or even the nuclei of atoms, could have held together. Instead, the matter rushing apart in this explosion consisted of various types of the so-called elementary particles, which are the subject of modern high­energy nuclear physics.

In the first book I shall describe all the positions of the spheres, along with the motions which I attribute to the Earth, so that the book will contain as it were the general structure of the universe. In the remaining books I relate the motions of the remaining stars, and all the spheres, to the mobility of the Earth, so that it can be thence established how far the motions and appearances of the remaining stars and spheres can be saved, if they are referred to the motions of the Earth.

In the sphere of natural science let us remember that we have always to deal with an insoluble problem. Let us prove keen and honest in attending to anything which is in any way brought to our notice, most of all when it does not fit in with our previous ideas. For it is only thereby that we perceive the problem, which does indeed lie in nature, but still more in man.

Increasing knowledge lessens the sphere of the supernatural.

It appears, according to the reported facts, that the electric conflict is not restricted to the conducting wire, but that it has a rather extended sphere of activity around it … the nature of the circular action is such that movements that it produces take place in directions precisely contrary to the two extremities of a given diameter. Furthermore, it seems that the circular movement, combined with the progressive movement in the direction of the length of the conjunctive wire, should form a mode of action which is exerted as a helix around this wire as an axis.

It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.

It seems perfectly clear that Economy, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Most persons appear to hold that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method—I know not what.

It seems to me that the idea of a personal God is an anthropological concept which I cannot take seriously. I also cannot imagine some will or goal outside the human sphere has been cited as a statement that precedes the last three sentences here, but this might have originated in a paraphrase, a transcription error, or a misquotation; it does not appear in any editions of the essay which have thus far been checked.

Jupiter is the largest of all the solar system’s planets, more than ten times bigger and three hundred times as massive as Earth. Jupiter is so immense it could swallow all the other planets easily. Its Great Red Spot, a storm that has raged for centuries, is itself wider than Earth. And the Spot is merely one feature visible among the innumerable vortexes and streams of Jupiter’s frenetically racing cloud tops. Yet Jupiter is composed mainly of the lightest elements, hydrogen and helium, more like a star than a planet. All that size and mass, yet Jupiter spins on its axis in less than ten hours, so fast that the planet is clearly not spherical: Its poles are noticeably flattened. Jupiter looks like a big, colorfully striped beach ball that’s squashed down as if some invisible child were sitting on it. Spinning that fast, Jupiter’s deep, deep atmosphere is swirled into bands and ribbons of multihued clouds: pale yellow, saffron orange, white, tawny yellow-brown, dark brown, bluish, pink and red. Titanic winds push the clouds across the face of Jupiter at hundreds of kilometers per hour.

Let him look at that dazzling light hung aloft as an eternal lamp to lighten the universe; let him behold the earth, a mere dot compared with the vast circuit which that orb describes, and stand amazed to find that the vast circuit itself is but a very fine point compared with the orbit traced by the stars as they roll their course on high. But if our vision halts there, let imagination pass beyond; it will fail to form a conception long before Nature fails to supply material. The whole visible world is but an imperceptible speck in the ample bosom of Nature. No notion comes near it. Though we may extend our thought beyond imaginable space, yet compared with reality we bring to birth mere atoms. Nature is an infinite sphere whereof the centre is everywhere, the circumference nowhere. In short, imagination is brought to silence at the thought, and that is the most perceptible sign of the all-power of God.
Let man reawake and consider what he is compared with the reality of things; regard himself lost in this remote corner of Nature; and from the tiny cell where he lodges, to wit the Universe, weigh at their true worth earth, kingdoms, towns, himself. What is a man face to face with infinity?

Like buried treasures, the outposts of the universe have beckoned to the adventurous from immemorial times. Princes and potentates, political or industrial, equally with men of science, have felt the lure of the uncharted seas of space, and through their provision of instrumental means the sphere of exploration has made new discoveries and brought back permanent additions to our knowledge of the heavens.

My first view - a panorama of brilliant deep blue ocean, shot with shades of green and gray and white - was of atolls and clouds. Close to the window I could see that this Pacific scene in motion was rimmed by the great curved limb of the Earth. It had a thin halo of blue held close, and beyond, black space. I held my breath, but something was missing - I felt strangely unfulfilled. Here was a tremendous visual spectacle, but viewed in silence. There was no grand musical accompaniment; no triumphant, inspired sonata or symphony. Each one of us must write the music of this sphere for ourselves.

My theory of electrical forces is that they are called into play in insulating media by slight electric displacements, which put certain small portions of the medium into a state of distortion which, being resisted by the elasticity of the medium, produces an electromotive force ... I suppose the elasticity of the sphere to react on the electrical matter surrounding it, and press it downwards.
From the determination by Kohlrausch and Weber of the numerical relation between the statical and magnetic effects of electricity, I have determined the elasticity of the medium in air, and assuming that it is the same with the luminiferous ether I have determined the velocity of propagation of transverse vibrations.
The result is
193088 miles per second
(deduced from electrical & magnetic experiments).
Fizeau has determined the velocity of light
= 193118 miles per second
by direct experiment.
This coincidence is not merely numerical. I worked out the formulae in the country, before seeing Webers [sic] number, which is in millimetres, and I think we have now strong reason to believe, whether my theory is a fact or not, that the luminiferous and the electromagnetic medium are one.

Nature … is an infinite sphere of which the center is everywhere and the circumference nowhere.

No mathematician now-a-days sets any store on the discovery of isolated theorems, except as affording hints of an unsuspected new sphere of thought, like meteorites detached from some undiscovered planetary orb of speculation.

Not only are there meaningless questions, but many of the problems with which the human intellect has tortured itself turn out to be only 'pseudo problems,' because they can be formulated only in terms of questions which are meaningless. Many of the traditional problems of philosophy, of religion, or of ethics, are of this character. Consider, for example, the problem of the freedom of the will. You maintain that you are free to take either the right- or the left-hand fork in the road. I defy you to set up a single objective criterion by which you can prove after you have made the turn that you might have made the other. The problem has no meaning in the sphere of objective activity; it only relates to my personal subjective feelings while making the decision.

Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.

Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.

Number, place, and combination … the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.

Oh! That the Chemist’s magic art
Could crystallize this sacred treasure!…
That very law which moulds a tear,
And bids it trickle from its source;
That law preserves the earth a sphere,
And guides the planets in their course.

Once regarded as the herald of enlightenment in all spheres of knowledge, science is now increasingly seen as a strictly instrumental system of control. Its use as a means of social manipulation and its role in restricting human freedom now parallel in every detail its use as a means of natural manipulation.

Only science, exact science about human nature itself, and the most sincere approach to it by the aid of the omnipotent scientific method, will deliver man from his present gloom and will purge him from his contemporary share in the sphere of interhuman relations.

Our knowledge must always be limited, but the knowable is limitless. The greater the sphere of our knowledge the greater the surface of contact with our infinite ignorance.

Our problem is that the climate crisis hatched in our laps at a moment in history when political and social conditions were uniquely hostile to a problem of this nature and magnitude—that moment being the tail end of the go-go ’80s, the blastoff point for the crusade to spread deregulated capitalism around the world. Climate change is a collective problem demanding collective action the likes of which humanity has never actually accomplished. Yet it entered mainstream consciousness in the midst of an ideological war being waged on the very idea of the collective sphere.

Poets say science takes away from the beauty of the stars—mere globs of gas atoms. Nothing is “mere.” I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination—stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern—of which I am a part. … What is the pattern, or the meaning, or the “why?” It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?

Saturated with that speculative spirit then pervading the Greek mind, he [Pythagoras] endeavoured to discover some principle of homogeneity in the universe. Before him, the philosophers of the Ionic school had sought it in the matter of things; Pythagoras looked for it in the structure of things. He observed the various numerical relations or analogies between numbers and the phenomena of the universe. Being convinced that it was in numbers and their relations that he was to find the foundation to true philosophy, he proceeded to trace the origin of all things to numbers. Thus he observed that musical strings of equal lengths stretched by weights having the proportion of 1/2, 2/3, 3/4, produced intervals which were an octave, a fifth and a fourth. Harmony, therefore, depends on musical proportion; it is nothing but a mysterious numerical relation. Where harmony is, there are numbers. Hence the order and beauty of the universe have their origin in numbers. There are seven intervals in the musical scale, and also seven planets crossing the heavens. The same numerical relations which underlie the former must underlie the latter. But where number is, there is harmony. Hence his spiritual ear discerned in the planetary motions a wonderful “Harmony of spheres.”

See in Nature the cylinder, the sphere, the cone.

Seeing and thinking have done much for human progress; in the sphere of mind and morals everything, and could the world have been saved by armchair philosophy, the Greeks would have done it; but only a novum organon could do this, the powerful possibilities of which were only revealed when man began to search our the secrets of nature by way of experiment, to use the words of Harvey.

Spherical space is not very easy to imagine. We have to think of the properties of the surface of a sphere—the two-dimensional case—and try to conceive something similar applied to three-dimensional space. Stationing ourselves at a point let us draw a series of spheres of successively greater radii. The surface of a sphere of radius r should be proportional to r²; but in spherical space the areas of the more distant spheres begin to fall below the proper proportion. There is not so much room out there as we expected to find. Ultimately we reach a sphere of biggest possible area, and beyond it the areas begin to decrease. The last sphere of all shrinks to a point—our antipodes. Is there nothing beyond this? Is there a kind of boundary there? There is nothing beyond and yet there is no boundary. On the earth’s surface there is nothing beyond our own antipodes but there is no boundary there

Starres by the Sun are not inlarg’d but showne.
Gentle love deeds, as blossomes on a bough,
From loves awaken’d root doe bud out now.
If, as in water stir’d more circles bee
Produc’d by one, love such additions take,
Those like to many spheares, but one heaven make,
For, they are all concentrique unto thee.

Study and, in general, the pursuit of truth and beauty is a sphere of activity in which we are permitted to remain children all of our lives.

Suddenly, from behind the rim of the moon, in long, slow-motion moments of immense majesty, there emerges a sparkling blue and white jewel, a light, delicate sky-blue sphere laced with slowly swirling veils of white, rising gradually like a small pearl in a thick sea of black mystery. It takes more than a moment to fully realize this is Earth . . . home.

That the machine of Heaven is not a hard and impervious body full of various real spheres, as up to now has been believed by most people. It will be proved that it extends everywhere, most fluid and simple, and nowhere presents obstacles as was formerly held, the circuits of the Planets being wholly free and without the labour and whirling round of any real spheres at all, being divinely governed under a given law.

The chemist works along his own brilliant line of discovery and exposition; the astronomer has his special field to explore; the geologist has a well-defined sphere to occupy. It is manifest, however, that not one of these men can tell the whole tale, and make a complete story of creation. Another man is wanted. A man who, though not necessarily going into formal science, sees the whole idea, and speaks of it in its unity. This man is the theologian. He is not a chemist, an astronomer, a geologist, a botanist——he is more: he speaks of circles, not of segments; of principles, not of facts; of causes and purposes rather than of effects and appearances. Not that the latter are excluded from his study, but that they are so wisely included in it as to be put in their proper places.

The cult of individual personalities is always, in my view, unjustified. To be sure, nature distributes her gifts variously among her children. But there are plenty of the well-endowed ones too, thank God, and I am firmly convinced that most of them live quiet, unregarded lives. It strikes me as unfair, and even in bad taste, to select a few of them for boundless admiration, attributing superhuman powers of mind and character to them. This has been my fate, and the contrast between the popular estimate of my powers and achievements and the reality is simply grotesque. The consciousness of this extraordinary state of affairs would be unbearable but for one great consoling thought: it is a welcome symptom in an age which is commonly denounced as materialistic, that it makes heroes of men whose ambitions lie wholly in the intellectual and moral sphere. This proves that knowledge and justice are ranked above wealth and power by a large section of the human race. My experience teaches me that this idealistic outlook is particularly prevalent in America, which is usually decried as a particularly materialistic country.

The development of the nucleoplasm during ontogeny may be to some extent compared to an army composed of corps, which are made up of divisions, and these of brigades, and so on. The whole army may be taken to represent the nucleoplasm of the germ-cell: the earliest cell-division … may be represented by the separation of the two corps, similarly formed but with different duties: and the following cell­divisions by the successive detachment of divisions, brigades, regiments, battalions, companies, etc.; and as the groups become simpler so does their sphere of action become limited.

The evolution of higher and of lower forms of life is as well and as soundly established as the eternal hills. It has long since ceased to be a theory; it is a law of Nature as universal in living things as is the law of gravitation in material things and in the motions of the heavenly spheres.

The facts of life do not penetrate to the sphere in which our beliefs are cherished; they did not engender those beliefs, and they are powerless to destroy them.

The highest reach of science is, one may say, an inventive power, a faculty of divination, akin to the highest power exercised in poetry; therefore, a nation whose spirit is characterised by energy may well be eminent in science; and we have Newton. Shakspeare [sic] and Newton: in the intellectual sphere there can be no higher names. And what that energy, which is the life of genius, above everything demands and insists upon, is freedom; entire independence of all authority, prescription and routine, the fullest room to expand as it will.

The interior parts of the earth and its internal depths are a region totally impervious to the eye of mortal man, and can least of all be approached by those ordinary paths of hypothesis adopted by naturalists and geologists. The region designed for the existence of man, and of every other creature endowed with organic life, as well as the sphere opened to the perception of man's senses, is confined to a limited space between the upper and lower parts of the earth, exceedingly small in proportion to the diameter, or even semi-diameter of the earth, and forming only the exterior surface, or outer skin, of the great body of the earth.

The main source of the present-day conflicts between the spheres of religion and of science lies in this concept of a personal God.

The mathematician lives in a purely conceptual sphere, and mathematics is but the higher development of Symbolic Logic.

The media need superheroes in science just as in every sphere of life.

The perfection of the heavenly spheres does not depend upon the order of their relative position as to whether one is higher than another.

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. … Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. … Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.

The soul seems to be a very tenuous substance … [and] seems to be made of a most subtle texture, extremely mobile or active corpuscles, not unlike those of flame or heat; indeed, whether they are spherical, as the authors of atoms propound, or pyramidical as Plato thought, or some other form, they seem from their own motion and penetration through bodies to create the heat which is in the animal.

The true foundation of theology is to ascertain the character of God. It is by the aid of Statistics that law in the social sphere can be ascertained and codified, and certain aspects of the character of God thereby revealed. The study of statistics is thus a religious service.

The truth in one sphere does not contradict the truth in another sphere. Truth is one and in harmony with itself.

The two revolutions, I mean the annual revolutions of the declination and of the centre of the Earth, are not completely equal; that is the return of the declination to its original value is slightly ahead of the period of the centre. Hence it necessarily follows that the equinoxes and solstices seem to anticipate their timing, not because the sphere of the fixed stars moves to the east, but rather the equatorial circle moves to the west, being at an angle to the plane of the ecliptic in proportion to the declination of the axis of the terrestrial globe.

The United States is the most powerful technically advanced country in the world to-day. Its influence on the shaping of international relations is absolutely incalculable. But America is a large country and its people have so far not shown much interest in great international problems, among which the problem of disarmament occupies first place today. This must be changed, if only in the essential interests of the Americans. The last war has shown that there are no longer any barriers between the continents and that the destinies of all countries are closely interwoven. The people of this country must realize that they have a great responsibility in the sphere of international politics. The part of passive spectator is unworthy of this country and is bound in the end to lead to disaster all round.

The wonderful structure of the animal system will probably never permit us to look upon it as a merely physical apparatus, yet the demands of science require that the evidently magnified principles of vitality should be reduced to their natural spheres, or if truth requires, wholly subverted in favor of those more cognizable by the human understanding. The spirit of the age will not tolerate in the devotee of science a quiet indifference. ...

Then if the first argument remains secure (for nobody will produce a neater one, than the length of the periodic time is a measure of the size of the spheres), the order of the orbits follows this sequence, beginning from the highest: The first and highest of all is the sphere of the fixed stars, which contains itself and all things, and is therefore motionless. It is the location of the universe, to which the motion and position of all the remaining stars is referred. For though some consider that it also changes in some respect, we shall assign another cause for its appearing to do so in our deduction of the Earth’s motion. There follows Saturn, the first of the wandering stars, which completes its circuit in thirty years. After it comes Jupiter which moves in a twelve-year long revolution. Next is Mars, which goes round biennially. An annual revolution holds the fourth place, in which as we have said is contained the Earth along with the lunar sphere which is like an epicycle. In fifth place Venus returns every nine months. Lastly, Mercury holds the sixth place, making a circuit in the space of eighty days. In the middle of all is the seat of the Sun. For who in this most beautiful of temples would put this lamp in any other or better place than the one from which it can illuminate everything at the same time? Aptly indeed is he named by some the lantern of the universe, by others the mind, by others the ruler. Trismegistus called him the visible God, Sophocles' Electra, the watcher over all things. Thus indeed the Sun as if seated on a royal throne governs his household of Stars as they circle around him. Earth also is by no means cheated of the Moon’s attendance, but as Aristotle says in his book On Animals the Moon has the closest affinity with the Earth. Meanwhile the Earth conceives from the Sun, and is made pregnant with annual offspring. We find, then, in this arrangement the marvellous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultation by the Sun and re-appearance. Indeed Mars in particular at the time when it is visible throughout the night seems to equal Jupiter in size, though marked out by its reddish colour; yet it is scarcely distinguishable among stars of the second magnitude, though recognized by those who track it with careful attention. All these phenomena proceed from the same course, which lies in the motion of the Earth. But the fact that none of these phenomena appears in the fixed stars shows their immense elevation, which makes even the circle of their annual motion, or apparent motion, vanish from our eyes.

There are those who say that the human kidney was created to keep the blood pure, or more precisely, to keep our internal environment in an ideal balanced state. This I must deny. I grant that the human kidney is a marvelous organ, but I cannot grant that it was purposefully designed to excrete urine or to regulate the composition of the blood or to subserve the physiological welfare of Homo sapiens in any sense. Rather I contend that the human kidney manufactures the kind of urine that it does, and it maintains the blood in the composition which that fluid has, because this kidney has a certain functional architecture; and it owes that architecture not to design or foresight or to any plan, but to the fact that the earth is an unstable sphere with a fragile crust, to the geologic revolutions that for six hundred million years have raised and lowered continents and seas, to the predacious enemies, and heat and cold, and storms and droughts; to the unending succession of vicissitudes that have driven the mutant vertebrates from sea into fresh water, into desiccated swamps, out upon the dry land, from one habitation to another, perpetually in search of the free and independent life, perpetually failing, for one reason or another, to find it.

There are three ruling ideas, three so to say, spheres of thought, which pervade the whole body of mathematical science, to some one or other of which, or to two or all three of them combined, every mathematical truth admits of being referred; these are the three cardinal notions, of Number, Space and Order.
Arithmetic has for its object the properties of number in the abstract. In algebra, viewed as a science of operations, order is the predominating idea. The business of geometry is with the evolution of the properties of space, or of bodies viewed as existing in space.

There are two processes which we adopt consciously or unconsciously when we try to prophesy. We can seek a period in the past whose conditions resemble as closely as possible those of our day, and presume that the sequel to that period will, save for some minor alterations, be similar. Secondly, we can survey the general course of development in our immediate past, and endeavor to prolong it into the near future. The first is the method the historian; the second that of the scientist. Only the second is open to us now, and this only in a partial sphere.

There is geometry in the humming of the strings. There is music in the spacing of the spheres.

There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.