Infinity

Ford, there’s an infinite number of monkeys outside who want to talk to us about this script for Hamlet they’ve worked out.

— Infinity

All things were together, infinite both in number and in smallness; for the small too was infinite.

— Infinity

Empedocles holds that the corporeal elements are four, while all the elements-including those which initiate movement-are six in number; whereas Anaxagoras agrees with Leucippus and Democritus that the elements are infinite.

— Infinity

Motion is supposed to belong to the class of things which are continuous; and the infinite presents itself first in the continuous--that is how it comes about that 'infinite' is often used in definitions of the continuous (what is infinitely divisible is continuous). Besides these, place, void, and time are thought to be necessary conditions of motion.

— Infinity

The Pythagoreans identify the infinite with the even. For this, they say, when it is cut off and shut in by the odd, provides things with the element of infinity. An indication of this is what happens with numbers. If the gnomons are placed round the one, and without the one, in the one construction the figure that results is always different, in the other it is always the same. But Plato has two infinities, the Great and the Small.

— Infinity

The physicists... always regard the infinite as an attribute of a substance which is different from it and belongs to the class of the so-called elements--water or air or what is intermediate between them. Those who make them limited in number never make them infinite in amount. But those who make the elements infinite in number, as Anaxagoras and Democritus do, say that the infinite is continuous by contact-compounded of the homogeneous parts.

— Infinity

That what is outside is infinite, leads people to suppose that body also is infinite, and that there is an infinite number of worlds. Why should there be body in one part of the void rather than in another? Grant only that mass is anywhere and it follows that it must be everywhere. Also, if void and place are infinite, there must be infinite body too, for in the case of eternal things what may be must be.

— Infinity

The problem of the infinite is difficult: many contradictions result whether we suppose it to exist or not to exist. If it exists, we have still to ask how it exists; as a substance or as the essential attribute of some entity? Or in neither way, yet none the less is there something which is infinite or some things which are infinitely many?

— Infinity

If 'bounded by a surface' is the definition of body there cannot be an infinite body either intelligible or sensible.

— Infinity

Anaxagoras gives an absurd account of why the infinite is at rest. He says that the infinite itself is the cause of its being fixed. This because it is in itself, since nothing else contains it--on the assumption that wherever anything is, it is there by its own nature. But this is not true: a thing could be somewhere by compulsion, and not where it is its nature to be.

— Infinity

To suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and an end of time, a magnitude will not be divisible into magnitudes, number will not be infinite. ...clearly there is a sense in which the infinite exists and another in which it does not.

— Infinity

The infinite turns out to be the contrary of what it is said to be. It is not what has nothing outside it that is infinite, but what always has something outside it.

— Infinity

Parmenides must be thought to have spoken better than Melissus. The latter says that the whole is infinite, but the former describes it as limited, 'equally balanced from the middle'. ...it is absurd and impossible to suppose that the unknowable and indeterminate should contain and determine.

— Infinity

What is one is indivisible whatever it may be, e.g. a man is one man, not many. Number on the other hand is a plurality of 'ones' and a certain quantity of them. Hence number must stop at the indivisible: for 'two' and 'three' are merely derivative terms, and so with each of the other numbers.

— Infinity

In the direction of largeness it is always possible to think of a larger number: for the number of times a magnitude can be bisected is infinite. Hence this infinite is potential, never actual: the number of parts that can be taken always surpasses any assigned number. But this number is not separable from the process of bisection, and its infinity is not a permanent actuality but consists in a process of coming to be, like time and the number of time.

— Infinity

With magnitudes the contrary holds. What is continuous is divided ad infinitum, but there is no infinite in the direction of increase. For the size which it can potentially be, it can also actually be. Hence since no sensible magnitude is infinite, it is impossible to exceed every assigned magnitude; for if it were possible there would be something bigger than the heavens.

— Infinity

Our account does not rob the mathematicians of their science, by disproving the actual existence of the infinite in the direction of increase, in the sense of the untraversable. In point of fact they do not need the infinite and do not use it. They postulate only that the finite straight line may be produced as far as they wish.

— Infinity

It is plain that the infinite is a cause in the sense of matter, and that its essence is privation, the subject as such being what is continuous and sensible. All the other thinkers, too, evidently treat the infinite as matter--that is why it is inconsistent in them to make it what contains, and not what is contained.

— Infinity

If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good.

— Infinity

Every material body has some natural movement, and can change its place. But an infinite body would occupy every place, and every place would be its own place. ...Every mathematical body must be imagined as having some shape. But shape is defined by some term or boundary, and nothing infinite can have a boundary.

— Infinity

Wallis rejected as absurd and inconceivable the now usual idea of a negative number as being less than nothing, but accepted the view that it is something greater than infinity.

— Infinity

In the entire history of Greek mathematics, all but the incomparable Archimedes and a few of the more heterodox sophists appear to have hated or feared the mathematical infinite. Analysis was thwarted when it might have prospered.

— Infinity

If a thing loves, it is infinite.

— Infinity

If the doors of perception were cleansed everything would appear to man as it is, infinite. For man has closed himself up, till he sees all things thro' narrow chinks of his cavern.

— Infinity

To see a World in a Grain of Sand And Eternity in an hour.

— Infinity

There is a concept which corrupts and upsets all others. I refer not to Evil, whose limited realm is that of ethics; I refer to the infinite.

— Infinity

There are no moral or intellectual merits. Homer composed the Odyssey; if we postulate an infinite period of time, with infinite circumstances and changes, the impossible thing is not to compose the Odyssey, at least once.

— Infinity

Anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist.

— Infinity

There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.

— Infinity

Each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.

— Infinity

The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.

— Infinity

I believe that there is no part of matter which is not — I do not say divisible — but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.

— Infinity

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.

— Infinity

And in that moment, I swear we were infinite.

— Infinity

The primary Imagination I hold to be the living power and prime agent of all human perception, and as a repetition in the finite mind of the eternal act of creation in the infinite I AM.

— Infinity

Great fleas have little fleas upon their backs to bite 'em,While these again have greater still, and greater still, and so on.

— Infinity

Anaximander gave up the idea that water or any other known substance might be the first principle, and held that this is of the nature of the infinite, that is, matter without any determinate property except that of being infinite. All things are developed out of this and return to it again, so that an infinite series of worlds have been generated and have in turn become again resolved into the abstract mass.

— Infinity

As to the query whether the finite parts of a limited continuum [continuo terminato] are finite infinite in number I will... answer that they are neither finite or infinite.

— Infinity

Nature doth, and in it alone is discovered an infinite wisdom, so that Divine Wisdom may be concluded to be infinitely infinite.

— Infinity

The Infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.

— Infinity

When we turn to the question, what is the essence of the infinite, we must first give ourselves an account as to the meaning the infinite has for reality: let us then see what physics teaches us about it.

— Infinity

All this arguing of infinities is but the ambition of school boys.

— Infinity

Even if there were exceedingly few things in a finite space in an infinite time, they would not have to repeat in the same configurations. Suppose there were three wheels of equal size, rotating on the same axis, one point marked on the circumference of each wheel, and these three points lined up in one straight line. If the second wheel rotated twice as fast as the first, and if the speed of the third wheel was 1/π of the speed of the first, the initial line-up would never recur.

— Infinity

The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes. They "shrank before the silence of the infinite spaces."

— Infinity

The Pythagoreans associated good and evil with the limited and unlimited, respectively.

— Infinity

Aristotle says the infinite is imperfect, unfinished, and therefore unthinkable; it is formless and confused. Only as objects are delimited and distinct do they have a nature.

— Infinity

The concept of the infinitely small is involved in the relation of points to a line or the relation of the discrete to the continuous, and Zeno's paradoxes may have caused the Greeks to shy away from this subject.

— Infinity

The relationship of point to line bothered the Greeks and led Aristotle to separate the two. Though he admits points are on lines, he says that a line is not made up of points and that the continuous cannot be made up of the discrete. This distinction contributed also to the presumed need for separating number from geometry, since to the Greeks numbers were discrete and geometry dealt with continuous magnitudes.

— Infinity

Because they [the ancient Greeks] feared infinite processes they missed the limit process. In approximating a circle by a polygon they were content to make the difference smaller than any given quantity, but something positive was always left over. Thus the process remained clear to the intuition; the limit process, on the other hand, would have involved the infinitely small.

— Infinity

Aristotle had considered the question of whether space is infinite and gave six nonmathematical arguments to prove that it is finite; he foresaw that this question would be troublesome.

— Infinity

In an infinite, eternal universe, the point is that anything is possible, and it's unlikely that we can even begin to scratch the surface of the full range of possibilities.

— Infinity

As there are an infinity of possible worlds, there are also an infinity of laws, certain ones appropriate to one; others, to another, and each possible individual of any world involves in its concept the laws of its world.

— Infinity

Outside the ordered universe [is] that amorphous blight of nethermost confusion which blasphemes and bubbles at the center of all infinity—the boundless daemon sultan Azathoth, whose name no lips dare speak aloud, and who gnaws hungrily in inconceivable, unlighted chambers beyond time and space amidst the muffled, maddening beating of vile drums and the thin monotonous whine of accursed flutes.

— Infinity

I fear what I have said of Infinities, will seem obscure to you; but it is enough if you understand, that Infinities when considered absolutely without any Restriction or Limitation, are neither equal nor unequal, nor have any Proportion one to another, and therefore the Principle that all Infinities are equal, is a precarious one.

— Infinity

For after all what is man in nature? A nothing in relation to infinity, all in relation to nothing, a central point between nothing and all and infinitely far from understanding either. The ends of things and their beginnings are impregnably concealed from him in an impenetrable secret. He is equally incapable of seeing the nothingness out of which he was drawn and the infinite in which he is engulfed.

— Infinity

Excessive qualities are prejudicial to us and not perceptible by the senses; we do not feel but suffer them. Extreme youth and extreme age hinder the mind, as also too much and too little education. In short, extremes are for us as though they were not, and we are not within their notice. They escape us, or we them. This is our true state; this is what makes us incapable of certain knowledge and of absolute ignorance.

— Infinity

I hold it equally impossible to know the parts without knowing the whole, and to know the whole without knowing the parts in detail. The eternity of things in itself or in God must also astonish our brief duration.

— Infinity

Unity joined to infinity adds nothing to it, no more than one foot to an infinite measure. The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice.

— Infinity

We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite, and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because He has neither extension nor limits.

— Infinity

When we would pursue virtues to their extremes on either side, vices present themselves insensibly there, in their insensible journeys towards the infinitely little; and vices present themselves in a crowd towards the infinitely great, so that we lose ourselves in them, and no longer see virtues.

— Infinity

We must relax our minds a little; but this opens the door to debauchery. Let us mark the limits. There are no limits in things. Laws would put them there, and the mind cannot suffer it.

— Infinity

All that is not thought is pure nothingness...And yet—strange contradiction for those who believe in time—geologic history shows us that life is only a short episode between two eternities of death, and that, even in this episode, conscious thought has lasted and will last only a moment. Thought is only a gleam in the midst of a long night. But it is this gleam which is everything.

— Infinity

Those who assumed innumerable worlds, e.g., Anaximander, Leukippos, Demokritos, and, later on, Epicurus, assumed that they came into being and passed away ad infinitum, some always coming into being and others passing away.

— Infinity

What does infinity mean to you? Are you not infinity and yourself?

— Infinity

Infinity is the end. End without infinity is but a new beginning.

— Infinity

Concerning the things needful to be known... we must first take care not to commit ourselves to a search, going back to infinity—that is, in order to discover the best method for finding out the truth, there is no need of another method to discover such method; nor of a third method for discovering the second, and so on to infinity. By such proceedings, we should never arrive at the knowledge of the truth, or indeed at any knowledge at all.

— Infinity

Things regarded in themselves, and in relation to God, are neither ugly nor beautiful. ...Perfection and imperfection are names which do not differ much from the names beauty and ugliness. ...This I know, that between finite and infinite there is no comparison; so that the difference between God and the greatest and most excellent created thing is no less than the difference between God and the least created thing.

— Infinity

By God, I mean a being absolutely infinite — that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality. Explanation — I say absolutely infinite, not infinite after its kind: for, of a thing infinite only after its kind, infinite attributes may be denied; but that which is absolutely infinite, contains in its essence whatever expresses reality, and involves no negation.

— Infinity

From the necessity of the divine nature must follow an infinite number of things in infinite ways—that is, all things which can fall within the sphere of infinite intellect.

— Infinity

Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.

— Infinity

In the Timaeus Plato had expounded a theory that outside the universe, which he regarded as bounded and spherical, there was an infinite empty space.

— Infinity

When you reach the top of the mountain, keep climbing.

— Infinity