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Life is not about finding our limitations, it’s about finding our infinity. Herbie Hancock
The mathematical objection is that as the clock is wound back and Hubble’s zero hour is approached all the stuff of the universe is crammed into a smaller and smaller space. Eventually, that space will become infinitely small. And in mathematics invoking infinity is the same as giving up. Or cheating. Horizon: What Happened Before the Big Bang? BBC 2010
Is the universe infinite? Might every event repeat again and again and again ... Is the Earth just one of uncountable copies tumbling through an unending void? Horizon: To Infinity & Beyond, BBC 2010
A google-plex has so many zeros that there is not enough space in the observable universe just to write the number down. ibid.
Graham’s number is so big it even made it into the Guinness Book of Records. ibid.
In an infinite universe anything that is possible has to happen. ibid.
While no-one likes the idea of space coming to an end, the consequences of an infinite universe are even more bewildering. ibid.
The universe is infinite. Horizon: How Big is the Universe? BBC 2012
No finite point has meaning without an infinite reference point. Jean-Paul Sartre
Civilisation is the process of reducing the infinite to the finite. Oliver Wendell Holmes
We must accept finite disappointment, but never lose infinite hope. Martin Luther King
Our knowledge can only be finite, while our ignorance must necessarily be infinite. Karl Popper
No matter what number you have in mind infinity is larger. Professor Carl Sagan & Ann Druyan, Cosmos: The Lives of the Stars, PBS 1980
I can’t help it, the idea of the infinite torments me. Alfred de Musset, L’Espoir en Dieu 1838
I always found something repulsive about it. Professor Doron Zeilberger, Rutgers University
Imagine that all of you are in Hades and I am the devil. I make the following proposition, I say: I’ve written down on a positive integer on a slip of paper, a whole number ... Every day you’re allowed one guess as to what that number is ... Professor Raymond Smullyan
If we didn’t have infinite there would be no mathematics at this time ... Infinite for us has become formal. Professor Jean DieuDonne
I could be bounded in a nut-shell, and count myself a king of infinite space, were it not that I have bad dreams. William Shakespeare, Hamlet II ii 251-252, Hamlet
The more you approach infinity, the deeper you penetrate terror. Gustave Flaubert
If the doors of perception were cleansed, everything would appear to man as it is – infinite. William Blake
To see a world in a grain of sand and heaven in a wild flower
Hold infinity in the palms of your hand and eternity in an hour. William Blake
If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all. Bertrand Russell
The last proceeding of reason is to recognize that there is an infinity of things which are beyond it. There is nothing so conformable to reason as this disavowal of reason. Blaise Pascal
The eternal silence of these infinite spaces makes me afraid. Blaise Pascal
I think that the leaf of a tree, the meanest insect on which we trample, are in themselves arguments more conclusive than any which can be adduced that some vast intellect animates Infinity. Percy Bysshe Shelley
All things were together, infinite both in number and in smallness; for the small too was infinite. Anaxagoras, cited John Burnet, 1920
The infinite presents itself first in the continuous. Aristotle
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. Morris Kline, Mathematical Thought From Ancient to Modern Times, 1972
The concept of infinity came in relatively late, even in Egypt, and ... its first fathers were more likely metaphysicians than theologians. In looking backward, as in looking forward, early man was quite unable to imagine endless time. Always he concluded that the animal creation, including his own kind, must have a beginning, and the earth he walked on, with it. Sometimes he ascribed the act of creation to the gods, or to one of them, and sometimes he laid it to a potent being of lesser dignity, usually to a totem animal. H L Mencken, Treatise on the Gods, 1930
Beneath the surface of the world are the rules of science. But beneath them there is a far deeper set of rules, a matrix of pure mathematics which explains the nature of the rules of science and how it is we can understand them in the first place. Dangerous Knowledge, BBC 2007
Georg Cantor: how big is infinity? ibid.
A whole hierarchy of different infinities. ibid.
All the analysis of infinite reality which the finite human mind can conduct rests on the tacit assumption that only a finite portion of this reality constitutes the object of scientific investigation, and that only it is ‘important’ in the sense of being ‘worthy of being known’. Max Weber
This is the Mandelbrot set. One of the most beautiful and remarkable discoveries in the entire history of mathematics. Yet it was discovered as recently as 1980 … This is going to change our view of the universe and give us a better understanding of its working. Arthur C Clarke, The Colours of Infinity, 1995
No matter how much we magnified it, a million times, a billion times, until the original set was bigger than the entire universe, we would still see new patterns, new images emerging, because the frontier of the M-set is infinitely complex. ibid.
It was not discovered until the era of modern computers. ibid.