A Quote by Galileo Galilei
The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
Related Quotes
The Infinite alone exists and is Real; the finite is passing and false. The Original Whim in the Beyond caused the apparent descent of the Infinite into the realm of the seeming finite. This is the Divine Mystery and Divine Game in which Infinite Consciousness for ever plays on all levels of finite consciousness.
When I speak of the aspiration towards the beautiful, of the ideal as the ultimate aim of art, which grows from a yearning for that ideal, I am not for a moment suggesting that art should shun the 'dirt' of the world. On the contrary! the artistic image is always a metonym, where one thing is substituted for another, the smaller for the greater. To tell of what is living, the artist uses something dead; to speak of the infinite, he shows the finite. Substitution... the infinite cannot be made into matter, but it is possible to create an illusion of the infinite: the image.
In this external world, which is full of finite things, it is impossible to see and find the Infinite. The Infinite must be sought in that alone which is infinite, and the only thing infinite about us is that which is within us, our own soul. Neither the body, nor the mind, nor even our thoughts, nor the world we see around us, is infinite.
More simply said, the finite does not add to the infinite but merely expresses the power of the infinite in a limited mode.
If you reject the infinite, you are stuck with the finite, and the finite is parochial... the best explanation of anything eventually involves universality, and therefore infinity. The reach of explanations cannot be limited by fiat.
The individual soul touches upon the world soul like a well reaches for the water table. That which sustains the universe beyond thought and language, and that which is at the core of us and struggles for expression, is the same thing. The finite within the infinite, the infinite within the finite.
What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.
To meditate with humility, consider existence. It is infinite. You are finite. You are a finite portion of infinite existence. Let this be your meditation.
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.
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.
The infinite being has assumed unto himself the mystery of finitude. And in him who is love the finite and the infinite are made one.
There are at least two kinds of games. One could be called finite, the other, infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.
Far be it from us to doubt that all number is known to Him 'Whose understanding is infinite' (Ps. 147:5). The infinity of number, though there be no numbering of infinite numbers, is yet not incomprehensible by Him Whose understanding is infinite. And thus, if everything which is comprehended is defined or made finite by the comprehension of him who knows it, then all infinity is in some ineffable way made finite to God, for it is comprehensible by His knowledge.
There's always going to be one more thing. Because that's what infinite feels like. And the difference between love and everything else is that it's infinite, it's built out of something infinite, or it feels like it is, anyway, which is the same thing to us. You think a million billion more things will come your way, a million billion more versions of everything. But no, everything that actually causes that infinite feeling, the circumstances of every infinite feeling, is so, so finite.
No contradictions will arise as long as Finite Man does not mistake the infinite for something fixed, as long as he is not led by an acquired habit of mind to regard the infinite as something bounded.
Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory.
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