A Quote by Hermann Weyl
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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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.
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.
Nothing is more human than for man to desire naturally things impossible to his nature. It is, indeed, the property of a nature which is not closed up in matter like the nature of physical things, but which is intellectual or infinitized by the spirit. It is the property of a metaphysical nature. Such desires reach for the infinite, because the intellect thirsts for being and being is infinite.
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.
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.
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.
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.
Since infinity is by its very nature infinite, then enlightenment by its very nature is infinite, and thus can be experienced in infinite ways, by itself or without itself
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.
God is Infinite and His Shadow is also infinite. The Shadow of God is the Infinite Space that accommodates the infinite Gross Sphere which, with its occurrences of millions of universes, within and without the ranges of men's knowledge, is the Creation that issued from the Point of Finiteness in the infinite Existence that is God.
God is infinite; and the laws of nature, like nature itself, are finite. These methods of working, therefore, - which correspond to the physical element in us, - do not exhaust His agency. There is a boundless residue of disengaged energy beyond.
I was a mathematician by nature, and still am - I just knew I didn't want to be a mathematician. So I decided not to take any mathematics courses.
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.
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.
Man always worships something; always he sees the Infinite shadowed forth in something finite; and indeed can and must so see it in any finite thing, once tempt him well to fix his eyes thereon.
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