September 13, 2011 Comments Off on Infinity
This sign, or the Western graph for the number 8 positioned horizontally, is a sign to denote the idea of infinitely great or infinity, referring to distances or numbers. Sometimes the concept of infinity in mathematical systems is expressed by the sign . As far as time is concerned the most common similar medieval symbol is the snake biting its own tail, or the empty circle, . It is as if represents a double endlessness or eternity.
Infinity (symbol: ∞) is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity. The word comes from the Latin infinitas or “unboundedness”.
The infinite, as the word indicates, is that which has no end, no limit, no boundary, and therefore cannot be measured by a finite standard, however often applied; it is that which cannot be attained by successive addition, not exhausted by successive subtraction of finite quantities. Though in itself a negative term, infinity has a very positive meaning. Since it denies all bounds — which are themselves negations — it is a double negation, hence an affirmation, and expresses positively the highest unsurpassable reality. Like the concepts of quantity, limit, boundary, the term infinity applies primarily to space and time, but not exclusively, as Schopenhauer maintains. In a derived meaning it may be applied to every kind of perfection: wisdom, beauty, power, the fullness of being itself.
The concept of infinity must be carefully distinguished from the concept of “all-being”. Infinity implies that an infinite being cannot lack any reality in the line in which it is infinite, and that it cannot be surpassed by anything else in that particular perfection; but this does not necessarily mean that no other being can have perfections. “All-being”, however, implies that there is no reality outside of itself, that beyond it there is nothing good, pure, and beautiful. The infinite is equivalent to all other things put together; it is the greatest and most beautiful; but besides it, other things both beautiful and good may exist (for further explanation, see below). It is objected that, if there were an infinite body, no other body could exist besides it; for the infinite body would occupy all space. But the fact that no other body could exist besides the infinite body would be the result of its impenetrability, not of its infinity. Spinoza defines: “Finite in its kind is that which can be limited by a thing of the same kind.” (Ethics, I def. ii). If he intended only to say: “Finite is that from which another thing of the same kind, by its very existence, takes away perfection”, no fault could be found with him. But what he means to say is this: “Finite is that, besides which something else can exist; infinite therefore is that only which includes all things in itself.” This definition is false.
Many confound the infinite with the indeterminate. Determination (determinatio) is negation, limitation (negatio, limitatio), says Spinoza. Generally speaking, this is false. Determination is limitation in those cases only where it excludes any further possible perfection, as for example, the determination of a surface by a geometrical figure; but it is no limitation, if it adds further reality, and does not exclude, but rather requires a new perfection, as for example, the determination of substance by rationality. The mere abstract being, so well known to metaphysicians, is the most indeterminate of all ideas, and nevertheless the poorest in content; the infinite, however, is in every way the most determinate idea, in which all possibilities are realized, and which is therefore the richest in content. According to Hobbs, we call a thing infinite if we cannot assign limits to it. This definition is also insufficient: infinite is not that whose limits we cannot perceive, but that which has no limit.
Wújí (Traditional Chinese: 無極; Simplified Chinese: 无极) (literally “without ridgepole”) originally meant “ultimate; boundless; infinite”
Know whiteness, Maintain blackness, and be a model for all under heaven. By being a model for all under heaven, Eternal integrity will not err. If eternal integrity does not err, You will return to infinity. (Daodejing 28, tr. Mair 1990:93)
In ancient India and Tibet the infinity symbol represented perfection, dualism, and unity between male and female. In the occult tarot it’s linked to magic and represents equilibrium or the balance of various forces. The uroborus (a circular serpent biting its tail – a UN symbol for “Human Settlements”) has been found in this shape. In modern times, it became a secular mathematical symbol for infinity in numbers, time or space (eternity). Source
The eighth dynamic is the urge toward existence and survival as INFINITY. The eighth dynamic also is commonly called God, the Supreme Being or Creator, but it is correctly defined as infinity. It actually embraces the “All-ness” of All.
Sanatan Dharma ( Hinduism)
God as the infinite, endless, unlimited with respect to space and time.
I understand that Buddhist philosophy argues for an infinitely continuing (forward and reverse) state of existence, with no centre, nor any permanent entity underpinning it. There has been no creation. Nothing that does not exist can be brought into existence and nothing that exists can ever disappear into nothingness.
That’s pretty mind-boggling, yet the idea of infinity is happily taken on board by many religious and non-religious people. But when we speak of infinity we really, I suspect, are thinking only of a very long time or a very great expanse of space. I don’t think we can really handle the idea of infinity, of something that just goes on and on and on…… In infinity, after all, all things become possible – indeed, inevitable. So in an infinite universe there is an infinite number of exact replicas of yourself currently reading an infinity of thaivisa.com postings on Buddhism and Infinity.
The medieval Kalam school of Islamic philosophers rejected the idea of an actual infinity, thereby, though still leaving the questions of temporal and spatial boundaries open, getting rid of an unhelpful and distracting construct. But mainstream Islamic, Christian, Hindu and Buddhist philosophers, to my knowledge, retain the idea.
Is it helpful, though? Is it best left to Mathematics as a theoretically possible construct, but in the “real” world of physics and human destiny discarded as an unhelpful conundrum?
If it is retained, does it imply that we’re living in an absurd universe (or infinity of universes)? If it is discarded, what can we then say about boundless continuity of existence, without permanence or any fixed point we could call a centre?
I was thinking about this after reading the comments of Matthieu Ricard (the monk) in “The Monk and the Philosopher”. Also John Barrow’s “The Infinite Book: A Short Guide to the Boundless, Timeless and Endless”.