An exercise in triviality.
I have been exercised of late by the use of “infinite” as an adjective and came to the conclusion that “infinite” should only be used to describe the unboundedness of things capable of being counted or measured (quantifiable or countable things). So, I reason, the number of terms in a numerical series, or physical things, or length or mass or time could be described as being “infinite”, because they could also be “finite”. The use of “infinite” to describe something qualitative which could never be finite was therefore illogical. (Not “wrong” but illogical because I take the position that no usage is ever “wrong” if it communicates what is intended to be communicated). But my “rule” is that “infinite” is usable only for things which must first be “finite”. Therefore “boundless” or “endless” should be more appropriate for non-quantifiable things. So “infinite sky” or “infinite space” would be better described as “endless sky” or “boundless space”. “Endless lines” not “infinite lines”, but “lines of infinite length”.
Georg Cantor even imparted qualities to “infinite”. Cantor described “cardinalities” of the infinite for different sizes of infinite sets. Of course, there are then an infinite number of cardinalities. He considered integers as being countably infinite, but he took the infinite set of real numbers – as being capable of being counted – but uncountable. But Cantor’s uncountable, various cardinalities of the infinite still apply only to quantitative things.
Early Indian mathematics distinguished between endless and innumerable and tried to classify infinites by considering loose bounds and rigid bounds:
…… two basic types of infinite numbers are distinguished. ……. a distinction was made between asaṃkhyāta (“countless, innumerable”) and ananta (“endless, unlimited”), between rigidly bounded and loosely bounded infinities.
In the hierarchy of words therefore I take “boundless” to be applicable to all things whereas I take “infinite” to apply only to quantifiable things.
But what happens now to “infinity” as a noun?
As a noun we give “infinity” many meanings. First as the quality or state of endlessness (limitlessness, boundlessness) and second as the number which is larger than any other and always larger than anything conceivable (∞). We therefore refer to the infinity of space or the infinity of meaning or the infinity of the stars. And in mathematics, ∞ is treated as a number (albeit with rather special properties) and can be used in mathematical operations as a number. But there is a third meaning or usage. We also use “at infinity” or “to infinity” as if it were a place. “Parallel lines meet at infinity”, we say in plane geometry. In calculus we speak of “limits at infinity”. We speak of points, planes and lines “at infinity” in projective geometry. The universe ends “at infinity”.
OED:
infinity (n.) late 14c., from Old French infinité. “infinity; large number or quantity” (13c.), from Latin infinitatem (nominative infinitas) “boundlessness, endlessness,” from infinitus boundless, unlimited” (see infinite). Infinitas was used as a loan-translation of Greek apeiria “infinity,” from apeiros “endless.”
infinite (adj.)late 14c., “eternal, limitless,” also “extremely great in number,” from Old French infinit “endless, boundless,” and directly from Latin infinitus “unbounded, unlimited,” from in– “not, opposite of” (see in- (1)) + finitus “defining, definite,” from finis “end” (see finish (v.)). The noun meaning “that which is infinite” is from 1580s.
To be finite is the opposite of being infinite. Infinity as a number, ∞, has mathematical zero as an inverse but ∞ when considered to be one end (?) of an endless series has -∞ at the other end. But what happens “at infinity”, where parallel lines meet and the universe comes to end. Most of the universe consists of apparently empty space, interspersed with sub-universes, galaxies, stars and star systems. But this space is not nothing. The space between electrons orbiting around the nucleus of an atom is not nothing either. These spaces may not contain matter but they still have attributes and properties. Gravity waves and magnetic waves can traverse them. Light – whether a wave or not – crosses them. Time exists within them. And with light traversing and a time interval, distance must follow. Space, therefore, has dimensions. And since we infer that some magic mass we call dark matter, and some magic energy called dark energy, abound, space also permits/allows/has dark energy and dark matter.
An infinite universe extends “to infinity”. Obviously it has to be nothing which lies beyond. And it is the properties or attributes of this “nothingness” which boggle the mind.
Clearly “empty” space does not serve as an illustration of the nothingness beyond. (It is not space I am told but space-time, where we can observe space as time passes but cannot observe time as space passes). A vacuum, anywhere, is void of matter but otherwise has the attributes of space and does not serve either. Even the Buddhist concept of emptiness, shunyata (Sanskrit where shunya = zero), is not entirely devoid of thought. We cannot say that light does not traverse nothingness because opacity to light would be an attribute. So would the non-passage of gravity waves through nothing also be an attribute. Time does not pass within nothingness. Time, in fact, cannot exist. Dimensions are undefined. No energy, no mass and not even any magic dark energy. No Laws of Nature. Nothingness cannot be imparted with any attributes or properties since then it would no longer be nothing. In fact, nothingness – by its very nature – must be incapable of being demonstrated, illustrated or even conceptualised.
Tom Mason commented on my previous post:
The universe is as it is, there is no boundary no edge. Also the so called expansion (or maybe it’s contraction) of our universe is not real — it is just a readily seen quirk due to the passage of time varying across the universe. The variation that is evident with the universe’s apparent smallness of its beginning and the apparent largeness of now.
And so I end with a circular and trivial argument and I have no better perception of nothingness:
“Nothing” is no thing – neither physical nor abstract. It cannot be conceptualised without becoming some thing. It has no properties and no attributes. No thing is nothing. Therefore nothing is no thing.
Except that nothing can exist beyond infinity and this nothing cannot even contain nothingness.
