Infinity cannot possibly mean what it suggests.
I often see people speaking of tangible things
has having the quality of 'infinity.'
Such as the universe, God..
Obviously I have no argument for infinity used in a strictly mathematical context or for infinity used figuratively, as an expression of incomprehensible enormity.
But infinity as used to quantify some physical measurement? Impossible.
First of all to even observe something infinite in order to measure it, you need an infinite amount of time. So assuming that you would be able to measure something as being infinite is necessarily presumptuous. Not only because the lifespan of a human construct is very small in comparison to eternity (infinitely small, actually), but because the point at which you finish measuring and can thus say "this measurement comes out to infinity" logically cannot come. I guess this is an ontological argument against the ontological validity of infinity.
Sure you can say, e.g., that an ohm meter
may measure infinite resistance. But it's only
reporting infinity because it's dividing the voltage it's trying
to push through by 0. It's expressed not directly as a
physical quantity, but in terms of a mathematical loophole.
Obviously this loophole arises only when we take zero to infinite precision. But can zero really be zero, as a physical quantity, to infinite precision? If it were truly zero then it couldn't be quantifying anything physical because that thing would not exist. This contradiction is probably incidental and circumventable, but not when you consider that measuring any value to infinite precision would not only require infinite time if it's supposed to correspond to something physical (and thus presuppose the existence of infinity in that respect), but also must presuppose that infinite precision even exists within the universe objectively. Sounds rather circular to me.. but hey, that's what infinity is, an infinite paradox. (As if there were any other kind.) Without a value to infinite precision (which is needed to mathematically derive an infinite quantity) being extracted directly from physical reality (as opposed to being constructed and originated within the context of a calculation, such as during division by zero) and plugged into a mathematical calculation, it is not justified to spit out an infinite quantity or a quantity to infinite precision and correlate it directly to physical reality as such.
When someone tries to prove infinity to me by
telling me to graph an equation approaching infinity, I lay the
burden of proof upon him and tell him to start graphing
and let me know when he reaches infinity.
Some people defend infinity by speculating that, wherever the edge of the universe is, there must be space around it, thus expanding the universe, and so on.. But this shows nothing other than an circular progression within the mind of the person making the argument. If such a person could just keep on speculating until he actually reaches infinite iterations, then I'd accept his logic..
Of course there are at least three other reasons this is invalid. 1. it's self-contradictory. Theyre projecting an absolute edge of space somewhere, and then saying it's not really the edge because there's got to be something outside of it. 2. Space is nothing in and of itself. it is merely a way of looking at things; a relationship among objects. Without objects to measure the 'space' between, one wouldn't even conceive of space. If you were an eye in an otherwise empty universe that saw blackness, you wouldn't think "I see space", you would think, "I see nothing." It's meaningless to say there's space outside the universe unless something occupies that space. So if the universe is infinite then it contains infinite mass, ergo infinite gravity. Or if not then at least it's logically impossible for us to know of it. And it's not possible to actually become directly aware of the universe from an outside perspective so as to justifiably conceive of space outside of the universe, because whatever is observing the universe from that point of view must be physical and part of the closed system and thus is itself an extension of the universe to that particular distance. 3. It's very possible that the universe is closed in four dimensions so that, in a sense, thinking you can travel to or beyond the edge of the universe is analogous to thinking you can walk to or beyond the edge of the earth. It just doesn't apply. This principle can apply in the time dimension too, in contradiction to those who extrapolate that time must have always existed or will always exist. Of course, so can the space is nothing principle. Time and space are analogous in that sense.
If an object of infinite mass existed, it would create a field of infinite gravity that would perpetuate infinitely throughout the universe and thus nothing could exist as it does.
If an object of infinite length or volume existed, we could logically never determine that it's infinite and speaking of the possibility of its infinity is about as relevant as speaking of another universe outside of this closed system, or of a nonphysical entity that is 100% disjoint with the physical and therefore cannot affect physical reality in any way.
If infinite precision existed, then Zeno's paradox would be completely valid and we would not be able to get from Point A to Point B in a limited timespan. People say one can get around that problem with calculus, but the fundamental logic behind it is undeniably valid. Math has simply been given ways to deal with its own inevitable construction of infinities. But plugging an infinite precision or quantity into math directly from physical reality and then spitting out a non-infinite quantity of non-infinite precision and correlating it to physical reality as such is just as invalid as the reverse. Therefore, since motion is possible, it must be invalid to presume that the infinity, or value of infinite precision used to derive an infinity, plugged into the calculation in order to collapse it, itself correlates with reality as such in the first place.
Richard A. Nichols III
see also: zErO, more on infinity and zero (brief/concise).