Interseting side note: Since the process of creating the infinitely large stone is defined solely by the concept of endlessness--it doesn't matter how rapidly God increases the size of the stone. If could increases it [1foot every second] or [1 inch ever million years] and in both cases the stone is equally infinite, because they will both continue to increase in size forever. However,
if we had two Gods who each chose to demonstrate their infinite powers by creating infinite stones, the God who was creating the [1foot every second] stone would probably impress a lot more of the [finite beings who happened to be watching the contest], than the God who was creating the [1 inch ever million years] stone. But would it be correct to say that the first God was truely demonstrating greater omnipotent power?
It seems to me that the answer is yes, but only if both Gods are actually competing to see which is the more powerful, and thus increasing the stone as fast as they can. But if this were true it would imply that they were no longer omnipotent--because there would be a limit on how fast they can increase the size of the infinite stones they are creating. If they are truely omnipotent, and there is no such limit, then we must assume that they are creating the infintely large stones at the rate of growth they have chosen because... well, because they have so chosen.
The fact that one God's stone is bigger at any given point in time says nothing about their infinite might, because over time both God's stone will become infinitely big. So no matter how much larger the quick-God's stone is--the slow-God's stone will eventually become just as large--although obviously by then the quick-God's stone will be much larger still. It makes a kind of sense, then, to suggest that the quick-God is progressing towards the concept of infinity faster than is the slow-God.
Removing Time
Actual Infinity is defined by endlessness--meaning that it is an endless process. But is there a
potential infinity--meaning one that is actually complete--and what characteristics would it have? The way I see it, with respect to the discussion of our current riddle, the potential infinity is that which will be--all the will be's that ever will be, condensed down into a single [now]. Obviously, what we have done is to [remove the concept of time] from the equation.
By doing so, however, we have necessarily changed what is vague about infinity. The [infinity that contained the process of time] was
temporally vague--because it was spread out over time--while having a very specific (i.e. infinitely precise) size at each specific point in time. When we remove time, what we are doing is to collapse all of those [sizes of the stone] down into a single [infinitely small point in time]. Thus, the size (or mass) of the stone has now become vague.
Mass occupies space--so we can see that infinity is fundamentally rooted in Einstein's parameters of Space and Time. We can choose to think of infinity from either of these apparently incompatible perspectives--but true infinity is equally defined by both.
It is worth noting that the [concept of progression] is still maintained, because the possible sizes of infinity that are contained in the now, are still [1 inch increments]. If we created a series of all the sizes of infinity--existing in the now--there wouldn't be any [steps of 1/2 inch].
What is interesting to note is that, since both Gods were increasing by [1 inch increments] a [timeless evaluation of their progress towards an infinitely large stone] would appear to be identical. Both God's would create exactly the same [sequence of stones with magnitudes that stepped up in one inch increments]--there would be no difference in size becasuse every stone that they would create over the endless stretch of time would become actualized in the temporal now; and we've already established that every stone size the quicker-God created woudl eventually be created by the slower-God. So without the reference of time--the speed at which they create is irrelevant.
But if one of the Gods had been increasing their stone by [1 inch every minute] and the other by [1 foot every minute]--then when we got rid of the temporal aspect, there would still be a difference in the sequences of stone sizes. In fact, there would be 12 size entries for the slow-God for every 1 size entry by the quick-god. So, once again, it would make sense to say that one was progressing towards infinity faster than the other.
