Something I've found interesting for the past few days (and off and on again before that) is the question of whether (and in what direction) time is infinite. In attempting to answer this question, both in religious discussions and philosophy classes, something interesting has come to my attention.

I always figured that time must be at least measurable in some small sense, at least its parts. For instance, it has been less than a minute since I started writing this post. "Less than a minute," defined more clearly, would be a great example of a finite period of time.

Time is full of these. In fact, you might say that the whole of time is composed of such finite parts, and therefore must itself be finite. Otherwise, to traverse the time from 1pm to 2pm, you would have to go through an infinite stretch of time, since infinity divided by anything is still infinity.

To put it differently, for time to be infinite, any smaller part of it would also have to be infinite, since infinity is indivisible.

However, it was pointed out to me recently by a math-loving friend of mine that there is such a thing as a "countable infinity," parts of which may in fact be finite without negating the fact that the whole is infinite. His example was the Fibonacci sequence, but since I don't know what that is, I will instead use "the set of all whole numbers" as an example. There is an infinite number of whole numbers; you could never count them all. And yet you can count some of them: for instance, "the set of all whole numbers from 1 to 5" (which of course, has five and only five members). This latter set is, undeniably, part of the former set; yet in this case, the part is finite whereas the whole is infinite.

Yet there are, of course, uncountable infinities. For instance, "the set of all numbers" is uncountable both in regard to its whole and in regard to its parts, since "the set of all numbers from 1 to 5" is still an infinite set (you can always divide it into smaller parts). Of course, "the number 5" is a part of "the set of all numbers," and so even here you can break the infinite whole into finite parts. Each finite number is a part of the infinite "set of all numbers." Still, the number of numbers in any segment of the set is infinite, and uncountable...you can only resolve this set to particular numbers, or points of the set.

This leads to a paradox when we move from numbers to time. Is time more like the set of whole numbers (divisible into certain finite segments), or the set of all numbers (divisible into certain finite points)? Or is it like neither, being completely irresolvable into individual moments, always divisible by a greater number? If it is, then my original criticism stands: how can you traverse an infinite number of moments in what is apparently measurable as a finite time? Because if time is infinitely divisible into smaller and smaller infinities, then the span of time from when I began this post to the present moment is both infinite and finite...five finite minutes, each full of infinity.

All that to say, I haven't really answered my question. Have a great day everyone!