manfred

Even in your example, infinity is just a concept - you can't really do anything an infinite number of times. Think about the act of actually doing it: after each act, your count will be finite. The use of infinity here is just a thought experiment; such thought experiments are useful in mathematics (such as determining limits - as you are doing here, or developing proofs by induction) - but does not map into reality.

The counter reflections are not infinite. Each is dimmer than the previous, because only a portion of the light is reflected each time. It eventually dims to nothing. I believe infinity is a valid and useful mathematical concept, but it is an abstraction that doesn't map directly into reality. For example: take one meter stick. In concrete terms, it can be divided into 100cm, 1000mm, 1,000,000 microns etc. In abstract terms, it can be said to consist of an infinite number of points. But a "point" is a concept of a dimensionless thing, which is not a real entity. You can't arrive at a point by successive division - there is always a finite length. You can't map points into reality, except in the mind. Nevertheless the concept of points, and of infinity, is useful because of the mathematical tools - such as calculus, which effectively utilizes these concepts. But it's an abstraction, not concretely real. Merged post follows: Consecutive posts merged Infinite is a generic term that can apply to anything. Eternal refers to infinite time. Eternity usually refers to an infinite past and infinte future, but in some contexts may refer to only one direction (past or future). This is an abstraction. You cannot map the elements of this set into concrete reality.

I realize "today" is a floating concept. Let me get more precise: I am breaking down time into discreet, measurable intervals and labelling them on a number line that stretches into the past (it also stretches into the future, but that is irrelevant). Replace "today" with t=0. the prior discrete interval is t=-1, etc, stretching into the infinite past. The argument is irrespective of the length of the interval, but using "day" is intended to help us visualize. Incidentally, this is just a variation of the Hilbert paradox.

A related question is: can the universe be infinitely old? Of course, if you believe the big bang is the absolute beginning, there being no predecessor event that caused the big bang - then you'll agree it has a finite age. Same if you believe in GOD. But some people propose that as an alternative to an eternal God, there is an eternal universe. The big bang could have been preceded by a big crunch, or the big bang was a 4 dimensional manifestation of a multidimensional entity. So in these types of scenarios, the universe (in the broadest sense: everything that exists) could be infinitely old. But I argue that the universe cannot be infinitely old. If it were infinitely old, we would never arrive at TODAY. Imagine "today" to be represented by a man who is waiting in a line to check into a hotel (one with an infinite number of rooms, of course). The line in front of him is infinitely long (there are an infinite number of days before him). No matter how many people check in at the front of the queue, the queue remains infinitely long (infinity -1 is still infinity). Hence, we never reach today. Therefore the age of the universe can't be infinitely old.