The infinity of Pi: an analogy
My theistic debater acquaintance, MG, from elsewhere, who just doesn’t accept the concept of a temporal infinity[#] (whether linear or circular, whether with cyclical events) on the basis that “Now” cannot be reached either from the starting point of an infinite past or by going backwards from an infinite future. I would argue that the everyday concept of mathematical Pi questions MG’s claim.
[#] Despite the fact that theists accept the concept that God is an eternal being without beginning or end.
[Note: I debated with MG the reason I think that there is a temporal infinity and as such any specific happening would have to ultimately repeat. I often used the analogy of walking around a sphere an infinite number of times and thus repeating being in a specific location at a specific “Now” or approaching “Now”. MG responds… ]
MG – “There is no reason to think that a repeating pattern will emerge. Just think of numbers like pi (an infinite set of numbers that never repeats or demonstrates any cyclical pattern).”
JP – Even on Pi you will find repetitive patterns. How many times will you find, say, 27, 33, 42, or 007 within the sequence Pi? Every time you find, say 42, it’s a repeat of the first 42! Even the number “4” is a single event that repeats randomly. In fact, you could think of Pi as a series, not necessarily in sequence, of ten separate ‘events’: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Nice try!
MG – “Even if it were repeated over and over again, it would still be true that it had been repeated a certain number of times. If that number is infinite, then a truly infinite number of events had to go through before the current one for that particle, and we are back in the same contradiction”.
JP – Go back and reread my analogy with the sphere and how you can go round and round an infinite number of times, participate in an infinite number of events, and still be within the distance of “The Present Moment”.
MG – “Pi can have the same number, but not in any CYCLE PATTERN.”
JP – And I said exactly that! Reread my post.
MG – “You were wrong about this. Admit it and move on.”
JP – I do not admit such a thing! The infinity of Pi (ah, you’ve admitted an infinity) is made up of a finite number of individual numbers (0 through 9). That’s a good analogy for there being an infinite number of individual finite events. Note that I have always said that infinity consists of an infinite number of finite events. You are just one finite event in a sequence of infinitely many finite events and collectively that is what infinity is. Going back to the Pi analogy: the number 4 is a finite event (as you are a finite event) within the infinite sequence we call Pi. The finite number 4 occurs an infinite number of times in the sequence we call Pi. The number 4 is therefore infinitely cyclical within the sequence Pi, but the number 4 itself does not have any specific cyclical pattern within the sequence Pi.
MG – “And as long as 4 does not present a cyclical regularity in pi, then pi counts as a complete counterargument to your cyclical time argument (for which you presented zero evidence).”
JP: As long as the 4 appears over and over again, either in an irregular pattern or a regular pattern, and as long as the 4 represents some kind of event, then translated into a cosmic setting, that event has happened again. and again.
Discussion:
*MG argues for an absolutely temporal finite Universe that required an actual creation and therefore a creator, and therefore God exists and God made him. However, perhaps even a finite Universe is infinite. By analogy, Pi has a finite beginning but apparently has infinite duration. Or, even if Pi eventually repeats or reaches finality, there is 1/3 that also has a finite beginning but is also infinite in duration. Therefore, even if our Universe had a finite beginning, it is still infinite if it does not have a temporary end.
*It would take you a temporal infinity of time to compute the entirety of Pi, but in attempting to do so, you would be SOMEWHERE within the sequence at any given moment, a moment you would call “Now”. In other words, you could have started time travel from an infinite amount of time ago and still be at a point we call “The Present Moment” or “Now.”
*Looking Infinitely Ahead: Let’s say for the sake of argument that the “Looking Infinitely Back” issues have been resolved in favor of MG. That is, the Universe had an absolute beginning a finite amount of time ago. Now there are the “Looking Infinitely Ahead” versions of the problems to be solved.
But doesn’t the issue of not being able to go from an infinite past to “Now” also work the other way around? Presumably, if he starts traveling, even mentally, back from an infinite future, he wouldn’t be able to travel back in time to get to “Now” either. This is relevant because as Pi [#], we have a finite beginning but, according to theists, we have eternal ‘life’ or eternal ‘life’; eternal ‘life’ or eternal ‘life’ in the afterlife. So how do you get back to “Now” from the infinite future? So, theists have the same infinity problem only in reverse.
[#] I’m not quite sure how you can have a one-sided infinity as in an infinite past that ends, or a finite beginning that never ends. However, Pi has a finite beginning but an (apparently) infinite ‘end’.
*If you can really have a one-sided infinity as at creation, thus an eternal ‘life’, or Pi, then you can logically have an infinite ‘beginning’ or a ‘beginning’ an infinite amount of time ago, and an end finite, or in other words what you can refer to as “Now”. If one, then the other. If the other – finite principle; infinite ‘end’ – then something can experience infinite time travel and arrive at the ‘Now’.