It is my belief that the infinite series may have much in common with Father Christmas. Impostors appearing in his guise are commonplace, but who can claim to have seen the real thing?
In general, infinity is a very abstract concept and it’s hard to relate it to practical or observable physics or reality.
In previous posts, I have implied that mathematical infinities can be applied to physical reality especially if some normalization is performed. On another thread, I was beginning to do this normalization through quantization (Planck Limits as a function or conversion.)
One aspect of this type of infinity is that you are dealing with the infinitely small/large or infinitely short/long or infinitely light/heavy.
To me, infinite series is a different animal. This application of infinity is much more difficult to relate to in practice. For instance; it is difficult to even find ways that this is used outside of mathematical (abstract) realms.
I found out that it is used in jpeg compression which surprised me because I always thought it was another more common technique that was being used. Apparently by storing the first few numbers of an infinite series, it can be used to restore “infinite” detail (a.k.a. fractal). Common sense tells me that this potential is still limited or quantized at the last step.
I found another physical application that seemed more useful: A bouncing ball. Forgive the pun but; this is more fun to play with. I think that it’s interesting to compare a bouncing ball on Earth to bouncing universes. On Earth, there are probably very few people that believe that the ball bounces forever while conversely, perpetually bouncing universes don’t put a strain on the senses.
I invite correction on the following: The Earth ball’s sequential repetitive cycles are reduced primarily by friction (molecular level collisions). To a lesser extent it is also reduced by heat generated with its repetitive collisions with the Earth…but these are merely the reducing agents. Friction will not suspend the ball in midair. I don’t think that the bouncing continues on down to a Planck level but I think that it is pretty close to a quantum level. Although I’m not prepared to declare exactly what happens just prior to the resting point; I do believe that something succeeds in bringing it to a halt. For all I know; maybe it’s ionic bonding at a molecular level. The most important aspect is that the ball comes to a rest. Bouncing universe, devoid of any losses probably results in a physical infinite series: (the incremental count of successive cycles).
Basically, I am trying to "prove" that; in at least one instance, finite is compatible with infinity in a possible physical reality.
However, I think that there are two instances: a quantized finite present is compatible with eternity.
