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This isn't a post about simulation hypothesis as some of the others.   This is simply a post to share some of the things I am currently thinking about the concepts of "infinity" and I haven't quite come up with any stable concept yet.    So you are getting these ideas literally within moments of when they first appeared on the drawing board of my mind.

We know of infinite constructs and they occur quite often in math with things such as the Fibonacci Sequence, Fractals, The Mandelbrot Set, the digits of PI, infinitely repeating decimal representation of some fractions, etc.

This can lead us to view most things as a representation of infinity.

We often can fall into the assumption that because, such unbounded numbers can exist that reality itself likewise must have no boundaries.    How can we represent a boundless number within a reality that has constraints?

There are some things to consider from this and like I said I am doodling around in my mind with these concepts right now.

What if the assumption that there are no bounds/constraints to reality is false?

This would not stop one from expressing numbers that appear to be endless.   The process of finding these successive digits in an endless number is actually quite simple math.   In fact all one needs generally is the rules and the previous number.   In some cases it might be a couple of the previous numbers or digits.

With that input you can create a cycle that effectively has no end, even though it is occurring within a constrained environment.

With this I posit that the existence of infinite constructs does not disprove the possibility that something has constraints.

We also cannot assume because we have not seen an end of the actual physical representations that there is no such end.   We can speculate that this might be true, yet if we do not encounter the end that does not mean there is not one.

The only thing we might be able to actually prove is that there is an END.    Because if there is an END then theoretically it is reachable.    If there is not an END you'd never know for certain as you simply may not have traveled far enough.

Yet the interesting thing here is that it is possible to represent infinite concepts in math within a constrained system.

I've stated the only thing limiting it in a computer is the amount of memory available to store the digits.    This number with our current capabilities would be vast beyond our imaginings.

However, there actually is no such constraint.    You cannot view all of the digits at once your mind simply cannot handle that, so in reality the computer need only display what you can perceive and you'd click NEXT or something to get the next set of digits.

A computer effectively could be designed to do this infinitely even though it be constrained by its memory limitations.   The only eventual failure would come with hardware or some other failure which might even be able to be repaired and continue.   So Time is the only true enemy here, not the infinite or not infinite nature of any constraints/borders.

What the computer would do would be no different than a mathematician calculating the next digits by hand.   It simply would be far faster.   So you could take the computer out of the equation and have a monastery full of  monks dedicated to providing the next digits of PI, or Fibonacci sequence, etc.

They could go on for infinity as long as a monk remained to do the job.    This would be true even if the monks themselves were in a constrained environment.

***Chew on that for a bit...  That's what I'm doing too...***

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