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...
Steem On!
Love this post. :-) A simple question that has come up many times with regards to infinity is that, if the universe is infinite, then the sky should be lit with all stars, should be not dark but alit with all stars and objects of the cosmos. Some scientists pose that this is proof that there was a big bang, a singularity, that is forever expanding, but stilll...infiinity would cause everything to have already existed, to make our night as light as our day. Perhaps we are on the "big crunch" event already, just not realizing it.
Infinity is fun, and the deeper you get into mathematics, the more fun it gets. There are concepts of different "sizes" of infinity, different "types" of infinity, and all sorts of other weird things.
Here's another thing that fits in your framework that you didn't mention: draw a line on a sphere that meets itself on the other side, like the equator of the Earth. Start walking on that line. It has no start, no end, and if you walk on it at a constant speed, you'll be walking for an infinite amount of time. You'll never reach the end. Does that imply that the line is infinitely long? Does it imply that the sphere is infinitely large? Clearly not the latter.
If you abstract this to one higher dimension, you could imagine that straight lines in the universe "wrap back on themselves" eventually as well. Just because you could travel in a straight line forever and not hit a wall does not imply that the universe is infinitely-large.
For the past 8 months I've been thinking about writing a series on infinity. Maybe now I'll have some motivation to make it happen...
Nice reply. I like the sphere example. That is another example of an infinite system that is not difficult to simulate. It was being told I couldn't deal with infinity in a simulation by someone and then them leaving before I could explain how that inspired this recent rash of posts. :)
(nom, nom, nom)
Clears throat...
Ok @dwinblood
"time" is the one thing that so far CANNOT be stopped!?
That's what I have been told. So I do want to help preserve "it"as best as I can. Now I am typing off the cuff as well so please bare with me. I like what you had to say about the monks. Now I am not a "REAL" monk at least not that I am aware of. However your "written words" are "IMPORTANT" to me and have successfully constrained me to this Steemit environment as if we were "both" monks just doing are jobs...
(passes the popcorn to Deva)
We are the monks of Fibonacci and Pi
Our job is to make sure the end is not nigh
Without Time there can be no action. For all action is related to Time in some way. So if Time stops, so too would action. This is how it seems to me. Now jumping back to the other posts... if this were a simulation then perhaps it could be paused, yet to those of us in the simulation we would never perceive such pauses as the perception of things is an action, and with time stopped there is no action. :)
(we might be attracting more monks and awakening minds who might be biting off more than they can chew, but I have taking my share of bites, so it's ALL good...let's continue! [unpause] )
The first few weeks of me discovering Steemit in 2017 let's just say I did not hit the pause button!!! Reading and Navigating my way through the platform for days upon days non stop upvoting, resteeming, posting, commenting, replying, etc...
Coffee was my fuel! I was like a brand new "code" released into the mainframe with plenty of "bytes" testing the parameters, boundaries, and borders without much constraint but my limitations to memory and my physical body being drained and consumed needing to [pause] sleep...
(fragmenting\defragmenting\processing\rebooting)
Ok!
Now where were we?
"if this were a simulation then perhaps it could be paused, yet to those of us in the simulation we would never perceive such pauses as the perception of things is an action, and with time stopped there is no action. :)"
Aaaaand ACTION!
[NEXT]