RE: Thinking about infinity
April 28, 2016 at 4:14 am
(This post was last modified: April 28, 2016 at 4:21 am by Ignorant.)
(April 27, 2016 at 12:10 pm)robvalue Wrote: Yes, if it could be divided up infinitely in reality, it would be a finitely "long" object, which could be made up of infinitely many parts of increasingly small lengths.
Of course, where you make the cuts is arbitrary, and it remains the sum of those parts whether or not you actually cut it. It's another way of viewing the same object.
In the same way: when you walk a metre, how many times have you passed the halfway point, if we recalculate it every time we reach that point based on the remaining length?
Right, I think this is one of Zeno's paradox's (or at least similar to it). I think it serves as a good example. The process you describe can proceed with an infinity of recalculations. So here's a few questions to consider:
Does/Can the infinity of "halfway points" actually exist as a reality on the length of one meter (somehow simultaneously "making up" the length of the meter, or do they exist notionally as a geometric series represents one which can always be added to, or like the coastline problem explained above)?
Consider a "reversal" of the recalculation. Could you ever "begin" to walk at all if your first distance you must pass is the infinitely smallest halfway point? <= Is that even logically coherent?
