
Balls In Barrels - fun with infinity - ColinWright
http://www.solipsys.co.uk/new/BallsInBarrels.html?HN0412
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mankyd
"Case 1 says it might be infinitely many, case two says it might be none."

What? Case 2 says that all the balls will be put back in. In both cases, there
will be infinitely many balls back in the barrel after midnight.

~~~
ColinWright

        Article: "Case 1 says it might be infinitely many,
                  case two says it might be none."
    
      > What? Case 2 says that all the balls will be put
      > back in. In both cases, there will be infinitely
      > many balls back in the barrel after midnight.
    

Yes, and in case 2 there will be none outside, which is what's being asked.

Quoting more completely:

    
    
        How many are outside of the barrel after midnight?
        We can't tell!
    
        Without being explicit, without actually naming the
        balls and saying which ones are being removed and
        replaced we simply cannot tell. Case 1 says it might
        be infinitely many, case two says it might be none.
    

Case two has all the balls in the barrel after midnight. That means there are
none outside, which is what's being asked.

Or have I misunderstood you?

~~~
mankyd
Ah, my mistake, you are correct. That being said, the example has another
flaw: it is based on completing an infinite number of finite time tasks in
finite time. That is to say, adding and removing an infinite number of balls
will take an infinite amount of time, but we're only given an hour to do it
in.

Note that this is different from Zeno's paradox, wherein the two racers each
have to move an infinite number of ever decreasing distances in ever
decreasing time (as opposed to constant amounts of time).

~~~
ColinWright
That's covered in the first part, where it defines an infinite sequence of
time stamps leading up to midnight. It assumes each task can be completed in
half the time of the one before, but if you're going to argue about that then
don't bother thinking about infinity at all.

