On Tue, May 4, 2010 at 12:44 AM, Brent Meeker <meeke...@dslextreme.com> wrote: > I notice I didn't respond to your first question in this post. So... >
I appreciate the response! >>>> On 5/3/2010 7:41 PM, Rex Allen wrote: >>>> So, given eternal recurrence, there are an infinite number of Rexs. >>>> And an infinite number of not-Rexs. Let's pair the Rexs off in a >>>> one-to-one correspondence with the not-Rexs. Then, let's go down the >>>> list and put an "A" sticker on the Rexs. And a "B" sticker on the >>>> not-Rexs. Then lets randomly arrange them in an infinitely long row >>>> and select one at random. What's the probability of selecting a Rex? >>>> What's the probability of selecting an "A" sticker? >>>> >>> >>> I suppose your intent is to assign equal measure to each position on >>> the list so, for any finite subsection of the list the measure of As >>> and Bs will be equal. >>> >> >> If that was my intent, what would your response be? >> > > The usual way of dealing with "infinity" is to use a measure that works for > finite cases and converges in the limit as the number is arbitrarily > increased. Notice that there is no way to "randomly arrange" the infinite > sets, except by some process that "randomly" selects elements and places > them on the list. So you're really back the generating frequency. Okay, so this is my point. So let's say we use a process to randomly distribute our newly-stickered Rexs and not-Rexs so that they are randomly arranged according to sticker-type. Even though we have now rearranged them...these are still the same Rexs and not-Rexs we started with when they were randomly arranged according to the 6-sided die. We haven't changed the relative number of Rexs and not-Rexs, we've just labeled them with an extra property and then rearranged them according to that additional property. They retain their original properties though. So, we still have a countable infinity of Rexs, and a countable infinity of not-Rexs. Who can be placed into one-to-one correspondence. SO...what difference does the "measure" make when deciding, as Carroll put it, "which infinity wins"? What does winning mean in this context? Okay, the not-Rexs have a greater frequency, but so what. They still don't outnumber the Rexs. Frequency seems like an arbitrary definition of "winning". Cardinality seems like the correct measure to decide who won. At least in the case of Rexs and not-Rexs, as well as with Boltzmann Brains and Normal Brains. The only way for the not-Rexs to "win" is to not allow the "eternal" part of "eternal recurrence." To keep it finite, where they win on cardinality. At the very least it seems like a defensible position...? -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.