How long is the song 'aleph-1 green bottles, hanging on the wall'?

[jack]

Poll #14435 Aleph-1 green bottles

Open to: Registered Users, detailed results viewable to: All, participants: 12

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How long is the song 'aleph-1 green bottles, hanging on the wall'

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omega-0, songs are inherently sequential
1 (8.3%)

omega-1, one verse per bottle
3 (25.0%)

omega-3, because... fish?
1 (8.3%)

Something else
4 (33.3%)

What?
3 (25.0%)

Comments

[ptc24]

I think if you're trying to get one verse per bottle, then your song might have to be a continuum in order to sing it all in time. FSVO "sing" and "time", of course.

You could invent a language where you use a precisely-timed note to convey an infinite amount of information, that lets you get aleph-null verses out of the way in finite time. Possibly you could even invent a really freakish sort of sound wave, where the amplitude at each instant represents a real (and thus a block of aleph-null verses), and you don't have to bother about boring things such as finite frequency or anything like that.

[jack]

Oh, I see! Right, that makes sense. (Assuming you're not picky about the verses coming sequentially.)

I'd assumed that if anything, you'd imagine a "more infinite" timeline :)

But does CH make a difference? Isn't aleph-c always at least as big as aleph-1, just CH says not bigger?

[ptc24]

I was thinking that if aleph-1 < c then aleph-1 might be a bit more tractable, possibly you wouldn't need a continuum. Of course my ideas about such scenarios are deeply hazy.