Earth is Probably Unique

[JimC]

Mathematicians can have a great old time with infinities.

Physicists invoke them at their peril.

[Brian Peacock]

Yeah, Hibert. As in Hibert's Grand Hotel - a hotel with infinite room that were always fully occupied. When a weary traveller arrives at reception one day in dire need of a room the manager, a quite brilliant man, says, "Of course sir, it will take but a moment to arrange" and he goes off to asks the person in room 1 to move to room 2, and the person in room 2 to move to room 3, and the person in room 3 to move to room 4, etc etc etc etc (an infinite number of times). The weary traveller is both pleased to have a room and to have been so fortunate to happen across such a marvellous manager. Later that day a rather flustered tour guide hurries into the building needing rooms for an infinite coach party of America tourists, to which the manager replies, "No problem sweet cheeks, it will take but a moment to arrange," and he asks the person in room 2 to move to room 4, the person in room 3 to move to room 6, and the person in room 4 to move to room 8, and each person room n to move to room 2n, and so on, until an infinite number of rooms become available.

It's just quirky way to explain how the idea of an infinite number being the largest possible value, or a value at all, is the wrong way to think about infinity.


So if the monkeys haven't come up with the complete works of The Bard after infinite attempts/time you can just ask them to continue and check back after infinite x 2 attempts/time, and so on and so on and so on (an infinite number of times). I still worry about al that monkey poop though.

[JimC]

I'm sure it's Hilbert...

[pErvinalia]

Yeah, Hibert. As in Hibert's Grand Hotel - a hotel with infinite room that were always fully occupied. When a weary traveller arrives at reception one day in dire need of a room the manager, a quite brilliant man, says, "Of course sir, it will take but a moment to arrange" and he goes off to asks the person in room 1 to move to room 2, and the person in room 2 to move to room 3, and the person in room 3 to move to room 4, etc etc etc etc (an infinite number of times). The weary traveller is both pleased to have a room and to have been so fortunate to happen across such a marvellous manager. Later that day a rather flustered tour guide hurries into the building needing rooms for an infinite coach party of America tourists, to which the manager replies, "No problem sweet cheeks, it will take but a moment to arrange," and he asks the person in room 2 to move to room 4, the person in room 3 to move to room 6, and the person in room 4 to move to room 8, and each person room n to move to room 2n, and so on, until an infinite number of rooms become available.

It's just quirky way to explain how the idea of an infinite number being the largest possible value, or a value at all, is the wrong way to think about infinity.


So if the monkeys haven't come up with the complete works of The Bard after infinite attempts/time you can just ask them to continue and check back after infinite x 2 attempts/time, and so on and so on and so on (an infinite number of times).

No one is debating that. You don't need to conceptualise infinity as a finite number to understand the probabilities involved and know that you can't be certain that the monkey (or monkeys, as long as we are talking about a finite number of monkeys) will ever output Shakespeare no matter how long you give them.

[JimC]

Give me a googleplex of monkeys typing for a googleplex of years, and I'm morally certain they will produce the entire posting output of Rationalia!

And, they'll also give a final assessment of what it actually tastes like!

(faintly of bananas is my bet...)

[Brian Peacock]

I'm sure it's Hilbert...

Oh 'ell.

[Brian Peacock]

Yeah, Hibert. As in Hibert's Grand Hotel - a hotel with infinite room that were always fully occupied. When a weary traveller arrives at reception one day in dire need of a room the manager, a quite brilliant man, says, "Of course sir, it will take but a moment to arrange" and he goes off to asks the person in room 1 to move to room 2, and the person in room 2 to move to room 3, and the person in room 3 to move to room 4, etc etc etc etc (an infinite number of times). The weary traveller is both pleased to have a room and to have been so fortunate to happen across such a marvellous manager. Later that day a rather flustered tour guide hurries into the building needing rooms for an infinite coach party of America tourists, to which the manager replies, "No problem sweet cheeks, it will take but a moment to arrange," and he asks the person in room 2 to move to room 4, the person in room 3 to move to room 6, and the person in room 4 to move to room 8, and each person room n to move to room 2n, and so on, until an infinite number of rooms become available.

It's just quirky way to explain how the idea of an infinite number being the largest possible value, or a value at all, is the wrong way to think about infinity.


So if the monkeys haven't come up with the complete works of The Bard after infinite attempts/time you can just ask them to continue and check back after infinite x 2 attempts/time, and so on and so on and so on (an infinite number of times).

No one is debating that. You don't need to conceptualise infinity as a finite number to understand the probabilities involved and know that you can't be certain that the monkey (or monkeys, as long as we are talking about a finite number of monkeys) will ever output Shakespeare no matter how long you give them.

Not my problem, thank doG. I'm just infinitely more concerned with the welfare of the monkeys than the probability of them producing excellent prose.

[JimC]

Give me a googleplex of monkeys typing for a googleplex of years, and I'm morally certain they will produce the entire posting output of Rationalia!

And, they'll also give a final assessment of what it actually tastes like!

(faintly of bananas is my bet...)

My bad - it is, of course, spelled googolplex

For the tiny minority of rationalians unaquainted with names for some very large numbers:

1 googol = 10100 , which is fairly big...

1 googolplex = 10googol , which is somewhat larger still...

[pErvinalia]

That's nearly as large as the number of manginas on rationlia!

[Brian Peacock]

Or the value of the US national debt.

[rainbow]

Or the value of the US national debt.

This is an actual example of infinity. The ceiling to the debt can be raised, so it really has no limit.

When the debt reaches infinity however, the dollar becomes worthless, and the debt disappears.

Problem solved.

[mistermack]

I've just read of an interesting problem relating to infinity. It's called Zeno's paradox of Achilles and the Tortoise.
He explains it like this. Imagine Achilles, and a Tortoise have a race. Achilles can run ten times as fast as the tortoise so he gives it 100m start.
When Achilles gets to the 100m mark, the tortoise has gone 10m. So the race continues.
When Achilles gets to the 110m mark, the tortoise is 1m ahead. And so on. Each time Achilles reaches where the Tortoise has been, the Tortoise is still ahead. Even if you repeat the calculation again and again a billion times, the tortoise would still be ahead of Achilles. You would have to repeat the process to infinity, for Achilles to catch up with the tortoise.

[Hermit]

Zeno constructed a whole set of them, all with the same conclusion. An arrow can never reach its target, and so on. Comparing what his paradoxes keep proving with what keeps actually happening, I have this sneaking suspicion that there is something fundamentally wrong with the paradoxes, notwithstanding the logic so impeccably utilised in them. [/derail]

[Svartalf]

The paradoxes of Zeno are actually pure sophistry, but well built, because the form is seemingly correct and it takes a reality check to see Achilleus outrace the tortoise and the arrow reach the target

[JimC]

The calculus of infinitesimals sorts it all out...