Warp wrote:
>   True. The event happens with *one* trial. You don't even need an infinite
> amount of them.

Selection bias. :-)

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> Warp wrote:
>>>   So exactly at which point are the works forced to appear, to fulfill
>>> the probability of 1?
> 
>> Infinity.  That's the point.
> 
>   In other words: Never. At no point is it forced to happen.

No. You're getting wrapped up in Zeno's paradox here.

>   The analogy is that the monkey will type Shakespeare's work for sure.
> Exactly when is this 100% certainty reached? Never.

Yes. After infinite time. But you're refusing to look at that case, trying 
to get to "after infinite time has passed" by looking one second at a time.

Assume you have an infinite number of monkeys, each typing one block of text 
the size of shakespeare, and they all finish within one day. Is Shakespeare 
in there?

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >   So at which point exactly will it happen with 100% certainty?

> When an infinite number of flips are flipped, and not before.

  In other words, never.

> >   "At infinity" is the same thing as "never" in this case.

> It has nothing to do with "time", so you are technically correct in saying 
> that it's physically impossible to do an infinite number of flips in a 
> non-infinite length of time.

  Thus the monkey analogy is technically flawed. Which is my original point.

> >> Resolve this discrepency, in your mind, and you'll understand why 
> >> shakespeare must appear.
> > 
> >   Once you explain to me the discrepancy that an event having zero
> > probability can happen.

> When you do it an infinite number of times.

  But it happens with only one attempt, not an infinite amount of them.

> Do you understand what I'm saying when I say you're confusing unbounded with 
> infinite?

  The monkey analogy is trying to make a connection between theoretical
math dealing with infinites and physical reality, which are at completely
different conceptual levels. I do not fully understand the math, but I'm
pretty sure I understand the physical process depicted by the analogy,
and I'm pretty sure the claim is flawed.

-- 
                                                          - Warp

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Darren New <dne### [at] sanrrcom> wrote:
> Assume you have an infinite number of monkeys, each typing one block of text 
> the size of shakespeare, and they all finish within one day. Is Shakespeare 
> in there?

  If all the monkeys press the key 'a', then obviously not.

  What forces any of the monkeys to press some other key?

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                                                          - Warp

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On Tue, 21 Apr 2009 09:15:29 -0700, Darren New wrote:

>>   So at which point exactly will it happen with 100% certainty?
> 
> When an infinite number of flips are flipped, and not before.

Disagree.  The point at which it will happen with 100% certainty is the 
point at which it happens, and not before. ;-)

Jim

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Warp wrote:
>> It has nothing to do with "time", so you are technically correct in saying 
>> that it's physically impossible to do an infinite number of flips in a 
>> non-infinite length of time.
> 
>   Thus the monkey analogy is technically flawed. Which is my original point.

Well, yes. You're saying "No, an infinite number of monkeys won't type out 
the works of shakespeare *because* there aren't an infinite number of 
monkeys in the universe."

Certainly the argument falls down if you don't accept the premise. So does 
the proof that 1+1=2, so I'm not sure what your point is.

>>>> Resolve this discrepency, in your mind, and you'll understand why 
>>>> shakespeare must appear.
>>>   Once you explain to me the discrepancy that an event having zero
>>> probability can happen.
> 
>> When you do it an infinite number of times.
> 
>   But it happens with only one attempt, not an infinite amount of them.

Because you're incapable of picking one number from an infinite number of 
possible numbers, in precisely the same way it's impossible to have one 
real-world monkey typing for an infinite length of time.

>> Do you understand what I'm saying when I say you're confusing unbounded with 
>> infinite?
> 
>   The monkey analogy is trying to make a connection between theoretical
> math dealing with infinites and physical reality, which are at completely
> different conceptual levels.

You're denying that the premise could possibly be true in the real world. 
That isn't how math works.

> I do not fully understand the math, but I'm
> pretty sure I understand the physical process depicted by the analogy,
> and I'm pretty sure the claim is flawed.

No, I'm pretty sure you don't understand "after an infinite amount of time" 
in the physical process sense of the word. I don't think anyone does, except 
maybe perhaps Hawking.

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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Warp wrote:
>> Do you understand what I'm saying when I say you're confusing unbounded with 
>> infinite?
> 
>   The monkey analogy is trying to make a connection between theoretical
> math dealing with infinites and physical reality,

So what you're saying is there aren't *really* an infinite number of 
positive integers, because if you count "one, two, three, ..." you'll never 
get to all the integers.

Yeah, OK, that's not what infinite means.

I'll agree that it's impossible to have an infinite number of monkeys. But 
if you *did*, they'd hit shakespeare with 100% certainty.

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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Warp wrote:
>   If all the monkeys press the key 'a', then obviously not.
>   What forces any of the monkeys to press some other key?

Randomness.  If you do an infinite number of trials and only get the 'a' 
key, then your process isn't random, by definition.

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >   If all the monkeys press the key 'a', then obviously not.
> >   What forces any of the monkeys to press some other key?

> Randomness.  If you do an infinite number of trials and only get the 'a' 
> key, then your process isn't random, by definition.

  Then there must be some kind of law of the universe which forces at
least some of the monkeys to type something else than 'a'.

  The probability that all of them will press 'a' is zero, but is this
a "different zero" from the one related to choosing one value from a
continuous range?

-- 
                                                          - Warp

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Warp wrote:
>   Then there must be some kind of law of the universe which forces at
> least some of the monkeys to type something else than 'a'.

No. It's part of the definition of infinity and random.

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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