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scott wrote:
> Hehe, I guess for some people it doesn't take much to "learn an awful
> lot" :-)
Uh, yeah...
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Kenneth wrote:
> getting grant money seems to be easier than I thought!
After the study to determine whether a duck's quack echos, nothing
surprises me any more. ;-)
Hmm, maybe we could get some kind of a grant? Maybe to determine whether
people can tell the difference between POV-Ray and the Real World?
...so basically, get paid to play with POV-Ray all day! :-D
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Mueen Nawaz <m.n### [at] ieee org> wrote:
> Which was my whole long winded point.
To make it clear: I was not saying anything *against* your arguments.
I was trying to complement them. :)
--
- Warp
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scott <sco### [at] scottcom> wrote:
> Isn't it mathematical fact that the probability of the works not appearing
> is zero in the limit condition?
In the exact same way as the probability of getting a specific value in
a continuous range is zero (for the sole reason that a continuous range has
an infinite amount of values).
Just because the probability is mathematically zero does not mean you
will not get any specific value.
--
- Warp
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scott <sco### [at] scottcom> wrote:
> Just to assume "the works" are W letter long, then the probability of a
> random sequnce R of length W exactly matching is 64^-W (assuming 64
> characters here). Then, the probability of R *not* matching is (1-64^-W).
> If we take N sequences of random letters, then the probability of finding
> "the works" is given by 1-(1-64^-W)^N, which *equals* 1 in the limit of N
> tending to infinity.
So exactly at which point are the works forced to appear, to fulfill
the probability of 1?
The answer is: They are never forced to appear. And that is not a
contradiction of the probability being 1 when dealing with infinity
(any more than a value in a continuous range having a probability of
zero is a contradiction that that value might be chosen at random).
--
- Warp
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> So exactly at which point are the works forced to appear, to fulfill
> the probability of 1?
In the limit of N --> infinity. If N is a finite number then the works are
not forced to appear, by saying N is infinite you are forcing them to
appear. Just think of "infinite" to mean "repeat until it does appear".
Saying "it might never appear" is not a valid argument, because an infinite
list of random sequences does not have a concept of "never", there are
always infinitely more sequences to come no matter how many you go through.
> The answer is: They are never forced to appear.
...unless N is allowed to be infinite, which the original problem states
quite clearly.
Or do you also disagree with 0.99999... with infinitely many 9's equals 1?
Perhaps you should read this page:
http://en.wikipedia.org/wiki/Limit_(mathematics)
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scott <sco### [at] scottcom> wrote:
> > So exactly at which point are the works forced to appear, to fulfill
> > the probability of 1?
> In the limit of N --> infinity.
That's, in fact, the exact same thing as saying "never".
And that's how it is: Each *individual* round of popping up values from
the RNG has a smaller-than-1 probability for the works to appear. Thus at
no point are the works *forced* to appear.
> > The answer is: They are never forced to appear.
> ...unless N is allowed to be infinite, which the original problem states
> quite clearly.
So at which point are the works forced to appear?
> Or do you also disagree with 0.99999... with infinitely many 9's equals 1?
Do you disagree that a probability of zero does not mean that the event
will never happen?
--
- Warp
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http://everything2.com/title/If%2520you%2520have%2520enough%2520monkeys%2520banging%2520randomly%2520on%2520typewriters%252C%2520they%2520will%2520eventually%2520type%2520the%2520works%2520of%2520William%2520Shakespeare
http://everything2.com/title/Monkey%2520Shakespeare%2520Simulator mentions a
site that I'd come across a while back that simulated this, but it's since
vanished.
--
Tim Cook
http://empyrean.freesitespace.net
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>> In the limit of N --> infinity.
>
> That's, in fact, the exact same thing as saying "never".
Ermm, no, it's saying that the probability will get as close to 1 as you
want, and in the limit it will *equal* 1. Exactly the same as saying
0.999999... can get as close to 1 as you want, and in the limit is actually
*equal* to 1.
> And that's how it is: Each *individual* round of popping up values from
> the RNG has a smaller-than-1 probability for the works to appear. Thus at
> no point are the works *forced* to appear.
For a finite number of tries, no.
>> Or do you also disagree with 0.99999... with infinitely many 9's equals
>> 1?
No go on, please answer this one, because it's the same thing. At which
point does 9/10 + 9/100 + 9/1000 suddenly equal 1? Answer: when you extend
the series to infinity.
> Do you disagree that a probability of zero does not mean that the event
> will never happen?
A probability of zero means an event does not happen by definition, however
if you try an infinite number of times it might not necessarily never
happen.
A good example has already been mentioned, of choosing an exact number
between 0 and 1. The probability is zero for any specific number, but if
you sum up the infinite number of probabilities between say 0.2 and 0.3, you
will get a non-zero probability.
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scott <sco### [at] scottcom> wrote:
> >> Or do you also disagree with 0.99999... with infinitely many 9's equals
> >> 1?
> No go on, please answer this one, because it's the same thing. At which
> point does 9/10 + 9/100 + 9/1000 suddenly equal 1? Answer: when you extend
> the series to infinity.
I really can't understand why you are so fixated with that question.
I never doubted or denied its veracity. My reply clearly implied that it
is indeed so.
> > Do you disagree that a probability of zero does not mean that the event
> > will never happen?
> A probability of zero means an event does not happen by definition, however
> if you try an infinite number of times it might not necessarily never
> happen.
You don't have to try an infinite number of times to get a value from
a continuous range. You only have to try once. And the value you get had
a probability of zero of being chosen. Yet it was chosen.
> A good example has already been mentioned, of choosing an exact number
> between 0 and 1. The probability is zero for any specific number, but if
> you sum up the infinite number of probabilities between say 0.2 and 0.3, you
> will get a non-zero probability.
You are not choosing a range of values. You are choosing *one* value at
random.
--
- Warp
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