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Invisible <voi### [at] dev null> wrote:
> http://news.bbc.co.uk/1/3013959.stm
getting grant money seems to be easier than I thought!
KW
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> http://news.bbc.co.uk/1/3013959.stm
>
> WTF-O-Meter: 2.8
Hehe, I guess for some people it doesn't take much to "learn an awful lot"
:-)
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> A true evenly-distributed random number generator and an infinite amount
> of time is a lot, lot closer to fulfilling the claim, and the probability
> of the works coming up is unlimitedly high, but there's still no absolute
> guarantee.
>
> (Many people think that in this last case the works *will* eventually
> appear with absolute certainty, but that's just the gambler's fallacy.)
Isn't it mathematical fact that the probability of the works not appearing
is zero in the limit condition?
Like if you ask what is the probability of getting no heads when a coin is
tossed N times, it is 2^-N, which is *equal* to zero in the limit as N tends
to infinity. That's what I was taught at school/university anyway.
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> Since there is an infinite amount of different finite sequences of
> letters, the probability of one specific sequence (in this case the works
> of Shakespeare) to appear is, mathematically speaking, zero.
Sorry Warp, but that's just bad math.
One way to explain why you are wrong is that yes, there are an infinite
number of finite length sequences of letters, but then there are also an
infinite number of finite length sequences that *contain* the works (plus
other junk). So the probability calculation is infinity/infinity, not
1/infinity.
If you restrict the problem down to finite sequences of the same length as
"the works", then now there are only a finite number of possiblities, and
exactly 1 of them will be "the works".
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.
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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] ieeeorg> 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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