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Also there was only one computer. The original scenario had a 1:1
monkey-typewriter ratio.
--
Tim Cook
http://empyrean.freesitespace.net
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>> My personal favourit is the quote about this being cheaper and more
>> entertaining than reality TV. ;-)
>
> Cheaper? Certainly. More entertaining? Well, is there really any fundamental
> difference between them? ;-)
...which is kind of my point...
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>>> And whoever said it was a theory in the
>>> first place? :-D
>> Actually there's no law of mathematics or physics which says that an
>> infinite number of monkeys will produce the works of Shakespeare (especially
>> given that the problem is incomplete: The amount of time is unspecified).
>
> That's what I was getting at... it's not really a theory, more a
> pop-thought-experiment. And a badly-formulated one, as you've pointed out.
More like, it's a precise mathematical statement, rendered casually as
"if you gave a monkey infinite time to randomly type stuff"... which is
rather less precise. And quite probably wrong in a number of ways. (For
starters, monkeys don't type statistically random text...)
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Tim Cook <z99### [at] gmail com> wrote:
> Also there was only one computer. The original scenario had a 1:1
> monkey-typewriter ratio.
What is the "original scenario"?
As far as I know, the compeltely original statement is: "One million
monkeys hammering on one million typewriters for one million years will
eventually produce the entire works of Shakespeare."
Of course that statement is patently false in all possible interpretations.
Later the falsity was attempted to be fixed by changing the "one million
years" to "an infinite amount of time".
Of course if you change it to an infinite amount of time, then the one
million number becomes superfluous. One monkey and one typewriter would
essentially say the exact same thing.
The spirit of the metaphor is, of course, that the "monkey" is really
a true evenly-distributed random number generator. While in this situation
the probability of the works popping up approaches 1, and the works will
thus almost surely pop up at some point, it's still not a guarantee. The
probability *approaches* 1, it never becomes it.
--
- Warp
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Warp wrote:
> probability *approaches* 1, it never becomes it.
I think if you mean "the probability as the time approaches infinity" then
yes. I think if you look at the actual result with infinite time provided,
you get the probability 1. It's not like you have different probabilities;
there's only one situation under consideration: an infinite amount of time.
Given that truly random sequences are normal, and in a normal sequence every
block of a particular length occurs with equal probability, and we're
talking an infinite sequence, it follows that the bard is in there
somewhere. If I'm not mistaken about the math of it.
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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Invisible escreveu:
> http://news.bbc.co.uk/1/3013959.stm
>
> WTF-O-Meter: 2.8
Yep, completely missing the point: it's just a thought experiment of
sorts. They should get more luck from a computer simulation with
cellular automata and let it run for a few millenia on common alphabet.
Eventually scanning through the generated texts we could see out of
order streams resembling the complete works, mangled among gibberish.
--
a game sig: http://tinyurl.com/d3rxz9
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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> > probability *approaches* 1, it never becomes it.
> I think if you mean "the probability as the time approaches infinity" then
> yes. I think if you look at the actual result with infinite time provided,
> you get the probability 1. It's not like you have different probabilities;
> there's only one situation under consideration: an infinite amount of time.
Just because the limit of the probability is 1 doesn't say anything about
whether the works will surely appear with complete certainty at some point.
It only says that the probability for them to appear is larger and larger
as the amount of time is increased.
To understand what I'm talking about, consider the opposite:
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.
Since the probability for them appearing is zero, does that mean that
they will never appear?
No, it doesn't mean that. The zero is just a consequence of calculating
the limit of the probability against infinity. It says nothing about what
will *surely* happen or not happen.
> Given that truly random sequences are normal, and in a normal sequence every
> block of a particular length occurs with equal probability, and we're
> talking an infinite sequence, it follows that the bard is in there
> somewhere. If I'm not mistaken about the math of it.
There is an infinite amount of sequences *not* containing the works of
Shakespeare. What stops the RNG from generating *all* of those other
sequences before generating Shakespeare's works?
Also, even if the RNG has already produced all the possible letter
combinations with as many letters as there are in Shakespeare's works,
that doesn't mean that the works are next. When we pop out the next set
of letters, there's still a really small probability for them being the
works of Shakespeare. Even if the RNG would have already produced all the
possible other combinations a billion times, it still doesn't make the
probability of Shakespeares' works popping out any more probable. Past
events do not affect future randomness.
Yes, it's extremely unlikely that popping up all the possible distinct
combinations of letters (amounting to the total number of letters in the
works) a billion times will not produce Shakespeare's works, but this
probability is still larger than zero. There is no guarantee.
--
- Warp
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nemesis wrote:
> Eventually scanning through the generated texts we could see out of
> order streams resembling the complete works, mangled among gibberish.
No, all the text is already there. It's your *brain* that's running in the
wrong order.
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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nemesis <nam### [at] gmailcom> wrote:
> Yep, completely missing the point: it's just a thought experiment of
> sorts. They should get more luck from a computer simulation with
> cellular automata and let it run for a few millenia on common alphabet.
> Eventually scanning through the generated texts we could see out of
> order streams resembling the complete works, mangled among gibberish.
I think sampling the noise produced by a resistor would be a better
way of simulating the "monkeys".
--
- Warp
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Warp wrote:
> It only says that the probability for them to appear is larger and larger
> as the amount of time is increased.
Right. And I'm talking about when you actually consider the end result, and
not the limit.
I don't think you can look at a limit as n -> infinity and say what the
answer is at infinity by analogy.
> 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.
Err, no. There are an infinite number of sequences that are as long as
Shakespeare, and only a finite number of *possible* sequences. If all
sequences are equally likely, they'll all appear an equal number of times.
> Since the probability for them appearing is zero, does that mean that
> they will never appear?
I think you're mistaken that the probability is zero.
>> Given that truly random sequences are normal, and in a normal sequence every
>> block of a particular length occurs with equal probability, and we're
>> talking an infinite sequence, it follows that the bard is in there
>> somewhere. If I'm not mistaken about the math of it.
>
> There is an infinite amount of sequences *not* containing the works of
> Shakespeare. What stops the RNG from generating *all* of those other
> sequences before generating Shakespeare's works?
Nothing. Nor does doing so keep Shakespeare's works from being generated.
You need to address the theorems about normal numbers. There's actual math
here not relying on intuition about infinitites.
> Also, even if the RNG has already produced all the possible letter
> combinations with as many letters as there are in Shakespeare's works,
> that doesn't mean that the works are next. When we pop out the next set
> of letters, there's still a really small probability for them being the
> works of Shakespeare. Even if the RNG would have already produced all the
> possible other combinations a billion times, it still doesn't make the
> probability of Shakespeares' works popping out any more probable. Past
> events do not affect future randomness.
COrrect. I think you're failing to account for infinity.
> Yes, it's extremely unlikely that popping up all the possible distinct
> combinations of letters (amounting to the total number of letters in the
> works) a billion times will not produce Shakespeare's works, but this
> probability is still larger than zero. There is no guarantee.
A billion? Sure. Infinity? I don't think so. Anything less than infinity? Sure.
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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