You only need either an infinite number of monkeys, or infinite time. Using both is a waste. Infinite monkeys will produce <whatever> instantly.
Now you need to define 'place'. If your using the planet as a reference point, then yes lightening does indeed hit the same place multiple times (this was an old wifes tale anyhow). But if you consider the movement of the planets, the solar system, and our home galaxy, it's harder to indeed say it hits the same place twice.
An infinite universe, by it's definition, is a flattened version of a multi-verse. So yes, if our universe is infinite then there are actually infinite peple writing this reply (as there are infinite people who mis-spelled something different than I, etc).
If the universe is infinite, if it's finite, all bets are off.
Random to the state of the observer
As nobody else concisely answered you, I'll speak up. We're talking about finite probability here, not infitesimal probability. If an event only occurs once within an infinite population, its finite probability is zero, and it essentially will never happen. (If it's observed once to exist, it will never happen again, so it's impossible to actually discover one.)
DrPizza
Administrator Elite Member Goat Whisperer
Yes, but would an infinite number of monkeys, in an infinite amount of time, be able to type out the expansion of square root of 3?
Java has a psedu-random number generator. If you were to generate numbers one at a time for 2^32 times the sequence would repeat it self.
DrPizza
Administrator Elite Member Goat Whisperer
Well, I made my brain hurt first, I figured others could suffer the same fate. It seems that any time I hear infinitity outside of calculus class, I immediately think, "well, what size of infinity? Aleph Nought, continuum, or some other size of infinity?" Oddly, in calculus class, the thought rarely occurs to me.
Here's an idea:
Every time the next number is generated (or every so often), provide the possibility of changing the seed based on some other psedu-random decision. eg. is the time from 00:00 1/1/1970 GMT odd or even.
My feeling is that their is no limit to the number of possibilities. Of course, like any random number generating algorithm, it is not truely random.
This theorem is rather moot when factoring in quantum mechanics. According to the latter, eventually, the typewriter would have spontaneously pushed all the exact right keys to compose Shakespeare's works. Better yet, the typewriter and monkey are not even required, since ink will magically appear on the paper to form the exact letters/words of the plays.
If the universe were truly infinite, then everything has already happened infinite numbers of times already... EVERYTHING. Each combination of particles, each person, each thought, each event... has already happened an infinite number of times.
That's one of the whole problems with infinity that people generally don't think about. We tend to think of infinity as having a starting point and moving FORWARD towards the infinite, but something truly infinite should be infinite forwards or backwards... and if it is infinite backwards, that means that at ANY point, an infinite amount of time has already passed, so anything that is a possibility would have already happened... again and again and again.... ad infinitum!
Joe
- May 27, 2002
- 12,653
- 205
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Originally posted by: Netopia
If the universe were truly infinite, then everything has already happened infinite numbers of times already... EVERYTHING. Each combination of particles, each person, each thought, each event... has already happened an infinite number of times.
That's one of the whole problems with infinity that people generally don't think about. We tend to think of infinity as having a starting point and moving FORWARD towards the infinite, but something truly infinite should be infinite forwards or backwards... and if it is infinite backwards, that means that at ANY point, an infinite amount of time has already passed, so anything that is a possibility would have already happened... again and again and again.... ad infinitum!
Joe
so... how many times have you posted this answer? 3? or is it 4?
LOL.... well, since I believe that the universe isn't truly infinite, I'll say I've only done it once. I can't PROVE that, one way or the other, but I believe that to be the truth.
Joe
Joe
For some perspective on just how improbable this is, check out this passage from "Programming the Universe" by Seth Lloyd:
It would take a billion billion [10^18] monkeys, each typing ten characters per second, for each of the roughly billion billion seconds [15 billion years] since the universe began, just to have one of them type out [the phrase] "hamlet. act i, scene i".
And that is not even paying attention to capitalization. In other words, infinity is a very very long time...
**edit** for clarity
It would take a billion billion [10^18] monkeys, each typing ten characters per second, for each of the roughly billion billion seconds [15 billion years] since the universe began, just to have one of them type out [the phrase] "hamlet. act i, scene i".
And that is not even paying attention to capitalization. In other words, infinity is a very very long time...
**edit** for clarity
forrestroche
Senior member
- Apr 25, 2005
- 529
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EXACTLY. It is also true, that if you flipped a coin an infinite number of times, and assumed that tails = 0, and heads = 1, eventually a string of binary code will be produced that, if fed into my digital LCD screen, would produce video images of every time that I had "mistreated" myself, EVER, IN MY WHOLE LIFE, and the wierdest thing, is that it would be JUST A COINCIDENCE.
That's a fact.
forrestroche
Senior member
- Apr 25, 2005
- 529
- 7
- 81
It's also a fact that that sequence would be produced not just once, but an INFINITE NUMBER OF TIMES. Along with sequences seemingly depicting every instance in which every human being had ever picked his (or her) nose, EVER.
forrestroche
Senior member
- Apr 25, 2005
- 529
- 7
- 81
This is actually a fallacy. It could take the first monkey to sit down exactly 22 keystrokes to write that line (a few less than me, with my imperfect typing skills). Or it might happen next week. Assuming the math is correct, I think you mean that over this period of time, the probability approaches 1 that the event will occur.
I must also point out that infinity is not a "long" time. "Long" implies finite. A long time may be a long time, but it is certainly not an infinite time. And your use of 15 billion years to suggest how "long" infinity is, is misplaced as well. 15 billion years, as a measure of time, when compared to infinity, is in fact, INFINITELY SMALL. It does not help us comprehend infinity, unless perhaps we are suggesting that relatively speaking 15 billion years is no more signifigant than a nano-second (which is true).
In an infinite amount of time, the monkeys will type Shakespeare an infinite amount of times.
Anything that is possible happens an infinite amount of times, when your time boundary is infinity.
Anything that is possible happens an infinite amount of times, when your time boundary is infinity.
It depends on the conditions of the randomality. If each time he its the key is a random process, then the overall set of key hittage could end up under a pattern in which the same rubbush is just repeatadly typed infinitly. If overall his typing is random, in that he doesn't repeat any typing in a pattern, then yes somewhere down the line he would type something from Shakespeare.
Its my belief that the probability starts over with each key pressed. And with the length of the works being so long, the probability is NEXT to zero of this being possible.
But, given inifinite time, it COULD happen.
But like I said, the probability starts over each time the monkey presses a key, and just because a long time has been spent on it does not mean the correct sequence is getting closer to happening.
Theoretically, given infinite time, this monkey could fail an infinite amount of times.
But, given inifinite time, it COULD happen.
But like I said, the probability starts over each time the monkey presses a key, and just because a long time has been spent on it does not mean the correct sequence is getting closer to happening.
Theoretically, given infinite time, this monkey could fail an infinite amount of times.
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