So a monkey with a typwriter will write the words of Shakespeare in an infinite lifetime.
But will it?
Say i flip a coin and it lands on head. I do it again 500 times and it lands on heads every time. In theory i could flip it again and again forever and it might never land on tails.
So if a coin was flipped on a table. Is it possible it will never land on tails in an infinite lifetime?
No, it will almost surely write the words of Shakespeare.
> almost surely
so the coin might never land on tails in an infinite flips
Here's a puzzle for you op
Say you turn a light on and,wait 30 seconds, turn it off, wait 15 seconds, turn it on again you keep switching the light after half the time previous has passed. You do this for 60 seconds. By that time you've switched the light an infinite number of times.
Is the light on or off afterwards?
>Is it possible it will never land on tails in an infinite lifetime?
No. In an infinite number of flips the distribution will be 50/50. Within that infinite string of flips you will have stretches of thousands of heads in a row, with just as many tails in a row.
Untrue. There is a probability of every single slip being the same, and this has the exact same probability as any other configuration of flips.
i see your analogy that infite isnt a number of times so the light will keep flicking forever.
My analogy would be the same but instead of flicking it on and off, u close your eyes and randomly hit 1 side of the switch, so it might stay as it is or it might change. Is there a chance it will never change if that happened for an infinite amount of time?
how do people like you dress themselves?
So whats the answer lol
Is the chance so low that it becomes 0?
Suppose the monkey is typing nonnegative integers.
Actually, suppose that there's a function from a set I mapping i to monkey m_i that types nonnegative integers ad countable infinite.
Could you build any real number in [0, 1) from what some monkey typed?
If each monkey eventually typed any finite sequence of nonnegative integers, then his resulting real number will be a normal number.
But not all real numbers in [0, 1) are normal.
atheists 1 x 0 probabilists
How long did it take the first monkey to write Shakespeare, all I gave was consciousness. Yes.
Coin flip isn't at all possible. Thereotically, "But will it" to and yes. The universe eventually expands until it IS so that it cannot, then collapses swirls inward upon and into itself until it ISN'T to the point that it must and bursts outward again. Perceivable in spilt seconds and eons always in all ways. But it's been the same again and again, we just choose new eyes each time and remembering and forgetting and changing what we Will.
nigga you high as fuck
it's (1/2)^n for however many trials. e.g. chance that you flip a coin 10 times and it's heads every time is (1/2)^10
>So if a coin was flipped on a table. Is it possible it will never land on tails in an infinite lifetime?
The probability of the coin never landing tails after infinite flips is undefined, but the limit of that probability as the number of flips approaches infinity is 0. After any finite amount of flips, there will be a non-zero (but small) probability that every flip was heads.
>Could you build any real number in [0, 1) from what some monkey typed?
No, the mapping would not be surjective.
Then either these random monkeys are useless or real numbers are a meme.
Why I shouldn't kill myself?
It's like pottery
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Veeky Forums so 4chanit the media endorsin it they just just trying to BRTHR
Yes. what you're saying makes sense.
Similarly, we are either alive, or dead. It's a binary state. If you are alive in this moment, you could be dead in the next. Therefore we have 50:50 chance of living or dying every second of our lives
The correct formulation is the Probability that it writes the works of Shakespeare approaches 1.
You are right the chance that the first n characters will be all "a" exists, but it goes down rapidly as n grows large.
> I do it again 500 times and it lands on heads every time. In theory i could flip it again and again forever and it might never land on tails.
Here the chance that it lands tails approaches(!) 1.
Of course not.
Shakespeare's works contain information.
Monkeys who randomly type letters into the PC will not create information.
Where is it supposed to come from?
If you take it from an abstract point of view, yes, given enough iterations and enough permutations, one will emerge that is exactly like on of Shakespear's works.
But in reality, this will not work. NEVER EVER. We will run out of type inc, or electricity, before anything meaningful happens.
Please stop listening to autists.
Same with evolution.
Pick a probability, P, as close to 1 as you want (not exactly 1).
If you hand me a FINITE string, w, I can give you a positive integer, N, such that after N coin flips, your string will have at least probability P of occurring as a substring of the N flips.
The monkey will also write a version of all of Shakespeare's works where you, the reader, are in the story fucking every one of his characters.
yeah, also monkeys don't live forever so they'll die before infinite time runs out
>establish several breeding colonies of monkeys
>examine output of each monkey for similarity to the Bard
>kill the most dissimilar
>50,000 years later, you have your shakespeare
asymptotically the probability is 0
I cant give an practical example because the situation you sketched is not practical to begin with
It should be “can” and not “will”, unless you include infinite timelines.
>code Shakespeare into DNA
>no useful proteins come out
Well I guess Shakespeare contains "no information"
Nice bait btw
[math]\frac{1}{\infty}=0[/math]
Monkeys can't even type.
Whomst'd've ever see a monkey do such?
Surely the monkey would become kill first
I think a good parallel to OP's question is;
>If Pi goes on forever and contains every sequence of numbers possible, does it contain an infinite series of 1s? (Or any arbitrary number)
The answer as far as I know is no, but I don't know why. Maybe because it inhibits other series from existing since it goes on forever?
The probability of the flip being heads or tails every time, but the probability of getting thousands of heads in sequence is very low.
Don't post nonsense
It's an event with probability 0. Take that as you will.
This doesn't even require calculations or overthought.
>Is it possible it will never land on tails in an infinite lifetime?
Yes. It's exactly 50% likely that it will never land on tails in an infinite lifetime, and exactly 50% likely that it will at some point, provided your coin is evenly balanced and flipped properly.
Just like the probability of any given sequence that is thousands of terms long...
No, you idiot. It's 0 and 1, not 0.5 and 0.5
Saying that some event "happens with probability 0" doesn't mean that it cannot happen.
Coin-flipping infinitely many heads is one possible outcome, out of infinitely many possible outcomes. The probability for it to happen is 0.
"Almost surely" or "almost always" is well-defined when you have an infinite sample space. It's when you have a possible outcome, but its probability (aka its measure) is zero. Like the probability of writing out the digits of pi by just randomly writing digits.
That situation could never exist though, a monkey writing Shakespeare could.
Meant for Retaaaaard
You can do it as many times as you want and, indeed, it might never land on tails. However, if you do it infinitely many times it will always be 50/50.
The fucking point is that given infinite time, no matter how small the chances of an event are it will eventually occur. Of course however the monkey analogy is retarded, but there's no way the coin will keep landing on heads forever.
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