I believe somewhere in this long explanation is the answer!
1000 monkeys at 1000 computers typing randomly for infinite time...
- Thread starter Proteinboy
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I believe somewhere in this long explanation is the answer!
I think it's possible if we were to factor in some things.
If we were to do the following:
1) Create a program such that it resets each time the proper key isn't pressed for the play. For example, if "Hello World" was the target, then typing in, "Helo" would cause it erases everything and starts back with a empty screen.
2) Only allow 26 letters and 10 numbers, and allow the play to be written without cases, but with proper spaces. The monkeys are not allowed to press two buttons at once. Like Shift and A.
3) Monkeys can gain intelligence. For example, after a certain number of proper keystrokes, they are rewarded with something, and bad keystrokes are punished. This will cause them to learn which keys to press in what order.
Of course, just randomly expecting something to occur may never occur, even if infinite time is given. It's possible to flip a coin and not get heads or tails, but given infinite time, without any factor, this may never occur.
If we were to do the following:
1) Create a program such that it resets each time the proper key isn't pressed for the play. For example, if "Hello World" was the target, then typing in, "Helo" would cause it erases everything and starts back with a empty screen.
2) Only allow 26 letters and 10 numbers, and allow the play to be written without cases, but with proper spaces. The monkeys are not allowed to press two buttons at once. Like Shift and A.
3) Monkeys can gain intelligence. For example, after a certain number of proper keystrokes, they are rewarded with something, and bad keystrokes are punished. This will cause them to learn which keys to press in what order.
Of course, just randomly expecting something to occur may never occur, even if infinite time is given. It's possible to flip a coin and not get heads or tails, but given infinite time, without any factor, this may never occur.
using the same principle: it doesnt matter how small the odds, given infinite time, the desired outcome will occur,
if a coin was to be tossed an infinite amount of times, is it possible that every single time, it lands as heads? given there is a 50% chance
the chances just get infinitly smaller.
1/2 *1/2 *1/2 * 1/2 * 1/2 * 1/2 ...ect
so in you guys' theory, it could happen that the coin will always land on heads. then that also means that tails would never occur.
ever.
just like the play Hamlet could also never have to occur
if a coin was to be tossed an infinite amount of times, is it possible that every single time, it lands as heads? given there is a 50% chance
the chances just get infinitly smaller.
1/2 *1/2 *1/2 * 1/2 * 1/2 * 1/2 ...ect
so in you guys' theory, it could happen that the coin will always land on heads. then that also means that tails would never occur.
ever.
just like the play Hamlet could also never have to occur
i thought it was just like saying that it doesnt have to happen lol...
PB, what you described is called a series. There are lots of ways to evaluate different types of series, but in this case I believe you would take the sum. What you described looks like (1/2)^n. As n increases, the number gets smaller. When n=3, the number is (1/8). When n=2, the number is (1/4). When n=some crazy number, (1/2)^123443543674256 is pretty much zero.
If you take the sum, it looksl ike (1/2)+(1/4)+(1/8)+all the numbers that are close to zero as n reaches infinity. Okay so actually it turns out this is called an infinite geometric series, and the sum is a/(1-x) where a is the initial value 1/2 and x is the ratio of change, 1/2.*
Anyway my point is there will always be a value, the sum never goes to zero, no matter how many times you flip a coin. True, the odds of certain words being in consecutive order get smaller as the word count increases, but the odds are never really zero. Therefore, there is always a possibility.
*=Just take calc 2
If you take the sum, it looksl ike (1/2)+(1/4)+(1/8)+all the numbers that are close to zero as n reaches infinity. Okay so actually it turns out this is called an infinite geometric series, and the sum is a/(1-x) where a is the initial value 1/2 and x is the ratio of change, 1/2.*
Anyway my point is there will always be a value, the sum never goes to zero, no matter how many times you flip a coin. True, the odds of certain words being in consecutive order get smaller as the word count increases, but the odds are never really zero. Therefore, there is always a possibility.
*=Just take calc 2
Remember just because their is a probable chance of something happening does not mean it will. Take for instance when i used flipping a coin as an example. One could flip it say for all infinity and NEVER once hit tails. Does the chance decrease or increase with the number of times you flip it? NO, Does the chance of 1000 monkeys successfully rewriting it increase/decrease with time? NO, Just because there is a probable chance does not mean this "chance" will happen. For infinity these monkeys could type and still NEVER do it.
Its perfectly reasonable to assume the monkeys would NEVER successfully write it even if they continued on for ALL time.
Its perfectly reasonable to assume the monkeys would NEVER successfully write it even if they continued on for ALL time.
that doesnt matter. IF the monkies typed RANDOMLY for INFINITY they would eventually do it. If they dident write, they wouldnt do it, if they dident type randomly, they wouldnt do it, if they dident type for infinity, they wouldnt do it. The question states which circumstances that needs to be there in order for it to actually happen, if you take away one of those, it wont happen. So theres no need to speculate and say for example "ahh, the monkies would die, infinity doesnt exist, blablablablabla" when the premisis of the task IS that it exists, you say the magic word "IF". Thats a word that takes real life out of it. If i suddenly grew 10 feet tonight i would wake up tomorrow and bash my head in the cieling. Well its not possible you say, well i dont care, if i actually grew 10 feet, i would..
too late...
What I was actually saying was referring to the probability that nothing at all is typed, because the monkeys push the backspace key the equal number of times that they push the letter and number keys.
I don't know. I think this would work only with infinite monkeys. Why? Because the act of typing nothing at all is all encompassing. If you take one monkey and try this, it falls apart. What about the probability of pressing the delete key for an equal amount of letters? What about the probability of ending up only typing one letter for infinity? These probabilities DO exist and therefore, according to the math, should occur. The problem is, if you type nothing for infinity, it's not Hamlet. It's not ever work ever created. It's just a blank sheet.
Therefore this can only with with infinite monkeys. If there are infinite monkeys, there will be infinite monkeys who type nothing, infinite monkeys who type only one letter, infinite monkeys who type Hamlet, and infinite monkeys who write this exact post.
Who said we evolved from apes?
he said IF.
You'd have a better chance of getting hit by lightning while on your way to redeem you're 2nd jackpot winning lottery ticket.
I have returned to this topic. Let's see. One thing that needs to be taken into account is this. If a monkey takes a particular liking to a certain key, due to the noise it makes or something. It will subconsciously press that key more times. I'm not sure where I stand on this anymore.