videogames101
Diamond Member
- Aug 24, 2005
- 6,777
- 19
- 81
Well, I see a problem, money's hands are WAY to big to hit 1 key, making this whole theory impossible anyways...
Originally posted by: videogames101
Well, I see a problem, money's hands are WAY to big to hit 1 key, making this whole theory impossible anyways...
Originally posted by: CSMR
You have an upper bound with your formula, which is what you need. The probability of a monkey typing a particular countably infinite sequence eventually is zero. William Shakespeare's works are of finite length, not infinite.
Generative Rendering Theorem outdoes Infinite Monkey Theorem. While Infinite Monkey Theorem cannot guarantee that even a tome as short as the complete Works of William Shakespeare can be recreated by random chance even when time is not a limiting factor, Generative Rendering Theorem absolutely does guarantee that each and every Work stored in the British Library can be recreated, given timescales way beyond the lifespan of the universe, even if every electron had the computing power of the most powerful super computer imaginable, by doing nothing more than counting sequentially from zero to infinity and beyond!
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.
Generative Rendering Theorem
Those familiar with computers will know that files stored on disk have a size specified in terms such as kilobytes or megabytes. Well, what is a byte? A byte is a unit of storage analogous to a litre. A jug that can store a litre can store any volume of liquid up to and including a litre, any volume between 1-1000 millilitres, or even nothing at all. It is the same with a byte. A byte can store any number in the range 1-255, or it can store nothing at all (the number 0).
An author editing a text document sees nothing but text displayed on screen, yet all of the letters and other characters on display are actually stored as numbers in the txt file being edited. Each character has its corresponding number. Although there are several numbering standards used for storing text, one of the most common is ASCII (American Standard Code for Information Interchange). In ASCII, the letter C is stored in the txt file as the number 67, while the word CAT is stored in the txt file as the number sequence 67, 65, 84.
While a txt file containing only a C can most certainly be brought into existence by an author using a word processor, there is another process by which a txt file containing only a C can be brought into existence. This process called Generative Rendering exploits the fact that given one byte can store only the numbers 0 and 1-255 (or 0-255, as we programmers say) a program can be written that does nothing more than write out to disk all possible 1-byte txt files. Each of these txt files will contain a different number in the range 0-255. Among these txt files will be a file containing the number 67. When that txt file is loaded into a word processor, what is displayed on screen is C. This program a Generative Text Renderer is presented here in a language the layperson can understand:
10 for x = 0 to 255
20 write x to a txt file
30 next x
Bytes can be combined in such a way that working together two bytes can be used to store numbers in the range 0-65535. This is like having two jugs, each of which can store only 1 litre but which when working together can store up to 2 litres. The Generative Text Renderer can be modified to write out all possible 2-byte txt files. Each of these txt files will contain a different number in the range 0-65535. Among these txt files will be a file containing the two numbers 67 and 65. When that txt file is loaded into a word processor, what is displayed on screen is CA.
Similarly, three bytes working together can be used to store numbers in the range 0-16777215. The Generative Text Renderer can be modified to write out all possible 3-byte txt files. Each of these txt files will contain a different number in the range 0-16777216. Among these txt files will be a file containing the three numbers 67, 65 and 84. When that txt file is loaded into a word processor, what is displayed on screen is CAT.
Ninety-one bytes working together can be used to store numbers in the range 0-SomeHugeNumber. The Generative Text Renderer can be modified to write out all possible 91-byte txt files. Each of these txt files will contain a different number in the range 0-SomeHugeNumber. Among these txt files will be a file containing the ninety-one numbers
083 105 110 099 101 032 116 104 101 121 032 097 114 101 032 110 111 032 108 111 110 103 101 114 032 116 119 111 032 098 117 116 032 111 110 101 044 032 108 101 116 032 110 111 032 111 110 101 032 115 112 108 105 116 032 097 112 097 114 116 032 119 104 097 116 032 071 111 100 032 104 097 115 032 106 111 105 110 101 100 032 116 111 103 101 116 104 101 114 046
When that txt file is loaded into a word processor, what is displayed on screen is: Since they are no longer two but one, let no one split apart what God has joined together. Thats Matthew 19:6 by the way (NLT).
Generative Rendering Theorem outdoes Infinite Monkey Theorem. While Infinite Monkey Theorem cannot guarantee that even a tome as short as the complete Works of William Shakespeare can be recreated by random chance even when time is not a limiting factor, Generative Rendering Theorem absolutely does guarantee that each and every Work stored in the British Library can be recreated in very little time by supercomputers doing nothing more than counting sequentially from zero to infinity and beyond!
Can't we test this, just for fun?
IIRC, Java has a random number generator. If a programmer could develop a random letter generator I'm sure someone would be willing to run it on their computer.
Perhaps a contest in Distributed Computing on who gets Macbeth first?
hmm if you wrote an algorithm that would produce all possible text up to 1 million characters long. Would you then be able to capture all future books that were likely to be written? That would also mean that there were only a finite amount of ideas to be written about.
...Generative Rendering Theorem absolutely does guarantee that each and every Work stored in the British Library can be recreated in very little time by supercomputers doing nothing more than counting sequentially from zero to infinity and beyond!
hmm if you wrote an algorithm that would produce all possible text up to 1 million characters long. Would you then be able to capture all future books that were likely to be written? That would also mean that there were only a finite amount of ideas to be written about.
Well, if you have a monkey on a keyboard for an infinite amount of time, eventually it will hit the keys in a sequence that recreates (insert famous work here). In the timeframe of infinity, any event that even has the slightest probability of happening will - if it never happened, then there would be no way to attach a probability to it.
Well, if you have a monkey on a keyboard for an infinite amount of time, eventually it will hit the keys in a sequence that recreates (insert famous work here). In the timeframe of infinity, any event that even has the slightest probability of happening will - if it never happened, then there would be no way to attach a probability to it.
Here's a fun fact that I just remembered. If a drunk person leaves his home and, with equal probability, will go a step in either North/South/East/West. Barring death or other causes of death, given infinite time.... he will get back home.
However, if he was in space and could also go up and down, he's not guaranteed to get back home after infinite time.
why not? now it's just a 3-dimensional random walk. that still visits all the probability space infinite times, when taken to infinity.