Go Back   AnandTech Forums > Hardware and Technology > Highly Technical

Forums
· Hardware and Technology
· CPUs and Overclocking
· Motherboards
· Video Cards and Graphics
· Memory and Storage
· Power Supplies
· Cases & Cooling
· SFF, Notebooks, Pre-Built/Barebones PCs
· Networking
· Peripherals
· General Hardware
· Highly Technical
· Computer Help
· Home Theater PCs
· Consumer Electronics
· Digital and Video Cameras
· Mobile Devices & Gadgets
· Audio/Video & Home Theater
· Software
· Software for Windows
· All Things Apple
· *nix Software
· Operating Systems
· Programming
· PC Gaming
· Console Gaming
· Distributed Computing
· Security
· Social
· Off Topic
· Politics and News
· Discussion Club
· Love and Relationships
· The Garage
· Health and Fitness
· Merchandise and Shopping
· For Sale/Trade
· Hot Deals with Free Stuff/Contests
· Black Friday 2014
· Forum Issues
· Technical Forum Issues
· Personal Forum Issues
· Suggestion Box
· Moderator Resources
· Moderator Discussions
   

Reply
 
Thread Tools
Old 05-25-2006, 07:44 PM   #51
videogames101
Diamond Member
 
videogames101's Avatar
 
Join Date: Aug 2005
Location: 52375
Posts: 6,146
Default understanding probability theory... Infinite monkey theorem

Well, I see a problem, money's hands are WAY to big to hit 1 key, making this whole theory impossible anyways...
__________________
3570K
HD7870 (Tahiti LE)
videogames101 is offline   Reply With Quote
Old 06-12-2006, 08:45 PM   #52
thoro86
Banned
 
Join Date: Jun 2006
Posts: 692
Default understanding probability theory... Infinite monkey theorem

Quote:
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...
lol
thoro86 is offline   Reply With Quote
Old 06-13-2006, 01:02 PM   #53
theMan
Diamond Member
 
theMan's Avatar
 
Join Date: Mar 2005
Posts: 4,386
Default understanding probability theory... Infinite monkey theorem

Quote:
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.
true, the whole thing is too unspecific.
theMan is offline   Reply With Quote
Old 02-02-2013, 05:43 AM   #54
JudgeDracoAmunR
Junior Member
 
Join Date: Feb 2013
Posts: 1
Default

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!
JudgeDracoAmunR is offline   Reply With Quote
Old 02-02-2013, 07:28 AM   #55
Slammy1
Platinum Member
 
Slammy1's Avatar
 
Join Date: Apr 2003
Location: Metro East Saint Louis
Posts: 2,112
Default

All events are low probability when viewed from the perspective of the beginning. The probability that you or I exist let alone be having this particular conversation probably makes the monkey typing thing seem likely, yet here we are.
Slammy1 is offline   Reply With Quote
Old 02-02-2013, 07:40 AM   #56
Mark R
Diamond Member
 
Mark R's Avatar
 
Join Date: Oct 1999
Posts: 8,247
Default

Quote:
Originally Posted by JudgeDracoAmunR View Post
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!
FTFY
Mark R is offline   Reply With Quote
Old 02-02-2013, 02:20 PM   #57
koshling
Member
 
Join Date: Nov 2005
Posts: 43
Default

Of course, you don't actually NEED the monkey (or the typewriter) at all.

There is a non-0 probability that the atoms in some finite volume, with total mass sufficient to form the physical rendition of the complete works, will spontaneously re-arrange themselves into that particular arrangement of matter. Now the amplitude of that particular wave-function (which is where the probability of the arrangement derives from quantum mechanically) will be vanishingly small, such that it simply won't happen (almost certainly) within the lifetime of the universe. However, in principal it could.

In fact you don't even need enough atoms!! Depending on how long you want said complete works to last, it could pop out of the vacuum for a short period of time. Next to an event horizon it might even not annihilate immediately (Hawking radiation in the form of a copy of Shakespear), though it's chances of survival in such proximity seem minimal at best ;-)
koshling is offline   Reply With Quote
Old 02-02-2013, 03:22 PM   #58
Harvey
Administrator
Elite Member
 
Harvey's Avatar
 
Join Date: Oct 1999
Location: Sherman Oaks, Ca.
Posts: 34,327
Default

Well, as long as we're dragging up a seven year old necro thread...

If an infinite number of rednecks riding in an infinite number of pickup trucks fire an infinite number of shotgun rounds at an infinite number of highway signs, they will eventually produce all the world's great literary works in Braille.
__________________

There are traitors and terrorists among us. They call themselves "Republicans." They are a greater threat to the U.S. than Al Qaeda and all the Al Qaeda wannabes. They have infested our democratic institutions with the sole objective of thwarting the will of the majority of our citizens.

And Whos's Watching Over Who's Watching Over You?
Tell me, who's telling who's telling you what to do what to do?
Harvey is offline   Reply With Quote
Old 02-05-2013, 11:27 PM   #59
m1ldslide1
Platinum Member
 
m1ldslide1's Avatar
 
Join Date: Feb 2006
Location: PDX
Posts: 2,322
Default

Quote:
Originally Posted by forrestroche View Post
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.
Seriously considering making this my new sig.
__________________
One's mind, once stretched by a new idea, never regains its original dimensions.
--Oliver Wendell Holmes

Crunching for Team AnandTech!
m1ldslide1 is offline   Reply With Quote
Old 02-11-2013, 08:29 AM   #60
Mushkins
Golden Member
 
Join Date: Feb 2013
Posts: 1,026
Default

Quote:
Originally Posted by JudgeDracoAmunR View Post
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!
That has nothing to do with probability, that's just simple iteration.
Mushkins is offline   Reply With Quote
Old 02-11-2013, 11:12 AM   #61
DSF
Diamond Member
 
Join Date: Oct 2007
Location: Baltimore, MD
Posts: 4,872
Default

Considering that he just joined the forums and this is his only post, something tells me he bounces around the interwebs searching for discussions on the Infinite Monkey Theorem and pastes his stock post in.
DSF is offline   Reply With Quote
Old 02-11-2013, 12:38 PM   #62
JTsyo
Diamond Member
 
JTsyo's Avatar
 
Join Date: Nov 2007
Location: NJ
Posts: 9,110
Default

Quote:
Originally Posted by Harabec View Post
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.

Last edited by JTsyo; 02-11-2013 at 12:44 PM.
JTsyo is offline   Reply With Quote
Old 02-11-2013, 01:41 PM   #63
koshling
Member
 
Join Date: Nov 2005
Posts: 43
Default

Quote:
Originally Posted by JTsyo View Post
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.
...and how would you filter out the 'useful' outputs from the dross?
koshling is offline   Reply With Quote
Old 02-11-2013, 03:32 PM   #64
Ben90
Platinum Member
 
Join Date: Jun 2009
Posts: 2,823
Default

The bound for the length of a story approaches infinity. Example:

JTsyo pooped his pants. But he woke up and realized it was just a dream. Then he woke up again and realized he was dreaming about a dream. Then he woke up again and realized he was dreaming about dreaming about a dream. Then he woke up again and realized he was dreaming about dreaming about dreaming about a dream...
Ben90 is offline   Reply With Quote
Old 02-11-2013, 04:11 PM   #65
TuxDave
Lifer
 
TuxDave's Avatar
 
Join Date: Oct 2002
Posts: 10,442
Default

Quote:
Originally Posted by JudgeDracoAmunR View Post
...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!
Oh is that all? Just pick up a supercomputer that can count off to infinity in very little time? So simple...


...
__________________
post count = post count + 0.999.....
(\__/)
(='.'=)This is Bunny. Copy and paste bunny into your
(")_(")signature to help him gain world domination.
TuxDave is offline   Reply With Quote
Old 02-11-2013, 06:05 PM   #66
ksheets
Senior Member
 
ksheets's Avatar
 
Join Date: Aug 2000
Location: BFE Ohio
Posts: 604
Default

Quote:
Originally Posted by JTsyo View Post
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.

Been to a Movie Theatre lately?
__________________
"I just quit. I stopped grass then -- I mean, pretty much -- and decided to get off the couch," -Brad Pitt.
ksheets is offline   Reply With Quote
Old 02-14-2013, 02:22 PM   #67
nOOky
Senior Member
 
nOOky's Avatar
 
Join Date: Aug 2004
Posts: 770
Default

Reading this made me dizzy, so I did the following. Since Chuck Norris has reportedly counted to infinity, twice, I decided to calculate in my head exactly where PI starts repeating. I can tell you that it starts with a 1, and ends with a 7. I'd type the characters down, but I'm no monkey at the keyboard with infinity on his side.

PM me if you really want the result.
__________________
System 1: i7-2600K @ 4.4GHz, Asus P8P67 PRO, 2X8 G-SKILL DDR3 1600, Hyper 212+, Sapphire 7970, Samsung 840 Pro 256GB - Win 8 Pro, Kingston HyperX 3K 120GB - Windows 7, all in a HAF-X with an Asus VW266H.
System 2: FX6300 @ 4.5, Asus M5A97 R2.0, 2 x 4 G-Skill 1600, Corsair Force GT 180 - Windows 8, HD6870, 32" Panasonic monitor 1080p.
System 3: Asus laptop, Windows 8. Intel 160GB SSD, G50Vt-X5.
nOOky is offline   Reply With Quote
Old 02-14-2013, 09:33 PM   #68
drinkmorejava
Diamond Member
 
drinkmorejava's Avatar
 
Join Date: Jun 2004
Location: MA
Posts: 3,410
Default

This reminds me of a problem I had at work today. The life of a part was predicted to be something like 10^31 hours...which is only a few orders of magnitude greater than the age of the universe.
drinkmorejava is offline   Reply With Quote
Old 02-15-2013, 03:12 AM   #69
Fayd
Diamond Member
 
Fayd's Avatar
 
Join Date: Jun 2001
Location: Around
Posts: 7,603
Default

Quote:
Originally Posted by A5 View Post
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.
more to the point, because it's infinity, it's "insert EVERY work ever produced", recreated infinite times with certainty.
__________________
Hold me closer Tony Danza
Count the Headlights on the Highway
Lay me down in sheets of linen
You've had a busy day today.
Fayd is offline   Reply With Quote
Old 02-15-2013, 03:17 PM   #70
TuxDave
Lifer
 
TuxDave's Avatar
 
Join Date: Oct 2002
Posts: 10,442
Default

Quote:
Originally Posted by A5 View Post
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.
__________________
post count = post count + 0.999.....
(\__/)
(='.'=)This is Bunny. Copy and paste bunny into your
(")_(")signature to help him gain world domination.
TuxDave is offline   Reply With Quote
Old 02-16-2013, 12:30 AM   #71
Fayd
Diamond Member
 
Fayd's Avatar
 
Join Date: Jun 2001
Location: Around
Posts: 7,603
Default

Quote:
Originally Posted by TuxDave View Post
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.
__________________
Hold me closer Tony Danza
Count the Headlights on the Highway
Lay me down in sheets of linen
You've had a busy day today.
Fayd is offline   Reply With Quote
Old 02-16-2013, 12:47 AM   #72
IDNeon
Junior Member
 
Join Date: Feb 2013
Posts: 2
Default

The probability that theonkey will hit the right combination of keys is a permutation of the required character posible and the number of times the choice of character is made.

Since the probability approaches infinity and 1/infinity approaches 0 one can say the entire point is academic and the actual probability is zero.

This is also true for genetic drift and is one of my several throttle to disprove evolution
IDNeon is offline   Reply With Quote
Old 02-16-2013, 11:53 AM   #73
jimhsu
Senior Member
 
Join Date: Mar 2009
Posts: 702
Default

Probability as summarized by Nassim Taleb (paraphrased):

You ask a question to a statistician and an everyday guy on the street: "If I flip a fair coin 20 times and it lands heads, what is the probability of getting a head on the next flip?"

Statistician: 0.5 obviously, since it's a fair coin.
Guy: You call that "fair"? It's almost definitely going to be a head.

----

In academics, the only acceptable answer obviously is the statistician's. In the real world ... well you're not so sure.

On topic, the probability that your keyboard is ruined by monkey urine is almost certainly higher than the probability that your monkey composes the first word in a Shakespeare play. (independent demonstrated experiment, n=6). The distribution of letters produced was also highly non-random.

Last edited by jimhsu; 02-16-2013 at 11:59 AM.
jimhsu is offline   Reply With Quote
Old 02-19-2013, 11:10 PM   #74
sao123
Lifer
 
sao123's Avatar
 
Join Date: May 2002
Location: Steeler Nation
Posts: 11,987
Default

7 years later, all my monkeys are on strike due to insufficient banana's and poo flinging breaks
__________________
Quote:
Originally posted by: Eaglekeeper
Most anyone in the US that grew up in the city/inner city does not have the skills/knowledge to properly survive off the land.

Originally posted by: Dank69
It's (expletive deleted) easy. Throw seeds on the ground. Plants sprout. Pick hamburgers. Repeat.
sao123 is offline   Reply With Quote
Old 02-20-2013, 02:04 AM   #75
TuxDave
Lifer
 
TuxDave's Avatar
 
Join Date: Oct 2002
Posts: 10,442
Default

Quote:
Originally Posted by Fayd View Post
why not? now it's just a 3-dimensional random walk. that still visits all the probability space infinite times, when taken to infinity.
Yeah that's what I would've initially guessed but its not true. You do not have a 100% probability of randomly walking back to the origin over infinite time give that you are traveling in 3 or more dimensions. So you will not hit the origin an infinite number of times. You may in fact never get back!

http://mathworld.wolfram.com/PolyasR...Constants.html

To convince yourself you could write a program that terminates when you return to the origin and two out of three runs your program will run forever.
__________________
post count = post count + 0.999.....
(\__/)
(='.'=)This is Bunny. Copy and paste bunny into your
(")_(")signature to help him gain world domination.

Last edited by TuxDave; 02-20-2013 at 02:08 AM.
TuxDave is offline   Reply With Quote
Reply

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -5. The time now is 06:34 AM.


Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2014, vBulletin Solutions, Inc.