The Infinite Monkey Principle

[Q.G.]

I'm sure that it's not. So is anyone who's done any amount of science.

You think so?
Perhaps, then, there's a lot of science you haven't looked into yet?

 

[Pete H]

No. Infinity most certainly does not exist, in a different way that 2 does not exist.

Perhaps you could define "exist" in both senses then?

The infinite monkey thing is an expression of a very human yet completely unfounded optimism, the believe that given an infinite chance (there's another concept that is more confusion than anything else) that something might happen, it must. It's an expression that given (albeit ludicrous) the right circumstances, nothing is impossible. And that makes us feel just great.

This seems over-stated to me. If the thought experiment says "if you have enough monkeys in a race one of them will arrive at the finish before it started running" then it is nonsense and will not happen however many races one tries. However, finding that a randomly generated text reproduces the works of Shakespeare does not violate any physical principles. If you restrict the maximum text length to something at least the length of Shakespeare's works, then there is a very small but finite probability of generating his works randomly. So generate enough random texts, and you have probability 1 of having produced Shakespeare's works. It still doesn't mean that you have, but it's incredibly unlikely that you haven't.

 

[st23]

I guess I see that monkeys could have a chance, given enough time, to complete the works Shakespeare. I was joking about their incompetence, and I'm sure they could learn to type all of the keys. Even if they are not as random as a computer, it could take a billion years to the power of a billion instead of the billion years for a computer, but it is statistically possible though perhaps outrageously improbable.
I think that probability can be kind of like philosophy at times, isn't this correct? It works but we don't know why. If you flip a coin there's a one in two chance it will be heads. If you get tails, and you flip it the second time there's still only a 1 in 2 chance it will be heads. If you flip it the second time and get tails, your third attempt will still be a 1 in 2 chance to get heads and so on. There is no guarantee you will ever flip heads, but somehow we do. And if we do it enough times we get a nice bell curve showing that it all averages out.

Pete H, I'm sorry if my first response seemed disrespectful, I re-read it and it sounded abrupt. I should learn not to post something at 3:00 in the AM when I've just gotten up to go to the bathroom.
Steve

 

[Nicholas Lindan]

As said before, infinity would not be needed to generate the entire works of Shakespeare at random, just a really, really long time.

Say, oh, 14 billion years or so? And a really, really big Universe. Wonder if an Alien on another planet has written Hamlet?

There is a proposition that (1 + oo) is not equal to (oo + 1). Never quite understood the logic behind it.

It is a subject that requires a lot of beer.

 

[Q.G.]

This seems over-stated to me. If the thought experiment says "if you have enough monkeys in a race one of them will arrive at the finish before it started running" then it is nonsense and will not happen however many races one tries. However, finding that a randomly generated text reproduces the works of Shakespeare does not violate any physical principles. If you restrict the maximum text length to something at least the length of Shakespeare's works, then there is a very small but finite probability of generating his works randomly. So generate enough random texts, and you have probability 1 of having produced Shakespeare's works. It still doesn't mean that you have, but it's incredibly unlikely that you haven't.

Physical principles?

That's the problem.
Talk about something, a situation, how impropable it may be, but something that could almost happen.
Then physical principles are brought in to 'explain' what could happen.
With that the entire thing is immediately lost in flights of fancy ever more fancifull than the already extremely stretched flight of fancy we began with.

You will also have probability 1 that no text at all is produced by the same infinite number of monkeys.
Just a matter of rephrasing the question.

Something that is lost the moment "physical principles" or mathematics, logic or anything else that doesn't care about anything else but a (conceived) harmonious relation between meaningless symbols is brought in.

 

[Q.G.]

I think that probability can be kind of like philosophy at times, isn't this correct? It works but we don't know why.

No, it's not correct.
Philosophy never works. All it does is take things apart so that they too don't work anymore. That's the beauty, and power, of it.

Probability does work.
Just as luck does. Because it's just another name for luck.

 

[Pete H]

Physical principles?

That's the problem.
Talk about something, a situation, how impropable it may be, but something that could almost happen.
Then physical principles are brought in to 'explain' what could happen.
With that the entire thing is immediately lost in flights of fancy ever more fancifull than the already extremely stretched flight of fancy we began with.

Anything violating physical principles must be a flight of fancy. The typing monkeys are a flight of fancy, but you can replace them with a computer generating random texts if you prefer, without changing the basic argument.

You will also have probability 1 that no text at all is produced by the same infinite number of monkeys.
Just a matter of rephrasing the question.

Quite possibly one or some of them will produce a blank text, and you may also come across the Bible, Das Kapital, and many other well-known works included in the random texts. So what?

Something that is lost the moment "physical principles" or mathematics, logic or anything else that doesn't care about anything else but a (conceived) harmonious relation between meaningless symbols is brought in.

What is lost? I don't understand this.

 

[Q.G.]

Anything violating physical principles must be a flight of fancy. The typing monkeys are a flight of fancy, but you can replace them with a computer generating random texts if you prefer, without changing the basic argument.

The flight of fancy i meant was the one that flies away from a situation towards featureless principles.

Russel's paradox was mention in passing. Another thing that only exists in principle, not a problem (like most paradoxes - perhaps even all, but saying that would presume knowledge of every paradox that is know and every paradox we might not yet know of. And ... [etc.]) in 'real life'.

Yes, we could replace the typing monkeys with computers. But why would we?

Quite possibly one or some of them will produce a blank text, and you may also come across the Bible, Das Kapital, and many other well-known works included in the random texts. So what?

The 'so what' was that the probability will be 1 (is it then still a probability? A confused concept, "probability") that no text at all will be produced.

Basically, anything that relies on things like "infinity" is a "what if?" thing with an impossible "if".
Sure, it's possible in flights of fancy. So what?

What is lost? I don't understand this.

What is lost is the grasp of the fact that we do not live in a world that consists of featureless and meaningless symbols, that can be juxtaposed and jumbled any way we like.
Yes, you can do whatever you want, 'in principle'. Especially if iffy concepts like infinity (or probability) are dragged in.
But so what (again)?
Those monkeys will not type Shakespeare. They can't even try. The entire thingy hinges on the impossibility of infinity, relies on the impossibility of infinity to make something impossible possible...

I'll have a plain coffee, no sugar, please.

 

[st23]

The entire thingy hinges on the impossibility of infinity, relies on the impossibility of infinity to make something impossible possible...

The OP mentioned infinity but it doesn't involve "infinity." The monkeys are given as much time as they please to finish, but they have to finish at some point to complete the work. This is not infinity to finish. Its a really, really, really long time... as much time as they want. Discussions about the possibility of infinity are irrelevant.

Getting a computer to randomly generate an "A" will take a certain amount of time. Getting it to randomly generate the word "And" will take even longer. But the probabilities of this can be calculated based on the possible combination of letters. How long does it take to generate a specific sentence? A specific paragraph? A specific chapter? A book? ... etc. This probably takes too long to carry out in our lifetime ... but it is possible.

Monkeys are much much slower than computers, but if they type randomly why could they not achieve the same thing in a vastly greater time? Nobody is suggesting that we try this, just theorizing that it is possible. Why monkeys and not a golf ball bouncing around a room with a typewriter? Of course, what could be cuter than a monkey?

Steve

 

[lxdude]

Yes, we could replace the typing monkeys with computers. But why would we?

Because computers don't bite, they don't spend time picking bugs off each other (though they might still need debugging), and they don't throw disgusting stuff at you.

 

[ntenny]

Because computers don't bite, they don't spend time picking bugs off each other (though they might still need debugging), and they don't throw disgusting stuff at you.

That is not at all my experience of them!

-NT

 

[st23]

It might be helpful to think of a computer trying to generate the letter "N". To do this it could generate random letters (this could be done by generating random numbers and assigning letters to it, a typical computer programing student assignment).

It could generate random numbers till it found an "N". It may take more than 26 tries because it may generate three B's or four z's etc before it gets to the "N" depending on how "random" your number generator is (yes computer programming students have to test their programs and results to see how evenly distributed or "random" they are ).

Worst case scenario that takes the most time: "N" is the last letter you end up generating and you have generated every other letter at least once, possibly a lot of times if you weren't very "random." You now have a set of 26 letters, every possible combination, but at least you got your "N"

If you want to generate the word "and" - you start generating random letters till you get the three in a row you are looking for. worst case senario is you have every possible three letter combination possible, some many times. This includes "aer" "for" "aaa" "dog", etc and the word "and" that you were looking for. You may get the word "and" sooner so you don't have to bother creating every single combination. You may get it on your 5th, 100th, or even your first try.

Want a copy of a ten thousand letter paper you wrote back in high school? You can do it it the hard way and generate ten-thousand-letter documents at random and review each one to see if its the one you want. You may end up with every possible combination of letters for a ten-thousand-letter document (which is a huge number of documents!) but you would have yours. You would also have the papers of all your classmates who had the same ten-thousand-letter assignment, and all the papers they could have written in ten thousand letters, and a whole lot of garbage... way more garbage than you could read in a lifetime. (your paper you wrote in High School may have been crappy, but lets not call it garbage, too, for sake of clarity )

Someone could calculate all the permutations/combination's of letters possible in a ten-thousand letter document, so it is a finite number for the maximum number of documents you might need to generate. It would take a very long time, even on a computer (unless the computer gets it on it's first random try .. but who is that lucky )

Is that easy with a computer? yes
Does it take a lot of time? yes

Is that easy with a few monkeys typing random letters on typewriters? No. But it is possible.
Would it take a lot of time? Yes, an extremely long time. Don't give the monkeys or their descendants a deadline and they should do fine (we know monkeys don't work well with stress ) Don't expect results for millions of years and you will both be happy.

Extrapolate that to the works of Shakespeare.

Why would anyone propose the question of a monkey, a typewriter and Shakespeare? It generates a lot of thought. Now we can ask if the monkey could use a word processor, which one should it use?

 

[Vaughn]

Anything violating physical principles must be a flight of fancy. The typing monkeys are a flight of fancy, but you can replace them with a computer generating random texts if you prefer, without changing the basic argument.

An old sci fi short story -- two computer techs are walking towards their waiting plane in the evening somewhere in Tibet. They were just checking on a computer and printer they had sold to a Buddhist sect. This sect holds that once they have written the 9 billion names of god (all possible combinations of the letters of their alphabet), then Mankind had fullfilled their purpose and the world will end. To this end, they bought the computer and printer and were busily pasting the Names into the Book -- saving a lot of time compared the handwriting they have been doing for centuries.

The techs were in a bit of a hurry to leave -- the 9 billionth name was due at any time and they did not want to be around to catch any blame it the world just continued to go on normally. As they climb the stairway into the plane, one looks up and notices the stars going out.

Love that story -- Asminov, I believe. Infinity is a concept, not a thing -- and a concept perhaps only a handful of people alive have any clue about. We do not understand it, we will never understand it, so we might as play the fools that we are and think about an infinite number of monkeys doing their infinite things.

"Reality is the leading cause of stress amongst those in touch with it." Jane Wagner

 

[Q.G.]

The OP mentioned infinity but it doesn't involve "infinity." The monkeys are given as much time as they please to finish, but they have to finish at some point to complete the work. This is not infinity to finish. Its a really, really, really long time... as much time as they want. Discussions about the possibility of infinity are irrelevant.

You'd only think so if you ignore what it is all about. Which is that something impossible will happen, wil become possible, given "as much time as they want", or rather as much time as it takes.
And given the impossibility, it needs another impossibility. That of infinity.

The entire thing is exactly the same as someone asking silly people to pay large amounts of money, promising that for that they will become extremely sharp witted. All they then need to do is wait a bit, until tomorrow, in fact. And when they start complaining after about a week or two (they weren't the brightest, remember?) that it doesn't happen, he tells them they just have to wait a bit longer. Hadn't he told them that they had to wait until tomorrow, and wasn't it still today, and not tomorrow yet?

Getting a computer to randomly generate an "A" will [...]

... change the premise completely.
What a computer does or does not do depends on what we tell it to do. Both through hardwiring and software.

Do you really believe that computers and "random" go together?
In one of my many lives, i have actually had the task of explaining 13 and 14 year olds that they do not, and they understood.

It might be helpful to think of a computer trying to generate the letter "N". To do this it could generate random letters (this could be done by generating random numbers and assigning letters to it, a typical computer programing student assignment).

Those kids were amazed, at first, how i could predict the entire "random" number sequence they were generating. Until they understood the way "random" numbers were produced.
"Randomness" in computers is just as mythical an entity as infinity is.

 

[Perry Way]

That is not at all my experience of them!

-NT

When I lived in the outback mountains of Central Coast California, my nearest neighbor, half a mile away, had a monkey as a pet. It would sit over the front doorway like on the edge of a ledge and masturbate when visitors came over.

When I was a little boy, I remember a pirate with a monkey, and the monkey would take from you and go into your pockets and everything.

That is my experience with them! But still I love monkeys. And so would everyone if they read the Ramayana.

 

[kossi008]

"Random" is the second un-needed proposition that people here get hung up on, just as "infinite".

I don't remember exactly anymore how Borges' story went. But if you fix the number of pages per book, the number of characters per page and the number of characters in the character set, and then *methodically* go through all the permutations that this allows, you will have generated all books ever, allowing for sequels (Hamlet might be two books, e.g.) and translations and transscriptions and such. If you are picky, then let's say, you will have generated all books in English containing no pictures, or so.

You start with the book that contains all A's, then exchange the last letter for a 'B' and so on... There is no magic involved here. It just takes an incredibly long, but finite time to do this. And again to find anything useful among the generated books... so much so that it is pointless to try.

 

[st23]

You'd only think so if you ignore what it is all about. Which is that something impossible will happen, wil become possible, given "as much time as they want", or rather as much time as it takes.
And given the impossibility, it needs another impossibility. That of infinity.

if something is impossible giving it infinity does not help. giving the monkeys no deadline is not the same as waiting for infinity to "happen." If it is impossible for monkeys to type Shakespeare's works it has nothing to do with the fact that we will not reach the end of time.

As an aside question, when do you think time will end?

... change the premise completely.
What a computer does or does not do depends on what we tell it to do. Both through hardwiring and software.

Do you really believe that computers and "random" go together?
In one of my many lives, i have actually had the task of explaining 13 and 14 year olds that they do not, and they understood.



Those kids were amazed, at first, how i could predict the entire "random" number sequence they were generating. Until they understood the way "random" numbers were produced.
"Randomness" in computers is just as mythical an entity as infinity is.

Computers can generate a sequence of numbers that will have an even distribution which can come as close as anything else to generating a TRUE? random number, whatever that is. I think the "randomness" of a sequence of numbers can be tested using math to see how it conforms to certain equations. I believe this is our definition of random in statistics. Some sets of numbers are more "random" because they are closer to the ideal curve (or line) when put on a graph.

I think "random" is kind of an enigma that we do not truly understand. If it is possible for a human to generate a TRULY random number using math, a computer could do it. This is a shortcoming of humanity, not computers. Neither should feel inadequate though. Its not easy to solve as far as I know, but I haven't done in depth research on the topic.

Yes SOME of the "random" sequences are repeatable because this is extremely helpful in duplicating results in experiments, simulations, etc. The fact that the numbers are evenly distributed is the important thing.

It is possible to generate a sequence of numbers that is NOT repeatable by, for example, using a number from the system clock as a variable (this adds a somewhat "random" element because the computer reads the clock at an unspecified and different time). You must have been using an extremely simple number generator to be able to guess the next number, and you were most likely using the same equation as the computer and doing the math yourself, which may astonish 1st graders but does not point out any weakness in computers.

There are some algorithms that generate very "random" appearing sequences that would give a even distribution of numbers or "letters" adequate for most purposes, including ours. I hope you explain this to future students.

 

[st23]

"Random" is the second un-needed proposition that people here get hung up on, just as "infinite".

I don't remember exactly anymore how Borges' story went. But if you fix the number of pages per book, the number of characters per page and the number of characters in the character set, and then *methodically* go through all the permutations that this allows, you will have generated all books ever, allowing for sequels (Hamlet might be two books, e.g.) and translations and transscriptions and such. If you are picky, then let's say, you will have generated all books in English containing no pictures, or so.

You start with the book that contains all A's, then exchange the last letter for a 'B' and so on... There is no magic involved here. It just takes an incredibly long, but finite time to do this. And again to find anything useful among the generated books... so much so that it is pointless to try.

You are correct that random is not needed. You could systematically generate all the possible text by sequence, which would be much faster.

The premise of using monkeys is that by evenly distributed random characters one could also generate the needed variations, although at a much slower pace. I think this is to demonstrate the effects of probability.

 

[Q.G.]

if something is impossible giving it infinity does not help. giving the monkeys no deadline is not the same as waiting for infinity to "happen."

Who is waiting for infinity to happen?

I suspect you're thinking is far too complicated.
An impossible problem is (' by definiton') easy to solve, using an impossible solution.
In fact, given that the problem is impossible, only impossible solutions to it exist. That's why it is impossible in the first place.

If it is impossible for monkeys to type Shakespeare's works it has nothing to do with the fact that we will not reach the end of time.

Who suggested that it would?

As an aside question, when do you think time will end?

Do you think it will?

Time is another of those things we don't understand. So i have no thoughts about whether it will end or not, because i know i don't know.
Augustine (at least, i believe it was him - time has clouded my memory ) perhaps gave the best 'explanation' of time: the past only exists in our memory. The future only in our expectation. The present does not exist (or if you would like to think it does: it is infinitessimal small).

Computers can generate a sequence of numbers that will have an even distribution which can come as close as anything else to generating a TRUE? random number, whatever that is. I think the "randomness" of a sequence of numbers can be tested using math to see how it conforms to certain equations. I believe this is our definition of random in statistics. Some sets of numbers are more "random" because they are closer to the ideal curve when put on a graph.

In short: computers can't 'do' randomness.

You seem to suggest that something can approach randomness. It's like being pregnant, though. Or like being unique.

You can 'bend' definitions to make them fit what you can have. But that's nothing else but cheating.

I think "random" is kind of an enigma that we do not truly understand. If it is possible for a human to generate a TRULY random number using math, a computer could do it. This is a shortcoming of humanity, not computers. Neither should feel inadequate though. Its not easy to solve as far as I know, but I haven't done in depth research on the topic.

The word "generate" holds a gigantic clue.

If i can generate something (no matter how), it is not random.
And there's nothing to prevent me generating the same thing again. And again. And again. So it's very deterministic, very predictable, that human/computer generated randomness. So not random.

But is it a shortcoming? That would suggest that, even though impossible, it doesn't have to be impossible.
You have started on your way to postulating something impossible to find a solution to yet another impossible problem. Perhaps using the concept of, oh... what shall be pick, "inifinity" can help you solve this?

Yes SOME of the "random" sequences are repeatable because this is extremely helpful in duplicating results in experiments, simulations, etc. The fact that the numbers are evenly distributed is the important thing.

Important, for what?
The thing to keep in mind is that those sequences may be anything, but random.

It is possible to generate a sequence of numbers that is NOT repeatable by, for example, using a number from the system clock as a variable (this adds a somewhat "random" element because the computer reads the clock at an unspecified and different time). You must have been using an extremely simple number generator to be able to guess the next number, and you were most likely using the same equation as the computer and doing the math yourself, which may astonish 1st graders but does not point out any weakness in computers.

There are some algorithms that generate very "random" appearing sequences that would give a even distribution of numbers or "letters" adequate for most purposes, including ours. I hope you explain this to future students.

[/QUOTE]

I did indeed use a simple random generator. The one built-in to the implementation of a (i believe it was) C compiler.
But you're wrong looking for more complex thingies. Complexity is not an issue.

Except (there's always an exception or two) that it gets easier to fool people into believing that a generated series of numbers could be random, the more complex the way the numbers are generated.
And that it becomes more work to generate a 'random' series.

As i explained the kiddies then.

Being "adequate" is not a substitute for lacking randomness. Something that is not random is not random. No matter how well it may suit your needs.

 

[ntenny]

An impossible problem is (' by definiton') easy to solve, using an impossible solution.
In fact, given that the problem is impossible, only impossible solutions to it exist. That's why it is impossible in the first place.

I've completely lost track of what you're talking about in this bit. Are you saying that it's *impossible* for a monkey to type _Hamlet_? Or that it's impossible to assemble infinitely many monkeys? (And just as well, too.) Or something else entirely?

In short: computers can't 'do' randomness.

_Pace_ von Neumann and the famous quote, this is only true if you define "computers" sufficiently restrictively. Quantum effects are, as far as we know, truly random. (It's possible that there's something deterministic going on that we don't get, but a lot of experimental results in QM suggest otherwise. If the collapse of a wavefunction isn't "random", it's almost certainly something entirely new that we don't have a word for.) Those effects show up in the real world in phenomena like "flicker noise" in electronics, and it's easy enough to hook up a simple circuit as a peripheral to a computer and use its noise as a source of random numbers.

You could argue that this isn't the *computer* "doing" randomness, and in a literal sense you'd be right, but you might as well say "computers can't display images" (because it's the monitor, not the CPU, that does the display).

The reason quantum-randomness peripherals are uncommon isn't that there's something "impossible" about them, it's just that there's hardly any need for them. For *almost* everything people do with computers, a pseudo-RNG is good enough, but that's not the same as saying it's the *only* thing that can be done.

You can 'bend' definitions to make them fit what you can have. But that's nothing else but cheating.

Only if there's a "right" definition in the first place. By the way, if you've never tried to articulate exactly what "random" means, in good tight unambiguous terms, you may want to give it a try. Not only is it a surprisingly slippery concept, I think you'll find that you can't get there without a concept of infinity.

-NT

 

[Joe VanCleave]

Setting aside the issue of what constitutes "true" randomness (which I suspect can't ever be proven, unless given unlimited time and computational power), a more interesting question concerns "cryptographic" randomness; this is the kind of random sequence desired for use in, for instance, a so-called "one time pad" Vernon cipher to achieve an unbreakable encryption.

Any sequence of supposedly "random" numbers generated by an algorithm are not sufficiently random for cryptographic purposes. Therefore, any computer-generated string of numbers, if based on an algorithm, cannot be random enough for cryptographic security. Such so-called "pseudo-random" number sequences, if used cryptographically, are essentially "string ciphers", and are very susceptible to cracking.

All software-based pseudo-random number generators are not cryptographically secure.

Interestingly, some one time pad systems were partially broken. This was achieved either by unrandom key sequences (many Soviet-era OTPs were generated by humans (not monkeys) typing on typewriters, which inevitably gave rise to nonrandom sequences of keystrokes); reusing the keys (therefore not truly "one time") or cross-referencing contextual information suspected to have been within the message. One such project had the code name of "Venona", and over a period of decades contributed to some understanding of Soviet espionage activities; but most of the Venona material remains unbroken to this day, a tribute to the security of a cryptographically secure OTP system, when used properly.

~Joe

 

[Q.G.]

I've completely lost track of what you're talking about in this bit. Are you saying that it's *impossible* for a monkey to type _Hamlet_? Or that it's impossible to assemble infinitely many monkeys? (And just as well, too.) Or something else entirely?

All that too, yes.

What i am saying is that suggestions that we do not need infinity is not true.
At least not as long as you want to stay with the things as it was set out.

We can change all that, start talking about another thing entirely. But then we would be, uhm... talking about another thing entirely.

So what i am saying was that an impossible problem cannot be solved. A solution would be impossible.
So 'is' (among other thingies) infinity. So infinity provides the perfect solution. We need infinity to have our monkeys type Shakespeare.
But (and that's where the thing falls down nonetheless) only as a possibility. Given an impossible solution to an impossible problem, there is no chance in hell that they will actually type Shakespeare, not ever.

It's all a play of words (pun intended). Possible, because the words are meaningless.
The fact that there is an infinite possibility that the infinite number of monkeys might hit the keys in the exact sequence needed to write Hamlet does not mean that it will happen.
The probability that they will only hit the space bar over and over again is just as great.
So is the probability that they will evolve and become (still illiterate) bicycle repairmen.
And that...

As mentioned many posts earlier, what we have here is that old ex falso sequitur qiudlibet, in an infinite way.
As mentioned here (and before too) we need that falsehood, infinity, to have our quodlibet follow.

This thing is like most paradoxes too: extremely easy to find your way out of the connundrum if only you 'get real', and break out of the confines set by the limited scope set by the vocabulary used.
We are not supposed to even try to understand what the terms used really mean (if anything), because that breaks the spell and spoils the sport.
But why would we not?

_Pace_ von Neumann and the famous quote, this is only true if you define "computers" sufficiently restrictively.

See? You understand how these games work.

But it is not. "Random" and the-result-of-something-we-do (directly or by proxy) are two things that will never meet.

There is no magic in computers.

Quantum effects are, as far as we know, truly random. (It's possible that there's something deterministic going on that we don't get, but a lot of experimental results in QM suggest otherwise. If the collapse of a wavefunction isn't "random", it's almost certainly something entirely new that we don't have a word for.) Those effects show up in the real world in phenomena like "flicker noise" in electronics, and it's easy enough to hook up a simple circuit as a peripheral to a computer and use its noise as a source of random numbers.

Again, you are giving meaning to terms using things we do not understand.

You could argue that this isn't the *computer* "doing" randomness, and in a literal sense you'd be right, but you might as well say "computers can't display images" (because it's the monitor, not the CPU, that does the display).

And again this bending thingy: "You can 'bend' definitions to make them fit what you can have. But that's nothing else but cheating."

The reason quantum-randomness peripherals are uncommon isn't that there's something "impossible" about them, it's just that there's hardly any need for them. For *almost* everything people do with computers, a pseudo-RNG is good enough, but that's not the same as saying it's the *only* thing that can be done.

And again: "Being "adequate" is not a substitute for lacking randomness. Something that is not random is not random. No matter how well it may suit your needs."

Sure. Noone says it can't be done, ever...
Get the picture?

Only if there's a "right" definition in the first place. By the way, if you've never tried to articulate exactly what "random" means, in good tight unambiguous terms, you may want to give it a try. Not only is it a surprisingly slippery concept, I think you'll find that you can't get there without a concept of infinity.

I know that it is a slippery concept. I think you'll find i have tried to convince, was it you?, that it is.

We do not need a "right" definition (again a slippery term is introduced to make the murky even more murky) to bend the definition we have and use. No.

 

[Q.G.]

The problem with cryptography is that if we use truly random keys (supposing that such things can exist) to code something, it will be impossible to have a key to decode it.
All we could do then is try anything (how long will that take?) and hope for the best. No guarantee that it will work. And if it does produce something, some fluke key produces something we could recognise as a thing of the sort that was coded, we have no way of knowing that it really is what we think it is, or something else completely.
So thank heavens that we can't produce truly random keys.

Unless, of course, you jot the key down on a scrap of paper and share that with the receiver. Which we of course do.

 

[st23]

Quote:
Originally Posted by st23
if something is impossible giving it infinity does not help. giving the monkeys no deadline is not the same as waiting for infinity to "happen."

Who is waiting for infinity to happen?

You said something to the effect that infinity is impossible. I am stating (over and over for some reason) that infinity doesn't have to exist for the proposed monkey experiment. The monkeys don't need forever. Just a a long time. Forget about infinity is what i am saying.

I suspect you're thinking is far too complicated.
An impossible problem is (' by definiton') easy to solve, using an impossible solution.
In fact, given that the problem is impossible, only impossible solutions to it exist. That's why it is impossible in the first place.

No, an impossible problem is not easy to solve. It is impossible to solve, by the definition of impossible. That's what impossible means. If it were possible to solve with an "impossible solution?????" as you say, it would not be impossible, by the definition of the word impossible. And to tell you the truth, an "impossible solution" is impossible, by the definition of the word impossible that you used to describe it. That's called logic. Not a meaningless group of symbols. Its how we form coherent arguments.

if you think the monkey experiment is impossible you should give reasons or use logic, not just repeat that it is impossible.



Originally Posted by st23
If it is impossible for monkeys to type Shakespeare's works it has nothing to do with the fact that we will not reach the end of time.

Who suggested that it would?

Didn't you suggest that because infinity is impossible the experiment was impossible? I can't scroll back now for an exact quote. I was stating that if the experiment is impossible, it is impossible for some other reason, like monkeys cant type all the keys, etc. Has nothing to do with infinity existing.

In short: computers can't 'do' randomness.

You seem to suggest that something can approach randomness. It's like being pregnant, though. Or like being unique.

You can 'bend' definitions to make them fit what you can have. But that's nothing else but cheating.

I'm not bending definitions and a sample of data can be appear more random than others.

Which of these data sets 0 to 10 is more random:

{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

{1,4,8,2,9,1,3,2,0,7,8,1,7,3,9,5,2,7,8,4,1,1,3,1,4,5,6,3,2,3,5,7,8,2,1}

The word "generate" holds a gigantic clue.

If i can generate something (no matter how), it is not random.
And there's nothing to prevent me generating the same thing again. And again. And again. So it's very deterministic, very predictable, that human/computer generated randomness. So not random.

Did you even read what I posted. I said it is possible to generate a "random" (note the quotes) sequence that is not repeatable by taking a value from the system clock. I suppose you could reset the clock and make sure the process runs at the same speed down to the millisecond. But as I said earlier... weather or not the characters generated fit you puristic vision of "random" is not important in the very least. It has to fit an even distribution of letters that for all practical purposes does what a "real" random number generator does. It can be repeatable. It can be repeatable by a first grader. It does not matter. It has to give a somewhat even distribution of letters. Therefor, you can't disregard the monkey experiment based on weather these are "REAL" random numbers or not as you did shown below:

But is it a shortcoming? That would suggest that, even though impossible, it doesn't have to be impossible.
You have started on your way to postulating something impossible to find a solution to yet another impossible problem. Perhaps using the concept of, oh... what shall be pick, "inifinity" can help you solve this?

 

[MattKing]

An old sci fi short story -- two computer techs are walking towards their waiting plane in the evening somewhere in Tibet. They were just checking on a computer and printer they had sold to a Buddhist sect. This sect holds that once they have written the 9 billion names of god (all possible combinations of the letters of their alphabet), then Mankind had fullfilled their purpose and the world will end. To this end, they bought the computer and printer and were busily pasting the Names into the Book -- saving a lot of time compared the handwriting they have been doing for centuries.

The techs were in a bit of a hurry to leave -- the 9 billionth name was due at any time and they did not want to be around to catch any blame it the world just continued to go on normally. As they climb the stairway into the plane, one looks up and notices the stars going out.

Love that story -- Asminov, I believe. Infinity is a concept, not a thing -- and a concept perhaps only a handful of people alive have any clue about. We do not understand it, we will never understand it, so we might as play the fools that we are and think about an infinite number of monkeys doing their infinite things.

"Reality is the leading cause of stress amongst those in touch with it." Jane Wagner

Actually it was Arthur C. Clarke .

Here is a link to the Wikipedia entry about the story (one of my favourites):
http://en.wikipedia.org/wiki/The_Nine_Billion_Names_of_God

And a further link to an online version:

http://lucis.net/stuff/clarke/9billion_clarke.html

This story has already made an appearance in the "deleted" thread here on APUG.