Infinite Universe and random number generators.
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Of course that is assuming you have an infinite amount of time... I wonder if we truly understand the thought of "infinite" :)
Rocky <>< Recent Blog Post: CubeTube – Power work are from ambient light!
Rocky Moore wrote:
I wonder if we truly understand the thought of "infinite"
I very much doubt it. It's too much an unreal concept for the human brain to comprehend. Although, there was one particular mathematician on the recent Horizon program who vehemently dismissed the possibility of infinity because he couldn't get his head round the idea. His theory was, that if you kept adding one to a number you would eventually go full circle and end up at zero. Weird or what? But as it can't be proved that infinity actually exists, he might well be right.
No trees were harmed in the posting of this missive; however, a large number of quantum states were changed.
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I got this idea from the Infinite monkey theorem, which states that: "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare." On that basis, that means that if the Universe really is infinite, then somewhere there must be a random number generator that keeps producing the same number over and over again simply because in an infinite Universe, however small the chance/probability is, a random number generator that produces the same number every time must exist. My head hurts :) Does anyone understand what I'm trying to explain?
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
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Lloyd Atkinson☺ wrote:
if the Universe really is infinite
It isn't, more than likely.
Lloyd Atkinson☺ wrote:
there must be a random number generator that keeps producing the same number over and over again
If you have an infinite number of [fair] generators, this is possible. The problem you are having is because of the way humans perceive probability. Think of a coin tossed three times. Three heads is just as likely as three tails, two heads with one tails and two tails with one heads. All possible outcome sets have equal probability, it is just psychologically more notable if the three heads come up. This principle extends to your number generator.
Lloyd Atkinson☺ wrote:
because in an infinite Universe, however small the chance/probability is, a random number generator that produces the same number every time must exist.
Only if an infinite number if generators exist. The probability of a generator being created over a unit of space (and/or time) can change in such a way that even in an infinite universe an non-infinite number of generators exits. [edit] Wasn't this a Dilbert or XKCD cartoon? [Edit 2] Both! http://xkcd.com/221/[^] http://www.random.org/analysis/dilbert.jpg[^]
Dalek Dave: There are many words that some find offensive, Homosexuality, Alcoholism, Religion, Visual Basic, Manchester United, Butter.
modified on Saturday, February 27, 2010 1:07 PM
Keith Barrow wrote:
The probability of a generator being created over a unit of space (and/or time) can change in such a way that even in an infinite universe an non-infinite number of generators exits.
if you're talking about a truly infinite universe then even considering varying probabilities of the existence of random number generators, you still end up with an infinite number of random number generators; it's just a smaller infinity than the size of the universe, but no less infinite.
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I got this idea from the Infinite monkey theorem, which states that: "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare." On that basis, that means that if the Universe really is infinite, then somewhere there must be a random number generator that keeps producing the same number over and over again simply because in an infinite Universe, however small the chance/probability is, a random number generator that produces the same number every time must exist. My head hurts :) Does anyone understand what I'm trying to explain?
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
:-) Interesting 'Infinite Monkey Theorem' :) . I think that it should be possible as few reverse engineering tools might use this concept. Karthik Balaguru
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Keith Barrow wrote:
The probability of a generator being created over a unit of space (and/or time) can change in such a way that even in an infinite universe an non-infinite number of generators exits.
if you're talking about a truly infinite universe then even considering varying probabilities of the existence of random number generators, you still end up with an infinite number of random number generators; it's just a smaller infinity than the size of the universe, but no less infinite.
That's not fair .. I was just starting to get a handle on this conversation .. just :)
The only thing unpredictable about me is just how predictable I'm going to be.
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OriginalGriff wrote:
Didn't spot the little flaw in the idea too quickly...
Recently on the BBC's Horizon programme, they showed a computer program that generated random letters to type the works of Shakespeare... it had been running about two weeks and had managed to type the grand total of the first sentence of his works :-O
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
First Folio Edition? Original or modern spelling?
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I got this idea from the Infinite monkey theorem, which states that: "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare." On that basis, that means that if the Universe really is infinite, then somewhere there must be a random number generator that keeps producing the same number over and over again simply because in an infinite Universe, however small the chance/probability is, a random number generator that produces the same number every time must exist. My head hurts :) Does anyone understand what I'm trying to explain?
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
IMHO, No. I don't think you would ever have a fair random umber generator that would always produce the same number. You could have one that would produce a very very long sequence that was all that same. As the odds of this are very small but still greater than zero. But the odds that a single random number generator produces a specific infinite sequence, such as all the same number, is zero. So it doesn't matter how many generators you have the probability still approaches zero.
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I got this idea from the Infinite monkey theorem, which states that: "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare." On that basis, that means that if the Universe really is infinite, then somewhere there must be a random number generator that keeps producing the same number over and over again simply because in an infinite Universe, however small the chance/probability is, a random number generator that produces the same number every time must exist. My head hurts :) Does anyone understand what I'm trying to explain?
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
I recently read the book Programming the Universe, by Seth Lloyd. I think it was this book, that talked about the infinite monkey theorem. And the probability that the monkeys could write shakespear given a keyboard with only letters numbers and puncutation, would be (1/(number of keys on the keyboard)^(number of letters in a shakespear book)) which is an enourmously small chance. One is more likely to create a simulated Universe in a very powerfull computer that will be able to output a Universe the same as ours. and also, a random number generator that produces the same number every time, is not a random number generator at all, by the definition of random.
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I got this idea from the Infinite monkey theorem, which states that: "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare." On that basis, that means that if the Universe really is infinite, then somewhere there must be a random number generator that keeps producing the same number over and over again simply because in an infinite Universe, however small the chance/probability is, a random number generator that produces the same number every time must exist. My head hurts :) Does anyone understand what I'm trying to explain?
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
Yes, that is what it means. A problem though with pseudo random number generators, I think, is that normally they don't produce such sequences. I think their internal structure simply prohibits that, which is not how it is supposed to be when you think of it from the perspective you describe. But, of course, in practical reality it does not matter, and they do produce at least relatively long unlikely such sequences, which is good enough. Another funny consequence of this perspective is that somewhere in Pi (at least if we can consider it a normal number (see http://en.wikipedia.org/wiki/Normal_number[^]) we will find encoded in say unicode the works of Shakespeare. We will also find mpeg4 encoded movies, very professionally made, of your life, even the part which has not yet happened. There will also be one such version of your life, but where you have a carrot instead of your normal nose. Somewhere there will also be found a perfect explanation of life, the universe, and everything. And so on and so forth. Magnus
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Rocky Moore wrote:
I wonder if we truly understand the thought of "infinite"
I very much doubt it. It's too much an unreal concept for the human brain to comprehend. Although, there was one particular mathematician on the recent Horizon program who vehemently dismissed the possibility of infinity because he couldn't get his head round the idea. His theory was, that if you kept adding one to a number you would eventually go full circle and end up at zero. Weird or what? But as it can't be proved that infinity actually exists, he might well be right.
No trees were harmed in the posting of this missive; however, a large number of quantum states were changed.
Digital Thunder wrote:
His theory was, that if you kept adding one to a number you would eventually go full circle and end up at zero. Weird or what?
When I do that, I get negative numbers first. I suppose I should use Unsigned types.
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Keith Barrow wrote:
The probability of a generator being created over a unit of space (and/or time) can change in such a way that even in an infinite universe an non-infinite number of generators exits.
if you're talking about a truly infinite universe then even considering varying probabilities of the existence of random number generators, you still end up with an infinite number of random number generators; it's just a smaller infinity than the size of the universe, but no less infinite.
a "smaller infinity"??? Now my sides hurt!!! What do you get when two moron atoms are bonded to one oxygen atom? An oxymoron!
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I got this idea from the Infinite monkey theorem, which states that: "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare." On that basis, that means that if the Universe really is infinite, then somewhere there must be a random number generator that keeps producing the same number over and over again simply because in an infinite Universe, however small the chance/probability is, a random number generator that produces the same number every time must exist. My head hurts :) Does anyone understand what I'm trying to explain?
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
Here's the text version: http://thedailywtf.com/Articles/Quite-Contrary.aspx[^]
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I got this idea from the Infinite monkey theorem, which states that: "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare." On that basis, that means that if the Universe really is infinite, then somewhere there must be a random number generator that keeps producing the same number over and over again simply because in an infinite Universe, however small the chance/probability is, a random number generator that produces the same number every time must exist. My head hurts :) Does anyone understand what I'm trying to explain?
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
Your reasoning is incorrect. First, the universe is REALLY big, but it is not infinite. So there can only be a finite number of random generators that we have to work with. Second: The probability of getting N heads in a row decreases exponentially with N. The probability of getting infinite heads in a row is exactly zero. If we allow an infinite number of random generators, then we still get zero probability. This is by L'Hopital's rule: the probability of successive heads decreases toward zero more quickly than number of generators increase toward infinity. I did not have time to read the other comments. My humble apologies if I am repeating something that has already been said.
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I remember one april fools day seeing a site that had a new compression algorithm. Represent a file as binary. That's 1s and 0s. 0 means nothing, so throw them away. All you have are 1s, so just compress that, and you get a super small file. I spent a day arguing with a guy at work that this was awesome, b/c he was too dumb to see it was a joke.
Christian Graus Driven to the arms of OSX by Vista. Read my blog to find out how I've worked around bugs in Microsoft tools and frameworks.
:laugh: :thumbsup:
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
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a "smaller infinity"??? Now my sides hurt!!! What do you get when two moron atoms are bonded to one oxygen atom? An oxymoron!
DragonsRightWing wrote:
a "smaller infinity"??? Now my sides hurt!!!
Whats infinity take one, infinity, or a different number? ;P
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
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Rocky Moore wrote:
I wonder if we truly understand the thought of "infinite"
I very much doubt it. It's too much an unreal concept for the human brain to comprehend. Although, there was one particular mathematician on the recent Horizon program who vehemently dismissed the possibility of infinity because he couldn't get his head round the idea. His theory was, that if you kept adding one to a number you would eventually go full circle and end up at zero. Weird or what? But as it can't be proved that infinity actually exists, he might well be right.
No trees were harmed in the posting of this missive; however, a large number of quantum states were changed.
I saw the Horizon programme too! :) Thats vaguely why I started thinking about Infinity ;P
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
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I saw the Horizon programme too! :) Thats vaguely why I started thinking about Infinity ;P
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
If I remember correctly, the conclusion of the program was that there are an infinite number of universes of infinite size. This begs a couple of questions: where does one universe meet another (for there to be more than one universe there surely has to be a boundary and if there is a boundary they can't be infinite) and secondly, if space is infinite (to fit these infinite universes in) is the volume of space larger than the sum of its universes (so is one infinity bigger than another)? I'm going to consult my good friend Jack Daniels and have a think about this. :laugh:
No trees were harmed in the posting of this missive; however, a large number of quantum states were changed.
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Your reasoning is incorrect. First, the universe is REALLY big, but it is not infinite. So there can only be a finite number of random generators that we have to work with. Second: The probability of getting N heads in a row decreases exponentially with N. The probability of getting infinite heads in a row is exactly zero. If we allow an infinite number of random generators, then we still get zero probability. This is by L'Hopital's rule: the probability of successive heads decreases toward zero more quickly than number of generators increase toward infinity. I did not have time to read the other comments. My humble apologies if I am repeating something that has already been said.
You have forgotten the Physics Shop at the Other End of the Universe. There you can purchase bottled portions of infinity, along with useful frictionless surfaces and massless beams. Bottles of space, under the brand "Really really really BIG", are also available. Unfortunately, they are out of stock of bug-free code.
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DragonsRightWing wrote:
a "smaller infinity"??? Now my sides hurt!!!
Whats infinity take one, infinity, or a different number? ;P
I know you believe you understood what you think I said, but I am not sure you realize what you heard is not what I meant.
If infinity = infinity-1, then 0=-1, a contradiction (subtract infinity on both sides). But it gets worse: Consider the sequence { (2*x)/x }, as x diverges to infinity. It would seem that infinity / infinity = 2. Or maybe not. What if I replace my sequence by { (3*x)/x }, or for that matter { (n/x)/(1/x) } then 0/0 = n = anything you like. Infinity might have some standard notion of divergence of a sequence, but there is a reason why we don't define operator arithmetic on infinity, and don't include "infinity" on the line of real numbers, and much of it has to do with problems like this. In any case, a lot of these concepts becomes easier for anyone who has had a bit of introductory calculus. It has taken very smart people a long time to come up with suitable notions of infinity that is mathematically viable. If you look at the kind of definitions that we take for granted (e.g. the epsilon-delta definition for limit: "For every epsilon, there exists a delta such that | x - a | < delta implies | f(x) - L | < epsilon."), you can see for yourself that it's not easy to come up with an understanding of infinity that you can mathematically manipulate. (Exercise: Work out how infinity comes into play in the above definition). It gets even worse, because even though the rational numbers have infinitely many numbers between 0 and 1, it's still not nearly big enough to describe sqrt(2)/2. So take a little calculus. Some of these concepts aren't as hard as you might think. To answer your question, infinity and infinity minus one are both infinite, but they are not equal, because infinity is not equal or even unequal to anything, including infinity. It's simply undefined, and for good reason. Anyways, these are just my 2c. There are a lot of books and people out there who can describe this very much better than I can in my feeble attempt.
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You have forgotten the Physics Shop at the Other End of the Universe. There you can purchase bottled portions of infinity, along with useful frictionless surfaces and massless beams. Bottles of space, under the brand "Really really really BIG", are also available. Unfortunately, they are out of stock of bug-free code.
