In the beginning ...

[Sean]

I have a problem with the whole monkeys and typewriters thing. For me the issue is randomness.

In a simplified version the monkey can have a die which he rolls repeatedly. Logically he will roll a six given infinite time but as the process is random it is not an absolute certainty that he will roll a six.

[MajGenl.Meade]

Sean

If that is the case, then it is equally not an absolute certainty that he will roll a 5. Or a 4, Or a 3. Or a 2. Or a 1. Which leaves us uncertain as to whether the die will ever stop rolling?

Put another way. You are saying that in infinite time it is certain he will roll 5 numbers but not certain that he'll roll a 6? If he cannot certainly roll a six given infinite time, then it was impossible for him to roll a 6. The issue is not solved by saying that since time is infinite he has infinite time ahead of him to roll everything but a 6, just by chance. Infinity to come is not "longer" than infinity past. They are equally as "long".

Your statement is of course unexceptionable as regards finite time. (Actually I think that randomness is the reason he will roll a 6. It certainly would not be random if he continually rolled a 1 - with unloaded dice). But I think you'll find that mathematical certainty is much stronger for a monkey rolling a 6 on day one than it is for life to emerge on earth - and yet the "nature-alone" folks say that given enough time, that life was a "certainty". (And as proof some of them offer the fact that we are here aren't we?)

I reject the contention of the always existing universe since an actual infinite is impossible. The monkeys cannot type all the works of Dawson and presumably would have the good taste not to do so

Regards
Meade

[Sean]

I'm not saying it is certain that he will roll the other five numbers... I chose 6 as an example. I agree that the odds against a 6 would be staggering over infinity but there is no absolute certainty.

It certainly would not be random if he continually rolled a 1 - with unloaded dice.

Why not? That's the beauty of total randomness. A series of 1s could happen just as easily as any other series of numbers.

I also don't believe that a 'certainty' can be strong or indeed weak. A certainty is an absolute. Anything else is a likelihood.

[thestoat]

Sean - the dice idea is great since it distills the argument right down. The odds of throwing a six are not zero - they are finite. Now, if the probability of throwing a 6 was 0% (ie impossible) then it won't happen. If the probability was 100% (ie definite) then it will happen every time. In between, then it is possible it will happen.

Get the monkey to throw. Not a six? No worries, throw again - we have time.

Throw again and again and again. Infinity never ends so the throwing never ends. If,after 9999999999999999999999999 millennia (which we could approximate to an infinite time), a 6 has not been thrown then mathematically the probability of throwing one tends to 0% (ie impossible). If it was not possible then it should be discarded as a possible outcome.

[Sean]

I agree totally with what you wrote Stoat. My only issue is absolute certainties being assigned to probabilitie (no matter how small or large. It's a contradiction in terms.

Should this be another thread?

[Andrew D]

Given sufficient time (and hardware), the hypothetical monkeys WILL type randomly every possible combination of letters that exists. One of those combinations is "The God Illusion". Admittendly that only took one monkey but the point is made. In infinite time, the monkeys MUST "eventually" hit upon any and all combination of letters.

So you keep saying. But saying something does not make it so.

It seems abundantly clear to me that something which is claimed to be "possible" but never actualises, even given infinite time to do so, is a thing for which the claim of "possible" is false. It is on a par with flying horses. Nothing can remain "possible" for infinity - because by definition if it does not happen (is unable to actualise) in infinite time then there is no time in which it is able to happen. A thing that cannot happen is an impossible thing.

Same wild leap again: "Does not happen" does not mean "is unable to actualise". "Does not happen" means merely "does not actualize". "Does not happen" and "cannot happen" are simply not synonymous.

I did not "put forward oscillating universes to explain away the problems of infinity". No problem with infinity has yet been articulated. I put forward the idea of an infinitely cyclical universe to point out that entropy also does not create an problem with infinity.

If you think that in infinite time, all possible events must happen, prove it. Repetition is not proof.

[Andrew D]

Throw again and again and again. Infinity never ends so the throwing never ends. If,after 9999999999999999999999999 millennia (which we could approximate to an infinite time), a 6 has not been thrown then mathematically the probability of throwing one tends to 0% (ie impossible). If it was not possible then it should be discarded as a possible outcome.

"Tends to 0%" does not mean "becomes 0%". (Just as "does not happen" does not mean "cannot happen".)

Take any number. Cut it in half. Cut it in half again. And again. And again. The results progress toward zero. But even if you do it an infinite number of times, the result never is zero.

"Impossible" does not mean "unlikely". Or "extremely unlikely". Or "really really really really ... really really really unlikely". "Impossible" means that the likelihood is a perfect zero. Not tending to zero -- actually being zero.

There is still no proof in this thread (or anywhere else that I have seen) that in infinite time, every possible thing must happen. If you know of such a proof, please produce it. Up to now, you have just been saying so. And merely saying so -- even if you say so over and over for an infinite period of time -- does not make it so.

[quaddriver]

There is still no proof in this thread (or anywhere else that I have seen) that in infinite time, every possible thing must happen. If you know of such a proof, please produce it. Up to now, you have just been saying so. And merely saying so -- even if you say so over and over for an infinite period of time -- does not make it so.

I have seen such proof, that the probabilty of ANY event is never zero.

therefore in infinte time, even the small probability events must occur.

you would need to contact Dr RA Blackburn at IBM (rab1@us.ibm.com IIRC) to see the same proof I did. of course he has a phd in math specializing in probability and I do not so he could have been giving me the probability of blueberry pancakes for all I know. Its up to you to believe what the eggheads say

[Andrew D]

There must be something in between the premise and the conclusion. As far as I can see, the premise -- "the probability of ANY [possible] event is never zero" -- leads to a quite different conclusion: Even after an infinite amount of time, the probability of any possible event is still not zero.

Take this from the flip side. If the probability of any possible event is never zero, then the probability of the nonoccurrence of that event is never 1 (or 100%). If the probability of the nonoccurrence of an event is never 1 (or 100%), then there is always some possibility that the event will not occur. Which rather proves my point: If there is always some possibility that the event will not occur, then it is not true that the event must occur.

[Andrew D]

This:

Throw again and again and again. Infinity never ends so the throwing never ends. If,after 9999999999999999999999999 millennia (which we could approximate to an infinite time), a 6 has not been thrown then mathematically the probability of throwing one tends to 0% (ie impossible).

is just flat-out wrong.

First, 9999999999999999999999999 millennia are not aproximately an infinite time. On the contrary, 9999999999999999999999999 millennia are an infinitesimal fraction of an infinite time.

Second, the odds of throwing a six never change. On the first throw, the odds of throwing a six are one in six. On the hundred-billionth throw, the odds of throwing a six are one in six. If I have thrown a six a hundred-billion times in a row, the odds of my throwing a six on the next throw are one in six. If in a hundred-billion throws, I have never thrown a six, the odds of my throwing a six on the next throw are one in six. Whatever you may think of the next bit, this bit is just straightforward probability mathematics.

If in an infinite number of throws, I have thrown as six every time, the odds of my throwing a six on the next throw are one in six. If in an infinite number of throws, I have never thrown a six, the odds of my throwing a six on the next throw are one in six.

Yes, after an infinite number of throws, I can still throw again. Consider a ray (the geometrical figure). If a ray starts at point X and continues through point X-1, then it extends infinitely on the negative side of X. I can extend the ray in the positive direction so that it starts at point X+1 and extends through point X-1 and infinitely thereafter on the negative side of X. Either (a) by extending the ray to begin at point X+1, I have made the infinitely long ray even longer or (b) the distance between X and X+1 is zero. For the latter to be true, zero must equal one. That is babbling nonsense, so if must be that I have made the infinitely long ray even longer.

If you have doubts about that, just ask yourself: "How many minutes are there in an infinite number of hours?"

[rubato]

Claiming that in an infinite span of time all events which have even the smallest probability of happening must necessarily happen is a bizarre misunderstanding of nature and frankly just wrong.

The chance that all of the water molecules in lake tahoe will at some point vibrate in exactly the same direction at the same time is very very small. But if they were to do so the entire volume of water could fly out of the lake, over the peaks of the Sierra range, and land somewhere in Northern California. But no rational person believes that such things "must" happen if we just wait long enough. If all of the atoms in the sun (which is very very hot and hence has a shit-load of thermal energy which can be translated into motion) were to do something similar the sun would shoot off across the galaxy at an enormous speed driving it out into empty space or across the galactic center where mayhem is likely to ensue.

Probability is just a way of calculating something; it does not require that thing to exist.

yrs,
rubato

[Scooter]

why do I have the feeling that this will lead into a discussion of whether 0.99999... is or is not equal to 1

[Rick]

the sun would shoot off across the galaxy at an enormous speed

Isn't the Sun shooting off across the galaxy at enormous speed already?

Small digression, please carry on...

[MajGenl.Meade]

Claiming that in an infinite span of time all events which have even the smallest probability of happening must necessarily happen is a bizarre misunderstanding of nature and frankly just wrong.

The chance that all of the water molecules in lake tahoe will at some point vibrate in exactly the same direction at the same time is very very small. But if they were to do so the entire volume of water could fly out of the lake, over the peaks of the Sierra range, and land somewhere in Northern California. But no rational person believes that such things "must" happen if we just wait long enough. If all of the atoms in the sun (which is very very hot and hence has a shit-load of thermal energy which can be translated into motion) were to do something similar the sun would shoot off across the galaxy at an enormous speed driving it out into empty space or across the galactic center where mayhem is likely to ensue.

Probability is just a way of calculating something; it does not require that thing to exist.

yrs,
rubato

Very true. But of course the real point is not that a "probable" thing must happen but that a "possible" thing must happen. If rational minds conclude that all the molecules of water in Lake Tahoe etc etc is never going to happen if we wait long enough - I agree and it is not possible.

AGD your constant repetition is equal to mine. You prove something instead of just contradicting any premise. (That isn't an argument; yes it is; no it isn't). Prove to me that if a "possible" thing cannot occur in infinite time (nay, "will not" occur for you are certain of it) that it is actually possible and not impossible. If a possible thing may not occur in inifinite time, when may it occur please? And don't say it does not have to occur. That is simply begging the question. Please make it clear if you are arguing that there is a true infinity of time (without beginning and end) or that there isn't.

Is not an oscillating universe one which expands and then contracts and then re-expands? I fail to see your "cyclical" as being any different. But since you keep repeating it without evidence perhaps you could cut a little slack there

Cheers
Meade

[thestoat]

First, 9999999999999999999999999 millennia are not aproximately an infinite time. On the contrary, 9999999999999999999999999 millennia are an infinitesimal fraction of an infinite time.

Yes of course that is true, but *in context* 9999999999999999999999999 millennia may be approximated to infinite time. This is because it takes a second to roll a dice and there are many, many seconds in 9999999999999999999999999 millennia. These sort of approximations happen all the time in the maths of physics

[thestoat]

If you have doubts about that, just ask yourself: "How many minutes are there in an infinite number of hours?"

... you do realise there are different sizes of infinity, don't you? (In your example, though, the answer is the same infinity).

[MajGenl.Meade]

I think this thread is one size of infinity.

[thestoat]

It's getting that way ...

[Andrew D]

Prove to me that if a "possible" thing cannot occur in infinite time (nay, "will not" occur for you are certain of it) that it is actually possible and not impossible.

Why would I set about "proving" something that is based on a premise which I do not accept and for which no support has been forthcoming? I am not asserting that a possible thing cannot occur in infinite time. Nor am I asserting that a possible thing will not occur in infinite time. I am asking you to support your assertion that every possible thing will (must) occur in infinite time. Thus far, you have not.

If a possible thing may not occur in inifinite time, when may it occur please? And don't say it does not have to occur. That is simply begging the question.

It is not begging the question at all. It is getting directly to the heart of the matter. You asserted that an infinite regress of time is impossible, because everything that could possibly happen must have happened. I asked you to demonstrate the truth of that assertion. Thus far, you have not.

Please make it clear if you are arguing that there is a true infinity of time (without beginning and end) or that there isn't.

I am asking you to support your assertion that an infinite regress of time is impossible. Thus far, you have not.

Is not an oscillating universe one which expands and then contracts and then re-expands? I fail to see your "cyclical" as being any different.

To me, oscillating at least connotes moving back and forth between two points, whereas cycling at least connotes reptition along a path leading in one direction. A pendulum oscillates; a wheel cycles. At the moment, in the present context, I do not see that the difference matters. But perhaps at some point it will.

[Andrew D]

First, 9999999999999999999999999 millennia are not aproximately an infinite time. On the contrary, 9999999999999999999999999 millennia are an infinitesimal fraction of an infinite time.

Yes of course that is true, but *in context* 9999999999999999999999999 millennia may be approximated to infinite time. This is because it takes a second to roll a dice and there are many, many seconds in 9999999999999999999999999 millennia. These sort of approximations happen all the time in the maths of physics

If the present context were a discussion of approximately infinite time (whatever that might mean), then such an approximation might be correct. But we are discussing infinite time, not approximately infinite time, so such approximations have no place in the discussion.

If you have doubts about that, just ask yourself: "How many minutes are there in an infinite number of hours?"

... you do realise there are different sizes of infinity, don't you?

I do realize that not all infinite numbers are equal, yes.

(In your example, though, the answer is the same infinity).

In my example, the correct answer is that the number of minutes in an infinite number of hours is an infinite number sixty times greater than that infinite number of hours. In order for the number of minutes in an infinite number of hours to equal that infinite number of hours, a minute would have to equal an hour. But the essential nature of a minute is to be one-sixtieth of an hour (or, if you prefer, the essential nature of an hour is to be sixty minutes). A minute cannot equal an hour, so the number of minutes in an infinite number of hours cannot equal that infinite number of hours.