In an infinite amount of time...

Yes.

The easiest way to conceptualize this is to invert the question. If something doesn't happen in an infinite amount of time, how can one say it was possible in the first place (and keep a straight face)?
 
I disagree. Searching through the space of possibilities in infinite time doesn't necessitate an exhaustive search, does it? Why would it?

If John puts his hand on the trigger, the ship will sink. This is possible, yet throughout all eternity John fails to put his hand on the trigger, because John knows it would be bad. One infinity later (argh!) and the ship is still floating.

'Course, this touches on some issues both in metaphysics and probability that I'm wholly unqualified to address. Not to mention ship design.
 
I would be inclined to agree with PogoPedant, as for example it is possible for life to arise on another planet and develop exactly the same as this one, to the point where someone identical to me arises, surely? And if this happens, surely, in an infinite time, it is possible for it to happen a million times, or even a trillion times? And since it's not impossible, only improbable, for someone to play the lottery every week and win every week, surely that must happen to one of my 'twins'? So in the face of this absurdity, I would say that just because something is possible, does not mean it has to happen, even in an eternity. But I would like to hear otherwise.
 
Originally posted by PogoPedant
If John puts his hand on the trigger, the ship will sink. This is possible, yet throughout all eternity John fails to put his hand on the trigger, because John knows it would be bad. One infinity later (argh!) and the ship is still floating.
Click to expand...
I think our disagreement is more semantic than anything. I have no problem with, given an infinite amount of time, John never pulling that trigger. I would just say that the conclusion, therefore, is that the act, however possible it may have seemed, was impossible.

[Originally posted by metropolis_part_one[/I]
I would be inclined to agree with PogoPedant, as for example it is possible for life to arise on another planet and develop exactly the same as this one, to the point where someone identical to me arises, surely? And if this happens, surely, in an infinite time, it is possible for it to happen a million times, or even a trillion times? And since it's not impossible, only improbable, for someone to play the lottery every week and win every week, surely that must happen to one of my 'twins'? So in the face of this absurdity, I would say that just because something is possible, does not mean it has to happen, even in an eternity. But I would like to hear otherwise.
Click to expand...
You have come with some astronomical (or, to use your word, absurd) improbabilities, but I think you've failed to give proper credit to the word eternity. It's hard to think about, but you are talking about a literally endless amount of time.

My question still stands. In what sense is something that never occurs, given an eternity to do so, possible?
 
Marquis de Carabas said:
My question still stands. In what sense is something that never occurs, given an eternity to do so, possible?
Click to expand...
Marquis,
Are you saying I'm never going to get to date another woman?
 
I agree with Pogo. "anything that can happen" is an ambiguous concept, which has a lot of metaphysical baggage attached to it.

A clearer statement would be the following:

"Any event which has a non-zero probability of happening given the opportunity to happen, will happen an infinite number of times, if given an infinite number of opportunities."

This phrasing makes clear two important points:

1) That there is an implicit assumption of the event in question being probabilistic. As soon as we start arguing about deterministic scenarios, the above statement goes out the window.

2) That what is important is opportunities, not time. For example, an event may be possible, in the sense that it has a nonzero probability of happening given the opportunity, but such opportunities may have a measure zero probability of occurring in any finite period of time. This could result in an event have a non-zero probability of happening a finite number of times, in an infinite period of time. Likewise, scenarios could be imagined in which an infinite number of opportunities for an event occur in a finite period of time.


Dr. Stupid
 
This reminds me of bad statistical reasoning along the lines of:

If there is a 1% chance of an event occuring and the event hasn't occured the past 99 tries, we are garenteed that it will occur on the next try. It's due.
 
Originally posted by Atlas
Marquis,
Are you saying I'm never going to get to date another woman?
Click to expand...
Your question carries the implicit premise that you've dated a first woman. Let's get past that before we worry about another one. :D


And what Stimpy said is essentially what I am getting at, but phrased much more clearly. I was working under the assumption that by "possible" one meant there was some probability of the event occurring.

I still think that time is important to the question, however, since every opportunity is an outcome of some number of prior events. So if the events that lead to an opportunity are possible, the opportunity itself becomes possible. Tracing back the logic, therefore, and event whose opportunity could not arise (i.e. whose opportunity was dependent upon one or more events whose probability was zero) is an impossible event (p=0).

The infinite amount of time allows for all events, and the opportunities they allow, and the events they allow, to happen.
 
Originally posted by Upchurch
This reminds me of bad statistical reasoning along the lines of:

If there is a 1% chance of an event occuring and the event hasn't occured the past 99 tries, we are garenteed that it will occur on the next try. It's due.
Click to expand...
The reasoning differs greatly, though. One might say infinitely. :D
 
Marquis de Carabas said:

The reasoning differs greatly, though. One might say infinitely. :D
Click to expand...
It's a metaphore. "Possible" events and "necessaraly occuring" events are very different things.

For example, it's possible that I will become blind next Thursday, February 19, 2004. Given an infinite amount of time, will I necessarily become blind next Thursday, February 19, 2004?
 
Originally posted by Upchurch
For example, it's possible that I will become blind next Thursday, February 19, 2004. Given an infinite amount of time, will I necessarily become blind next Thursday, February 19, 2004?
Click to expand...
Given an infinite amount of time, I would say there would arise a man, calling himself Upchurch on a message board of some entity known as the JREF who would go blind on what, to him, was Thursday, February 19, 2004. If this never occurred, in an infinite span of time, then I would label the event impossible.

I still think that it's all coming down to semantics, but I would like to know in what sense an event that does not occur in an infinite amount of time is known as "possible." The definition I'm using for possible is p/=0. If you're using a different one, please let me know.
 
An infinite number of monkeys might write the works of Shakespear, but they might not, they might write romance novels instead...

An infinity of possibility does not allow for finite impossibility!
 
No. There are lots of situations in the realm of probability studies that there is a calculatable percentange chance that something will happen in an infinite amount of time. You might google for such terms as "infinite" "random" and "walk".
 
Russ,

A brief scan of some pages I googled on infinite, random, and walk have led me to at least temporarily cede defeat on this one. I've got a lot of reading to do it seems. Thanks for giving me something to think about.

--Marquis
 
Marquis de Carabas said:
The definition I'm using for possible is p/=0.
Click to expand...
If an event occurs exactly once in an infinite number of trials, then the probability is zero. Possible doesn't mean nonzero probability. Look up "sets of measure zero" somewhere.
 
The idea said:

If an event occurs exactly once in an infinite number of trials, then the probability is zero. Possible doesn't mean nonzero probability. Look up "sets of measure zero" somewhere.
Click to expand...


Wouldn't it just be an infinitely small fraction? If the probability is 0, then it never could have happened, right? Or is that what you're getting at?
 
sorgoth said:
Wouldn't it just be an infinitely small fraction?
Click to expand...
What kind of number system are you using? Probability is the limit of a ratio. The ratio involves the number of hits on the top and the total number of trials on the bottom. If, as the total number of trials increases beyond any specified bound, the number of hits stays at the number 1, then the limit of the ratio is zero.

sorgoth said:
If the probability is 0, then it never could have happened, right?
Click to expand...
No, the whole point is: no! It's a mistake to use "probability zero" as a shorthand for "impossible." Those are different concepts.
 
metropolis_part_one said:
I would be inclined to agree with PogoPedant, as for example it is possible for life to arise on another planet and develop exactly the same as this one, to the point where someone identical to me arises, surely? And if this happens, surely, in an infinite time, it is possible for it to happen a million times, or even a trillion times? And since it's not impossible, only improbable, for someone to play the lottery every week and win every week, surely that must happen to one of my 'twins'? So in the face of this absurdity, I would say that just because something is possible, does not mean it has to happen, even in an eternity. But I would like to hear otherwise.
Click to expand...
To follow your line of thoughts: If you have not only trillions of twins, but an infinite number of them, one of them will indeed win the lottery week after week. :p
 
You must log in or register to reply here.

Back
Top Bottom