I was thinking about the so-called theory that if the universe is infinite then somewhere theres another me surfing another web and wasting time on another message board.
Isn’t that a load of bunk? I mean whos to say that the universe beyond our range of detection isn’t just an infinite series of giant Pikachus each a slightly different shade of yellow?
I mean saying that the universe is infinite surely doesn’t say anything about the probability of anything exisiting or happening does it? It strikes me as 2nd rate philosophy no doubt involving a large spliff.
In an infinite universe, everything possible is likely (or maybe certain, I can’t remember), but people often miscontrue this as meaning that anything can happen, even if it is logically or physically impossible.
Current cosmology posits a finite number of atoms in the universe, although the the chrarcteristics of spacetime are such that, from any position in the universe, the rest of the universe looks similar in expanse: A finite universe which looks infinite.
If this stuff was easy it wouldn’t be interesting!
There must be an infinitely large set of events that do not happen anywhere; in fact this set would be much larger than the set of events that do happen, even though both sets are infinite…
does that make any sense, or am I completely wrong?
Any set of events with a non-zero probability is I believe guaranteed to happen within an infinite number of sets of events.
If this is true, then only those sets of events that have zero possibility would not happen.
It can be argued that in an infinite probability space even some zero probability events can occur. This can be shown considering this simple Gadanken experiment.
Choose at random an infinite list of numbers each from 0-9 in value, and write this down. What is the probability that the number you write down is 00000… continuing in an infinite row of zeros? Clearly the probabiliyt is 0 for that event, considering further for any infinite grouping of numbers 912345678476… the probability of getting that particular grouping is 0. Yet you non the less got a grouping if you did the experiment, and that grouping must also have had a 0 probability.
If you have a variable with a continuous pdf (probability distribution function), the probability of obtaining any given value is zero. But, when you perform an experiment you must obtain a value, even if the probability is zero.
So, of course events with zero probability happen all the time.
Metagumble: You seem to have a good intuitive grasp of the subject, and a flair for metaphor (LOL at Pikachu…)
Bippy: Well explained. But wouldn’t it be fair to say almost any interesting event almost certainly will have probability zero? For instance, what are the chances I’m sitting at my computer typing right now? Assuming it’s equally likely that any of an infinite number of possible people could be doing it instead, the probability must be zero.
Not mathematicians replace ‘countablely’ by ‘infinitely’ and ‘un’ by 'a bigger ’
I would say that it depends on the size of the universe, and the events. For instance, if your universe has uncountablely many locations, and the number of possible events at a location is countable, then every event ‘certainly’ occurs somewhere (indeed, infinitely often). Conversely, if you have uncountably many possible events, and countably many locations, almost all events don’t happen anywhere.
What actually happens? Let us assume the universe is infinite in extent and planets are spaced out a bit. Then there are countably many planets. Does life has positive probability? You’d be tempted to say so, (in which case it would occur infinitely often given an infinite number of planets). But thinking about parallel universes and that philosophical argument I can’t remember the name of says otherwise.
at the same time, there are any number of events that have probability 1 that don’t happen. consider:
p(~a) = 1 - p(a).
in the previous example, p(a) = 0, yet p(a) happened. therefore ~(~a), so though p(~a) = 1, we have ~(~a).
so that means, basically, that nothing is guaranteed. even if it has a probability of 1. that doesn’t make a whole lot of sense without any measure theory, does it?
DAMN my post got eaten by hamsters. Short version:
I don’t think it is a load of bunk at all. An infinite universe has infinite events, therefore every single possible event happens. The only two possible probabilities for an event become zero (impossible) or one (possible and certain). If you agree that you are browsing the SMDB etc etc then it is a possible event. Hence, it has a probability of 1. So there would be in fact another finite amount of OPers out there browsing the SDMB.
And I think this points strongly in favor of a finite universe.
If you have an infinite sequence of 1’s, then it is not possible ever to find anything other than 1’s. But if you have a an infinite sequence of numbers like pi for example, then any finite sequence, no matter how big, can be found in it. Same thing.
Sérgio you cannot ask a pdf the probability of a single point and expect to get a meaningful answer.
This simply isn’t true. It’s perfectly reasonable (although it has probability 0) that an event with probability 1/2 of occuring at any point in time never happens in an infinite amount of time. Think of flipping a coin an infinite number of times–you may never get heads.
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It’s interesting that you’d mention this as a property of pi, when there’s currently a decent amount of research going on to discover whether pi is actually like this.
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The probability of a single point is 0. Why is that not meaningful?
FWIW, any standard text on probability theory will confirm that Sérgio is exactly right.
Ramanujan I didn’t get a word of what you said. What was the “previous example”? If a happens, then p(a) can never be 0. Any argument that says otherwise is invalid. And when you say therefore something, a logic statement must be made. ~(~a) is not a statement, it defines an event (the event a in this case).
If an event has zero probability, then it does not happen. Am I wrong so far?
I don’t make any claims here. But I could make the same argument with a random sequence of natural numbers. What exactly is this research trying to prove? That pi is random? Are you saying it is not enough that it has been proven that there isn’t any repeating pattern in pi? How about:
a) If any finite sequence of natural numbers does not repeat (proven), there are infinitely many different sequences.
b) If there are infinititely many finite sequences, there is any finite sequence.
What he said is correct. Any integral evaluated on a single point is zero. I said it was not meaningful because it will assign 0 probability to events that may have a positive probability. Why would you ask a question for which you know the answer is wrong? Secondly I said it because I remember my probability and statistics teacher in college saying it (I don’t mean to carry any weight but it made sense to me).
If an event has zero probability, then it does not happen. Am I wrong so far?
I don’t make any claims here. But I could make the same argument with a random sequence of natural numbers. What exactly is this research trying to prove? That pi is random? Are you saying it is not enough that it has been proven that there isn’t any repeating pattern in pi? How about:
a) If any finite sequence of natural numbers does not repeat (proven), there are infinitely many different sequences.
b) If there are infinititely many finite sequences, there is any finite sequence.
What he said is correct. Any integral evaluated on a single point is zero. I said it was not meaningful because it will assign 0 probability to events that may have a positive probability. Why would you ask a question for which you know the answer is wrong? Secondly I said it because I remember my probability and statistics teacher in college saying it (I don’t mean to carry any weight but it made sense to me).
Yes, if you mean that it cannot happen. Read the posts by Sérgio, Ramanujan and ultrafilter again.
Also:
No. What about
0.12112111211112111112…
This is an infinite non-repeating decimal which does not contain every sequence; for example it does not contain the sequence 23.
Yes, if you mean that it cannot happen. Read the posts by Sérgio, Ramanujan and ultrafilter again.
Also:
No. What about
0.12112111211112111112…
This is an infinite non-repeating decimal which does not contain every sequence; for example it does not contain the sequence 23.
First, apologies to people hoping to be enlightened by this thread. There’s some rather technical mathematics going on behind the scenes that doesn’t help anyone understand what some of us are talking about. One of the things measure theory is about is studying generalisation to cases like this one:
Sorry, Pedro, actually no. (And kudos to you for starting from first assuptions.)
In finite cases this is true. But if, for instance, you pick a random number between 0 and 1, then, as the probability of picking any specific number is zero, but some number is picked.
First, apologies to people hoping to be enlightened by this thread. There’s some rather technical mathematics going on behind the scenes that doesn’t help anyone understand what some of us are talking about. One of the things measure theory is about is studying generalisation to cases like this one:
Sorry, Pedro, actually no. (And kudos to you for starting from first assuptions.)
In finite cases this is true. But if, for instance, you pick a random number between 0 and 1, then, as the probability of picking any specific number is zero, but some number is picked.
(LOL at Pikachu…)