Is Everything Inevitable if Time is Infinite?

True, and the probability for any of them is zero.

Damn! I knew I should have just gone to the library to check out Hamlet. Anybody want to buy 1,000 monkeys? How about 1,000 typewriters?

The way the question is set up, it seems to invite counterexamples. But to be conclusive, these counterexamples have to be demonstrably impossible. This then invites a laundry list of post hoc stipulations why these counterexamples are wrongly impossible. We seem to be approaching a definition of “possible event” as “one that will occur, given world enough and time.”

Here is the OP and below are some counterexamples with some reasons given for rejecting them:

“Assuming the universe has no end can we assume everything will happen, subject to its inviolable laws?”

We cannot assume the following will happen. We can assume they will not:

I will root for the Yankees.
I will play center field for the Dodgers. Violates the “unconstrained by space and time”

A centaur will marry a mermaid. Violates something, I don’t think there’s an inviolable physical law against it, but we can easily extend our prohibition to fictional beings.

Let P be the sentence, “If a centaur marries, he marries a mermaid.”
The sentence P will be falsified. Violates the “no logical funny business” condition.

If the universe is endless, we understand that to mean “events never stop happening,” or the OP has no force at all. That means that either there is at least one event of infinite duration. or there are an infinite number of overlapping finite ones.
If there is an event of infinite duration, then the termination of that event never occurs. Violation: pettifoggery: That amounts to saying the universe is endless means the event of the unverse ending will not occur.

Tristram Shandy meets Jorge Borges:

As technology improves and parts of the universe fall off, it becomes possible to record every event that occurs every day. These records are compiled, copied, and bound such that there is a binder for every subset of all the days that have occurred.

The number of binders is the power set of the (infinite) number of days (or pick your unit of time), so even though there are an infinite number of days, there are not enough to record, file and bind the calendars.

A set cannot be put into a one-to-one relation with its power set. (It doesn’t matter how small the unit of time is, or how many binders can be done in that unit.) Violation: excessively contrived, unrealistic, not the kind of event we are talking about, too mathy, boring.

So it does seem to me that we are getting close to a definition of “thing” or “happen,” or “will” that amounts to saying “If the universe is endless, everything will happen that possibly can,” along with a definition of “everything that can possibly happen” as “everything that will happen in an endless universe.”

I’d like to see some examples of events that do occur that are unconstrined by space and time, because it seems like we have eliminated a priori impossible events and contingent events. What’s left?

The beginning of time and therefore space is roughly measurable. Since they have a starting point they cannot be infinite. One could argue that they may continue on infinitely, but even that argument seems specious given their starting point will always exist. Doesn’t this mean time and space will always be finite - big yes, but bounded and finite?

First you are thinking of the Big Bang like it was a point that exploded and expanded into space. If space is infinite, then it was always infinite; it didn’t start small and grow to infinity. And the Big Bang was infinite as well in that case, filling all of space as they appeared.

And second, having a definite beginning doesn’t keep something from being infinite; if you start counting from 1 upwards that’s a definite beginning of an infinite sequence.

I understand this distinction. My interest is more in pointing out the paradox and the implications of that paradox, for observers within a given universe.

For instance, using the example of flipping a fair coin, if we look at all possibilities across all universes, we’ll get a 50/50 probability of Heads and Tails. That’s obvious. Now assume that we’re only able to observe these events experimentally within a single universe of possibilities. If I happen to be in a particular universe where we don’t get that probability distribution, perhaps we get 75/25 or even get an infinite series of Heads, we’re now in an interesting predicament. Thus, even though it is 50/50 across all universes, given that I’m experimenting in a universe where we get an infinite series of Heads, it doesn’t make sense to describe that even as 50/50 in that universe, and I could argue that it is, in fact, impossible for it to come up Heads, else I’d be in a different universe, one that is defined by some other infinite series besides one that is all Heads.

The same could be said of any of these particular infinite series. If we’re in one that is defined with a 50/50 probability, but never has a sequence of a Million Heads, then we’re still going to end up seeing everything that is possible, as even we were to see a series of a Million Heads, we would be in a different universe.

So, I guess my point is that, sure, if we’re evaluating across all possible infinite series, we could see any sequence, ones that particularly include or exclude certain artifacts. But practically, we can only exist in a single one of these series, so we can really only meaningfully define possible as a subsequence that contained in the actual sequence. Hence, though an infinite sequence of Heads is possible in one sequence across all possible sequences, it doesn’t make sense to say that in the actual sequence; I swear I flipped a Tails at least once.

nevermind, merged into new thread, doesn’t make sense

George329, it looks like you started this thread three different times. I’m not sure if that’s because you were posting in more than one forum or if you just lost track of an older version, but please don’t do that. I’ve merged all three threads.

If an event has a probability of occurring that is greater than zero, over an infinite number of trials, there is a 100% probability that event will occur. So you are basically saying something like “Having seen a white swan, I can affirm that the event that no white swans exist will not occur.”

Over an infinite number of flips, a sequence of a million heads will inevitably occur. However, an infinite sequence of heads will not inevitably occur, because its probability is not greater than 0. (The joint probability of independent events occurring is the product of their individual probabilities, but 1/2 raised to the infinite power is not greater than zero. It is 1 over 2 to the infinite power, which is not a positive number.) Since flipping a tail has a probability greater than zero, it is inevitable that there will be no infinite sequence of heads.

on a side note is time seperate from everything
if everything ends because its done everything it can does the infinite time end or does it tick on.
if it does the mecanhics of time cannot be thought of as part of everthing in the beginning.it really is seperate.all most grand father clock sitting outside our universe ticking away.

if you take the coin and put 2 heads “sides”.you will see you can no longer say not all

possibltiys can happen.if i get a machine to flip the coin on to a surface that is dead smooth

then eventaully i will be able to know that heads will always apppear.any deviancy from it say a

breeze or a crack on the suface i shall find the cause and again beable to know which side will

be face up.
so i coin flip can not be used as a event that has two different outcomes from the same cause.
you have to find something without a cause to beable to have a diffent possibltiy.