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Time Likely To End Within Earth's Lifespan, Say Physicists

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Re: Time Likely To End Within Earth's Lifespan, Say Physicists

#51
post #6

"If the universe lasts forever, then any event that can happen, will happen, no matter how unlikely." That's just plain mathematically wrong. There are many kinds of infinity ( http://en.wikipedia.org/wiki/Aleph_number ), and the set of all possible events has a much, much higher cardinality than an infinite axis of time. This is similar to saying that, since the set of integers is infinite, it must contain Pi.

This does not seem wrong to me.

"Among other things it depends crucially on an important assumption about the laws of physics: that we ought to be able to understand why they work, not just observe that they do work"

IANAP but,

In assuming that there are discrete laws of physics, we also assume there is a subset of all 'possible' events; events that 'can happen'. (Given a certain arrangement of the universe at T1, there is a set of possible arrangements of the universe at T2).

If we assume finite time, the set of events that will happen is a subset of the set of events that can happen. This is because the set of events that can happen is infinite and the set of events that will happen is finite. If both are infinite, then they are the same set.

Infinite time makes it apparent that all of the events that can happen will happen an infinite number of times, because events that can happen are events that will happen, and an event that can happen is never eliminated from the set of events that can happen by having been an event that will happen.

Re: Time Likely To End Within Earth's Lifespan, Say Physicists

#52
post #6

"If the universe lasts forever, then any event that can happen, will happen, no matter how unlikely." That's just plain mathematically wrong. There are many kinds of infinity ( http://en.wikipedia.org/wiki/Aleph_number ), and the set of all possible events has a much, much higher cardinality than an infinite axis of time. This is similar to saying that, since the set of integers is infinite, it must contain Pi.

To give a specific example: In three and more dimensions, if you start a random walk outside some sphere there is a non zero probability that the event "the brownian motion enters this sphere" never happens. Funnily, in dimension one and two this is not true.

Interesting. Are you talking about a continuous walk, or a walk on the integers? Is there an intuitive explanation for this? I get that in 1 dimension you will visit all points if you wait long enough, but two? And why does it change at 3?

Re: Time Likely To End Within Earth's Lifespan, Say Physicists

#53
post #9
post #6

"If the universe lasts forever, then any event that can happen, will happen, no matter how unlikely." That's just plain mathematically wrong. There are many kinds of infinity ( http://en.wikipedia.org/wiki/Aleph_number ), and the set of all possible events has a much, much higher cardinality than an infinite axis of time. This is similar to saying that, since the set of integers is infinite, it must contain Pi.

the set of all possible events has a much, much higher cardinality than an infinite axis of time. Are you sure of that? How would you prove it? It seems intuitively right, but intuition has a habit of being wrong, when it comes to infinities.

Events happen at the same time. At any one given point in time, there are trillions (probably much more than that) of events happening. In fact, wouldn't the set of all events be uncountably infinite?

Now that I think about it, we're talking about all possible events, which is even bigger. For any given event, there is theoretically an infinite amount of alternative possible events. Therefore, for each of the trillions of events at any given point in time, there is an infinite set of other possible events.

Re: Time Likely To End Within Earth's Lifespan, Say Physicists

#54
post #51
post #6

"If the universe lasts forever, then any event that can happen, will happen, no matter how unlikely." That's just plain mathematically wrong. There are many kinds of infinity ( http://en.wikipedia.org/wiki/Aleph_number ), and the set of all possible events has a much, much higher cardinality than an infinite axis of time. This is similar to saying that, since the set of integers is infinite, it must contain Pi.

This does not seem wrong to me. "Among other things it depends crucially on an important assumption about the laws of physics: that we ought to be able to understand why they work, not just observe that they do work" IANAP but, In assuming that there are discrete laws of physics, we also assume there is a subset of all 'possible' events; events that 'can happen'. (Given a certain arrangement of the universe at T1, th…

"In assuming that there are discrete laws of physics, we also assume there is a subset of all 'possible' events; events that 'can happen'. (Given a certain arrangement of the universe at T1, there is a set of possible arrangements of the universe at T2)."

False. Possibilities can be mutually exclusive, so if one occurs, the other can't. Yet, after the fact, we considered them both to be events that could have happened.

(Unless you subscribe to absolute determinism, but I don't believe that's clear to be the case. Also, IME, discussions of determinism mechanisms in, e.g. quantum mechanics, tend to talk more about whether that's where Diety lives.)

Re: Time Likely To End Within Earth's Lifespan, Say Physicists

#55
Time Likely To End Within Earth's Lifespan, Say Astrologers

There is a 50 per cent chance that time will end within the next 3.7 billion years, according to a new astrological model of the zodiac.

Look out into space and the signs are plain to see. According to a certain reading of our tarot cards; Cronos created Heaven and Earth when he sneezed for the first time 13 billion years ago; therefore; Heaven and Earth have been expanding ever since. And the best evidence of the expansion of the Cronos' sneeze comes from observation of the Cronos' germs in distance reaches of the cosmos; therefore; cosmos' expansion is accelerating.

That has an important but unavoidable consequence: it means that the cosmos will expand forever. And a cosmos that expands forever is infinite and eternal. This is obviously because the creator of the cosmos the eternal and infinite god Cronos is infinite and eternal.

Today, a group of astronologist rebel against this idea. They say an infinitely expanding cosmos cannot be so because the laws of astrology do not work in an infinite cosmos. For these laws to make any sense, the cosmos must end, say the Trimagistus Nuovo Raphaello Bousso at the University of California, Berkeley and few pals. And they have divined when that is most likely to happen.

Their divination is deceptively simple and surprisingly powerful. Here's how it goes. If the cosmos lasts forever, then any event that can happen, will happen, no matter how unlikely. In fact, this event will happen an infinite number of times.

This leads to a problem. When there are an infinite number of instances of every possible divination, it becomes impossible to determine the probabilities of any of these divined events to occur. And when that happens, the laws of astrology simply don't apply; the absurd laws of physics take over. "This is known as the "measure problem" of eternal inflation," say Bousso and buddies.

In effect, these guys are saying that the laws of astrology abhor an eternal universe.

The only way out of this conundrum is to divine some kind of divine intervention that brings an end to the cosmos. Then all the probabilities make sense again and the laws of astrology regain their power to divine.

When might this be? Bousso and co have consulted Cronos' assistant in charge of human affairs, a Mr. Prometheus, and this is the reply they got: "Time is unlikely to end in our lifetime, but there is a 50% chance that time will end within the next 3.7 billion years," said Mr. Prometheus who started it all when he stole the light from Gods to give it to humans and that was about 3.7 billion years ago. So if no symmetry breaking occurs; Bousso and Co's 3.7 billion year prediction for the end of time is as good as proved by Einstein's General Relativity.

But Mr. Prometheus had one cautionary statement: "The time will end for humans; not for gods. I am sorry" said Mr. Prometheus, a good friend of humanity since the beginning.

3.7 billion years is not so long! It means that the end of the time is likely to happen within the lifetime of the Gaea and the Hyperion.

But Buosso and co have some comforting news too. They don't know what kind of divine intervention will cause the end of time for humanity but they do say that we won't see it coming. They point out that if we were to observe the end of time in any other part of the cosmos where the authority of Cronos has been usurped; we would have to be causally ahead of it, which is unlikely because the God Mnemosyne hates to remember what she had not forgotten.

In other words we'll run headlong into this divine intervention before we can observe its effects on anything else.

The imminent end of time is a little unsettling but the argument is by no means astronologically sound. Among other things it depends crucially on an important assumption about the laws of astrology: that we ought to be able to understand why they work, not just observe that they do work. And that's a physical point of view rather than an astrological argument. And you cannot trust physicists to explain anything; because for them if it is Wednesday it must be a wave; if it is thursday it must be a particle.

So Buosso and buddies raise some interesting questions but nothing to lose any sleep over. At least, not for another 3.7 billion years Cronos will not bother to end time for human beings.

Ref: arxiv.org/abs/1009.4698: Eternal Inflation Predicts That Time Will End

Re: Time Likely To End Within Earth's Lifespan, Say Physicists

#56
post #40

Earlier quoted context omitted.

I think you're missing the point. While it's _extremely_ unlikely that the next random number produced would be Pi, in an infinite scale it can (and theoretically would) happen because it is, in fact, possible to occur.

No, it theoretically would not happen. Proof: let X[n] be the set of numbers with non-zero probability of being produced at the n'th trial. X[n] must be countable, since sum(X[n]) = 1 and the sum of any uncountably infinite set of non-zero numbers must be infinite. Let X = union(X[n], n=0...infinity). X is countable, being the countable union of countable sets. The reals are uncountable. Thus, most real numbers will…

I'm not entirely sure I understand the logic here, and being not a math student myself I'm sure my original statement is likely to be wrong.

However, I don't see how the set of numbers found in an infinite number of trials would be countable.

Edit: I googled some about this and can say I definitely learned some math today..

Re: Time Likely To End Within Earth's Lifespan, Say Physicists

#58
post #56

Earlier quoted context omitted.

No, it theoretically would not happen. Proof: let X[n] be the set of numbers with non-zero probability of being produced at the n'th trial. X[n] must be countable, since sum(X[n]) = 1 and the sum of any uncountably infinite set of non-zero numbers must be infinite. Let X = union(X[n], n=0...infinity). X is countable, being the countable union of countable sets. The reals are uncountable. Thus, most real numbers will…

I'm not entirely sure I understand the logic here, and being not a math student myself I'm sure my original statement is likely to be wrong. However, I don't see how the set of numbers found in an infinite number of trials would be countable. Edit: I googled some about this and can say I definitely learned some math today..

Countably infinite - like the integers. I.e., if you start counting the integers (1, 2, 3, etc), you will eventually reach any given integer.

Count the first element from set 1, first element from set 2, second element set 1, second element set 2, first element set 3, third element set 1, etc. Eventually you will count every element from every set.

You can't do that for the real numbers.

Re: Time Likely To End Within Earth's Lifespan, Say Physicists

#59
post #53
post #9

Earlier quoted context omitted.

the set of all possible events has a much, much higher cardinality than an infinite axis of time. Are you sure of that? How would you prove it? It seems intuitively right, but intuition has a habit of being wrong, when it comes to infinities.

Events happen at the same time. At any one given point in time, there are trillions (probably much more than that) of events happening. In fact, wouldn't the set of all events be uncountably infinite? Now that I think about it, we're talking about all possible events, which is even bigger. For any given event, there is theoretically an infinite amount of alternative possible events. Therefore, for each of the trillio…

Certainly there's an uncountably infinite number of possible events. The question is whether that's an uncountable infinity with larger cardinality than the uncountable infinity of instants in which they could be happening.

As far as I'm concerned having read the thread up to this point the question is still open... though my personal prejudice is still that it's not true that every event must happen.

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