Time Likely To End Within Earth's Lifespan, Say Physicists(technologyreview.com)
technologyreview.com
Time Likely To End Within Earth's Lifespan, Say Physicists
http://www.technologyreview.com/blog/arxiv/25807/?ref=rss
63 comments
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.
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 point, and what's interesting is that it doesn't rely on the cardinality arguments above. Both the set of points visited by the walker and the set of points in the universe have the same cardinality, but that doesn't mean that the walker visits all points.
(In fact I suspect he can never visit more than a vanishing subset of them, but I could be wrong, and I'm sure somebody has figured this out already...)
(In fact I suspect he can never visit more than a vanishing subset of them, but I could be wrong, and I'm sure somebody has figured this out already...)
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?
This is for continuous walk.
As you say, in one dimension you will visit all the points.
In two dimension the random walk is dense, so you pass arbitrarily close to every point in the plane.
As the dimension increases beyond two, it gets less and less likely that you hit the target sphere. In some way, space gets bigger and bigger as the dimension increases.
Suppose the d dimensional "target" sphere is very small and very close to the starting point of the path. Let some time pass, and suppose that the Brownian motion does not hit the sphere and has increased by 1 in every direction. Then the distance to the sphere is sqrt(d), which grows unbounded as d increases: if you don't hit the target immediately, on average you will be further away from it in higher dimension. So the probability of touching the target after that diminishes as the dimension increases.
I don't have an intuitive explanation of why 3 is the critical dimension though.
As you say, in one dimension you will visit all the points.
In two dimension the random walk is dense, so you pass arbitrarily close to every point in the plane.
As the dimension increases beyond two, it gets less and less likely that you hit the target sphere. In some way, space gets bigger and bigger as the dimension increases.
Suppose the d dimensional "target" sphere is very small and very close to the starting point of the path. Let some time pass, and suppose that the Brownian motion does not hit the sphere and has increased by 1 in every direction. Then the distance to the sphere is sqrt(d), which grows unbounded as d increases: if you don't hit the target immediately, on average you will be further away from it in higher dimension. So the probability of touching the target after that diminishes as the dimension increases.
I don't have an intuitive explanation of why 3 is the critical dimension though.
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.
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.
I have a machine that flashes a light on or off once a second, at random. You can view streams of output from the machine as possible events. Now, suppose an infinite amount of time has passed (aleph-null, by definition). Have I seen every possible sequence?
Well, take the set of aleph-null length sequences (all aleph-null of them [1]) and put them in an order. Now construct the following sequence: invert bit 1 from sequence 1, invert bit 2 from sequence 2, ... etc.
Note that this sequence was never produced by the machine, since we enumerated all the sequences it produced, but they are all different to this one. So, by a standard diagonalisation, the set of events is higher cardinality.
[1] How many aleph-null length sequences come out of the machine? Well, they have to be continuous, so the only obvious aleph-null length sequence is the total sequence the machine produces. However, you can drop an entry from the beginning of the sequence to get another aleph-null length sequence. And so on, making a total of aleph-null.
Well, take the set of aleph-null length sequences (all aleph-null of them [1]) and put them in an order. Now construct the following sequence: invert bit 1 from sequence 1, invert bit 2 from sequence 2, ... etc.
Note that this sequence was never produced by the machine, since we enumerated all the sequences it produced, but they are all different to this one. So, by a standard diagonalisation, the set of events is higher cardinality.
[1] How many aleph-null length sequences come out of the machine? Well, they have to be continuous, so the only obvious aleph-null length sequence is the total sequence the machine produces. However, you can drop an entry from the beginning of the sequence to get another aleph-null length sequence. And so on, making a total of aleph-null.
Interesting attempt, but I'm not convinced by the part of the argument where you divide the complete output of the flashy light box into aleph-null sequences, each of length aleph-null.
Mostly, I'm unconvinced that an "event" which takes an infinitely long time to complete actually counts as an event. Usually when we talk about events they're localised in space and time.
Mostly, I'm unconvinced that an "event" which takes an infinitely long time to complete actually counts as an event. Usually when we talk about events they're localised in space and time.
Well, it's kind of a Catch-22.
This proof is dependent upon the lemma that time is infinite. On the other hand, the set of events we're looking for is the one where time ends. Therefore by assuming the lemma we have no need for the proof.
OTOH, if we're looking at another event that's not so confusing (one that's not the end of time), the proof holds water. It's a pretty sweet proof that I think is similarly used to prove that the set of real numbers is uncountable.
This proof is dependent upon the lemma that time is infinite. On the other hand, the set of events we're looking for is the one where time ends. Therefore by assuming the lemma we have no need for the proof.
OTOH, if we're looking at another event that's not so confusing (one that's not the end of time), the proof holds water. It's a pretty sweet proof that I think is similarly used to prove that the set of real numbers is uncountable.
No, what I'm saying is that an event which takes an infinitely long time to happen (ie an infinite series of one-second flashes) isn't a proper "event", which as used at least in relativity, is something that happens in finite space and time.
But there's no need to argue about the definition of event. I'll say instead that I'm interested in knowing whether infinite time implies that all finite-length events must eventually happen (and indeed, happen an infinite number of times as the paper claims).
But there's no need to argue about the definition of event. I'll say instead that I'm interested in knowing whether infinite time implies that all finite-length events must eventually happen (and indeed, happen an infinite number of times as the paper claims).
Yes, sorry, there is definitely a theorem that if you have an infinite sequence, uniformly distributed over an alphabet, then the probability of seeing any finite sequence is 1. I think that, given some assumptions, you can model the universe as an infinite numerical sequence, so you should see all finite events.
However, the assumptions here seem tricky. Uniform distribution of probability seems unlikely, and if the universe is anything like the game of life, there are garden of Eden states with no predecessor state, which an evolving system cannot reach, even in infinite time.
Cardinality is indeed tricky. I had thought that all finite sequences would be greater than aleph-null, but apparently it isn't.
However, the assumptions here seem tricky. Uniform distribution of probability seems unlikely, and if the universe is anything like the game of life, there are garden of Eden states with no predecessor state, which an evolving system cannot reach, even in infinite time.
Cardinality is indeed tricky. I had thought that all finite sequences would be greater than aleph-null, but apparently it isn't.
if they universe is composed of a single axis by which information is sorted, then infinite time should produce all possible combinations. However, if the universe has some 'structure' to it, it might become ordered at some point, exchanging chaos for order. In a universe that becomes ever more ordered and unique. This isn't like saying infinity - infinity, or infinity/infinity, this is more like there are a set of the infinite, and there is a set of the finite, and they are two distinct sets without one influencing the other.
Order and Chaos need not be interchangeable.
There is an interesting book called "Sync" which discusses the presence of spontaneous order from chaos. He also talks about how order can turn back into chaos, but the important part of the book is that there are cases where chaos will not turn into order, and order will not turn into chaos, meaning that the stability of the two create two distinct sets, one that contains the identity of the universe and one that allows it to change.
Some of you may have read Wolframs work as well which shows that simple rules can lead to ordered stable systems. That stability is the definition of uniqueness.
Sync, it's the one book I recommend all my thinking friends read. http://amzn.to/a8s5Dl
It changed my life, and my world view.
So, I am comfortable saying that no act of randomness by any number of chimpanzees ( as they are now ) will randomly produce a work of William Shakespeare. WS, wasn't just a man, he was a man in a time with billions of events that influenced that moment when he composed those works. There was a structure and a path to those influences, and it wasn't such a frail construct that randomness happened upon it, but rather there was a beautify symmetry that occurred and allowed that to come to pass.
Another way to look at it, is that random/ chaotic signals will not sum up to collapse a bridge. however an ordered marching army has in many cased taken down the bridge.
Order and Chaos need not be interchangeable.
There is an interesting book called "Sync" which discusses the presence of spontaneous order from chaos. He also talks about how order can turn back into chaos, but the important part of the book is that there are cases where chaos will not turn into order, and order will not turn into chaos, meaning that the stability of the two create two distinct sets, one that contains the identity of the universe and one that allows it to change.
Some of you may have read Wolframs work as well which shows that simple rules can lead to ordered stable systems. That stability is the definition of uniqueness.
Sync, it's the one book I recommend all my thinking friends read. http://amzn.to/a8s5Dl
It changed my life, and my world view.
So, I am comfortable saying that no act of randomness by any number of chimpanzees ( as they are now ) will randomly produce a work of William Shakespeare. WS, wasn't just a man, he was a man in a time with billions of events that influenced that moment when he composed those works. There was a structure and a path to those influences, and it wasn't such a frail construct that randomness happened upon it, but rather there was a beautify symmetry that occurred and allowed that to come to pass.
Another way to look at it, is that random/ chaotic signals will not sum up to collapse a bridge. however an ordered marching army has in many cased taken down the bridge.
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.
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.
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.
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.
Their statement makes sense: If you have a non zero probability of something happening, say P, and N times that it could happen, then you would expect it to happen about P * N times. Lets let E = P * N. Now as N goes to infinity the number of times you expect it to happen does as well. Both go to a countable infinity (Aleph 0 as you linked) which is a problem when it comes back to defining P. Normally we would say P = E / N but this doesn't make sense when E and N are both the same 'size' of infinity.
> This is similar to saying that, since the set of integers is infinite, it must contain Pi.
Not exactly. Pi has no chance of occurring in an infinite set of integers.
Not exactly. Pi has no chance of occurring in an infinite set of integers.
Okay, so how about "Given a number generator that produces numbers for an infinite amount of time, it will produce Pi"
This, of course, is impossible.
This, of course, is impossible.
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 NOT eventually be produced.
(It's true, pi in particular could be in X, but the vast majority of numbers could not be in X.)
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 NOT eventually be produced.
(It's true, pi in particular could be in X, but the vast majority of numbers could not be in X.)
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..
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.
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.
By a similar argument, at least half of all natural numbers are completely random.
4 - 4/3 + 4/5 - 4/7 + ...
I'm pretty sure that is the message he was trying to convey. He is saying the scientist's point doesn't make any sense.
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.
"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.
"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.)
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.)
Well, there IS an integer that contains all the digits of Pi
3141592...
3141592...
No, that "integer" would need to have an infinite number of digits, and no integer has an infinite number of digits.
So you are saying that their is a largest integer with a finite number of digits? Lets call that integer N, wouldn't 10*N have one more digit than N?
You are confused: yes there are infinite integers, but every single integer has a finite number of digits.
Edit: (Several people have said the same thing so maybe I can add something else)
I think another point of confusion might be the difference between "arbitrarily long" and "infinitely long". The number pi is infinitely long, a single integer can be arbitrarily long.
What's the difference? Pi has infinite digits. It is an irrational number. We can never "see" all the digits of pi, because no matter how far out we go there are always more digits.
With an integer, this isn't the case. There are infinite integers, but this property is defined on the set, not on any single element in the set of integers. Every integer (a single element in the set of integers) is finite. All of them, no matter what. They all have an end.
That said, what "arbitrarily long" means is that for any length you choose, there are integers that long (or longer). Say we choose a length 5, then 10000, 10001, 10002, ... all have length 5 or greater, but every one of them has an exact length. It just happens to be greater than 5. You can do this for any length: 1000, 10^1000, whatever. Anything. Choose any number as big as you can even imagine. Try to imagine numbers bigger than anything you can even imagine. There are integers that long, and infinitely more integers longer than that. But every single one of them has an exact, finite length.
Edit: (Several people have said the same thing so maybe I can add something else)
I think another point of confusion might be the difference between "arbitrarily long" and "infinitely long". The number pi is infinitely long, a single integer can be arbitrarily long.
What's the difference? Pi has infinite digits. It is an irrational number. We can never "see" all the digits of pi, because no matter how far out we go there are always more digits.
With an integer, this isn't the case. There are infinite integers, but this property is defined on the set, not on any single element in the set of integers. Every integer (a single element in the set of integers) is finite. All of them, no matter what. They all have an end.
That said, what "arbitrarily long" means is that for any length you choose, there are integers that long (or longer). Say we choose a length 5, then 10000, 10001, 10002, ... all have length 5 or greater, but every one of them has an exact length. It just happens to be greater than 5. You can do this for any length: 1000, 10^1000, whatever. Anything. Choose any number as big as you can even imagine. Try to imagine numbers bigger than anything you can even imagine. There are integers that long, and infinitely more integers longer than that. But every single one of them has an exact, finite length.
This is all true, assuming one uses a standard model for the integers. Non-standard models[1] are more interesting, but I'm not sure if one could say anything about the number of digits of a non-standard number.
[1] http://en.wikipedia.org/wiki/Non-standard_model_of_arithmeti...
[1] http://en.wikipedia.org/wiki/Non-standard_model_of_arithmeti...
Integers can have an arbitrarily large but finite number of digits. They cannot have an infinite number of digits. There is a big difference.
I guess we are in the realm of cardinality of infinity which I don't quite get. I would think an infinitely big integer would have an infinite number of digits. So you are saying:
log(infinity) < infinity
log(infinity) < infinity
Once again, there is no such thing as an infinitely big integer. You seem to be having difficulty with the fact that:
1. There are an infinite number of integers, but
2. Every integer is finite
Start counting 1,2,3,4... Do you ever get to the end? No, this proves that there are infinitely many integers. But do you ever get to an infinite number? No, you'll stay in the set of finite integers forever.
1. There are an infinite number of integers, but
2. Every integer is finite
Start counting 1,2,3,4... Do you ever get to the end? No, this proves that there are infinitely many integers. But do you ever get to an infinite number? No, you'll stay in the set of finite integers forever.
No, there is no largest integer with a finite number of digits.
There are infinitely many integers, but every integer is finite.
There are infinitely many integers, but every integer is finite.
> Well, there IS an integer that contains all the digits of Pi
1234567890 does:)
1234567890 does:)
From the sounds of it, this is a far from accepted idea that's just now coming out in like it's first paper or something, so don't start planning your End of Time Party. There's still a lot of verification and research and math between this being published and it becoming the consensus among physicists.
It's not even a paper, it's just a manuscript on the arXiv, yet to pass peer review, if indeed it ever will.
I had a quick skim of the manuscript, and remain skeptical... a bunch of it doesn't even seem to make sense:
If it does occur in Nature, eternal inflation has profound implications. Any type of event that has nonzero probability will happen infinitely many times, usually in widely separated regions that remain forever outside of causal contact. This undermines the basis for probabilistic predictions of local experiments. If infinitely many observers throughout the universe win the lottery, on what grounds can one still claim that winning the lottery is unlikely? To be sure, there are also infinitely many observers who do not win, but in what sense are there more of them? In local experiments such as playing the lottery, we have clear rules for making predictions and testing theories. But if the universe is eternally inflating, we no longer know why these rules work.
I had a quick skim of the manuscript, and remain skeptical... a bunch of it doesn't even seem to make sense:
If it does occur in Nature, eternal inflation has profound implications. Any type of event that has nonzero probability will happen infinitely many times, usually in widely separated regions that remain forever outside of causal contact. This undermines the basis for probabilistic predictions of local experiments. If infinitely many observers throughout the universe win the lottery, on what grounds can one still claim that winning the lottery is unlikely? To be sure, there are also infinitely many observers who do not win, but in what sense are there more of them? In local experiments such as playing the lottery, we have clear rules for making predictions and testing theories. But if the universe is eternally inflating, we no longer know why these rules work.
From the comments it sounds like it's related to string theory, which itself is on shaky theoretical ground. Guess we have to think out the box to progress physics, just need these kind of articles to use appropriate language to give a good idea of how far off many of these types of theories are to being proven.
> don't start planning your End of Time Party
Rats, there goes my idea for building a Restaurant at the End of the Universe!
Rats, there goes my idea for building a Restaurant at the End of the Universe!
Woit's take on the Not Even Wrong blog:
http://www.math.columbia.edu/~woit/wordpress/?p=3185
http://www.math.columbia.edu/~woit/wordpress/?p=3185
And linked from that, Lubos Motl's even less charitable take:
http://motls.blogspot.com/2010/09/bousso-et-al-catastrophe-i...
Much like most other doomsday prophets and other kinds of crackpots, the authors are completely unable to understand the point and the arguments that they're assuming something fundamentally wrong in their very first axioms - and that's why everything they write down has to end up being a complete nonsense.
Instead, they obviously expect a long sequence of follow-up papers that will discuss whether the Universe will cease to exist in 5.31 or 5.32 billion years and worship the amazing prophets, Bousso et al., who have predicted this amazing doomsday. This is also clear from a staged dialogue included in the paper where a semi-dumb person asks various questions about the doomsday that the authors would clearly like to be discussed in other people's papers.
http://motls.blogspot.com/2010/09/bousso-et-al-catastrophe-i...
Much like most other doomsday prophets and other kinds of crackpots, the authors are completely unable to understand the point and the arguments that they're assuming something fundamentally wrong in their very first axioms - and that's why everything they write down has to end up being a complete nonsense.
Instead, they obviously expect a long sequence of follow-up papers that will discuss whether the Universe will cease to exist in 5.31 or 5.32 billion years and worship the amazing prophets, Bousso et al., who have predicted this amazing doomsday. This is also clear from a staged dialogue included in the paper where a semi-dumb person asks various questions about the doomsday that the authors would clearly like to be discussed in other people's papers.
I've skimmed the paper and it's quite readable. The problem arises because probability doesn't make sense in an infinite universe. To make sense of it the authors consider a small patch of finite size and then let that finite size go arbitrarily large. In this picture probability is well defined but our space and time will always have an edge. However this is just a model, not an expected version of reality. The same thing happens in quantum field theory where the theory doesn't make sense at arbitrarily high energy so we just impose a cut off and ignore energies above a certain scale. This doesn't mean we think physics just stops there. Instead, it's just a way to parameterise our ignorance about what comes beyond.
This theory is well across the line from science and into religion.
How is this: "we'll run headlong into this catastrophe before we can observe its effects on anything else."
any different than this:
"But of that day and hour knows no man, no, not the angels of heaven, but my Father only." http://bible.cc/matthew/24-36.htm
How is this: "we'll run headlong into this catastrophe before we can observe its effects on anything else."
any different than this:
"But of that day and hour knows no man, no, not the angels of heaven, but my Father only." http://bible.cc/matthew/24-36.htm
The difference is "Father knows".
"Earth's lifespan" is slightly misleading if we're talking about inevitable future catastrophes of physics. What's more important is the lifespan of earth as a hospitable planet and that's significantly less time (since the sun is heating up). From http://en.wikipedia.org/wiki/Sun#Life_cycle
"...the Sun is gradually becoming more luminous (about 10% every 1 billion years), and its surface temperature is slowly rising. ... The increase in solar temperatures is such that already in about a billion years, the surface of the Earth will become too hot for liquid water to exist, ending all terrestrial life".
So (using the numbers from this article) we have about 1 billion years to get off this rock, leaving another 2.7 billion on other planets before time ends. Not a bad run if we can make it. :)
We have about 1 billion years to get off this rock
Or we could just move this rock.
Or we could just move this rock.
"Any type of event that has nonzero probability will happen infnitely many times(...). This undermines the basis for probabilistic predictions of local experiments. If infnitely many observers throughout the universe win the lottery, on what grounds can one still claim that winning the lottery is unlikely? To be sure, there are also infnitely many observers who do not win, but in what sense are there more of them?"
The first sentence is wrong, as pointed out by zeteo, but the rest does not make any sense either.
Take continuous random walk starting at zero at t=0. There are an infinite number of paths that reach each value at time t=1. Yet we can say the the probability that the random walk is positive at t=1 is one half. And by "say" I mean give a solid mathematical definition of this fact, not some hand waving argument.
The first sentence is wrong, as pointed out by zeteo, but the rest does not make any sense either.
Take continuous random walk starting at zero at t=0. There are an infinite number of paths that reach each value at time t=1. Yet we can say the the probability that the random walk is positive at t=1 is one half. And by "say" I mean give a solid mathematical definition of this fact, not some hand waving argument.
This is based upon a false assumption. Not every possible thing need happen given infinite time. There's an infinite number of things that can happen, and each thing that happens takes a finite amount of time to happen. Infinite time is not enough for infinite things to happen.
> If the universe 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.
Umm... this does not follow. Their argument surely must be more convincing than this nonsense.
Umm... this does not follow. Their argument surely must be more convincing than this nonsense.
I'm not a physicist and I'm baffled. Doesn't entropy imply that all events cannot happen? Wouldn't an event happening infinite times clearly and unambiguously violate the effects of entropy?
This doesn't really affect anything here at all. It may be neat that they're predicting time to end over 3 billion years from now, but I can guarantee we'll all be long dead by then.
Well, that makes sense. <i>Time</i>'s circulation has been dropping for years anyway.
Less arXiv on HN, please.
Less of the whole arXiv, or just the subset of the arXiv which is crazy?
The problem is that you need to be a domain expert to tell which parts are crazy. It's not a general consumption resource.
True. Though the best heuristic that a non-physicist can apply is that if something on the arXiv sounds interesting, it's probably crazy.
Non-crazy papers have titles like Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization and Towards finite density QCD with Taylor expansions and tend to be of interest to around four people in the world, of whom three may or may not be the authors.
Non-crazy papers have titles like Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization and Towards finite density QCD with Taylor expansions and tend to be of interest to around four people in the world, of whom three may or may not be the authors.
Right, and "Eternal Inflation Predicts That Time Will End" totally fails that test. (I don't mean to sound like I'm attacking you -- I agree with you. This is re: the OP)
Is this code for "Less Science Topics" or is there something wrong with arxiv.org?
arxiv is a preprint database that anyone can submit to. It's the 4chan of scientific papers. Experts in the field often have a hard time making sense of what's going on there. Granted, there is good stuff -- but only if you already know exactly what you're looking at. ArXiv is not a place for the general public. Wait until the papers clear peer-review for that.
This can be easily averted. Destroy the Earth.
I will leave the validation arguments to the people who know something more than the highschool physics I know. But "End of Time" wtf can that mean?
Take a shot sci-fi fans.
Take a shot sci-fi fans.
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
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
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.