## we live at the beginning of the time when life is possible

Here is another fishy coincidence. This is from Lawrence Krauss' A Universe from Nothing

 The catalyst for this new gestalt originates from the argument I gave in the last chapter: dark energy is measurable today because “now” is the only time in the history of the universe when the energy in empty space is comparable to the energy density in matter. Why should we be living at such a “special” time in the history of the universe? Indeed, this flies in the face of everything that has characterized science since Copernicus. We have learned that the Earth is not the center of the solar system and that the Sun is a star on the lonely outer edges of a galaxy that is merely one out of 400 billion galaxies in the observable universe. We have come to accept the “Copernican principle” that there is nothing special about our place and time in the universe. But with the energy of empty space being what it is, we do appear to live at a special time
He doesn't reflect on why this has happened, he just states it.

 Quote by Haelfix Take the population of the earth. It is a fact that because population seems to move on an exponential growth curve, a person born at any time t will note something rather odd. That is that the number of people living in his or her era, is roughly the same order of magnitude as the number of people in history that are dead.

This is a separate issue, namely, why there are so many patterns in our number system. All of that I find much more problematic and much more spooky than the fact that we live in the beginning of the habitable age.

 Recognitions: Science Advisor It is not really a seperate issue. The crux of the problem is in determining whether you are 'typical' or 'atypical' in the statistical sense of the word. Defining what that means precisely is thorny, as I tried to illustrate. Certain assumptions need to be put into the system before you can make a mathematically rigorous statement (its like wondering what the probability is to pull a small O(1) integer out of the set of all positive integers) For instance, if you lived in a universe where there was an exponentially growing distribution of life giving planets, then it doesn't matter when you were born. The value 't' is irrelevant, b/c no matter what value 't' takes (young, old, very old), you will always be in an era where there were about as many observers before as there are in the present. However if you don't realize that you are in an exponentially growing phase, and instead simply try to put a uniform probability measure on the space, you end up making all sorts of wrong conclusions.

 Quote by Haelfix Certain assumptions need to be put into the system before you can make a mathematically rigorous statement (its like wondering what the probability is to pull a small O(1) integer out of the set of all positive integers)
The odds of picking a small O(1) integer out of the set of all integers is infinitely small. The odds of picking an integer near zero from integers 1 to 10^20 is finite. So your analogy breaks down there.

 For instance, if you lived in a universe where there was an exponentially growing distribution of life giving planets, then it doesn't matter when you were born. The value 't' is irrelevant, b/c no matter what value 't' takes (young, old, very old), you will always be in an era where there were about as many observers before as there are in the present. However if you don't realize that you are in an exponentially growing phase, and instead simply try to put a uniform probability measure on the space, you end up making all sorts of wrong conclusions.
This is a law of mathematics. It's like asking what are the odds of the circumference being 3.14 times greater than the diameter. It's always going to be 3.14. These two issues are not related. To demonstrate that they are not related let me try to sum up succinctly the two different issues:

1. the abundance of patterns in the set of all real numbers
2. the fact that we live right at the beginning of the habitable zone

Those two subjects are not related.

 Recognitions: Science Advisor Except that the universe, galaxy formation and so forth is not necessarily bounded in time or in space. That would be an extra assumption that you would need to justify. Worse, as in any physical system described by unitary physics there is a Poincare recurrence time, and indeed there might be all sorts of processes that produce galaxies and observers at very late times quite independant of that.

 Quote by Haelfix Except that the universe, galaxy formation and so forth is not necessarily bounded in time or in space. That would be an extra assumption that you would need to justify.
Quite simple, the BB occurred 13.7 billion years ago, so time and space are bounded by the present and the BB.

 Worse, as in any physical system described by unitary physics there is a Poincare recurrence time, and indeed there might be all sorts of processes that produce galaxies and observers at very late times quite independant of that.
Might does not imply is. You have an argument from ignorance here. Whenever you see the word could or might in an argument, then you know it's an argument from ignorance. The fact of the matter is, anything could happen. Seriously, could the universe end tomorrow? Sure. Could the gravitational constant change? Sure. So when you posit that x can happen you're not making a positive assertion, you're just stating a tautology, we already know that anything can happen.

 Recognitions: Science Advisor Obviously we are talking about boundedness into the future and not the past! The Friedman-Robertson-Walker and eventual DeSitter solution that is under discussion here only has a boundary at timelike infinity, and its eventual fate is unclear. http://en.wikipedia.org/wiki/Future_...nding_universe The reason I use the word 'might' is b/c the exact physics at very late times (see the Wiki for what that means) is complicated and in fact significantly more complicated than what that page shows. I'd rather not get into the exact details as it very much depends on parts of physics that are not entirely understood. One thing that we do know, is that if the laws of physics satisfy the conditions necessary for Liouvilles theorem and its quantum analogue to hold, then there absolutely will be a recurrence time, and you won't have any sort of finite probability measure available to use.

 Quote by Haelfix Obviously we are talking about boundedness into the future and not the past!
We're talking about a point in time in the future when matter will not be able to hold together. Some people put that at 10^31, others much higher, the point is though there is a boundary. Even if there is not, it is still fishy that we live at the beginning of the habitable age.

 Recognitions: Science Advisor Sorry, there is no consensus at all on whether the universe is or is not compact spatially, or what boundary conditions one imposes.. In fact, it is not even clear whether there is a boundary in the past, as it is quite easy to write models that go beyond the standard big bang. As I have said, assuming that indeed we are dealing with some sort of infinite set, then it is no more or less fishy that we happen to pull the number 3 out of a hat as opposed to a number like a googol. This is one of the difficulties with doing cosmology in a universe that might admit astronomically large distance scales and/or time scales and is very much a contemporary problem in modern cosmology.

 Quote by Haelfix Sorry, there is no consensus at all on whether the universe is or is not compact spatially, or what boundary conditions one imposes..
We certainly have much more evidence that the universe will continue to expand forever and that matter one day will not hold together than any other model. Even if matter continues to exist forever that merely makes things even more fishy.

 In fact, it is not even clear whether there is a boundary in the past, as it is quite easy to write models that go beyond the standard big bang.
The evidence overwhelmingly suggests the BB began 13.7 bya. Even if there is some odd pieces of evidence that conflict with that thesis the BB is certainly the best explanation given the evidence. To advocate anything other than the best explanation is tantamount to irrationality.

 As I have said, assuming that indeed we are dealing with some sort of infinite set, then it is no more or less fishy that we happen to pull the number 3 out of a hat as opposed to a number like a googol.
Not every integer is special. What's fishy is when you pick a special number from an infinite set such as pi or e. Numbers at the beginning are special. The number one for instance is much more special than 1,254,785,854

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 Quote by robertjford80 We certainly have much more evidence that the universe will continue to expand forever and that matter one day will not hold together than any other model.
As I said, it is significantly more involved than you might imagine. For one, quantum mechanics becomes involved when we start talking about astronomically big time scales. Further the eventual heat death of the universe does not mean that galaxies will no longer form. The picture to have in mind is of two liquid canisters mixing. Eventually they reach an equilibrium mixed state, and seem to stay that way, but over very large timescales eventually they go back to their starting configuration (or arbitrarily closely)

 Quote by robertjford80 The evidence overwhelmingly suggests the BB began 13.7 bya. Even if there is some odd pieces of evidence that conflict with that thesis the BB is certainly the best explanation given the evidence. To advocate anything other than the best explanation is tantamount to irrationality.
Yes, although I don't think this means what you think it does. In particular the evidence for the BB says nothing about whether there is a singularity in the past.

 Quote by robertjford80 Not every integer is special. What's fishy is when you pick a special number from an infinite set such as pi or e. Numbers at the beginning are special. The number one for instance is much more special than 1,254,785,854
This is the incorrect albeit very common notion that I have been trying to unsuccessfully dispel since the beginning. This is very wrong mathematically!

 Quote by Haelfix As I said, it is significantly more involved than you might imagine. For one, quantum mechanics becomes involved when we start talking about astronomically big time scales. Further the eventual heat death of the universe does not mean that galaxies will no longer form. The picture to have in mind is of two liquid canisters mixing. Eventually they reach an equilibrium mixed state, and seem to stay that way, but over very large timescales eventually they go back to their starting configuration (or arbitrarily closely)
I don't see what you're driving at. Either way, if there is or is not a boundary in the future for life existing that doesn't dispel the fact that there is something fishy about finding ourselves at the beginning of the habitable age.

 Yes, although I don't think this means what you think it does. In particular the evidence for the BB says nothing about whether there is a singularity in the past.
We have no evidence that life existed before the CMB, hence there is no reason to believe it.

 This is the incorrect albeit very common notion that I have been trying to unsuccessfully dispel since the beginning. This is very wrong mathematically!
Look, it's quite obvious that there are some numbers that are special and some that aren't. Since you can't understand that, there is no point in dialoguing.

 Moreover, the thesis that no numbers are special is an extreme minority view. If you're going to prove that it should be a majority view then you're going to have to do better than a mere assertion.

Recognitions: