## October 24, 2010

### The Godot We Know part Bet

As noted before, it's critical to all physical arguments for the existence of God to prove that the age of the universe is not only finite but *young*, in a relative sense. The reason for this is the heart of Father Spitzer's argument:

- Of all the imaginable sets of physical constants (such as the speed of light in a vacuum, the gravitational constant, Planck's constant, etc.) that define a universe, there are extraordinarily more sets that define a universe in which life as we know it
*is not*possible, than there are sets that define a universe in which life*is*possible. That is, if you randomly define the physical constants,**you'll almost certainly end up with a universe where life as we know it simply cannot exist.**

It takes a very special set of constants for life even to be possible.

For example, if gravity decreased by the *cube* of the distance from matter, rather than the square of the distance (as it does in our universe), gravity probably wouldn't be strong enough to pull matter together into planets, stars, solar systems, and galaxies. We would have a slurry of molecules permeating the universe, and we cannot really imagine life arising from such a uniform putty.

- So if we assume that physical constants
*randomly*assume values around the time of a Big-Bang event, the odds of any one particular universe, defined by a random set of constants, being "life-friendly" (allowing life to arise) are vanishingly small. Pick a random universe and it almost certainly cannot give rise to life. - Yet we know
*at least one*universe allowed the existence of life, because, well,*here we are*! - Now, if a literally
*infinite time*is available for repeated universes to emerge, then every possible value for the physical constants will appear at some point; every possible*combination*of values will appear at some point; and that means that every possible life-friendly universe is certain to appear -- at some point. It won't happen often, but many, many life-friendly universes will eventually emerge. - However, if there is only a
*limited, finite time*available for emerging universes; and if that finite time is relatively small, compared to the odds against a life-friendly universe; then the odds are vanishingly small that*any*life-friendly universe would ever emerge, anywhere, anytime... there's just not enough time.

This is an important concept. If some event is very, very improbable -- a life-friendly universe created by a random arrangement of universal constants -- then it will only happen if you have an enormous number of attempts. If you flip a coin enough times, eventually it will land on its edge and balance there, landing neither heads nor tails. But you can only expect that if you flip an enormous number of coins.

Since a life-friendly universe is much less likely than a coin landing on edge, the number of times a (random) universe would have to emerge in order for even a single one of them to be life-friendly is so large, we humans would have a hard time distinguishing it from infinity. It's *that big*.

- Thus, if any such life-friendly universe emerges in a short length of time (see point 3), we should conclude the constants are
*not*set randomly but are severely constrained,**so as to favor those values that lead to a universe in which life can form,**and subsequently evolve into intelligence and sentience.

If you flip a coin only four or five times, and it lands on edge, you'd have to conclude that there was something "funny," something non-random, about that particular coin. Same if you shuffled a deck -- and found all the cards arranged by suit and number, from the two of clubs up to the ace of spades. It must have been rigged somehow!

- Therefore, the life-friendly coherence and order we observe in our own universe implies a strong possibility, at least, that some
*intelligent being*created, or at least designed our universe...*if*, that is, only a finite and relatively short period of time has been available for universes to emerge.

So to be able to conclude that our universe was tailor-made by a designer, there must be an anomaly: A short period of time in which universes can be created via Big Bang events, therefore only a small number of universes -- but we've already gotten one that can sustain life. That's so improbable, **the only plausible explanation is that... something or somebody has been busy loading the dice!**

That's why it's critical to Spitzer's argument to show that the past age of any collection of universes is both finite and fairly young: Because if the age of a collection of universes is infinite, or even very large compared to the odds against, then it's no surprise that we get the occasional life-friendly universe; sheer random probability can explain it, and there's no need to invoke an intelligent designer.

But we really ought to define what we're talking about. What constitutes "the universe?" What is a "collection of universes," how can there be more than one? And what does it mean to talk about a universe "emerging?"

There are several major competing cosmological conjectures; let's look first at the standard model, where there is only one universe (our own); then we'll look at alternative models that allow for many universes:

- Standard Big Bang Theory (SBBT): There is only one universe; it began with the (one and only) Big Bang about 13.7 billion years ago (13.7 Ga), and has been expanding ever since. For a while, the rate of expansion was slowing down; but for the last several billion years, the rate has been increasing. This universe may "exist" forever, in a sense, even after the heat death (complete entropy) of all matter and energy; but it had a definite starting point (for space, time, matter, energy, and every other state or condition) not very long ago.
*Past-expanded*BBT: So-called because such conjectures envision a multiplicity of universes, in sequence or parallel, making any conceivable creation event much longer ago than 13.7 billion years... which means there is more "past;" or to put it another way, these conjectures*expand*the available past, possibly infinitely far into the past.

It's easy to see how SBBT implies a starting point a finite number of years ago: Observation shows us that our universe is finite in size. And we can calculate the rate of expansion of our universe by observing the speed at which other galaxies are moving away from our own galaxy, the Milky Way.

Picture a balloon with little dots all over it. As you inflate the balloon, every dot gets farther away from every other dot. You can determine the rate you're inflating the balloon by picking one dot (call it Home), then measuing how quickly all the nearby dots are receding from Home.

Anyway, with those two parameters -- the current radius and the rate of expansion -- it's a simple mathematical exercise to "run the movie backwards," and see how long ago it is since the radius of the entire universe was zero. That, then, is how long ago the Big Bang occurred.

But what about these "past-expanded" BBTs? What kinds of universes do we have to imagine? Let's take the easiest one first.

**Nomenclature note:**As PBBTs envision multiple, possibly infinite universes, I will use the normal term universe to mean only a single universe, similar to our own; I will use the science-fictional term Multiverse to mean the collection of all of the universes, past, present, and future, envisioned by a particular model. I hope this will avoid confusion.

I'll write more about the actual argument Father Spitzer makes in later posts. For right now, I just want to introduce the various conceptualizations of "past-expanded" Multiverses that cosmologists discuss. Starting with...

### Cyclic Multiverse

Picture a universe very much like ours; but in this universe, there is enough matter that eventually gravity will slow the expansion, slower and slower, until finally the universe stops expanding altogether -- and begins a slow and stately collapse. (As best astronomers can determine, this *does not* describe our own universe, where expansion is not slowing. Take this as a hypothetical.)

The collapse gets faster and faster, until finally all matter and energy, space and time come crashing together in what cosmologists call the Big Crunch. In the end, we are left with a point of zero-radius that contains the entire universe... which then, at some point, explodes outward with another Big Bang, starting the cycle all over again.

This occurs over and over for an indeterminate number of times, either a very, very large finite number of cycles, or else an infinite number of cycles. We must ask three questions about such a Multiverse in order to determine whether it implies a designer or creator:

- Is it possible for such a Multiverse to have already cycled an
*infinite number of times*in the past?

If Yes, then out of that infinity of universes (one for each cycle), we should see plenty of life-friendly universes emerge through sheer, random chance. End of discussion; we cannot conclude that the existence of a life-friendly universe means anything at all, and certainly not a creator or designer. (If you deal an infinite number of poker hands, you'll necessarily get an infinite number of royal flushes... no stacking the deck required.)

- But even if an infinite past of cycles is
*not possible*-- meaning there is a beginning point to this cyclic Multiverse -- is that start point be so long in the past, has enough time elapsed, have enough universes emerged, that it's*still plausible*that one of those universes could have randomly achieved life-friendly physical constants?

Sticking with our analogy, you don't need an infinite number of poker hands. The odds of dealing yourself a royal flush are about 1 out of 650,000; if you deal 50 million hands -- each time shuffling the deck, then dealing five cards off the top -- it's almost dead certain you'll get a royal flush... in fact many royal flushes. But as big as 50 million is, it's still a finite number.

Of course, it would take a very long time to deal that many hands; at five seconds per hand with no rest periods, it would take almost eight years. So how long for a random universe to emerge that is capable of supporting life? Physicists believe the time required would be much, much longer than the full expected lifespan of our universe, from its birth in the Big Bang to its heat death, when entropy is universal and complete. So much longer, in fact, that in comparison to the time required to randomly produce a mix of physical constants that would allow for life, **the lifespan of our own single universe would be indistinguishable from zero.**

That's a very, very long time... *unreasonably* long, as it turns out.

Here's a peek into a future post: The best physical estimates show that you cannot have that many Big Bangs. Each time you cycle, entropy increases; that is, more energy ends up in cosmic background radiation and less in stars and planets and such with each successive universe; every new universe is closer to heat death than its predecessors.

Long before you could "deal yourself" enough universes to get one that supports life, the entire cyclical Multiverse would have "bottomed out," reached the point of maximal entropy. And at that point, the universe no longer collapses.

Thus most cosmologists believe that a cyclic Multiverse cannot run long enough to produce a life-friendly universe by random chance; so if our own, observably life-friendly universe is part of such a chain of universes book-ended by successive Big Bangs and Big Crunches, the physical constants are not being generated by random chance: As above, **something or somebody is stacking the emergence deck.**

But we still cannot conclude that it's a "somebody," not a "something," because there is yet another possible explanation for the non-randomness of physical constants and the bias towards life-friendly universes:

- If the cyclic Multiverse sits within a larger "Metaverse," and if that Metaverse has its own rules and physical laws... do those external laws limit or constrain the
*possible values of the physical constants*, so that it's much more probable that life-friendly universes will form than we have been imagining? In other words, is the emergence of*life-friendliness*driven by the physical laws of the Metaverse, such that the emergence of life-friendliness is*not a random function*?

In your hometown, you have probably noticed a curious phenomenon that appears not to be altogether random: Over a six-month period, temperatures tend to get warmer and warmer; but then, over the next six-month period, they tend to get cooler and cooler. Clearly this is not random; if temperatures changed entirely by random, you would expect periods of several years of hotness, followed perhaps by a cooling period of only six days, before things start to heat up again.

It's tempting to conclude that the Temperature Gods simply like to make the thermometer go up and down in a fairly regular fashion. But there is an alternative explanation: Your hometown sits within a larger system -- planet Earth, whose axis tilts with respect to its orbit around our sun, Sol.

As a result of this entirely natural cause, half the year your hometown is tilting towards Sol, while the other half it's tilting away. This explains the phenomena of summer and winter, respectively... with no anthropomorphic, intelligent deity required.

So even if we conclude that life-friendly universes can only emerge from a cyclic Multiverse via *non-random* processes, that still doesn't mean we have found our proof of God: It's possible there are other, purely natural (not supernatural) causes of non-randomosity.

Review the key points of a physical argument for God:

- There are many more imaginable life-unfriendly universes than life-friendly universes.
- So the odds of any one, specific universe being life friendly are vanishingly small.
- But we know at least one has emerged, because we're sitting in it.
- With literally infinite time, all possible universes, including the life-friendly ones, will eventually emerge, even by random chance.
- Assume finite time, and a relatively short finite time at that; then the odds of any life-friendly universe
*ever*emerging through random chance are also vanishingly small. - Putting (3) and (5) together implies that our own universe (at least!) was initiated by non-random processes.
- And that non-randomness makes it plausible, at least, to argue that our universe was created or designed by an intelligent being. (To discharge our assumption in (5), we must add, If only a
*finite, relatively short*period of time has been available for universes to emerge.)

(And remember likewise that commenter **Nerys Ghemor** is correct: These teleological debates are all versions of the "God of the gaps" argument: Science can't explain X at this moment, so X must have been ordained by God.

(However, these physical conjectures sit at a much more sophisticated level than, e.g., Michael Behe's "intelligent design" foolishness. The Spitzer conjectures invoke what appear to be universal physical constraints, such as the Heisenberg Uncertainty Principle, Einstein's General Relativity, and the stochastic nature of quantum mechanics, rather than the "known unknown" (to use Donald Rumsfeld's wonderful phrase) of the exact mechanism of some otherwise plausible sequence of events, like the evolution of the eye or the bacterial flagella. If the Spitzer conjecture is to fail, it must do so due to *unknown* unknowns, not known unknowns.)

The next two types of Multiverse we'll poke around in are (a) a Multiverse like an ocean filled with bubbles, where each bubble is a separate universe; and (b) a Multiverse comprising many more dimensions than the four we can detect (three spatial dimensions, plus the dimension of time, or duration); each universe is a "membrane," or spatial cross-section of some smaller number of dimensions within the larger-dimension Multiverse.

This kind of Multiverse has many other membranes (which impatient physicists call "branes"), and they can flutter around in the Multiverse and bang into each other, with catastrophic results for inhabitants.

More later, as I become inspired (i.e., less lazy than usual).

Hatched by Dafydd on this day, October 24, 2010, at the time of 3:50 AM

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## Comments

The following hissed in response by: Sabba Hillel

Actually, given the logical point that the Creator would have created **time** as well, there is no point involved for the definition of "the time it would take to create this universe". Before the creation of the universe "time" itself would not exist. We apparently define time as something that we sense in order to differentiate between events in this universe. Thus, "before" the big bang is a meaningless concept. Similarly, we cannot say that there is a certain amount of "time" in between creations.

Actually, there is no **reason** for G0d to have created the universe at any particular "moment" in its existence. He could have created it five seconds ago with this message on your computer screen, or 5 billion years ago and allowed it to continue until the current moment, or 5,771 years ago in order to start things moving with the advent of Mankind as we know it. Since the definition of the Creator includes Omnipotence, and there is nothing in the rules of the Universe to prevent it, we cannot argue for any particular "moment" of creation.

This is like starting a computer model with all variables set to 0, or starting it with the variables set to what they would be after a particular run. Given no round off errors, once the simulation starts running, there would be no way of determining at which point it actually started, aside from the log records which would not "exist" within the universe of the simulation.

Actually, for free will to exist (and one of the beliefs in Judaism is that free will is part of the purpose of the universe), it is a **requirement** that there be no **absolute proof** of creation. If such absolute proof (as opposed to valid arguments) existed, it would remove our free will.

The above hissed in response by: Sabba Hillel at October 24, 2010 7:11 AM

The following hissed in response by: Sabba Hillel

But we still cannot conclude that it's a "somebody," not a "something," because there is yet another possible explanation for the non-randomness of physical constants and the bias towards life-friendly universes:* If the cyclic Multiverse sits within a larger "Metaverse," and if that Metaverse has its own rules and physical laws... do those external laws limit or constrain the possible values of the physical constants, so that it's much more probable that life-friendly universes will form than we have been imagining? In other words, is the emergence of life-friendliness driven by the physical laws of the Metaverse, such that the emergence of life-friendliness is not a random function?

In your hometown, you have probably noticed a curious phenomenon that appears not to be altogether random: Over a six-month period, temperatures tend to get warmer and warmer; but then, over the next six-month period, they tend to get cooler and cooler. Clearly this is not random; if temperatures changed entirely by random, you would expect periods of several years of hotness, followed perhaps by a cooling period of only six days, before things start to heat up again.

It's tempting to conclude that the Temperature Gods simply like to make the thermometer go up and down in a fairly regular fashion. But there is an alternative explanation: Your hometown sits within a larger system -- planet Earth, whose axis tilts with respect to its orbit around our sun, Sol.

This argument does not deal with creation because the creation claim is then set back to involve the "Metaverse". A similar argument was once proposed by Isaac Asimov stating that the Big Bang could have occurred because of the collision of two protoUniverses. He then went back several more levels. However, what he did not seem to realize was that no matter how far he went back, he was still left with the creation of the

**original**setup.

This is like various fantasy stories or mythologies involving "gods". Since they do not fit the definition of G0d, (omnipotent, omniscient, etc), all this does is push the existence of G0d back a level. For example, if gods created this universe, then G0d would be the Creator of the Universe that contained gods who had the specified powers.

The above hissed in response by: Sabba Hillel at October 24, 2010 7:19 AM

The following hissed in response by: snochasr

I'm still looking for an explanation of how a different value for Planck's constant, or the speed of light, would make a universe "life friendly" or not. I can see how such things might make a particular planet uninhabitable, or habitable, but in our galaxy alone there are a very large number of life-friendly planetoids, and one assumes a very large number that are "near habitable" should their environment change for any reason.

The above hissed in response by: snochasr at October 24, 2010 10:28 AM

The following hissed in response by: BlueNight

I'm a young-earth creationist, but I don't rely on a "God of the gaps" mindset. That's too much like convicting everyone who comes before the court without an alabi: guilty before proof. There are too many examples of that mindset failing to be reliable. (Ben Franklin's lightning rod, and churches' refusal to install them, is the primary modernist myth of this sort, whatever its historicity.)

Creation science is primarily forensic and social, and thus circumstantial. There are examples of faith healings which any mentalist or hypnotist would recognize instantly as belonging to their disciplines. That's not to say God wasn't involved, but rather God may have arranged things so that an "accidentally" invoked hypnotic trance caused a psychosomatic healing. That's also not to say the black swan, a physical miracle, doesn't exist.

Cosmologically, if we assume the existence of sequence as something present universally, we have three options:

1. "The world rested upon an elephant and the elephant rested upon a tortoise" and from there it's "turtles all the way down" (infinite regress of finite variety).

2. "The world rested upon an elephant and the elephant rested upon a tortoise" supported by a mammoth, a Brachiosaurus, an airplane, a bowling ball, Atlas, a pair of roller skates, and so on down (infinite regress of infinite variety).

3. The unmoved mover, sentient or not, sapient or not, involved or not, exists.

If sequence itself, as something that can be recognized logically, simply does not exist "outside" of our universe/multiverse/metaverse/omniverse, then all bets are off.

The above hissed in response by: BlueNight at October 24, 2010 12:41 PM

The following hissed in response by: Dafydd ab Hugh

**Sabba Hillel:**

We're using a lot of loose shorthand here, but cosmologists have more rigorous formulations.

For time in a Multiverse, substitute Multitime, a measure of duration of the cycle itself. The questions are (a) whether Multitime has already been running for an infinite or finite duration as of a particular moment; and (b) if Multitime has only achieved finite duration, then has has it been long enough to allow the cycle to have already produced such a large number of random universes that it's plausible one could have had, through sheer random chance, physical constants that allow for the formation of life.

For the turtles-turtles-turtles objection, bear in mind that the Metaverse -- in which some Multiverse is (or Multiverses are) cycling through creation of many universes -- might have different physical laws from the interior universes that emerge.

That's my point: What seems not only random but wildly improbable within an individual universe might be, not merely likely, but *absolutely determined* by the larger Metaverse that contains the smaller universes.

We must consider these possibilities in order to be (reasonably) complete in our reasoning.

**Snochasr:**

I already gave one example, but I'll alter it slightly: If you change the value of the Gravitational Constant, you can end up with gravity so intense that the universe would expand after the Big Bang, slow, then contract back into the Big Crunch in a very short period of time. That time could be too brief to form the coherence of solar systems and planets, let alone allow sufficient time for life to form.

Contrariwise, you could make gravity so tenuous a force that those structures never form, because gravity cannot overcome the initial momentum imparted to each molecule by the Big Bang. You get a semi-uniform smear of molecules fairly evenly distributed throughout the universe; I cannot see how life could form under such circumstances.

Planck's Constant is basically a measure of the energy quantum: If it were larger, so that particles had to build up a much larger batch of energy before being able to emit any of it, then particles might not be able to exchange energy. That might mean no molecules could form, electrons couldn't move up or down their electron shells, and so forth. Or if Planck's Constant were much smaller, the exchanges might become so continuous that again, structure could not form, as everything would be breaking up and reforming too rapidly for any coherence.

The speed of light sets the upper limit of relative velocity. If it were much faster, particles would have hurried away from their fellows so quickly, they would get out of range of gravity and could not be tugged back to form stars and planets. Contrariwise, if the speed were too slow, it would take so long for photons created by stellar fusion at the core of a star to random-walk their way out to the surface that the universe would be entirely dark... possibly long enough that the star would have already burned out and collapsed before the first photon could escape.

See, you monkey around with those constants and everything falls apart. There are, of course, ranges within which everything can still be made to work, such that life (as we know it) can exist; but the ranges where this is *not possible* are very much larger.

Dafydd

The above hissed in response by: Dafydd ab Hugh at October 24, 2010 12:57 PM

The following hissed in response by: Karl

And a major part of the "fine tuning" argument assumes that the range of possible values for these variables is very large compared with the "life-friendly" range. It may be that according to as-yet-undiscovered laws, the value of the gravitational constant is constrained to either "life-friendly" values or very close.

In a recent issue of Sci-Am, it turns out that varying one parameter gives you a universe capable of supporting life only in one narrow region, if you vary more than one at once, you get other islands of life-supporting universes. The universe may be fine tuned, but there may be more than just the one station available.

The above hissed in response by: Karl at October 24, 2010 5:57 PM

The following hissed in response by: BlueNight

And of course we're defining life solely in terms of chemistry. In a universe where matter is diffuse but universally dense, an electromagnetic pattern might result from Brownian motion and eventually evolve into sentience. As long as motion and potential difference can exist, goes the theory, life might appear vastly different than we've ever seen.

As a Christian, I don't expect it, but there are a lot of things I've been told not to expect which I have seen.

The above hissed in response by: BlueNight at October 24, 2010 7:13 PM

The following hissed in response by: snochasr

I'm getting quite an education, but I think I also need a lot of imagination to envision how some of these "constants" could ever be other than what they are. Why do we consider these "constants" as mere "variables" that are set to a random initial value (or perhaps at some "Designer's" whim) at the time the whole universe is set in motion? Why wouldn't the gravitational constant ALWAYS be as the square of distance? A 10-dimensional universe I can understand, with one of those dimensions being the "brane number," but the other dimensions would need to be the same, therefore producing the same physical constants across (this form of) the multiverse, would they not?

The above hissed in response by: snochasr at October 25, 2010 6:59 AM

The following hissed in response by: Robert

Sabba Hillel, we can equally well ask where God came from. The traditional answer is that he is an unmoved mover, which is indeed the only way to terminate the infinite regress, but there's no reason to believe that an unmoved mover, a first cause, must necessarily be a sentient entity, let alone of all the properties attributed to God. The attempted proofs of that are riddled with gaps, bridgeable only by faith.

The whole line of argument used in the book being discussed appears to be misunderstanding probabilities at a basic level. You have to specify the outcome you're looking for, before tossing the coin, rolling the dice, or whatever.

Suppose I toss a coin 1000 times, taking maybe 20 minutes. There are approximately 10^100 possible outcomes, 1 followed by 100 zeroes, so the chance that any one of them happens is 1 in 10^100, ludicrously small. If everyone in the world tossed coins non-stop until the sun dies, the chances of anyone duplicating my coin toss sequence are still only around 1 in 10^80.

Clearly, since my coin toss sequence is so ludicrously improbable, it can't be the result of pure chance. Something must have intervened to pick the sequence -but this logic is false. Whatever sequence I came up with would be equally unlikely. If I had specified the sequence in advance, then we could safely concluded the coin was rigged, and only if I had.

Howe, results like the proportion of heads tossed, or the proportion of time the coin came up the same way twice running, are meaningful ultimately because of averaging.

Applying this logic to the state of the universe, we see we have to be very careful about what we measure the probability of. Looking for the chances of getting a universe exactly like ours si like looking for the chance of a particular sequence of coin tosses, the wrong type of question. What we need to know if the probability of ending up in a universe that can support life of any kind, not necessarily as we know it, and that calculation is currently beyond us.

The above hissed in response by: Robert at October 25, 2010 10:22 PM

The following hissed in response by: Dafydd ab Hugh

**Robert:**

Suppose I toss a coin 1000 times, taking maybe 20 minutes. There are approximately 10^100 possible outcomes...

I believe it's actually closer to 10^301:

- We begin with the exact number of outcomes, which is 2^1,000;
- To estimate this, we can use the fact that, by definition, 2 = 10^(log 2);
- The log of 2 just about = 0.301;
- So 2^1,000 = (10^0.301)^1,000;
- Which = 10^(0.301 x 1,000);
- Which = 10^301.

That is, the total number of possible outcomes from flipping a coin 1,000 times is just about ten trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion... which by a curious coincidence is almost exactly how many counterfeit dollars Barack H. Obama will have spent by January 20th, 2013 -- his last day in office.

On a more serious note, suppose we define a "habitable universe" as one that can support life as we know it; and suppose that habitable universes correspond to those in which that thousand-flip coin toss yields a sequence that contains at least 800 heads.

I'm not willing to sit down and calculate the odds of one of those uinverses (sequence of coin flips) coming up habitable (containing >= 800 heads). But I *am* willing to bet $50 that the odds of a habitable universe popping up in even 10^100 trials of the thousand-flip coin toss is *less than* the odds that all the air molecules in my office will randomly, simultaneously move to the right side of the room, leaving the left side in vacuum. Any takers?

Therefore, if you try your thousand-flip coin toss a few times, and a habitable universe pops up... you can bet your bottom dollar that the coin is unfairly weighted, biased in favor of habitability, instead of being truly random.

That is the syllogism; the trick is to make a reasonable estimate of the odds of each vital constant being within the habitability range, then combining all those odds into one probability that *all* vital constants simultaneously fall into the habitability range.

Dafydd

The above hissed in response by: Dafydd ab Hugh at October 26, 2010 1:16 AM

The following hissed in response by: Robert

It is 10^300, that was an arithmetical slip.

More importantly justify looking only at the odds of life as we know it, not of all life? I think not.

Like any specific coin toss sequence, life as we know it can only be identified as special after the fact. There's not to single it out, other than the fact that we're an example of it, just as there's nothing to single out a specific coin toss sequence, other than that I happened to toss it.

For meaningful results, we must consider only those outcomes which could have been identified as special before the fact, like getting 1000 heads. That's a significant result, because the total number of heads will be normally distributed, so is much more likely to be 500+/-30 than to be 1000. In the case of a random distribution of universes, life in general is something that can be picked out as special before the fact; life as we know it isn't, not unless there are only a finite number of forms of life that can exist, a claim which would not be easy to prove.

Incidentally, the chance of the air molecules in your room end up in the same half is something like 2^(10^28) - 6*10^23 molecules per litre, i.e Avogrado's number, 1000 litres in a cubic metre, a room 2x4x2 metres. 2^(10^28) = approx 10^(3*10^27). The chance of getting over 800 heads from the thousand flips is at 1/2^(10^3), the chance of getting exactly 1000 heads, so it is massively greater than the odds of the air in your room doing that. You'd lose that $50 dollar bet.

This aside, the arguments for the smallness of the habitable zone for life as we know it are pretty weak. As noted by Karl, it's it tacitly assumed that only one parameter is varied at a time. If the points supporting as we know it lie near some curve, or even a straight line askew to these parameters, varying just one at a time will massively underestimate the proportion of habitable universes, and there's no good reason to think that they don't.

The other problem is the neglect of feedback effects. Above you mention the case of weaker gravity. It doesn't matter how weak gravity is, a uniform distribution of matter is unstable, and will collapse. (Look up the Jeans Instability). This collapse will only stop when the central pressure is high enough. You can then calculate from there what happens for weaker gravity. It turns that that over a significant range, the central pressure gets high enough to cause fusion, hence stars as we know them.

Because gravity is weaker, the stars end up being cooler than in our universe, and lasting longer. At a rough estimate, if gravity were 10 orders of magnitude weaker, the result would be be stars weighing about 10^15 solar masses, just enough to compress their cores to fusion heat, with a life span around 10^20 years, and 10^5 times the radius and brightness of our sun, but only slightly cooler than our sun. Orbiting at around 300 AU would give comfortable earth-like conditions for a 100 quintillion years.

Make gravity too weak, and the stars won't ignite at all. If some of the other parameters vary too, you might find matter decaying before the stars have time to collapse, and there are many other complications.

However, the simple fact remains that something determined by negative feedback, like the core temperature of stars, isn't going to be sensitive to physical parameters. A star will always be exactly hot enough to produce pressures high enough to support its own weight - any hotter and it expands, cooling itself; any cooler and it contracts, warming up - and this would remain so even if neutrons were 10% heavier.

Life, of course, is a prime example of a process dominated by negative feedback.

The above hissed in response by: Robert at October 26, 2010 5:54 AM

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