Camp Quest West

I'll be appearing at Camp Quest West this year. For those who haven't heard of it, Camp Quest is a national organization that endeavors to reproduce all the great trappings of Church Camp for atheists, providing a place godless kids can spend a week in the wild, learning stuff, having fun, gobbling early morning flapjacks, roasting strange things over a campfire, putting on silly skits, staying up all hours of the night playing Twister. Well, okay I made up the last bit (Cherry 2000 fans, huzzah). But you get the picture. No prayers, no bible lessons, no making God's eyes out of popsicle sticks.

Instead, alongside all the traditional fun stuff, there are educational activities that teach about critical thinking, science, freethought history, things you need, things that make you go (obscure TNG trivia fans, huzzah--but no, they won't kidnap your kids and force them to build advanced engines and weaponry, and you won't need strange alien gases to fool them into giving them back--I know, I know, you were hoping). See Wikipedia for more.

Camp Quest has summer camps in Ohio, Minnesota, Michigan, the Smoky Mountains, Ontario Canada, and yes, California (that's Camp Quest West). The latter's camp site is in the Sacramento region. It runs from Sunday July 12 to Saturday July 18 (2009). I don't know if it's full up yet, but if you have means and interest, and kids to be rid of for a week, it's worth a thought. Though camps are always expensive, and Camp Quest is no exception, so keep that in mind. They are fully non-profit, but there is considerable overhead for this sort of thing, as you might imagine (though they could reduce costs considerably if wealthy benefactors donated annual subsidies--hint, hint--currently they do get some coverage from small donors like me, just not enough yet to cover all costs).

Sometime during that week (possibly Tuesday) my good friend David Fitzgerald and I will pop by to run a game I designed for the campers, History or Hogswallop!?, which evolved from activities we ran for previous camps. As it's described in their May newsletter:

History or Hogswallop is coming to town!

Author and historian Dr. Richard Carrier and his loyal sage David Fitzgerald will present History or Hogswallop!?, an exciting team game that pits all your wits against the wildest claims in history. Can you figure out how to uncover the truth? Will your team win the prize? Find out, when you play History or Hogswallop!?

Dr. Carrier developed this game last year based on previous years at Camp Quest, when presenting challenging questions about ancient history led to a lot of fun for all. Gigantic ships, famous battles, and crazy claims were described, and campers had to work together to come up with smart ideas how they'd find out if any of these stories were true.

Now we've got a whole new batch of crazy claims, and a slick new way to run an action-packed competition among teams of campers, this time for a prize. Every player will learn a lot about history and historical method, without any boring lectures. What's more, their intelligence and ingenuity will be challenged, and their skills as a skeptic honed. Some will even get a good bit of exercise!

It's only for campers. But I thought it couldn't hurt to mention Camp Quest West, if perchance any readers out there are parents or know parents who'd love to send their kids to a freethought summer camp this year. It's a great project I love to support.

Appearing in Sacramento

I will be giving yet another reprise of my talk on Not the Impossible Faith in Sacramento (California) this June 14 (2009) for Atheists and Other Freethinkers. This will be their usual meeting time and place, Sunday 1pm to 4pm in Room 10 at the Sierra 2 Community Center, 2791 24th Street, just south of Broadway (see map). Parking is available on the street or in the rear (off 4th Avenue). It's open to the public (but donations are always appreciated) and I will be selling and signing books afterward (where you'll get a better deal than online). For a description of the talk see my announcement for last month's Berkeley appearance.

Appearing in San Francisco

The San Francisco Atheists have asked me to give an encore presentation of my discussion of J.P. Holding and my book Not the Impossible Faith in San Francisco (California). This will be in the banquet room at Schroeder's (240 Front Street, when you walk in just head all the way to the back room) on the Saturday of May 30 (2009) at 6pm. It's open to the public, but you will be expected to buy a drink or meal from the hosts (and please tip generously). I will be selling and signing books afterward, but be advised, supply is limited! For what this talk will be about, see Appearing in Berkeley.

Statistics & Biogenesis

Today, critics compel me to compose a long and dull commentary on probability and biogenesis, which will nevertheless be terrifyingly important to some people. The rest of you can skip all the way down to the last section marked "conclusion" and just read that. Everyone else, bear with me. In Sense and Goodness without God I briefly summarized the conclusion and justification for a naturalist theory of the origin of life (on pp. 166-68). Among the points I make is this:

"All the planets around all the billions of stars in all the billions of galaxies are organized at random with practically infinite variation, and because there are so many, the law of big numbers prevails: every possible planet that could be (given the universe and its physical laws) probably has been, is, or will be. Thus, that one or more planets should have all the right properties for biogenesis is probably a foregone conclusion, and our planet is known to be one of those rare few. Though we have none of the information we need to calculate any of the relevant statistics, this is still a reasonable conclusion, for two reasons."

...which two reasons I then go on to summarize, followed by a bibliography for further reading and confirmation of that summary, which includes Richard Carrier, "The Argument from Biogenesis: Probabilities Against a Natural Origin of Life" in Biology & Philosophy (19.5, November 2004, pp. 739-64). I have discussed these issues before, most notably in my debate with Wanchick (see Atheistic Cosmological Argument, and then search for my sections on the CDA here and here and on the ACA here) and in my past blog entry on Yockey. In the latter I discussed the role of probability thresholds in determining when an improbable event is too improbable to be considered a chance event. I also discussed this in my article for Biology & Philosophy, where I demonstrate why we can't ascertain the relevant statistics, but that we can ascertain some of their limits, and as it happens, they correspond to my argument in Sense & Goodness.

An Irrational Complaint

In his negative (and arguably delusional) review of my book on Amazon.com, Christian apologist David Marshall claims the argument I summarized in Sense & Goodness is without logical and scientific foundation. Of course, he failed to mention that I cited numerous books and articles by scientists and others in support of my conclusions and that I specifically directed my readers to these works in the bibliography. Instead, he claims my "discussion of biogenesis is terribly glib" (glib here being in As*hole Dialect a synonym for "brief"), and then claims I "[don't] seem to notice, let alone deal with any of the real problems in this field," even though that is exactly what the bibliography does.

Among other things, Marshall complains that, taken hyper-literally, I can't mean what I say, since (for example) extremely bizarre planets (like, oh, let's say, gigantic mushy balls of spontaneously-formed bunny rabbits) surely are too improbable to have occurred even once in the known expanse of space and time (though he didn't put it that way--he's not particularly funny). But then, anyone who takes words in a book hyper-literally is probably a fundamentalist. The rest of us act like normal people. Of course, literally I wrote that every possible planet (on known physics) probably has been, is, or will be, and if the universe continues forever, and that disturbing bunny-planet is physically possible, it will indeed exist eventually. But obviously, from context, that isn't what I was talking about. I was only referring to the possibility of biophilic planets, i.e planets capable of harboring the origin and evolution of life.

I'll certainly grant that literally every possible planet has not yet been realized (e.g. every possible pattern of alternating red and yellow striations as viewed from space), but every possible general configuration probably has (e.g. a planet almost certainly exists with some pattern of alternating red and yellow striations), and I say "probably" here because some extremely bizarre general configurations will not be realized. But we don't generally care about them. Because as the scientists I cite explain, a planet being biophilic corresponds to a likely general configuration, one that has almost certainly been realized many times in the known universe (for many reasons, some of which I summarized). As I go on to argue in the book, this conclusion is supported by considerable evidence in many ways, most especially by the fact that nothing required for biogenesis is observably uncommon (p. 167), so we needn't even consider the probability of the extremely bizarre (like planets made of clumps of spontaneously-formed animals).

Nevertheless, Marshall also claimed my use of "The Law of Big Numbers" is just a "pseudo-scientific phrase," thereby proving his ignorance of the basic math. For this is a formally proven concept in statistical theory, taught in every introductory college course in statistics (e.g. see the textbook discussion of The Law of Large Numbers by professor of statistics Philip Stark at UC Berkeley). According to this law, as the number of occasions increases, the probability of an event approaches 100% (if it has any probability of occurring at all). It's just a matter of time--or, more exactly, of the number of opportunities, which are spread not just across time, but space as well.

In the case of biogenesis, this law entails that if the probability of biogenesis is (let's say) 1 in 10^40, but there are 1 in 10^50 trials, then the number of biogenesis events will almost certainly not be zero. In fact it will approach 10^10, or ten billion biogenesis events, scattered across the universe. But even if there are just 1 in 10^50 events (not just of mixing organic molecules, but everything else), the Law of Large Numbers still entails we should expect that ten billion or so events (give or take) will occur in this universe which have a probability of 1 in 10^40. Since one of those events could as easily be the origin of life as anything else, if life has a 1 in 10^40 probability of originating by natural accident, then we cannot conclude (at least from observing a single instance of it) that life didn't so arise. That's what I argue in Sense & Goodness (i.e. that the natural probability of biogenesis is small, but the number of events, and even trials, in this universe has been vast). The Law of Large Numbers does indeed entail my conclusion from the premises, and the works I cite establish the premises.

Marshall nevertheless says I don't deal with the "real" problems in biogenesis, yet I refer readers to where I did (my article in Biology & Philosophy) and where others have (naming several books by experts on the subject). My own article on biogenesis is 26 pages long. My section on the subject in Sense & Goodness is 2 pages long. So in effect, Marshall irrationally wants a me to expand every section of my book 13-times-over, merely because he wants every little item discussed. Such a demand is quite irrational. Satisfying it would make the book an unbuyable (and unreadable) 5,700 pages long! Instead of attempting something so absurd, as I explain in the introduction of Sense & Goodness (p. 5), all my claims are backed up by the works cited in the bibliographies. Therefore, if you want to know how we deal with the problem of obscure issues like homochirality, you need to consult the bibliography. Had Marshall done so, as my book explicitly instructed him to do, then he would have known I have an entire section on homochirality in my cited article, supporting the generalizations in the book (the topic is also discussed by some of the other authors I cite). And so, too, for anything else of importance.

Dembski's Filter

Though I and others pointed out much else that was wrong with Marshall's remarks (on this and other subjects) in comments on Amazon responding to Marshall's review (producing a long and boring thread that must surely rival in size most you are likely to find on Amazon, and that eventually became pointless as he continued ignoring or misrepresenting almost anything we said), there is one issue worth further elucidation, since it is often not understood. And that's the difference between trials and events, and how and why cosmic probability thresholds pertain to both.

One of the most useful books in this regard, you may be surprised to hear, is by the notorious creationist William Dembski. In fact, I highly recommend his book No Free Lunch. In it he discusses the issues of probability and information theory that pertain to ascertaining when an event is too improbable to be a coincidence, and thus must be either a product of physical necessity (like crystallization or planet formation) or intelligent design (like excavated coins or arrowheads). Contrary to what his many critics claim (though they raise many valid issues and concerns one should be aware of: e.g. see "Not a Free Lunch But a Box of Chocolates" by Richard Wein), Dembski is right about the logic of his argument, and is only wrong in two respects:

(1) First, in trusting the creationist biochemist Michael Behe, Dembski (also a creationist but only a mathematician) mistakenly concludes there have been mutation events in the history of evolution with a random increase in information content greater than 500 bits (which he rightly argues would be unbelievably improbable). But there is no confirmed evidence of this, no evolution expert believes any such event has occurred, and Behe has never published his demonstrations of irreducible complexity (supporting such a claim) in any peer reviewed journal and has never conducted any experiments or laboratory research necessary for such a demonstration to be scientific.

Dembski fully agrees that increases in information of less than 500 bits can and often do arise by chance, and that in fact this happens routinely in evolution, and if that's all there has been, he would agree evolution by natural selection is sufficient to explain all life on earth. Similarly, I fully agree that if, instead, Behe is right (and there has been at least one spontaneous increase in specified information content greater than 500 bits in the development of any genome), then Dembski is right, and some degree of intelligent engineering of single-celled life billions of years ago would be the best explanation of observed phenomena. But until Behe (or anyone) actually scientifically confirms such an observation, this is merely a hypothetical. Indeed, it's worse than that, really, since scientists have shown the evidence is very unlikely to favor Behe, even if he ever does do any actual scientific research on the matter (e.g. see "Irreducible Complexity and Michael Behe"). Either way, without this evidence, Dembski's argument cannot reach his desired conclusion, no matter how correct his method.

(2) Second, in focusing exclusively on the role of a probability filter, Dembski underplays the fact that Intelligent Design is usually identified by much more direct means, which curiously fail to confirm ID in the very case in question (the origin and evolution of life). For example, if I receive a brief email from my wife asking me to buy some eggs, the probability that such an email could have been typed and sent at random (such as by her cellphone accidentally being switched on in her purse and its buttons being pushed by jostling against her lipstick and ladysmith revolver) might be nowhere near any probability threshold at all--it could be well within the realm of cosmic probability or even earthly probability (indeed, I'm sure some such random event has happened at least once, somewhere at some time, to someone on earth)--yet I still don't conclude this message from her is an accident.

Though I fully believe such a random event could happen (and my only folly in trusting it in such a case would be buying some eggs we didn't need, a tragedy my wife and I would have no problem rectifying by baking some cookies and cake), I base my conclusion that she intelligently composed and sent the message instead not on the improbability of it being sent otherwise, but on my past observations of my wife's interests and behaviors. From considerable direct evidence I know she exists and how she communicates with me and that we often do need eggs and she often asks me to buy things we need. I have ample confirmed evidence that sending intelligently designed messages to me is exactly the sort of thing she does. I also have ample confirmed evidence that most such electronic text messages (in fact, in my own experience, all of them sent to me so far, numbering easily in the hundreds) turn out to have been intelligently designed and not randomly composed (a fact I have also confirmed by strong and abundant independent evidence).

Similarly, if we had the same evidence that God makes things, we wouldn't need to prove something was improbable to conclude he made it: if we knew for a fact he does things like that, and he told us outright what he did, we would be as justified in concluding he did it, as I am justified in concluding my wife sent me an emailed request for eggs. If, for example, the Bible had an accurate description of the genetic code for a bacterial flagellum and stated correctly that it was inserted into single-celled organisms two billion years ago, and God personally spoke to us still today, affirming what the Bible said, about this and many other things besides, especially things we then confirmed independently, then we would have very strong evidence for ID (see my more detailed example in Why I Am Not a Christian, particularly "Christianity Predicts a Different Universe," although the whole article pertains).

Of course, God in such a scenario could still be lying, but we could rule that unlikely the same way I rule unlikely the possibility that my wife is lying about her wanting eggs: all I would need is considerable past experience confirming my wife's general honesty in such matters (= considerable past experience confirming God's general honesty in such matters). And sure, we might still debate who "he" really is and how he does what he does. But once we'd ruled out lying and other causes of the data, there would be no question in such a case that life was probably at least partially engineered by someone remarkable, no matter how he did it or who he really was.

But I must still take issue against Dembski's critics here: his error lies not in adopting the wrong method or ignoring other methods, it lies in not recognizing the fact that his opponents are also correctly applying the same method, just without the math. For what makes the conclusion about my wife's email valid is the improbability of the whole conjunction of affairs (e.g. all the evidence I have of my wife's interests, powers, and behaviors, and of all the past correspondences between text messages sent to me and independent evidence confirming they were not randomly composed = all the evidence we could have had of God's interests, powers, and behaviors, and of all the past correspondences between divine messages sent to us and independent evidence confirming they were not likely hallucinatory, etc.). We conclude such a collection of evidence cannot exist by chance accident (it's too improbable), therefore we conclude it is all meaningful data that indicates just what we conclude it does (e.g. that my wife exists and has those interests, powers, and behaviors, and now wants me to buy eggs = that God exists and has those interests, powers, and behaviors, and once deliberately engineered the bacterial flagellum), and this is what warrants the conclusion that a particular event or message sent to us is not random noise but intentionally designed.

If we were to do the math, I am quite certain we would find the improbability of such a collection of background evidence arising by chance must be way beyond any probability threshold, thus confirming the merits of Dembski's probability filter. Provided we do indeed rule out both physical necessity (as Dembski agrees we must) and random chance (which is what the threshold is for), intelligent design does become the most likely explanation.And this is in fact how we actually infer intelligent design in the world, even though we are unaware of it. The trouble is, in the case of biogenesis, we don't have the vastly improbable set of background evidence that, for example, makes my wife's egg message unlikely to be random. There is simply no direct evidence at all of God's acting in or on the world (at least none comparable to what I have with respect to my wife doing so), much less of God's specifically splicing engineered strips of genetic code into bacteria, or deliberately assembling self-replicating proteins to jump-start life on earth.

In other words, all Dembski has is the mere improbability of random assembly. Thus, he must find all the improbability exceeding the threshold entirely in that singular event itself, whereas I do not have to do this in the case of my wife's message. For the improbability in that case is spread out over the total conjunction of the entire field of pertinent background evidence warranting the conclusion that this particular message was intentional. That's why that specific message need not be very improbable as a chance event (and indeed, it would only require the accidental production of barely 100 bits of information). Rather, it's the conjunction of its content, with all the other evidence warranting my interpretation of it, that's too improbable to regard as accidental (since the total specific information content of all of this is far and away more than 500 bits). But Dembski lacks that. Which is why he needs to find evidence of at least one instance of a spontaneous specified information gain of over 500 bits, somewhere in the history of genetic evolution (outside, of course, human genetic engineering). But as no one has actually found such a thing, his desired conclusion lacks scientific support.

Line of Argument

1. The Borel and Dembski Thresholds (1 in 10^50 and 1 in 10^150, respectively) indicate the least likely thing that can happen in the known universe purely by chance. This is explained by William Dembski in No Free Lunch and in my own work (as cited above).

2. That least likely chance event can be anything, literally anything (as Dembski himself correctly argues): a galaxy cluster accidentally arranged to spell out a section of the Hebrew alphabet, a rock formation on a distant planet exactly identical in topography to a recreational water park in San Dimas, a talentless child randomly striking piano keys and reproducing part of a Bach concerto purely by accident (which is an example similar to one Dembski himself uses), or (as Dembski also acknowledges) the accidental linking of amino acids in a self-replicating sequence, or any mutation producing a sequence that confers amazing biological advantages (like a complex organ)--all provided the probability of any of those things matches the threshold.

3. Therefore (as Dembski again correctly argues), if we witness such an event, and it is a singular event (i.e. we only see it once), then we cannot argue that it's too improbable to have happened by chance, because at least one such event will in fact happen by chance in the known universe, and the event we are witnessing may indeed be that one chance event.

4. Only if we saw several such events (producing a combined improbability so high it falls well above the threshold and therefore whose conjunction is not likely to happen anywhere in this universe purely by chance) or an event that all by itself is so improbable it exceeds the threshold, can we argue that intelligent design is the more likely explanation of why that event occurred (and then only if we can rule out physical necessity, as Dembski himself explains).

5. We have already discovered in the lab self-replicating peptides and proteins of such a low complexity that the probability of their accidental combination is far below these thresholds. And we have ample scientific reason to believe these are not the only such combinations possible or even close to being the only ones (and the more possibilities there are, the more likely an accidental production of a self-replicator becomes). For example, one such peptide has a probability of accidental combination of 1 in 10^41 (see Carrier 2004 for these and other scientific facts and references, also Carrier 2005, pp. 167-68). That means we can expect roughly a billion such accidents to occur in the known universe under the Borel threshold (since 10^50 - 10^41 = 10^9 = one billion), and roughly 10^109 such accidents under the Dembski threshold (that's a 1 followed by 109 zeroes--which is, by the way, a lot).

6. Therefore, even if forming that one replicator were the only possible way to get life started by accident (and the science proves it is not), we still cannot claim such an event wasn't one of the billion or more random accidents (of all sorts) that are already expected to occur by chance in this universe. For it could well be one of them, as Dembski agrees. He might argue the actual probability must be much lower than his threshold. But if it isn't, even Dembski concedes that in such a case we cannot argue to an event's Intelligent Design merely from its improbability. And he is right.

7. The scientific facts now prove the combination of attributes necessary to produce a biophilic planet is not highly complex, and certainly far less complex than even the simplest self-replicating peptide. This is demonstrated by Peter Ward and Donald Brownlee in Rare Earth: Why Complex Life Is Uncommon in the Universe (2000), and others (see the bibliographies in Carrier 2004 and 2005).

8. Therefore, whatever the improbability of accidentally generating a biophilic planet in the known universe may be, science proves it must be much lower than the improbability of randomly assembling a self-replicating peptide or protein.

9. The improbability of randomly assembling a self-replicating peptide or protein is scientifically certain to be lower than 1 in 10^41 (as discussed under point 4 above), so a fortiori the improbability of accidentally generating a biophilic planet in the known universe is scientifically certain to be much lower than 1 in 10^41.

10. 1 in 10^41 is well below the Borel and Dembski thresholds.

11. Therefore, the probability that a universe, of the size and age we observe this universe to be, would produce a biophilic planet by accident (without any intelligent design), is well below the Borel and Dembski thresholds, as is the probability that such a universe would then produce a self-replicating peptide or protein by accident (without any intelligent design).

12. Whatever is below the Borel and Dembski thresholds cannot be attributed to Intelligent Design based solely on its improbability.

13. Other than its improbability, there is nothing else about the origin of life that is indicative of Intelligent Design.

14. Therefore, the origin of life affords no evidence of Intelligent Design.

Q.E.D.

Working It Out

We have two different statistical considerations here: the probability of getting life given a certain number of trials, and the probability of getting life in this universe regardless of the number of trials. In the first case, if we randomly combine amino acids into 10^50 combinations of sufficient length, then the Law of Large Numbers entails the probability will be virtually 100% that one of them will be the self-replicating string that has a probability of 1 in 10^41. In such a condition, the appearance of self-replicators is inevitable on Naturalism. It effectively has a final probability of 100%. Scientific evidence suggests we are actually in that situation, and Ward & Brownlee argue that we are. But in the second case, we could have only one random combination of amino acids of sufficient length, occurring only one single time in the whole age and expanse of the universe, and still we cannot infer design, even if that one single instance is the self-replicating string that has a probability of 1 in 10^41.

This is because even though that latter result would be remarkably lucky (though only from our subjective point of view), at least a billion events exactly that improbable will already inevitably happen in this universe, so we cannot be surprised to have found one of them. For the final probability that such an improbable event will occur in the known universe is virtually 100%. That doesn't mean the probability that this universe would produce life is 100%. That probability (in this completely artificial "one single chain of amino acids formed in the whole universe" scenario) remains 1 in 10^41. It's just that so many things happen in this universe, that some event of that unlikelihood is guaranteed to happen. In other words, whatever the probability of biogenesis is, it will be the same exact probability as a billion other things that will in fact inevitably happen without intelligent design, and since none of them will have been intelligently designed, we cannot infer merely from this event being one of them that it, unlike them, was intelligently designed.

But as I explain in Sense & Goodness, we are definitely not in this artificial "one single chain of amino acids formed in the whole universe" scenario. Nor are we in a universe where biophilic planets are rare. To the contrary, as Ward & Brownlee explain, we are in a "buttload of amino-acid chains formed in the whole universe" scenario, and though ideal planets may be rare (arguably no more common than one per dozen galaxies), biophilic ones are not. We observe this universe contains at least a hundred billion galaxies (10^11), and there are certainly a great many more than that, we just can't see them because they are beyond our horizon. Each galaxy contains on average a hundred billion stars (10^11), which harbor altogether many more planets and moons of significant size.

Of course many stars have no planets or moons, but those that do will usually have a great many of them (due to the nature of how they form). Our star alone has over fifteen of them (at least eight planets and seven moons with planetoidal mass). And as Ward & Brownlee explain, seven of those were biophilic at one point or another in our star's history (three currently are: Earth, Ganymede, and Titan; two possibly are: Europa and Callisto; and two once were: Mars and Venus). Titan, especially, looks remarkably like Earth (a recent photograph is shown to the right), though it's habitable zones would still be subterranean. Earth, meanwhile, would probably look a lot more like Mars or Venus had life not taken hold and begun altering and regulating its atmosphere. If our solar system is not unusual in having over a dozen planets and moons in a variety of configurations (and there is no reason to believe it is), then on average there is likely to be at least one biophilic planet or moon for every star (which does not mean one in every planetary system, as many will have none, but some, like ours, will have many).

So 10^11 galaxies x 10^11 biophilic planets and moons = 10^22 biophilic planets and moons. Currently. But stars form in the known universe at a rate of 10^12 per year and live an average of ten billion years, so there have actually been a great many more biophilic planets in the known history of this universe (which spans over 13 billion years so far), and there will be a great many more as time goes on. So our count remains conservative. The more relevant time scale is the planetary period of opportunity. The window for life to originate and take control of a planet is at least half a billion years (since the substantial changes in conditions needed to close that window take at least that long to develop).

On any given biophilic planet or moon there will be at least a million cubic kilometers of region suitable for biogenesis (10^6). The earth's oceans alone exceed a billion cubic kilometers and don't even exhaust all possible venues for life. Even a planet or moon with only a 1500 km radius (the smallest we should count) will have 9 million viable cubic kilometers if only a single kilometer of depth is considered across or near its surface. In reality, the viable regions would be scattered about at different depths and locations (individual pools of sludge or sheets of chemically reactive clay or undersea volcanic vents, etc.), but the total volume will be at least 10^6 km^3 for any given planet or moon we consider, most of which will be far larger than 1500 km in radius (the earth alone is four times that).

The number of amino-acid chains of sufficient length that must randomly form per cubic kilometer (of every viable area in the universe) every year in the available window, for the near certainty that a polymer with a probability of 1 in 10^41 would form somewhere in the universe by now, is only 100,000 (10^5), per the equation completed below, using all the estimates above, which we know are all far below what they must in fact be. That's just one random chain forming every ten thousand cubic meters in a whole year (since a cubic kilometer is a billion cubic meters, and 10^9 / 10^5 = 10^4 = 10,000).

Even if there is only one volcanic vent or active sludge pool or plate of reactive clay or any comparable chemical system per planet, and we exclude all other locations, so that to get the same result an average of 10^11 chains must form at each localized system per year, such systems can easily do that. A single liter can contain over 10^20 amino acids (less than a kilogram of organic material), and in highly active systems their chaining is not only natural and inevitable, but rapid. If every amino acid in such a mass formed one link per minute (which is slow: the rate in biological systems is many per second), it would take less than an hour to form chains as long as the simplest self-replicators we already know about, and in that hour at least 10^9 chains of such length would form (if every stage halves the available amino acids available for the next stage). If no autocatalytic system or self-replicating protein or peptide arises, they would start chaining to each other (producing more experiments) or dissolving and linked anew (also producing more experiments), either way recycling and continuing the process. It would only take 100 days of this to have tried 10^11 chains, and that's with only a single liter undergoing all this chemistry. So one way or another, 100,000 trial chains per cubic kilometer of viable area is well within natural means.

Following here is the calculation I just ran through, for the number of biogenesis trials (not just events of any kind) that we can expect there to have been. The only unknown variable is N. All the others are known for a fact to be the values here assigned or higher:

G (Number Galaxies Known) x S (Average Number of Stars per Galaxy) x B (Average Number of Biophilic Planets or Moons per Star) x K (Number of Cubic Kilometers per Planet or Moon in Which Amino Acids Could Form and Chain) x N (Number of Amino-Acid Chains That Likely Will Form per Cubic Kilometer of Viable Area per Year) x Y (Average Number of Years a Prebiotic Window Will Last) = G(10^11) x S(10^11) x B(1) x K(10^6) x N(10^5) x Y(5 x 10^8) = 5 x 10^41

Thus, if N = 10^5 (and as just argued, it seems entirely reasonable to believe it must be at least that), then the Law of Large Numbers entails any specific peptide of probability 1 in 10^41 has already appeared at random in this universe at least five times over (give or take a few). And since there are certainly many different simple self-replicating molecules (not just one), biogenesis must have occurred many more times than that. The exact math can be much more complicated (as I explain in my article for Biology & Philosophy), but no matter how you run the numbers, some peptide chain with a probability of 1 in 10^41 has definitely appeared many times in the known universe, and there are certainly many self-replicating peptides no more complex than that.

The Talk.Origins Archive has a collection of articles for further reading on this subject (in its Abiogenesis FAQs), and that is amply supplemented by Dr. Robert Hazen's Origin of Life 101. Plus, again, the bibliographies in Carrier 2005 and 2004.

Conclusion

The way I framed all this in Sense & Goodness was much briefer and more colloquial. But the basic argument was that the way we would expect things to be if biogenesis was an inevitable random accident (and therefore well within the threshold even for trials, not just events), is exactly what we observe, a coincidence that suggests the conclusion: natural biogenesis was a likely outcome of the universe. But things would be different if we could predict that this is also exactly what God would do. If we could deduce from the definition of God that he would make the universe so vastly big and old, and so numerously populated with stars and planets and moons, and wait ten billion years or so before thinking to create life somewhere, and then do this with a single-celled (or even pre-cellular) string of commonplace naturally-chaining organic molecules of relatively simple construction, and then noodle around with these single-celled life forms for three billion years before thinking of the idea of assembling them together to make multicellular life forms (or if God had already clearly communicated all this to us before humans could have guessed it, or if he otherwise proved he did all this), then we could say that Intelligent Design was more likely than natural accident (as I believe a proper Bayesian argument would show).

But the evidence all goes the other way: for all of these things are 100% expected if life was a natural accident, but not at all expected if a God did it (much less a God who had specific plans in mind for humans, who are neither single-celled nor essentially strings of proteins), since a God has so many other ways to do it (in fact, infinitely many, if we grant his omnipotence--and in any case, so many more obvious and efficient ways to do it, and thus more expected ways of doing it...I can think of five just sitting here). And that completes the actual argument in my book: even though we cannot ascertain the exact probability of biogenesis (p. 166), all the evidence is exactly as expected if it was indeed an accident (and thus had a probability within a reasonable threshold, pp. 166-67), but not at all expected (in other words, not at all predictable) if it was intelligently designed. In fact nothing points to the latter at all, except the event's improbability.

Yet as demonstrated here, there have surely been enough trials (events of amino-acid chaining) in enough places to make biogenesis not just a likely accident, but virtually inevitable. And yet even at its most improbable (if we imagine just one chain of amino acids randomly occurring in all the universe to date), it still wouldn't be improbable enough to conclude it was an act of design. For even by the creationist William Dembski's own calculation, over 1,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000 events have occurred in this universe, purely by accident, that are even less probable than that. And if they weren't designed, why would life be?