Is There a Probability for the Universe? New Thoughts about the Anthropic Coincidences


The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language, where their voice is not heard.”
—Psalm 19 (KJV)

“It is a strange fact, incidentally, that religious apologists love the anthropic principle. For some reason that makes no sense at all, they think it supports their case. Precisely the opposite is true. The anthropic principle, like natural selection, is an alternative to the design hypothesis. It provides a rational, design-free explanation for the fact that we find ourselves in a situation propitious to our existence.”  
—Richard Dawkins, The God Delusion


The illustration above is a diagram of the “Triple Alpha Process” describing the nuclear synthesis of carbon-12 nuclei in giant stars from three helium nuclei (alpha particles).   It’s one of those “special” events or features that are called “anthropic coincidences.”   These anthropic coincidences, regarded as unlikely events  (low probability events, but see below) are the basis for the  “Anthropic Principle,”that our universe is finely tuned to support carbon-based life. It’s known in several versions ranging in acronym form from Weak Anthropic Principle (WAP), to the Strong Anthropic Principle (SAP), the Christian Anthropic Principle (CAP) and, not least, the Completely Ridiculous Anthropic Principle (you do the acronym).

My interest in this was reignited by Bob Drury’s fine post about why it’s not correct to use probability arguments about the Anthropic Principle, fine-tuning of the universe.   Many believers in God argue that when the Anthropic Coincidences are combined, the exceedingly small joint probability of them happening together supports the proposition of a creating God.   As I will try to demonstrate below and as Bob Drury pointed out, this reasoning is incorrect.

Nevertheless, I also believe that these anthropic coincidences help us to believe in God. I take the point of view of the psalmist  in Psalm 19,  quoted above: “The heavens declare the glory of God.”   I’ll argue that if probability is taken as a measure of the degree of belief (how much you would be willing to bet on the truth of a proposition), then it can be applied to the Anthropic Coincidences to support belief in a creating God.


I’ve discussed the Anthropic Principle in several other posts on this blog:   Philosophic Issues in Cosmology 6The Theology of Water,  and Are We Special: The Anthropic Coincidences.  The arguments presented in these posts can be classified as shown below.   The categories listed are discussed in greater detail (with examples) in the linked posts and references given therein.

  • Features of the universe–e.g. space dimensionality 3; the mass/energy content of the initial universe that enabled expansion but not immediate collapse; uniformity in very early universe;  size;
  • Finely tuned values for fundamental physical parameters–e.g. the mass difference between proton and neutrons that enables stability for nuclear processes; the carbon-12 excited state energy that by resonance enhances the probability of carbon-12 nucleus formation from a rare collision of three He nucle (see figure and linked referencei;
  • Nature of physical laws–e.g ratio of electromagnetic force to gravitational force; inverse cube force law for gravity; quantum mechanical laws that enable chemical bonding and (see below) the special properties of water;
  • “Accidental” geo-astronomical features–e.g. tilt of the earth’s axis enabling life-friendly climate, unusually large moon shielding earth from asteroid and meteor collision.

It must be emphasized that there are many more instances of such fine tuning–parameters for which the values have to lie between narrow limits to enable a life-supporting universe, and many more examples of geo-astronomical and chemical features.    George F.R. Ellis, in the reference linked above, specifies general conditions that must obtain for a universe to contain life as we know it.


Ellis points out a major objection to using probability arguments for the existence of the universe: the universe is a single datum—probability arguments are generally applied to samples from larger collections for which we have information about variability (if one holds a “frequentist interpretation” of probability, as below).  For example, if you’ve examined 20,000 crates of oranges and found 100 crates containing bad oranges, you’d be justified in putting a probability of  100/20,000 or .005 in finding a bad orange in the next crate.   But if you’ve only come across one crate of oranges, then it’s speculation to put a probability on finding a bad orange.  (But see below.)

Another error one finds is that some apologists list a string of fine tuning examples (call them a,b,c,d…x),  and then use the argument that P(a,b,c,d…x) = P(a) P(b) P(c)P(d)…P(x).  They say that the probability of the total set is the product of the probabilities for each member  of the set. This would be true if the events were independent, in other words if what happened for one event did not depend on what happened for another.¹  Such independence will not necessarily hold. Consider, for example, the properties of water that are life-friendly:

  • thermodynamic–high freezing and boiling points, high specific heat, etc.;
  • physical –surface tension, low specific gravity of ice, maximum density of liquid water at 4 deg C.

These properties all depend on the very unusual capacity of protons in a H2O molecule to form strong hydrogen bonds to oxygen atoms in other H2O molecules.   And that hydrogen bonding capability arises from quantum mechanics and the physical nature of electrostatic attraction.    So it is one feature, not many, for which a probability should entered. .And how do you assess the probability of quantum mechanics giving rise to hydrogen-bonding?


“But is it probable that probability brings certainty?
—Blaise Pascal, Pensees 496

I’m going to try a different approach, using probability as a measure of belief. (I apologize to those professional statisticians and mathematicians who will possibly be offended by my presumption.)   The approach is my take on Richard Jeffrey’s Subjective Probability.

Let’s start with a different definition of probability, based on strength of belief.   Consider the following examples for betting on a horse race.   You overhear a trainer telling a pal that “the next race is fixed for Trump’s Nag to win, with odds of 9/1”.    You bet $10,  expecting to win $90.    The defined probability, working from the odds ratio, is  1/(9+1) = 0.10.    The probability of losing your bet is then 1- 0.10 = 0.90.    The expectation value² is 0 = 0.10 x 90 + 0.90 x(-10).

The next step is to consider conditional probability, that is how the probability of an event depends on a linked event.   Let A represent the event that a stock price rises to $100.   Let B represent the event that information about the possible rise of the stock is given.    Then the conditional probability is denoted as p(A|B), the probability of event A given that event B occurs.   Note that there is no causal relation implied here–it’s only a matter of evidence.

Now to the meat of the matter.   Let F represent the proposition  “the universe is fine-tuned for carbon-based life to exist“;  G: “God exists“;  N: “God does not exist (or that “Naturalism= materialism” accounts for everything).    Then

  • p(G | F)  is a probability, a degree of belief, that F —> G, i.e. fine-tuning is evidence for the existence of God;
  • p(N | F)  is a probability that fine-tuning implies that God does not exist;
  • p(F | G) is the probability that if God exists then He can fine-tune the universe;
  • p(F | N) is the probability that a fine-tuned universe would occur in the absence of God;
  • p(G) is the probability—the degree of belief—that God exists;
  • p(N) is the probability—the degree of belief—that God does not exist.

Then straightforward manipulation³ yields

 P(G | F)) = [ P(G) ] [ P(F | G) ]
 P(N | F)      [ P(N) ] [ P(F | N)]

     1                     2             3

Term 1 is a likelihood ratio for degrees of belief: the ratio of “belief strength that fine-tuning implies the existence of God” to “belief strength that fine-tuning  implies no God;”  term 2 is a likelihood ratio,  “belief strength in God” to “belief strength in no God (naturalism);”   term 3 is a likelihood ratio “belief strength that God, if He exists, would create a fine-tuned universe to support life” to “belief strength that naturalism/materialism would yield a fine-tuned universe.”

Now certainly term 3 is a number much greater than 1, even if the exact value is indeterminate.   The value for term 2 will depend on the individual–for a Christian martyr, it would be a huge number;    for Richard Dawkins or Lawrence Kraus it would be a very small number.

Here’s the point: the value you impute to term 1, the likelihood ratio for belief that a fine-tuned universe is evidence for the existence of God, will be greater than  1 if you are not a hard core atheist.    If you’re agnostic—if you think that it’s a 50/50 proposition that God exists—then certainly fine tuning should convince you that God exists.   If you’re a strong believer in materialism/naturalism (Dawkins or Kraus), then term 2 would be small enough to swamp term 3, even if the latter is very large.

So the upshot is that if you do believe in God or if you’re an agnostic, fine tuning can be evidence for God’s creating hand.   If you’re an atheist—this will not be sufficient evidence.   And we come again to Grace given by the Holy Spirit as the mechanism for faith.


¹Further, if you do this with a large number of events, it will certainly not lead to useful information.   Consider a series of 50 independent events, each of which has a probability of 0.9.   Then the probability for all the events happening together is 0.9 ^ 50 = .0052. which is small, even though the probability for the events individually is large.

²The “Expectation Value” is the value you’d expect to get over a very large number of trials. For example, if you bet $1 on a single spot showing showing up on a toss of a fair die (six sides), and would get $3 if it did show up, then your expectation value would be (1/6) x $3 + (5/6) x(-$1) = -$1/3, a losing proposition.  (And the House always sets payoffs so that the expectation value for you is negative.)

³Consider p(F and G), the probability that both F and G occur (or that both F and G are true propositions).   Then a form of Bayes’ theorem is  that
p(F and G) = p(G | F) p(F) = p (F | G) p(G);

similarly p(F and N) =  p(N | F) p(F) = p (F | N) P(N);

Take the ratio of the two expressions.

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28 thoughts on “Is There a Probability for the Universe? New Thoughts about the Anthropic Coincidences”

  1. Pingback: How did life begin?

  2. Yes, the universe wouldn’t exist without these constants being exactly so, but that’s no guarantee that such a universe would have humans in it. Maybe in only one out of a million universes, has intelligent life (or any kind of life) developed. Conversely, maybe in only one out of a million universes did the constants work out in such a way that the universe survived, instead of imploding into nonexistence a trillionth of a second after its Big Bang.

    Fish can survive in winter because oxygen seeps through the ice covering the frozen pond. Is this God’s way of protecting the fish? No, it’s because if oxygen didn’t seep through, fish wouldn’t have survived, in fact there’d be no fish to begin with, and we wouldn’t be talking about it.

    That is the Anthropic Principle.

    A baby doesn’t have any conception of its being a separate being. Later it becomes aware of other people but thinks it’s the center of the universe. Later still a teenager realizes other people have wants and needs (but still his is the most important). A mature adult realizes he’s only one person in a world of about 7 billion that goes on with or without him. Similarly, humans used to think that there was only one world, later that the Sun and all the planets revolved around it . . . Now we realize that we’re just a tiny speck in a huge universe that goes on with or without us.

    The author holds to an earlier, less mature world view. He thinks that because we’re here, means the universe was created just for us. Not so. As Mark Twain put it years ago, it could have been created just for oysters — “but that would be just like an oyster to think so, since the oyster is the most self-centered creature on the earth, except Man”.

    1. Thank you for your comment, C..s. A good reply to your objections has been given by the philosopher Thomas Nagel in his book, Mind and Cosmos:
      “One doesn’t show that something doesn’t require explanation by pointing out that it is a condition of one’s existence. If I ask for an explanation of the fact that the air pressure in the transcontinental jet is close to that at sea level, it is no answer to point out that if it weren’t, I’d be dead.” Thomas Nagel, Mind and Cosmos.

    2. The answer to Nagel is, “We know for a fact that the transcontinental jet was made for humans, because it was in fact made *by* humans for that purpose, and specifically that is why the air pressure was designed for human capacities.”

      You can’t say that about the universe.

      “One doesn’t show that something doesn’t require explanation by pointing out that it is a condition of one’s existence.”

      This misstates the issue. I’m not showing that the universe doesn’t require explanation. In fact it can be explained in several ways. I’m simply rejecting the particular explanation that it was made just so that we could live in it.

    3. I don’t find your explanations (whatever they might be–you haven’t stated them) as satisfying as mine, that the universe is the creation of a super-intelligence, which we call God. And so my Bayes’ probability of belief explanation is vindicated.

    4. No, it’s not “vindicated”. Your feelings are simply guiding what you think is your reasoning.

      Psychologically many people (though a decreasing number) feel the need to posit a God who created the universe, even though logic does not require it. Similarly they feel the need to posit a Devil, even though the bad things that people do can all be explained by normal psychological processes. Maybe science seems too mundane an explanation to be satisfying. Or maybe the desire is more gut-based, coming from the same place that our fear of the dark comes from.

    5. Have you noticed that the ultimate center of observation of the universe is each individual human? In my case, that center of the universe is extremely important to me. Except for that center, the universe may as well not exist.

    6. No, but when I’ve observed the moon, it is only from my location, not from any out-of-body diagrammatic observational perspective, however useful such a diagram may be. My location is necessarily the center of observation whether I refer to what I observe as my backyard or the universe. When I say I drove to the grocery store, I think, however vaguely, of a diagram of my car moving along streets from my house to the grocery store. That is not what I observe. Because I am necessarily the ultimate center of observation, I observe the road, houses and fields passing by as I look out the windshield of my car. In that sense, I am necessarily always at the center of the universe. Analysis is posterior to observation and must be compatible with observation. We tend to think of the analytical depiction as the reality and our observation as needing to conform to it, rather than vice versa.

    7. Yes, and we are correct to do that. It is part of realizing you (or I) are not the center of the universe, part of living in community with others. We can never really know what another person senses, but by the use of communication (language, etc.) we trust that we get a pretty good idea, enough of an idea that we can take each other’s feelings into account so as to live together as a stable and functioning society, and also (pertinent to this discussion) trust other’s attempts to explain what we all think we see and sense.

  3. Pingback: MONDAY EXTRA – Big Pulpit

    1. Howard, thanks for the comment, but I don’t understand it. Could you please enlarge? Do you mean that if P(F)=0 you’re dividing zero by zero? That isn’t correct, so …?

    2. Sure you are. Oh, you’ve canceled it out, so it doesn’t appear in the version of the equations you display, but you have seen “proofs” that 1 = 2 based on subtle mistakes like that.

      But let’s back out and look at this qualitatively, which is what you were trying to do anyhow. Say “F” now means “Flaming Letters”: it is the claim that there are giant flaming letters across the sky (in the CMB, that is) that spell out “In principio erat Verbum.” Now that would be strong evidence for the existence of God, and of course God could have arranged for those letters to be there; then again, He might not choose to do so. However, in the absence of any firm evidence that the letters exist in the first place, no mathematical shell game about flaming letters God did not put in the sky will make for a convincing argument about God, one way or the other.

      So to be convincing, the fine tuning needs to be more obvious than the flaming letters. However, we do not have any information AT ALL about the probabilities involved in “fine tuning”, and without that information, we cannot be sure there is a fine-tuning “problem” to be solved in the first place. It’s less obviously problematic than the lack of flaming letters, but it’s the same issue.

    3. Well, I see where your objection comes from, Howard. On the other hand, being familiar with cosmology, physics, molecular biology, and knowing there could have been so many other ways for these to be and not support carbon-based life leads me to the conclusion that fine-tuning exists, even without a quantitative, frequentist assessment of probability. You of course can conclude otherwise, but you might ponder on the quote from Thomas Nagel below. By the way, as long as P(F) is not exactly equal to 0, the division to cancel it out is legitimate. That’s mathematics, not physics or philosophy.

    4. 1. Yeah, the carbon-based life thing. That’s a lot like making a fine-tuning argument on the basis that we’re having this discussion in English, but what if the particular events that gave rise to the English language had not occurred? It’s not obvious that there’s a problem, since there are, after all, other languages besides English. Are there other ways life could have existed without carbon-based chemistry? Sure. Don’t pretend that the constants might be different but the equations are beyond dispute.
      2. Ultimately, you are making the same kind of argument one makes for the existence of God based on witnessing the majesty of a storm, or of an earthquake, or of a fire: it belongs more to poetry than to math or physics. You should recognize it as such, because I think it is more convincing as poetry than as math, and you purpose here is to persuade. And besides, God was not in the storm, or the earthquake, or the fire.

    5. I’m not sure I understand your argument, Howard. Are you saying that since other forms of life which are not carbon-based might exist, that vitiates the Anthropic Principle? If that is your argument, then I would counter that we’re considering that we’re here as humans, biological entities based on carbon biochemistry. That’s the basis for a discussion. If that isn’t your argument, then I can’t really make any sense out of what you’re saying, and I won’t bother to go further in this exchange. It won’t contribute to my understanding and possibly not to the average reader.
      And my argument isn’t poetic, although I do hold to the poetry of Psalm 19A,
      “The heavens declare the glory of God.”

    6. You know, the most amazing thing happened to me tonight… I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing! — Richard Feynman

      You’re the one who brought up carbon-based biochemistry. I assumed you meant it to be more significant than Feynman spotting license plate ARW 357.

    7. The fact that there is carbon-based life, along with ancillary conditions for that, is a major component of the Anthropic Principle. And you’re using a frequentist interpretation of probability, which I said in the article doesn’t work for a single datum. I think this, on my part, concludes the discussion. You haven’t employed any arguments other than others have used, and I don’t find those convincing or enlightening. And evidently you don’t find mine either enlightening or convincing. So no point to further exchanges. (But I do believe that Thomas Nagel’s comment answers Feynman’s criticism.))

    8. No, I’m afraid I don’t find your arguments convincing. They start off with, “Isn’t it remarkable that the universe supports carbon-based biochemistry?” but have no real answer to the reply, “Well, maybe it’s not so remarkable,” other than that you and Nagel feel it in your bones. That’s as may be, but how you feel in your bones is poor material for math or physics. It’s fine for preaching to the choir, and might even be the basis for a fine hymn (there are many like that), but if you mean it as a tool for apologetics, I don’t think it will be very successful.

    9. Howard, I thought I would be gracious and let you have the last word. However, since you’ve descended to a personal level by implicitly impugning my intelligence (or motives) by the statement “but how you feel it in your bones….”, I’m not going to let that pass. I don’t know if you know enough physics to be familiar with the name Fred Hoyle–he was the famous cosmologist, an atheist who gave the derisive term “Big Bang” to the idea of creation of the universe from a singularity.
      He was also the one who predicted the existence of the excited C-12 nuclear energy level that facilitated the triple-alpha process above. And he was the one who made the following statement later:
      “A common sense interpretation of the facts suggests that a super-intellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.” Fred Hoyle

      I’ve given several specific instances in the article and other posts to support my contention that these anthropic coincidences are unusual. You, on the other hand, haven’t done much but say “tisn’t,” so I suggest that it’s you “who feel it in your bones,” not I nor Nagel.

      Please don’t comment again on any of my posts. If you do, I’ll delete it.

    10. Read this first, then delete it if you like.
      If I wanted to impugn your intelligence or your motives, I am rude enough to be direct about it. Instead, I meant exactly what I said: your approach is, at its core, more intuitive than deductive, and it will fail as an argument for the existence of God when used against people who (1) expect something more deductive, (2) do not already agree that God exists, and (3) have the same skills you do, and so do not consider you an authority based on your degrees. That’s not to say an intuitive approach is without merit, but its merit is not as an apologetics tool for scientists.
      If you are going to delete this, I suggest you delete the whole thread. Otherwise you look like an enormous … jerk … (which is exactly what I am now convinced you are) to anyone who stumbles across this thread. See? I’m direct enough to state this, even though I’m toning it down to just “jerk”.
      If I ever take notice of you again, it will only be because I have forgotten who you are. And frankly, I will forget you in short order, because you are not quite the center of the universe you seem to think you are. I’ll try to remember who and what you really are, though.

    11. What, an hour ago you were launching a personal attack on me and telling me you would delete any response, and NOW you want to have a civilized debate?
      That requires a mutual respect that no longer exists between us.

    12. To whom it may concern: I realize that civilized debate with Howard is a no-go proposition and, as I said in another comment, I forgive him for insulting me and taking this discussion to a personal level. My replies to his comments, particularly noting that Anthony Flew was converted by considering the Anthropic Coincidences, are for the benefit of the general reader of these comments.

    13. And I, for my part, stand by my statements. My disagreement with Bob Kurland was academic in nature. To briefly summarize, an argument based on fine tuning absolutely requires that the actual existence of fine tuning be established, or it fails to have rigor; Kurland somewhat acknowledges this, but thinks that, to paraphrase Potter Stewart’s opinion, “I know it when I see it” restores enough rigor for it to be persuasive. Again, I disagree; more importantly, my own experience leads me to suspect the kind of person for whom this argument might be intended — an atheist with a STEM background — would find this unpersuasive.

      At that point, I considered the matter closed. Kurland had made his case, I had made my objections, and the reader could make an informed decision whether or not Kurland’s position had either theoretical or practical merit.

      Sadly, Kurland then decided to turn this into a personal attack.

      No doubt all of us are jerks, to a greater or lesser extent. I know both Kurland and I are, and since you are reading this exchange, you have seen it, too. Please bear in mind that the Internet somehow draws the worst out of people — worse than traffic does, I suspect, and without the obvious restraint of not wishing to die in a car wreck or an act of road rage. Had this disagreement been dealt with face-to-face, it probably would have been much more civil, even without the fear of making a public scene.

      Nevertheless, the damage is done. The discussion cannot proceed as before, and what you have seen is more of an exhibition of our own sinfulness than any kind of evangelical tool. Kurland and I are both scoundrels in need of forgiveness; neither of us is exactly a dying martyr in a position publicly to forgive his persecutor.

      I apologize for my contribution to this ugliness. I wish it had not happened, and I wish we had not brought disgrace to the cause we both wish to advance. Please remember: the disgrace properly belongs to us and to us alone.

    14. No, I think I’ll let this stand because it shows how you really think. You haven’t replied to arguments specifically, nor to Fred Hoyle’s comment–who knows more physics and math than I do, and possibly you. And I forgive you for your insults, calling me a jerk. As Oscar Wilde said, “Always forgive your enemies; nothing annoys them so much.

    15. Sorry, but you are the one who made this personal. I respected you UNTIL YOU DID THAT. Leave this up if you’re man enough; it doesn’t mean you agree.

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