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The Probability of You Existing at All is Almost NON-Existent. A Brief Reflection on the Contingency of our Being and the Glory of God, Based on a Recent Math Article.

September 27, 2011

I was alerted to a fascinating article by Ali Binazir who sets forth mathematically the odds of you or I existing, just as we are genetically. It turns out that, when taking into consideration the astonishing number of possibilities of parents meeting, grandparents before them and on and on going back the generations, and adding also the vast numbers of sperm and ova in possible combination over a the lifetime of the marital acts, of all those generations, it would seem that the odds of me existing just as I do, are 1 in 102,685,000. That’s a number so huge it hurts to think about it.

To say that we are contingent beings, is a vast understatement. To say that some one or something is contingent is to say that the existence of same is not inevitable, but can only come about based on any number of previous things being true in a chain of being or causality. Hence I would not exist if my parents had not existed and met. Further, they would not exist if the parents had not existed and met, the chain going back many generations. Thus, my existence depends on a vast number of “meetings” going just right, or I am not here.

Consider some of the contingencies and requirements for your existence as set forth by Mr Binazir. Some of the numbers are based on hunches, but generally those numbers are on the conservative side. I am only publishing a small amount of his musings here. You can read his full article here: What are the Chances of You Being Born? and see how he comes up with these numbers.

So here are listed some of the probabilities of required events for you to be born:

  1. Probability of boy meeting girl: 1 in 20,000.
  2. Now let’s say the chances of them actually talking to one another is one in 10.
  3. And the chances of that turning into another meeting is about one in 10 also.
  4. And the chances of that turning into a long-term relationship is also one in 10.
  5. And the chances of that lasting long enough to result in offspring is one in 2.
  6. So the probability of your parents’ chance meeting resulting in marriage and kids is about 1 in 2000
  7. So the combined probability is already around 1 in 40 million
  8. Now things start getting interesting.  Why?  Because we’re about to deal with eggs and sperm, which come in large numbers. Each sperm and each egg is genetically unique because of the process of meiosis; you are the result of the fusion of one particular egg with one particular sperm.  A fertile woman has 100,000 viable eggs on average.  A man will produce about 12 trillion sperm over the course of his reproductive lifetime.
  9. Let’s say a third of those (4 trillion) are relevant to our calculation, since the sperm created after your mom hits menopause don’t count.  So the probability of that one sperm with half your name on it hitting that one egg with the other half of your name on it is 1/(100,000)(4 trillion)= 1/(105)(4×1012)= 1 in 4 x 1017, or one in 400 quadrillion.
  10. But because the existence of you here now on planet earth presupposes another supremely unlikely and utterly undeniable chain of events.  Namely, that every one of your ancestors lived to reproductive age we must also go further presuming 150,000 generations going back to man’s origin.
  11. Well then, that would be one in 2150,000 , which is about 1 in 1045,000– a number so staggeringly large that my head hurts just writing it down.
  12. But let’s think about this some more.  Remember the sperm-meeting-egg argument for the creation of you, since each gamete is unique?
  13. Well, the right sperm also had to meet the right egg to create your grandparents.  Otherwise they’d be different people, and so would their children, who would then have had children who were similar to you but not quite you.
  14. This is also true of your grandparents’ parents, and their grandparents, and so on till the beginning of human time.  If even once the wrong sperm met the wrong egg, you would not be sitting here noodling online reading fascinating articles like this one.  It would be your cousin Jethro, and you never really liked him anyway.
  15. That means in every step of your lineage, the probability of the right sperm meeting the right egg such that the exact right ancestor would be created that would end up creating you is one in 1200 trillion, which we’ll round down to 1000 trillion, or one quadrillion.
  16. So now we must account for that for 150,000 generations by raising 400 quadrillion to the 150,000th power: That’s a ten followed by 2,640,000 zeroes, which would fill 11 volumes of a 250 page book with zeroes.
  17. For the sake of completeness: (102,640,000)(1045,000)(2000)(20,000) = 4x 102,685,007 ≈ 102,685,000
  18. Probability of your existing at all: 1 in 102,685,000

Now, there are some assumptions you may quibble with. I would certainly add in (sadly) some probabilities related to being aborted, or miscarried. But even a simpler analysis yields astonishing numbers. One of my brothers made his own calculation regarding one of Binazir’s numbers:

My numbers are more simplistic.  But assuming 100,000 eggs/woman & 12T sperm/man, that creates 1.2 x 10^18 combinations for every man/woman pairing (i.e., signficantly more combos than 400T or 4 x 10^14 mentioned in the article).  If you assume 3B women on earth & 3B man, that means 3 x 10^14 eggs and 3.6 x 10^22 sperm currently on the planet, for a total combination of 1.1 x 10^37 pairings.  If you assume current population is 1% of the history of humanity, total combos go to 1.1 x 10^39.

Not only are you and I contingent, we are very improbable! Yet here we are! Mirabile visu! (wondrous to behold).

Theologically of course we are no accident or happenstance. God has always known us, intended us, loved us and planned for us. Scripture says,

  1. Before I formed you in the womb I knew you (Jer 1:5).
  2. Come, you who are blessed by my Father; take your inheritance, in the kingdom prepared for you since the creation of the world (Matt 25:34)
  3. For you created my inmost being; you knit me together in my mother’s womb.I praise you because I am fearfully and wonderfully made; your works are wonderful, I know that full well.My frame was not hidden from you when I was made in the secret place. Your eyes saw my unformed body. All the days ordained for me were written in your book before one of them came to be. (Psalm 139:13-16)

Yes, you’re here alright, and math can barely account for your existence, so tiny are the odds. But God has overseen every detail and knew you long before you were born. In fact he has been preparing a place for us in the kingdom, from before the creation of the world. Not only has he always known us, but he has known everything we would do, for every one of our days have been written in his book before one of them ever came to be.

The great mystery of our existence stretches back in time into the very heart and mind of God who has always known and loved us, has prepared for us and made a way for us. You are wonderfully and fearfully made and God has done a marvelous thing. You’re not just one in a million, you’re one in a 102,685,000

Photo Credit: Portland Glass

This video makes a moving point, but attributes our existence to luck. But you are not here by luck, you are here by the grace and will of God.

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Comments (49)

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  1. Chidi says:

    Loved it – thank you!

  2. Alan says:

    Excellent article and thank you for Mt 25:34!

    Showing that God knew us, and we had personhood even before our actual birth.

  3. Nick says:

    Glory to Divine Providence and Will, for He made us for Himself.

  4. sally says:

    And you could widen your perspective even further if you factor in the (im)probabilities that
    the universe would be created in a manner in which atomic and macro forces are so finely tuned,

    with an exquisite and improbable combination of balanced forces that make the formation of planets possible,

    and the even more improbable chance that any one of these planets would have the proper balance of characteristics to support life,

    and the vanishingly small chance that a life form would come into existence with the capacity to reason and reflect upon the astonishing improbability that they could have spontaneously emerged from a mindless interaction of mere matter, happenstance and chance.

    If you are interested in a discussion of implications of the compound nature of these improbabilities, I would recommend Fr. Robert Spitzer SJ — discussing the theistic implications of the anthropic principles demonstrably necessary for our universe to be able to support life: http://www.counterbalance.org/cosmcrea/spitzer-frame.html

  5. Shan Gill says:

    Lots of fun!

    However, probability mathematics is simply a tool for the finite mind of man to grasp the huge numbers in play in the universe. It should go without saying that God doesn’t rely on probability to operate His universe; He has knowledge of every quark and lepton – the probability required to describe our scientifically defined quantum universe does not exist for God. And if one enters the murky realm of probability, one can never move linearly to decisiveness. Decisiveness does not evolve from randomness; it exists as a function of intelligence.

    But that aside, the column was lots of fun!

  6. John C. Kovach says:

    An infant is a miracle from the moment of conception.

  7. John C. Kovach says:

    Yhis is often overlooked!

  8. Howard says:

    The numbers game is really not the way to go!

    Whether you’re talking about the existence of an individual or, like Sally, the fundamental forces of nature, you have the same problem: PROBABILITIES ARE *TOTALLY* MEANINGLESS EXCEPT IN THE CONTEXT OF A MODEL. So if your model is that the Earth is the only place where life like ours exists and that God really DOES play dice with the universe, you can use your argument; only I’m sure you don’t really believe that. If, on the other hand, you were a 19th-Century believer in determinism, you would believe that all free will is an illusion, for God as well as for man; we see things as they *had* to be. Today there are some cosmologists, and who knows how many people who just pick up fuzzy ideas from the media, who believe that there are an infinite number of universes, so that how ever small a probability may be, if it’s not zero, when multiplied by infinity it will happen an infinite number of times. Something similar is true of the many-worlds interpretation of quantum mechanics: whenever a choice is made, the universe splits, with one branch universe for each possible decision. All told then, the many-worlds interpretation means that if anything CAN happen, it DOES happen — in some branch universe.

    With respect to the the balance of the forces of nature, the situation is even more clear. What are the odds that the permeability of free space times the permittivity of free space is one over the square of the speed of light? Practically zero, if you think these are numbers drawn out of a hat; 1 (certainty), if you know they are a consequence of Maxwell’s Equations for electromagnetism.

    • 🙂 God love you Howard but I really don’t know what you are saying. My brain hurts, reading your last paragraph, yet it is one of the neatest paragraphs I have ever read.

      • Howard says:

        OK, let’s take this over to sports.

        What were the odds that the 1919 Chicago White Sox would lose the World Series? Pretty small, if you asked people who judged on appearances; a certainty, if you knew the fix was in. Until you know what kind of game is being played, a question about the odds is meaningless.

        • I’m still not sure what your point is.

          • sally says:

            If you watch Fr. Spitzer’s videotaped talk, you will see that he applies his theory to ALL/ANY possible universes, including ones that theoretically do not include carbon based life forms. He also considers the theory that at the moment of the big bang there could have been milliions of universes coming into existence, and applies the probabilities to those potential universes.

            He speaks only of conditions necessary for the existence of units and forces that have the capacity to build complexities of any sort that could possibly give rise to any kind of possible material life form. So if you watch his video (granted it takes an hour) you will see that he answers your questions.

      • Tom says:

        Here’s a picture to help each of you speak to the other:

        http://www.zazzle.com/and_god_said_maxwells_equations_tshirt-235628270699537542

  9. Jon White says:

    Seeminhg coincidence is God working incognito.

  10. Howard says:

    Math can deal with relentless determinism. Math can deal with mindless chance. Math has no way to deal with choices made by free will; yet it is free will, from God, man, and angels, that shapes reality.

    • Yes, but I do think math, in a case like this, can help record how highly contingent things, people and events are.

      • Howard says:

        Well … sorta. Again, probability can only deal with things that come from mindless chance, not from the mind of God.

        First, a silly illustration. It’s the middle of a season of MacGyver. He has only seconds left to defuse a bomb or he and several other people will die. He comes to the last step and has to cut a wire, but he can’t tell if he should cut the red wire or the yellow wire. He guesses red and cuts the wire with a silent prayer. What are the odds that he has cut the right wire?

        As far as the character is concerned, the odds are 50/50, and he has had a narrow escape from death. Sitting in your living room, though, you know that the writers are not going to kill the title character in mid-season. You knew he was going to cut the right wire. Chance was not involved.

        Now to something more serious. How contingent was the Blessed Virgin Mary? True, like any other created being, she is ultimately contingent, but it is sound theology to say that she in particular was planned from the creation of the world, and she was spoken of in the Garden of Eden. It wasn’t a lucky chance that she was born; chance had nothing to do with it.

  11. John says:

    If 10^2,685,000 is the number, then, ineffable is the word!

  12. teo matteo says:

    Howard, I dont know nuth’en bout permissability of free space (i do know that my bingo card has a free space smack dab in the middle of it!!) and I dont know ’bout Maxwell’s equations (but Maxwell smart was a really zany character on t.v. once) but i do know that your brain is move’n faster than the speed of light cuz there are some guys who says that einstein was wrong bout that..

  13. Vijaya says:

    Fun post even though stats and prob. were my least favorite topics in math. Good thing God doesn’t rely on probabilities, but carefully orchestrates everything, down to the lovely encounters beloveds have had throughout the generations.

  14. Napolitano says:

    An article from a Catholic perspective was published on this idea by Michael Pakaluk in the July 2011 Boston Pilot. “The Logic of the Gift” http://www.thebostonpilot.com/article.asp?ID=13550 It was written independently of Binazir’s blog post.

  15. R in Indiana says:

    Coincidentally, I am taking a nutrition class, and we are studying the intricate details of digestion. I am in awe as I look at the incredible complexity of the body, and how it works seemlessly every day for 75 years on average. We are fearfully and wonderfully made.

  16. Juan says:

    I actually have a problem with this logic.

    Assuming all of your numbers are correct that would be probability of me being here if their were no dependencies. But if I am not here then I would not be doing this calculations.

    If we can imagine infinite worlds, or just 1.1 * 10^2,685,000 worlds, one for each other outcome of your calculation then in all of those worlds I don’t exist or am somebody else.
    If I don’t exist then I can’t make this calculation.
    If I do exist and I do make this calculation then I think that wonderful large number is how improbable it is that I exist BUT in each of the worlds where I do exist I make the same calculation which means that if I make this calculation then I must exist so the probability of making the calculation and existing is 1.

    In other words every other alternate me (each odd in the calculation) makes the same calculation and gets to the same number so its not so wonderful.

    For me to realize that it is odd for me to exist I must exist so the probability of me existing is 1.

    In other words if you have 1 in a 1000 chance of getting the jackpot once you get the jackpot, or once you exist, then the chance of getting the jackpot is 1 because you already have the jackpot. In this case if you exist you got the jackpot so the odds of getting the jackpot are one.

    Well… that got a bit messy near the end, its been a long day…

    • I am not sure I follow you. But if it helps to see the large number not as odds but as an indicator of the kinds of things that had to fall in place for me to exist, then think of it that way. Bottom, I am the result of a lot of factors that fell into place.

    • Kerstin says:

      Juan, here is my thinking.
      You look at this from your own personal perspective. The calculation, however, when you look at it more closely, is based on the probability of the existence of any human being, not you or I in particular. Since you and I are part of that group, the calculation also applies to us. See the difference?

      Now, you do lose me with alternate worlds (presumably universes?) and existing there. Since we can’t penetrate the time horizon of our own universe, never mind the impossibility of ever knowing what is physically beyond our universe, this whole train of thought doesn’t quite fit of what we can know. It is speculation – a very popular one in some circles, but still speculation. The only thing we can perceive of what is beyond this universe is God.
      If you were thinking of other planets within this universe where there are Dopplegaenger, then the vast distances within pose an impenetrable barrier for us to ever know. Again, this is speculation. But it makes for great science fiction plots 🙂

      • Juan says:

        Well… ok maybe this way is better.

        If you are at the beginning of time and decide to calculate how probable is it that Juan will exist (if there is no guiding hand of course and God doesn’t intervene, etc…) then I will accept that the odds of Juan existing are 1.1 * 10^2,685,000.

        But if I exist then the probability of me existing is 1. Once that chance occurred then the chance of it occurring is 1 because you know it occurred.

  17. Dan says:

    What about all those other near-miss people who don’t exist but would’ve if just one thing would’ve been different? What about the might-have-beens? I wonder if God knows who they are.

  18. Kerstin says:

    Simply marvelous!
    I’ve thought about the improbability of mine or anybody’s existence before, but never did I think the number was this high!

  19. Paul Rimmer says:

    We are only improbable given a prima facia consideration of our existence, based on a very limited understanding we have of physical principles. There are certain string theories that reduce the number of possible universes to 10^500. If there exist deterministic physical laws that govern the state of our universe from the beginning until now (as appears may be the case), then the odds of me existing exactly as I am are 1 in 10^500. Much more likely than the calculations listed here. Newtonian principles would have the chance of my existence being incalculably small (much smaller than the calculation here). We have gone from almost impossible to 1 in 10^500 in only five hundred years. I intuit that the pattern will continue and that it will be discovered that there is a 100% chance of my existing exactly as I do. I suspect that the universe could not have existed any other way than it does.

    • Kerstin says:

      Paul,
      in Fr. Robert Spitzer’s book, New Proofs for the Existence of God, he cites the improbability of our universe existing the way it does is (10^10)^123. This number blew me away.

      • Paul Rimmer says:

        Even 10^500 is a very large number. The 10^(10^123) figure is actually the possibility of our universe being able to support life. I think the 10^(10^123) is not an accurate probability given our current knowledge, at least if certain string theories are the case. The 10^(10^123) is the estimate given the assumed range of physical constants; if the constants are unbounded, then even this number is far too small; the variation would be infinite. The mathematician Roger Penrose calculated this 10^(10^123). Ed Witten, physicist, calculated the 10^500 for the number of possible universes. I suspect that the trend will continue until we find that the probability is 100%, and that our universe in all its details could not have come about any other way than it has.

  20. Cynthia BC says:

    As an undergraduate at the University of Maryland in the mid-1980s, I took a genetics class as a “USP” requirement (I’ve long since forgotten what “USP” stands for). In the class we learned about various inherited conditions, but my takeway was that there are SO MANY opportunities for the reproductive process to go awry that the birth of a child truly is miraculous!

  21. Cynthia BC says:

    http://www.washingtonpost.com/national/health-science/sperm-donor-children-face-challenges-in-learning-their-medical-history/2011/07/01/gIQAX9hwzK_story.html

    Oh, and here’s an interesting article from Tuesday’s Washington Post. And people think sperm banks are a good idea because…???!

  22. Tom says:

    So what happens to the 2,685,000 people that don’t exist because I do? Can they be saved? If not, that’s a lot of pressure on me!

  23. Jer InCanada says:

    I think I understand what Juan is saying. Whenever I by a lottery ticket I always figure I have a 1 in 2 chance of winning….either the ticket is good or it isn’t. For that reason I always buy 2 tickets.
    Looking at your odds up there of my existing (i do exist by the way), 1 in 10^2,685,000, you might be interested to know that scientists estimate the total number of elementary particles in the universe at 10^90.

  24. Annette Strachan says:

    And, a lookalike exists, ” I saw you in church,” mistaken identity, fascinating, in two places at once. Choice.

    In Choice on YouTube Venerable Fulton Sheen compares Jesus and Barabbas but not physical similarities.

    Choice of good or evil is the theme, and lookalikes who choose the latter are a burden.

  25. Lulu says:

    I feel better reading this. Y’all need to be happy with the miracle that is you.

  26. James S says:

    Glory to god! God’s love for us can not be put into words. When you are feeling down, turn to Him.