The Probability of You Existing at All Is Unbelievably Low

I was alerted to a fascinating article by Ali Binazir, who sets forth mathematically the probably that each of us exists. It turns out that when taking into account the astonishing number of possibilities of parents meeting, grandparents meeting before them, and so on going back generations, and then adding the vast number of sperm and ova in possible combinations over decades of the marital act in all those generations, the odds of me existing just as I do are about 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 someone or something is contingent is to say that the existence of same is not inevitable but rather can only come about based on a number of previous things being true in a chain of being or causality. I would not exist if my parents had not existed and then met. Further, they would not have existed if their parents had not existed and met, and so on. Thus, my existence depends on a vast number of “meetings” going just right; if they hadn’t I would never have been born.

Consider some of the contingencies and requirements for your existence as set forth by Mr. Binazir. Some of the numbers are approximations, but generally they are on the conservative side. I am only publishing a small number of his musings, but you can read his full article here: What Are the Chances of You Being Born?.

The following analysis, paraphrased at some points, is taken directly from Mr. Binazir’s article:

The probability of father meeting mother is 1 in 20,000. The chances of them talking to one another is 1 in 10. The chances of that turning into another meeting is about 1 in 10. The chances of that turning into a long-term relationship is about 1 in 10. The chances of that lasting long enough to result in offspring is 1 in 2.

  • So, the combined probability is already only about 1 in 40 million.

Now let’s get down to some of the biological details: 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 about 100,000 viable eggs while a man will produce about 12 trillion sperm over the course of his reproductive lifetime.

  • Let’s say a third of those (4 trillion or 4 x 1012) are relevant to our calculation, since the sperm created after your mother hits menopause don’t count. So, the probability of that one sperm with half your name on it fertilizing that one egg with the other half of your name on it is 1 in (100,000) (4 x 1012) = 1 in 4 x 1017, or 1 in 400 quadrillion.

However, your existence presupposes another supremely unlikely chain of events. Namely, that every one of your ancestors lived to reproductive age, going back about 150,000 generations to the origin of man.

  • So, the chance of your particular chain of ancestors having remained unbroken for all that time would be 1 in 2150,000, which is about 1 in 1045,000.

Remember the sperm-meeting-egg argument for the creation of you, since each gamete is unique? 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. This is also true of your grandparents’ parents, and their parents, and so on back to the beginning of human time. That means that in every step of your lineage, the exact the right sperm had to fertilize the exact right egg such that you would ultimately be created.

  • To account for all 150,000 generations, we raise 400 quadrillion to the 150,000th power yielding 102,640,000. The probability is thus about 1 in 102,640,000.

To complete the analysis: (102,640,000) (1045,000) (40,000,000) = 4 x 102,685,007 ≈ 102,685,000.

Thus, the probability of your existing at all is about 1 in 102,685,000.

You may quibble with some of the Binazir’s assumptions above. I would certainly add in (sadly) that there is the possibility of abortion or miscarriage, but even a simple analysis yields an astonishingly small probability.

One of my brothers made his own calculation regarding one of Binazir’s assumptions and came up with a figure that would make the probability of existence even smaller:

My numbers are more simplistic, but assuming 100,000 eggs/woman & 12 trillion sperm/man creates 1.2 x 10^18 combinations for every man/woman pairing (i.e., significantly more combinations than the 400 trillion or 4 x 10^14 mentioned in the article). If you assume there are 3 billion women and 3 billion men alive today, that means 3 x 10^14 eggs and 3.6 x 10^22 sperm are currently on the planet, for a total of 1.1 x 10^37 possible pairings. If you assume the current population is 1% of the history of humanity, the total number of combinations increases to 1.1 x 10^39.

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

Theologically, of course, we are no accident; we do not exist by happenstance. God has always known us, intended us, loved us, and planned for us. Scripture says,

  • Before I formed you in the womb I knew you (Jer 1:5).
  • 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).
  • 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 all right, 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 each of us in the kingdom, from before the creation of the world. Not only has He always known us; he has known everything each of us would do, for every one of our days has 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.

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

10 Replies to “The Probability of You Existing at All Is Unbelievably Low”

  1. Here’s a thought experiment to help illustrate the unbelievably huge size of these numbers. Let’s say we have a insect that–mirabile dictu–we can send to the moon. Let’s say it’s a fly that moves at about 4 mph. The moon is about 240,000 miles from the Earth. So, round-trip time works out to be about 14 years…for the fly to go to the moon and back. That’s a pretty good trip. Now imagine that each time the fly comes back from the moon it brings with it a speck of moon dust the size of a grain of sand (let’s say 1 mg). And let’s say the fly decides to bring the ENTIRE MOON back to the Earth, one grain of sand at a time. That’s going to take a LONG time. An unimaginably long time. But let’s make it longer. Let’s say the fly takes a brief respite of one million years between trips. The question is, how long will it take for the fly to bring the entire moon back to the earth? The answer, if my math is right, (assuming a mass of the moon of 7.34 x 10^22 kg), is about 7.34 x 10^34 years. That’s a ridiculously huge number. But it’s not even remotely comparable with 10^2,685,000. And what’s even more profound is that 10^2,685,00 is not even remotely comparable with eternity.

    1. Is that an African fly or a European one? And I note that it is an unladen fly that moves at about 4 mph. How fast does a laden fly fly?

  2. I would caution anyone from drawing a religiously-minded conclusion from these probabilities and here’s why: While the probability of any one of us existing is very low, the probability that 350 million humans existing in the United States is very high. In other words, when seen in the aggregate, that probability is simply stating that it is very hard to predict _who_ will exist and not that someone will.

    This is similar to the probability of any one star turning super-nova. That probability is low but the presence of super-novae throughout the cosmos is not.

    Again, it is similar to the probability of winning the Loto: while my chances of winning are very small, the probability of someone (or someones) winning are much higher.

    Having said that, Monsignor Pope’s reflection should spur us to consider that while the Mind of God could think of a nearly infinite number of souls to create, he chose to create you and I. That should always be a great sense of wonder and a real source of gratitude.

    1. I think that was exactly Msgr. Pope’s point: that we are not accidents, that God “chose to create you and [me].” No need for “caution” about drawing any conclusion other that the one he quite explicitly drew.

  3. For perspective on the size of those numbers, there are only 10x 80 elementary particles in the observable universe.)

  4. Thank you, Monsignor.
    What impresses me is that at the moment our parents came together to form us, the Creator of the Universe stopped what He was doing to give, to each and every one of us, a soul unique to itself. No one else has had a soul like mine, no one will have a soul like it. Same to all of us. I would call that a personal relationship with God. Then, I hope and believe, that He has written my name on the palm of His hand, so whenever He looks at His hand, He thinks of me. Wowser.

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