A little while ago I had the privilege of attending TEDx San Francisco, organized by the incomparable Christine Mason McCaull. One of the talks was by Mel Robbins, a riotously funny self-help author and life coach with a syndicated radio show. In it, she mentioned that scientists calculate the probability of your existing as you, today, at about one in 400 trillion (4×10^{14}).

“That’s a pretty big number,” I thought to myself. If I had 400 trillion pennies to my name, I could probably retire.

Previously, I had heard the Buddhist version of the probability of ‘this precious incarnation’. Imagine there was one life preserver thrown somewhere in some ocean and there is exactly one turtle in all of these oceans, swimming underwater somewhere. The probability that you came about and exist today is the same as that turtle sticking its head out of the water — in the middle of that life preserver. *On one try.*

So I got curious: are either of these numbers correct? Which one’s bigger? Are they gross exaggerations? Or is it possible that they *underestimate* the true number?

First, let us figure out the probability of one turtle sticking its head out of the one life preserver we toss out somewhere in the ocean. That’s a pretty straightforward calculation.

According to WolframAlpha, the total area of oceans in the world is 3.409×10^{8} square kilometers, or 340,900,000 km^{2 } (131.6 million square miles, for those benighted souls who still cling to user-hostile British measures). Let’s say a life preserver’s hole is about 80cm in diameter, which would make the area inside

3.14(0.4)^{2}=0.5024 m^{2}

which we will conveniently round to 0.5 square meters. If one square kilometer is a million square meters, then the probability of Mr Turtle sticking his head out of that life preserver is simply the area inside the life preserver divided by the total area of all oceans, or

0.5m^{2}/3.409×10^{8}x106m^{2} = 1.47 x 10^{-15}

or one in 6.82×10^{14}, or about 1 in 700 trillion.

One in 400 trillion vs one in 700 trillion? I gotta say, the two numbers are pretty darn close, for such a farfetched notion from two completely different sources: old-time Buddhist scholars and present-day scientists. They agree to within a factor of two!

So to the second question: how accurate is this number? What would we come up with ourselves starting with first principles, making some reasonable assumptions and putting them all together? That is, instead of making one big hand-waving gesture and pronouncing, “The answer is five hundred bazillion squintillion,” we make a series of sequentially-reasoned, smaller hand-waving gestures so as to make it all seem scientific. (This is also known as ‘consulting’ – especially if you show it all in a PowerPoint deck.)

Oh, this is going to be fun.

First, let’s talk about the probability of your parents meeting. If they met one new person of the opposite sex every day from age 15 to 40, that would be about 10,000 people. Let’s confine the pool of possible people they could meet to 1/10 of the world’s population twenty years go (one tenth of 4 billion = 400 million) so it considers not just the population of the US but that of the places they could have visited. Half of those people, or 200 million, will be of the opposite sex. So let’s say the probability of your parents meeting, ever, is 10,000 divided by 200 million:

10^{4}/2×10^{8}= 2×10^{-4}, or one in 20,000.

**Probability of boy meeting girl: 1 in 20,000.**

So far, so unlikely.

Now let’s say the chances of them actually talking to one another is one in 10. And the chances of that turning into another meeting is about one in 10 also. And the chances of that turning into a long-term relationship is also one in 10. And the chances of *that* lasting long enough to result in offspring is one in 2. So the probability of your parents’ chance meeting resulting in kids is about 1 in 2000.

**Probability of same boy knocking up same girl: 1 in 2000.**

So the combined probability is already around 1 in 40 million — long but not insurmountable odds. 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. 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/(10^{5})(4×10^{12})= 1 in 4 x 10^{17}, or one in 400 quadrillion.

**Probability of right sperm meeting right egg: 1 in 400 quadrillion. **

But we’re just getting started.

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* – going all the way back not just to the first *Homo sapiens*, first *Homo erectus* and *Homo habilis*, but all the way back to the first single-celled organism. You are a representative of an unbroken lineage of life going back 4 billion years.

Let’s not get carried away here; we’ll just deal with the human lineage. Say humans or humanoids have been around for about 3 million years, and that a generation is about 20 years. That’s 150,000 generations. Say that over the course of all human existence, the likelihood of any one human offspring to survive childhood and live to reproductive age and have at least one kid is 50:50 – 1 in 2. Then what would be the chance of your particular lineage to have remained unbroken for 150,000 generations?

Well then, that would be one in 2^{150,000} , which is about 1 in 10^{45,000}– a number so staggeringly large that my head hurts just writing it down. That number is not just larger than all of the particles in the universe – it’s larger than all the particles in the universe *if each particle were itself a universe*.

**Probability of every one of your ancestors reproducing successfully: 1 in 10 ^{45,000}**

But let’s think about this some more. Remember the sperm-meeting-egg argument for the creation of you, since each gamete is unique? 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. This is also true of your grandparents’ parents, and their grandparents, and so on till the beginning of 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.

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.

So now we must account for that for 150,000 generations by raising 400 quadrillion to the 150,000^{th} power:

[4×10^{17}]^{150,000} ≈ 10^{2,640,000}

That’s a ten followed by 2,640,000 zeroes, which would fill 11 volumes of a book the size of *The Tao of Dating* with zeroes.

To get the final answer, technically we need to multiply that by the 10^{45,000 }, 2000 and 20,000 up there, but those numbers are so shrimpy in comparison that it almost doesn’t matter. For the sake of completeness:

(10^{2,640,000})(10^{45,000})(2000)(20,000) = 4x 10^{2,685,007 }≈ 10^{2,685,000}

**Probability of your existing at all: 1 in 10 ^{2,685,000}**

As a comparison, the number of atoms in the body of an average male (80kg, 175 lb) is 10^{27}. The number of atoms making up the earth is about 10^{50}. The number of atoms in the known universe is estimated at 10^{80}.

So what’s the probability of your existing? It’s the probability of 2 million people getting together – about the population of San Diego – each to play a game of dice with *trillion-sided dice.* They each roll the dice, and they all come up the exact same number – say, 550,343,279,001.

A miracle is an event so unlikely as to be almost impossible. By that definition, I’ve just shown that you are a miracle.

Now go forth and feel and act like the miracle that you are.

Think about it,

Ali B

*Thanks for visiting! You can find more of my writing here and here. I also wrote a book on how smart women can find more love, which turns out to be the highest-rated of its kind on Amazon (4.9/5 stars). The book on how smart men can be more successful with women is also alright.*

PS: Update 9/26/11: To all you smartypants out there who just can’t wait to tell me “the probably of existing of something that exists is 100%” and “this is all just hand-waving” — yes, Einstein, I know, and you’re *totally missing the point*. The probability of sentient life is not something that can be measured accurately, and hundreds of steps have been deleted for simplicity. It’s all an exercise to get you thinking, but some of you are so damn smart and obsessed with being right that you’ve lost the mental capacity to wonder and instead harp on the numerical accuracy of the calculation. And no matter how you slice it, it’s pretty remarkable that you and I, self-absorbed scallywags that we are, stand at the end of an unbroken chain of life going all the way back to the primordial slime. *That’s* the point. Now if you have something interesting to say, I’ll approve the comment, otherwise into the slag-heap of trolls it goes.

Update 11/10/11: Someone at imgur.com came up with this beautiful infographic, which apparently made the rounds of the planet while I was asleep. Click on it to get the full-size version.

I enjoyed the article. I always knew I was special.

In reply to Christopher Smyth: I am not a creationist and not a Christian in that sense. We are the result of coincidence and ripple effects, mutation and selection. I just have not found the right argument which explains that we exist as conscious things, capable of typing blogs, which has a prior probability of almost nothing. Nothing I have found on the internet has convinced me so far, including the Observer Selection Bias (wiki).

In reaction to Anon: We are talking about the prior probability, not the posterior probability, which is always 100%. The prior of 40 zero’s in a row is very very small. BTW so is the prior of every other outcome, but the outcome of 40 zero’s is very unique. If it happened you would start doubting the random number generator.

I’m getting a bit impatient; all blogs are missing one key point:

Yes, you are right…but you still shouldn’t feel that special. If you were never born, you would never know you existed (obviously). Therefore, in your realm of consciousness, the chance of your existence: a guaranteed 100%.

It is interesting that the odds are much higher against evolution occuring and yet evolution beat the odds! So for Christians to say that because they are here and beat the odds that God must be the reason. Wishful thinking Christians.

Absolutely fantastic, intriguing article, thanks for the lack of sleep. :)

I’m sure that you’re aware by the comments here that there are many Christians who think that you’ve proven that Man must have been created by a god. Just as importantly, they think that was your intention.

I disagree that this is what you accomplished and I disagree that this was your intention.

Please set me straight or set the Christians straight, as the case may be.

Thanks

Comment to Ali’s comment: If you widen the circle of observations to include other universes and other times, as you suggest, you increase the numerator of the probability fraction, but you also increase the denominator. The fraction remains astronomically small. Doesn’t it?

I like the simplicity of DimSum’s example, but we are not talking about a pot of identical sweets. What sets human life apart is the fact that we are probably at the very top the creation pyramid. If we limit ourselves to Planet Earth alone, our unique – to avoid the word “superior” – nature seems obvious. There could be even more “superior” collections of molecules out there in Universe, but that does not alter the fact that very very few collections of molecules are capable of typing this comment. I am not just any sweet in a pot, I am one of the 7.5 billion blue sweets in a pot of 400 trillion yellow sweets. I have been incredibly lucky. Incredibly lucky. So lucky that it is hard to imagine that this all happened by coincidence. But what other explanation could there be than coincidence? This is where I get stuck.

he odds are outrageous when you consider any of our man made concepts, but when you have infinite chances of universes forming, in the infinite concept of time, the odds suddenly look not so bad.

There may have been millions, billion

This is coming at the question of existence from completely the wrong angle.

Yes the probability of things happening as they did to produce ‘Me’ are astronomically large.

But ‘I’ am an output of those events happening – had they not happened and other sperm had met other eggs, there would be another copy of ‘Me’ saying “wow what crazy odds that I exist!”.

This is like taking a huge pot of sweets (400 trillion), picking one out and going “Omg it’s this exact sweet, what are the chances?!”

Similarly, the probability element looks at something incromprehensible from a particularly human view.

The odds are outrageous when you consider any of our man made concepts, but when you have infinite chances of universes forming, in the infinite concept of time, the odds suddenly look not so bad.

There may have been millions, billions, trillions or quadrillions of universes to exist where there was no life.

There is something suspect here. If you have two events A and B. If thoose events are independent between them. You can state the probability of A and B happens is the product of their probabilities separately. But ¿How do you decide thoose events are independent?

¿ Number of ways it can happen /Total number of outcomes is a good measure of probability in that case? ¿Number of Outcomes is fixed or changing?

A curious fact for example:

The propability to find a rational (in other words fractions) number in the interval [0,1] of real line is 0. ¿Coincidence or not ? ¿How probability to find the most ordinary kind of numbers would be zero?

This is a great article because it elicits something rare – deep, genuine astonishment and wonderment. At face value the odds strike one as so staggering as to be way beyond our ability to grasp in any meaningful way.

I respect and understand those who use such odds to shore up the case for an all-powerful Deity, but I fail to see how one can do that without including additional probabilities for the creation and mature development of said Deity to the point where it could go on to create a universe in which we emerge.

I can’t help but feel that there may be one or more factors which lower the probability at certain stages but I haven’t been able to put my finger on those yet.

What has been overlooked is that some of the steps to arrive at these odds are spread out over equally incomprehensible spans of time, so the notion of simultaneously rolling many trillion-sided dice in San Diego – a one off event – obscures the at times very slow accumulation of probabilities which make up the final figure. After all, the turtle has to have an equal opportunity to rise to the surface at any point in the ocean for it to have a non-zero chance of finding the life preserver.

This is an amazing article because I’ve mused upon this very bizarre event (my being born)- without your insanely complex math of probability of course – just based on the unlikelihood of my own parents meeting in the first place. My dad was born in Hungary, came to the USA at age 11, then joined the military thanks to WWII, went to England, where he met my mother… and they didn’t have me till 4 years after they were married. The other consideration is, what if “YOU” coming into being would require the egg of a woman in Prussia in 1760 meeting the sperm of a guy in Wyoming born in 1920. That YOU would never happen. We are all the product of a very precise moment in time, aided by a series of such events (our ancestors). So, indeed, we are miracles who can scoff at the staggering odds of winning the latest Powerball lottery. It also hurts any arguments about reincarnation.

This is the most lowering, and amazing thing I’ve ever perused. I’ve generally thought of myself as a decent and kind individual

I was truly stunned when you spent computing each one of those probabilities.

very good, i like it…

this fantastic keep doing the good work

absolutely fantastic, intriguing article, thanks for the lack of sleep ;)

still interesting

Nice Infography ! thanks for Share :)

The fact there are 7 billion people alive is evidence of there being a high probability humans will be born. I think we have to provide some understanding as to why it seems strange that there is such a small probability we are here, and yet we are. my fathers sperm all had different characterisitcs, some where Michael Phelps, some were Eddy the Eel. So, some of his sperm were better than others, and so we can eliminate a whole lot of sperm from the equation because of their unlikliness of helping my mother conceive me. In fact, I think we could keep eliminating sperm if we were to carefully scrutinise the capabilities and position of each sperm in the fallopian tubes etc. So, in short, i think if we were to look at every possible cause leading up to the effect that is you, there is actually a much higher probability of you being here than not. It is hard to loook past hard determinism here and not say that you were 100% likely to be born, because of the unbroken chain of causes that lead to effects, that is you, and hence why you are here. This of course, does not mean you cannot be grateful for your life and wonder at the miracle.

Food for thought

This one is just a crooked version of Zeno’s paradox.

This is the most humbling, and awe inspiring thing I’ve ever read. I’ve always thought of myself as a good and kind person, but this has inspired me to take better care of myself, others, and be the best of “me”i can. With those odds, and that we only happen once, I’m going to make the best, and the most of it I can. Thank you for this xo.

And what are chances for life on a planet?

– need water

– gravity. Enough gravity/rotation for holding on to water.

– temperature between 0 – 100

– sun

– moon

– asteroide collisions…

I believe there are no life in other galaxies. The survival of the fittest will always result in extinction of resources on planets. So the,BANG,asteroide collisions are the universe’ last life insurance for life on planet earth.

However, I do not believe in luck, but I do believe in God.

Sadly, I do believe in extinction

Despite the “Zero” probability, there are over 7 billion of us here?

Thank you, Sir! It is indeed very good way to look at the life! Absolutely not waste of time. That would be good if one calculated the odds of egg:sperm ratio connected that you exist and so your writing :)

“Ali, the scientific method is not the only path to knowledge. Everything that exists isn’t necessarily material. To assert otherwise requires a leap of faith. Just sayin”

No you are wrong. The scientific method is not a path to knowledge, but it is a path to understanding the world around us. If you can’t prove something, than it does not exist. All this other hoopla about things not being material is, with all due respect, hot fuzz. And to call the need to explain something using rationale evidence and thinking a leap of faith, is just pure ignorance. Just sayin.

Re: “Unfortunately, a concept that can be neither proven nor refuted is not scientific. “God” is such a concept. Care to define what that is? Otherwise it’s just fuzz.”

Ali, the scientific method is not the only path to knowledge. Everything that exists isn’t necessarily material. To assert otherwise requires a leap of faith. Just sayin’.

You’ve grossly underestimated the probability here. Since every action has a ripple effect, everything that has ever, or will ever take place in the universe will affect how the rest of the universe looks given enough time.

If I go left instead of right on a walk, everything I do will be slightly different. All my interactions will be different, and these minor differences will keep on growing until eventually the entire universe looks slightly different compared to how it would’ve looked if I’d turned right. This means that ALMOST everything that has ever happened in the entire universe had to happen in exactly the right way in order for you to be born.

The fact that you’re alive today is so astronomically improbable it’s not worth thinking about, and it angers me when people take life for granted.

Its odd that just today I was thinking about the odds on me being born, working out parents meeting, sperm and eggs, exactly as written above including ancestors etc. ,. I thought that there would only be me who thought of such things…

One of the most revered hindu saints has told that there are 3 things a soul can dream of and the first one is specified as being born as a human being… So I appreciate this article. Quite an interesting perspective… For those who disagree it is only a theory. You can read it until you are interested or just ignore it.

Thanks Ali, You just proved God!

I was really amazed by the time you spent calculating all those probabilities. I’m not really good at maths but I can tell you that your article is really friendly (probabilities for dummies). It was really great to learn how magical is to be alive. What were our chances? And we are here. Great article.

On top of this odds, add in the odds of this universe coming into existence , and having the things like gravity, and atoms set just right after that, even if these things were off by 1%, intelligent life or life, couldn’t exist. The odds of this universe being the way it is by mere chance is 0 if it is the only universe, the only explanation for it being the way it is through chance is if there is a infinite number of universes, and that makes even less sense as you then need a source for these infinite universes, some sort of machine capable of throwing out universes forever. And then the question arises where did this universe creating thing come from. The odds of these things being true get less and less as you go on.

The fact is, we are faced with overwhelming odds, that life cannot exist as it does, this universe cannot exist as it does, and me and you cannot exist, yet here we all are. Impossible odds of you being here, in a universe that has impossible odds of existing in its current state.

All the evidence points to a miracle, something that is beyond comprehension, something so far beyond this universe in terms of intelligence and power, that it is impossible for us to understand. This is what the Bible calls God. A infinite power and intelligence that exists outside of space and time, when you add up all the numbers, and realise that there is no chance of this actually happening, no chance of you even being here, or this universe as it is, all that is left is God. This is the data, the cold hard numbers, that do not lie. God has already been proven to exist through the numbers, the odds of things happening as they have.

If you want to continue to shut out the truth and run away from God, it’s up to you. But you will never find what you are looking for because you are being fooled and you are fooling yourself. You can only run away from the truth for so long, it will catch up with you one day, and then you will have to face the consequences and answer for the way you lived your life, there is no escaping it. Find Jesus Christ, now, today, while you have time, because one day your time will run out and he will not be able to save you.

Unfortunately, a concept that can be neither proven nor refuted is not scientific. “God” is such a concept. Care to define what that is? Otherwise it’s just fuzz.

You are a miracle, so is this universe and everything in it, the odds of this all happening the way it did, a universe capable of sustaining life, and you being here reading this, is zero. This is why the Bible tells us only the fool believes there is no God. Because only through intelligence can you have a universe, and concious human beings. It cannot happen any other way. Which is why science tries to come up with multi universe theories, only by trying to eliminate these odds can they take God out of the picture. Sadly for them, there is no multi universes , there is one, and it is capable of sustaining intelligent life,and has everything so precise, everything required for life, so precise, that the odds of it happening by chance are zero.

People get angry when you mention the odds, because it points to a intelligent designer, something that scares they life out of them because they have gambled everything on this intelligence not existing. The odds are overwhelmingly in favour of their being a all powerful God, and overwhelmingly against there not being a God. The chances of you being here today, right now at this minute in this universe, and all that is required to make that actually happen, is 0, the odds of God not existing is basically 0. This is what the numbers tell us, this is the facts.

Great article. Thank you Ali :)

I was doing my Saturday night study for tomorrow morning’s service (Psalm 131 “I am fearfully and wonderfully made” written by King David, when I ran across your blog post.

“…How precious also are thy thoughts unto me, O God! how great is the sum of them! 18 If I should count them, they are more in number than the sand…”

Psalms 139:17-18 (KJV)

I’m going to challenge my parishioners who Facebook to post a link to your post so they can get an idea of how much of a miracle they actually are…

I have found that the average Christian’s greatest handicap is the ability to critically understand scientific thought, when actually, contrary to commonly held opinion, the Bible and modern science have quite a lot in common.

I hope I pronounce your name correctly tomorrow… :D

High praise indeed, Rev! Hope the parishioners derive some benefit from it. You are also sending them to the fake Harvard Commencement address, yes? :)

In doing research for my own writing on celebrating our person and in particular our daily lives, I’ve stumbled on your post (in tandem, after watching Ms. Robbins’ talk and curious about the 1 in 4 trillion number). Just wanted to thank you for the post, and winding it down to a most spiritual inference; a lot of (scientific) supposition ends up leaving any prophetic insight off of the work. So, thank you.

Conceded, the chance of me being me, given I am human is of course 1:1. But that distracts from the other question, about me being human given that I consist of molecules. If someone can explain why that is not a turtle in a life preserver, then please rescue me. If not, save our souls.

I see many people agreeing that the probability of each of us being born a human being was astronomically small. It just is. I see no one taking it to the next level: If that probability was indeed that close to zero, then how do you explain that I am actually typing this? It cannot be sheer luck. Yes we can explain human existence by an accumulation of highly rare circumstances. But that does not explain that I am one of them, and not gas. There must be something at work that defies probability.

il Palazzo and other 1:1 believers: you are addressing a different issue. We are not like any other turtle, who has a 1:1 chance of being a turtle. We are that one turtle that is sticking its head through the life preserver. The chance of that happening given you are a turtle is less than 1:1. More likely that someone put that life preserver there on purpose. Frightening thought!