On my birthday, I had a strangely pertinent thought: what's the probability of being born?

In a recent talk at TEDx San Francisco, Mel Robbins, a riotously funny self-help author, mentioned that scientists estimate the probability of your being born at about one in 400 trillion.

"That's a pretty big number," I thought to myself. If I had 400 trillion pennies, I could probably build a decent-sized penny fortress with it.

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, with exactly one turtle in all of these oceans, swimming underwater somewhere. The probability that you came about is the same as that turtle sticking its head out of the water -- into the middle of that life preserver. On one try.

So I got curious: Are either of these estimates correct? Which one's bigger? Are they gross exaggerations? Or could they be underestimates of 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 341 million km (131.6 million square miles). Let's say a life preserver's hole is about 80cm in diameter, which would make the area inside about 0.5 square meter. 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 about 1 in 700 trillion.

One in 400 trillion vs one in 700 trillion? Pretty darn close, for such an unusual calculation. The scientists and Buddhists seem to agree.

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 500 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.)

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 1/10th of the world's population 20 years go (1/10th 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, or one in 20,000.

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

So far, so good.

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 two. So the probability of your parents' chance meeting resulting in kids is about one in 2000.

Step 2. Probability of same boy knocking up same girl: one in 2000.

So the combined probability is already around one in 40 million -- long but not insurmountable odds. Now things start getting interesting. We're about to deal with eggs and sperm, which come in large numbers.

You are the result of the fusion of one particular egg with one particular sperm. Each sperm and each egg is genetically unique because of the process of meiosis. 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 one in 400 quadrillion.

Step 3. Probability of right sperm meeting right egg: one 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 -- one in two. 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 , which is about one in 10 -- 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.

Step 4. Probability of every one of your ancestors reproducing successfully: one in 10

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, too. 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 their parents, 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 400 quadrillion.

So now we must account for those 150,000 generations by raising 400 quadrillion to the 150,000 power:

[4x10] ≈ 10

That's a ten followed by 2,640,000 zeroes, which would fill 11 volumes the size of my book. Multiplying it all together for the sake of completeness (Step 1 x Step 2 x Step 3 x Step 4):

Probability of your being born: one in 10

As a comparison, the approximate number of atoms in the known universe is 10.

So what's the probability of your being born? It's the probability of 2.5 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 proven that you are a miracle.