What are the chances of being born?
Scientists calculate the probability of your existing as you, today, at about
one in 400 trillion (4×1014).
“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 3.409×108 square kilometers, or
340,900,000 km2 (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 m2
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
0.5m2/3.409×108x106m2 = 1.47 x
10-15
or one in 6.82×1014, 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:
104/2×108=
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/(105)(4×1012)= 1 in 4 x
1017, 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 2150,000 ,
which is about 1 in 1045,000– 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 1045,000
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 150,000th power:
[4x1017]150,000 ≈ 102,640,000
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
1045,000 , 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:
(102,640,000)(1045,000)(2000)(20,000) = 4x 102,685,007
≈ 102,685,000
Probability of your existing at all: 1 in 102,685,000
As a comparison, the number of atoms in the body of an average male (80kg,
175 lb) is 1027. The number of atoms
making up the earth is about 1050. The
number of atoms in the known universe is estimated at 1080.
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.
Written by Ali Binazir
Scientists calculate the probability of your existing as you, today, at about
one in 400 trillion (4×1014).
“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 3.409×108 square kilometers, or
340,900,000 km2 (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 m2
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
0.5m2/3.409×108x106m2 = 1.47 x
10-15
or one in 6.82×1014, 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:
104/2×108=
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/(105)(4×1012)= 1 in 4 x
1017, 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 2150,000 ,
which is about 1 in 1045,000– 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 1045,000
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 150,000th power:
[4x1017]150,000 ≈ 102,640,000
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
1045,000 , 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:
(102,640,000)(1045,000)(2000)(20,000) = 4x 102,685,007
≈ 102,685,000
Probability of your existing at all: 1 in 102,685,000
As a comparison, the number of atoms in the body of an average male (80kg,
175 lb) is 1027. The number of atoms
making up the earth is about 1050. The
number of atoms in the known universe is estimated at 1080.
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.
Written by Ali Binazir
