24th
Are You Totally Improbable Or Totally Inevitable?
“If we have never been amazed by the very fact that we exist, we are squandering the greatest fact of all.”
— Will Durant, American writer, historian, and philosopher (1885-1981)
“Not only have you been lucky enough to be attached since time immemorial to a favored evolutionary line, but you have also been extremely — make that miraculously — fortunate in your personal ancestry. Consider the fact that for 3.8 billion years, a period of time older than the Earth’s mountains and rivers and oceans, every one of your forebears on both sides has been attractive enough to find a mate, healthy enough to reproduce, and sufficiently blessed by fate and circumstances to live long enough to do so. Not one of your pertinent ancestors was squashed, devoured, drowned, starved, stuck fast, untimely wounded or otherwise deflected from its life’s quest of delivering a tiny charge of genetic material to the right partner at the right moment to perpetuate the only possible sequence of hereditary combinations that could result — eventually, astoundingly, and all too briefly — in you. (…)
The number of people on whose cooperative efforts your eventual existence depends has risen to approximately 1,000,000,000,000,000,000, which is several thousand times the total number of people who have ever lived. (…)
We are awfully lucky to be here-and by ‘we’ I mean every living thing. To attain any kind of life in this universe of ours appears to be quite an achievement. As humans we are doubly lucky, of course: We enjoy not only the privilege of existence but also the singular ability to appreciate it and even, in a multitude of ways, to make it better. It is a talent we have only barely begun to grasp.”
— Bill Bryson, A Short History of Nearly Everything, Black Swan, 2003
“Statistically, the probability of any one of us being here is so small that you’d think the mere fact of existing would keep us all in a contented dazzlement of surprise.”
— Lewis Thomas, The Lives of a Cell, Bantam Books, 1984, p. 165.
“Life is one huge lottery where only the winning tickets are visible.”
— Jostein Gaarder, The Orange Girl, Orion Publishing, 2004
“’We are the lucky ones for we shall die’, as there is an infinite number of possible forms of DNA all but a few billions of which will never burst into consciousness.”
— Frank Close, a noted particle physicist who is currently Professor of Physics at the University of Oxford, The Void, Oxford University Press
“What are the odds that you exist, as you, today? Author Dr Ali Binazir attemps to quantify the probability that you came about and exist as you today, and reveals that the odds of you existing are almost zero.
Think about yourself.
You are here because…
Your dad met your mom.
Then your dad and mom conceived you.
So a particular egg in your mom
Joined a particular sperm from your dad
Which could only happen because not one of your direct ancestors, going all the way back to the beginning of life itself, died before passing on his or her genes…
So what are the chances of you happening?
Of you being here?
Author Ali Binazir did the calculations last spring and decided that the chances of anyone existing are one in 102,685,000. In other words (…) you are totally improbable.
— Robert Krulwich, Are You Totally Improbable Or Totally Inevitable?, NPR, Nov 21, 2011
“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.”
Click image to enlarge
— Ali Binazir, What are the chances of your coming into being?, June 15, 2011
A lovely comment by PZ Myers, a biologist and associate professor at the University of Minnesota:
“You are a contingent product of many chance events, but so what? So is everything else in the universe. That number doesn’t make you any more special than a grain of sand on a beach, which also arrived at its precise shape, composition, and location by a series of chance events. (…)
You are one of 7 billion people, occupying an insignificant fraction of the volume of the universe, and you aren’t a numerical miracle at all — you’re actually rather negligible.”
— PZ Myers, A very silly calculation, Pharyngula, Nov 14, 2011
‘Life is one huge lottery where only the winning tickets are visible’
“Thirteen forty-nine,” was the first thing [he] said.
“The Black Death,” I replied. I had a pretty good knowledge of history, but I had no idea what the Black Death had to do with coincidences.
”Okay,” he said, and off he went. “You probably know that half Norway’s population was wiped out during that great plague. But there’s a connection here I haven’t told you about. Did you know that you had thousands of ancestors at that time?” he continued.
I shook my head in dispair. How could that possibly be?
”You have two parents, four grandparents, eight great-grandparents, sixteen great-great grandparents — and so on. If you work it out, right back to 1349 — there are quite a lot.
“Then came the bubonic plague. Death spread from neighborhood to neighborhood, and the children were hit worst. Whole families died, sometimes one or two family members survived. A lot of your ancestors were children at this time, Hans Thomas. But none of them kicked the bucket.”
“How can you be so sure about that?” I asked on amazement.
He took a long drag on his cigarette and said, “Because you’re sitting here looking out over the Adriatic.
“The chances of of single ancestor of yours not dying while growing up is one in several billion. Because it isn’t just about the Black Death, you know. Actually all of your ancestors have grown up and had children — even during the worst natural disasters, even when the child mortality rate was enormous. Of course, a lot of them have suffered from illness, but they’ve always pulled through. In a way, you have been a millimeter from death billions of times, Hans Thomas.
Your life on this planet has been threatned by insects, wild animals, meteorites, lightning, sickness, war, flods, fires, poisoning, and attempted murders. In the battle of Stikelstad alone you were injured hundreds of times. Because you must have had ancestors on both sides — yes, really you were fighting against yourself and your chances of being born a thousand years later. You know, the same goes for the last world war. If Grandpa had been shot by good Norwegians during the occupation, then neither you nor I would have been born. The point is, this happened billions of times through history. Each time an arrow rained through the air, your chances of being born have been reduced to the minimum.”
He continued: “I am talking about one long chain of coincidences. In fact, that chain goes right back to the first living cell, which divided in two, and from there gave birth to everything growing and sprouting on this planet today. The chance of my chain not being broken at one time or another duirng three or four billion years is so little it is almost inconceivable. But I have pulled through, you know. Damned right, I have. In return, I appreciate how fantastically lucky I am to be able to experience this planet this planet together with you. I realize how lucky every single little crawling insect on this planet is.”
“What about the unlucky ones?” I asked.
”They don’t exist! They were never born. Life is one huge lottery where only the winning tickets are visible.”
— Jostein Gaarder, The Orange Girl, Orion Publishing, 2004.
(Illustration source)
See also:
☞ Richard Dawkins, Unweaving the Rainbow, Lapidarium notes
