There are about 100 billion stars in the Milky Way galaxy. In standard notation that’s

100,000,000,000

Since the Hubble Space Telescope has pushed our eyes ever farther into the observable universe, astronomers now believe that there are more than 200 billion galaxies. That’s

200,000,000,000

If our Milky Way is an “average” galaxy, then there must be more than 20,000 billion billion stars. That’s

20,000,000,000,000,000,000,000

or 20 sextillion. Astronomers are more sanguine, however. Latest estimates put the number of stars at more than 70 sextillion. That’s a lot of stars. If some tiny fraction of them, say 1 in a billion have planets orbiting them with conditions favorable to life, that’s still more than 70 trillion planets capable of supporting life.

Astrophysicists also tell us that the universe is 12 to 15 billion years old. Of course many, perhaps most, of the planets capable of supporting life haven’t been around that long. Perhaps, like the earth, they’ve been around for only 5 or 6 billion years. It’s also possible, however, that many planets now cold and barren were once warm and capable of sustaining life. Perhaps 5 billion years ago, when our earth was just starting, there were other planets billions of years old that were just starting to darken or grow cold, planets long since dead that were capable of sustaining life billions of years ago. Let’s suppose that over the course of billions of years, say 10 billion, the number of planets capable of sustaining life has remained relatively constant. Let’s also suppose that the probability that life would arise and thrive by chance alone on one of these planets is 1 in 10^{15} for every million years. That’s a very small number, much too small for human beings to observe, since we would have to observe trillions of planets over the course of billions of years to have any hope of seeing life happen. Nevertheless, the number of chances for life to arise on one of those 70 trillion planets over the course of 10 billion years would be:

70 × 10

^{12}×10 × 10^{9}× 10^{-6}= 700 × 10^{15}

Suddenly that 1 in 10^{15} chance doesn’t look so small. In fact, the probability that no life would arise on those planets would be

(1 – 10

^{-15})^{(700 × 1015)}

This is a number very slightly less that 1 raised to a truly enormous power. If it were 1 (i. e., if the probability of life arising by chance alone were really zero), then all argument would be over. The probability of no life would be 1. But since it is ever so slightly less than 1, raising it to a truly enormous power makes it approach zero. I don’t have the mathematics background to calculate this number, but I suspect it is very close to zero. If so, it means that the probability of life arising by chance alone somewhere in the universe would be virtually certain.

To see how this works lets take an easier example. Lets toss 10 pennies on a table and see how many land heads up. What is the probability that all will land heads up? Since each penny has a 50/50 chance of landing heads up, the probability that all 10 will land that way is:

0.5

^{10}= 0.0009765625

Now let’s say we get 300 people tossing 10 pennies each. (Of course, we would have to supply $30 to purchase the pennies, but let’s not worry about that just now.) What is the probability that none of them will have all the pennies come up heads? The probability is

(1 – 0.0009765625)

^{300}= 0.74593866970625976803095741268068

This means that there is a slightly greater than 1 in 4 chance that 300 people tossing 10 coins will see at least one toss where all the coins come up heads. If we increase the number of people to 1000, then the probability of at least one occurrence of all heads is greater than 60%. If we increase it to 10,000, then the probability of at least 1 throw of all heads becomes greater than 99.994%, very nearly certain.

So you see, when people talk about life arising by chance, it may indeed be a very small chance but multiplied over trillions of opportunities and billions of years. The only problem is, we don’t have the faintest idea what the chance of life arising on its own is. Maybe it’s on the order of 1 in 10^{15}, as I suggested. Maybe it’s 1 in 10^{15,000,000}. Maybe it really is 0. But if it is 0, then a larger and more difficult question presents itself: How can we possibly be if we can’t possibly have come to be?

## One response to “Odds for Life”

very good Chip. improbable but very good.