Probability and Scale

Here we should discuss probabilities in the context of very large numbers and Drake's Equation.

Inevitability of the Unlikely

It's may be a commonplace observation, but the universe is a big place. A very very big place. Most galaxies contains hundreds of billions of stars and there are hundreds of billions of galaxies. Relatively recent estimates suggest the universe may contain between 100 billion and 200 billion galaxies, though some estimate the count may be so high as 500 billion. Our own galaxy is believed to contain at least 100 billion stars, though most estimates fall in the range of 300 billion to 400 billion stars.

Let's arbitrarily assume that there are 200 billion galaxies, each containing an average of 200 billion stars. Our universe would then contain 40,000,000,000,000,000,000,000 stars!

In some ways, these numbers would be easier to conceive if they were simply infinite. Infinity is unlimited, which means it is undefined.  But one billion is not an infinite number. It is a definite, limited number whose contours evade concrete consideration. We can mathematically manipulate billions of billions, but our minds aren't big enough to think of such a vast number as a discrete series of individual components.

An interesting feature of such a large dataset, however, is that even the most unlikely of events take on a degree of inevitability.  Let us assume a one in a trillion chance of just the right kind of star developing just the right kind of planets under just the right kind of circumstance that life as we know it would come into existence.  Even still, the universe would contain an expected forty billion life-bearing stars!

We know that the probability that life such as ourselves could emerge from the cosmos is higher than zero. Our own existence confirms our possibility. If we live upon the only life-bearing planet in the universe, the probability of life's emergence would have to be very small, indeed.

Drake's Equation

Astronomers have devised a formula, Drake's Equation, for estimating the likelihood that SETI would discover an alien civilization. In many ways the equation is little more than a framework for structured speculations.  The probability that we would find life on another world is the product of several other probabilities that we can only estimate arbitrarily.  

The basic equation states that the number of civilizations in our galaxy that we could detect (N) can be estimated by multiplying the rate at which habitable stars are formed, the fraction of such stars that develop planets, the average number of such planets that would be habitable, the fraction of habitable planets that actually develop life, the fraction of life-bearing planets that develop sentience, the fraction of sentient lifeforms that develop detectable civilizations, and the length of time that such civilizations last.

No term of the equation is presently known with any real certainty, and our best guesses grow increasingly speculative as we walk deeper into the sequence.  We have some understanding of how often stars form and develop planets. We have yet to find exosolar life and have only developed a very limited range of technologies to detect it. It could be wildly improbable that life would develop anywhere or the galaxy could be teeming with sentient life that we are on the verge discovering any day now.