In the summer of 1950, physicist Enrico Fermi was having lunch with colleagues at Los Alamos National Laboratory, the New Mexico research site where he'd helped build the first atomic bomb. The conversation had started with a magazine cartoon about aliens stealing garbage cans and drifted into a discussion of unidentified flying objects and the possibility of faster-than-light travel. Fermi, who had a habit of doing quick order-of-magnitude calculations in his head, went quiet for a moment. Then he asked something like: "Where is everybody?"

He wasn't being flippant. Fermi was one of the sharpest back-of-the-envelope thinkers in twentieth-century physics — the kind of person who could estimate the yield of a nuclear blast by watching how far scraps of paper fluttered in the shockwave. His question was a real calculation, not a joke, and it goes like this: given how old and how big the galaxy is, intelligent life should have had plenty of time to spread across it. So if it exists anywhere else, why haven't we seen any trace of it?

To feel the force of that question, you need a sense of scale. The Milky Way — our home galaxy — is about 100,000 light-years across and contains somewhere between 100 and 400 billion stars. A light-year is the distance light travels in one year, roughly 5.9 trillion miles; it's a unit of distance, not time, despite the name. The galaxy itself is about 13.6 billion years old, and stars capable of hosting rocky planets have existed for at least 8 or 9 billion of those years — billions of years before our Sun formed.

Now think about colonization timescales. Suppose a civilization develops space travel and decides to expand, sending colony ships to nearby star systems. Those colonies grow, mature, and eventually send out colony ships of their own. Even if each ship travels at a modest fraction of the speed of light — nothing exotic, no warp drives — the expansion is like compound interest: the colonized volume grows exponentially, not just outward at a fixed crawl.