To fully appreciate the sheer magnitude of the vast distances in space and time that separate the Earth from whatever cousins she may count among the stars, imagine that the Earth itself is the Milky Way galaxy – and that a single human walking the Earth represents all of humanity, for her entire existence. In so doing, we can observe those vast distances at a scale we can more easily comprehend.
We find ourselves, then, on a Milky Way Earth – we, humanity, standing alone on an undistinguished hill. We, humanity, will live 100 years on this Earth, during which we may roam as we please. And we have a radio, with which we may try to locate and communicate with other folks who might be here with us on Milky Way Earth.
Our 100 years represent the entire period we might expect humanity – or any other intelligent civilization – to endure. We’ll call it 1,000,000 years. And if the Earth represents the Milky Way, then we can compare the Earth’s surface, with its 25,000-mile circumference, to the broad belt of stars that lie beyond the intensely radioactive core of the galaxy, where life can never begin. The circumference of that belt, at the point where our solar system sits, is around 240,000 light years. So,
100 years on Milky Way Earth = 1,000,000 actual years
1 mile on Milky Way Earth = 10 light years
We have another factor to consider: how long will the Milky Way be hosting intelligent civilizations? The galaxy had a beginning, and will have an ending. Can we arbitrarily call it 10 billion years? At our Milky Way Earth scale, that’s
1,000,000 Milky Way Earth years = 10,000,000,000 actual years
Any given civilization-person standing on Milky Way Earth, then – such as ourselves – can expect to be there for 1/10000th of Milky Way Earth’s existence. If we’re going to meet another person there, we need to encounter them during our 100 years (assuming their 100 years overlaps with ours). There could be 10,000 other people dropped onto our Milky Way Earth randomly across the 1,000,000 years it will exist – and still not be any two people on the planet at the same time.
Assuming two people on Milky Way Earth at the same time, they would have to literally run into each other while roaming the entire surface of the planet to achieve contact. The odds of that occurring, even if their 100 years overlapped completely, are less than one in a billion (given Earth’s surface area of almost 200,000,000 square miles, and an average walking vector of 50 miles per day).
Ah, but then we have a radio! If anyone is on Milky Way Earth at the same time we are, we can contact one another by radio, right?
Remember that we are scaled differently here; while a radio transmission from New York City to Los Angeles takes less than a second on real Earth, it would take almost 5 years on Milky Way Earth – 10 for a two-way exchange. [Put another way, the radio is slower than walking; its only virtue is that a radio signal covers more territory than a walking person’s field of vision.] (Scaled back out, the period on an exchange in real interstellar space would approach 100,000 years – 1/10th of the duration of an intelligent civilization.) Many of these exchanges would never complete after the initial message is received, as the sender stands a good chance of being extinct by the time a reply is received, depending on the distance.
To have a reasonable chance of contact by signal with a contemporaneous person on Milky Way Earth, its population density at the time we happen to exist there would need to be somewhere around 12 (Built in here is the assumption that we can only contact by radio those on the same side of the planet as we are, given that in the real universe we can’t receive and transmit through the galactic core, and given that interstellar space does not have an analog for the atmosphere off which we can bounce signals; to make radio contact with any human on the other side, we’d have to walk to that side and then start searching.)
To have a reasonable chance of actual face-to-face contact with a contemporaneous person on Milky Way Earth in 100 years of wandering, given a daily travel radius of 50 miles and 200,000,000 square miles of territory, its population density would need to be around 300.
For the signal contact to become a reasonable expectation, the galaxy would need to host more than 100,000 intelligent civilizations. For physical contact between civilizations to be a reasonable expectation, there would need to be well over 2,000,000.
Put another way: even if the galaxy teems with intelligent life across its duration, we are unlikely to hear from them or meet them. Time and distance work against us all...
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