## Thursday, April 16, 2020

### Life, the Universe, and Everything

This is a  post about John Conway and Enrico Fermi.

John Conway passed on recently, of COVID-19. He is one of those people, who if you know his work, you feel a little sad, and if you don't, you still feel a little sad but in more disconnected way. John Conway did many things, but he also created the Game of Life.

No, I'm not talking about the Milton Bradley/Hasbro game where you start with a car, you must get married and you load up on kids and you make life decisions that will end up in the wealthy retirement home (Much more the American Dream than Monopoly). No, this is a mathematical game about growth and death, which I first discovered in high school in an issue of Scientific America. It is played on graph paper (at the time) and later in computers, and is an interesting simulation. You draw a pattern on the graph paper, and you evolve it through some simple rules:
1. Any filled-in space with fewer than adjacent two filled-in spaces becomes empty (dies).
2. Any filled-in space with two or three adjacent filled-in spaces continues to exist.
3. Any filled-in space with more than three adjacent filled-in spaces becomes empty (dies).
4. Any empty space with exactly three adjacent filled-in spaces is filled in.
With these four rules, you can take any pattern and see how it evolves over time. Computers made this even easier (and engineering students, though wealthy in graph paper, quickly adapted it to computers).  So you can sketch any pattern, and follow their evolution until they stabilize, go extinct, or move off the board entirely.

Some patterns and parts of patterns go extinct - they don't have enough adjacent squares to survive. Some stabilize into a solid pattern that will no longer evolve - a two-by-two square is the simplest. Some stabilize into patterns that lose parts and gain other evenly - the most basic of these oscillators are "blinkers", a line of three vertical squares that, the next turn, become three horizontal squares, which then become three vertical squares until the end of time. And the last group moves out over time in a stabilizing pattern - the simplest version of these is the "glider", which moves slowly forever, until it rules into something else like a map edge or a stable pattern or glider.

OK, let's move on to Enrico Fermi, who is ALSO famous for many things, but the thing we want to talk about is Fermi's Paradox. The basics of this is the question - If the universe is ancient, and extraterrestrial life has had the chance to rise, evolve, and spread out, where are they? Even given the titanic distances of space, why haven't we encountered them?

This was formalized in the Drake Equation, which looks at the following factors:
${\displaystyle N=R_{*}\cdot f_{\mathrm {p} }\cdot n_{\mathrm {e} }\cdot f_{\mathrm {l} }\cdot f_{\mathrm {i} }\cdot f_{\mathrm {c} }\cdot L}$
where:
N = the number of civilizations in our galaxy with which communication might be possible;
and
R = the average rate of star formation in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
fl = the fraction of planets that could support life that actually develop life at some point
fi = the fraction of planets with life that actually go on to develop intelligent life
fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time for which such civilizations release detectable signals into space.
This is grist for many SF novels, with answers ranging from "they are already here" to "they are avoiding us" to "space is really, really big" to "something is out there eating civilizations" to "all these factors make N so small that we are effectively alone - did we mention that space is really, really big?".

We can argue the numbers, of which we really don't have a large enough sample size to even make a good guess, but, to quote the old joke - "Now we're just haggling." Another way of looking at this is through the lens of Conway's Life.

Some extraterrestrial life will not get to the point where it games sentience, or space travel, or communications, much the factors laid out in the Drake equation - they will die out. And some will reach a stable condition, either technologically or geographically, where they will enter a self-sustaining stasis - gaining a little, losing a little, but staying pretty much in the same location and tech level. And some will become gliders - leaving parts of their past behind them as they continue to evolve in a particular direction.

And these gliders would continue in a relatively stable state, until they hit something else - the edge of a map, another glider, or an existing stable system. And yet (if we are thinking in spacial terms), they are a straight line in a huge three-dimensional space - the chance of them hitting any particular point (like, say, our sun) is tiny. Yet in an infinite universe, or, just saying a extremely large sample size like our galaxy, it remains possible.

And I think that's where we are. I'm not sure if everything really connects here, or there are just similarities, and definitely don't have the maths to back any of this up (like I said "We're just haggling."). But it is an interesting thought experiment for the day, and unites Mr. Fermi and Mr. Conway.

More later,