We didn't encounter it by chance though; we encountered it by complex goal-directed physical processes that are known to produce extremely high distictiveness-to-kolmogorov-probability outputs.
As for the first replicator, we simply do not yet know how (or even when) that came about, though random chance does seem likely. So I guess if you add enough layers of "built the machine that..." then you do end up with pure randomness (probably). But I would conjecture that there's a lot less "informational distance" between the cosmos and the first replicator than there is between the first replicator and Adam Yedidia.
This was consciously aiming a gun at an explicitly-named remote target, ricocheting the bullet off an unprecedentedly-reasonable number of explicitly-chosen elements, and hitting the target.
Don't let semantics muddy the water about this achievement
The universe has produced things that basically must exist given the laws of physics (when certain chemicals exist together under certain conditions we know they will react in certain ways, etc).
We are one of those things, and the things we make are things that we are compelled to make by our very nature.
So it's not chance. Our universe as constructed necessarily gives rise to the things we see and experience.
Just because you have a random process choosing between outcomes A and B doesn't mean that there is a 50/50 chance you'll see either outcome.
For a related interesting result relating to this see the recent paper where they analysed the Drake equation using probability distributions.
Or perhaps this consists of (slight) evidence that favourable conditions for the evolution of intelligence are more common than we currently suspect.
This was not his first try. His other efforts all ended in "Poof".
But this effort yielded life that figured out the equations! So, the equations generated life smart enough to figure out the equations.
So, the equations were both (1) general enough to generate life and (2) simple enough that the generated life could figure out the equations.
IMHO, amazing juxtaposition!
Is this set of equations essentially the only possible set of equations with both (1) and (2)?
If you mean evolution, yes. But nothing about the big bang for example makes it a "goal directed process".
(In fact even evolution only looks that way from hindsight -- there's not some end goal there either).
This distinction, between chance and goal-directed physical processes, is artificial, though.
It's artificial because it was produced by humans.
:-)
The more precise statement is that you'd never encounter this number by uniform sampling within the range of objects of (some reasonable choice of finite size)