excuse me, but no. Our best-effort guesses might be the best we could literally do. But there is no need to be that literal, or literal at all. As long as the uncertainty range includes 0.5, it's OK, but merely a test of how much we know as a fact as opposed to intuitively. And at that, the equation can surely be blown up further. Why would it be optimal?
> If you then look at those outcomes together, you find that in over half of them, we are alone in the universe.
Since we do not really know, anything but P=0.5 should imply incorrect prior estimates. That might be more insightful than whether alien life exists or not.
The words "long" and "evidence" are gross overstatements, but the claim is trivially true if including the Asian origin in "contact". While there is no definite proof for extended contact beyond that, there is no final proof to the opposite either.
The basics are easy to look up. There is plenty of time for exchange in the at least 4000 years of immigration from Asia through the Bering Strait before it almost completely submerged at a time when the first civilizations already emerged, among them chinese.
Still though: Mezo America is far from there in time and space; Grid layout is kind of natural, because only a few space filling polygons exist; The linguistic evidence is very weak at the very least because of the time span, isolation, the lack of written records and corruption of oral tradition.
The search space is huge. A few attractive artifacts may just be noise in the signal. All it takes to satisfy the claim beyond the initial exchange is a single successful explorer.
That does sound anxious (and one could read aggression into it, too). But there are so many more emotions below and on top, that maybe they serve at least some coordination effort. Here you exaggerate the emotion for display, but you virtue signal that you are concerned and signal the concern itself, not to be anxious. So it's a reflexive emotion.
Such things remind me all too often of the fix point combinator and what not. But I'm anxious to miss the point, because at some point logical reasoning doesn't work anymore and leads into a trap, e.g. in case of greed.
What does that look like? A SAT problem takes a bunch of unknown variables (v_1, v_2 ... V_n) and logic operators (''not, and, or'' for example would be enough) to form a formula that combines these operators and variables, to asks us for an assignment (traditionally ''true'' or ''false'') to each variable respectively, so that the formula is satisfied; For example given the rules of sudoku find a filled sudoku. Or for xx+nx+m=0, and a given n and m, find x.
Then what is the model theoretic problem? Is it, if f(a,b)=((a and not b) or (b and not a)) is satisfied by e.g. (a=1,b=0), then we want to know all configs that satisfy it? The way I understand your post, you are saying we want to know if all combinations of a and b over {0, 1} satisfy the formula. I'm not sure that's not the same thing from a different perspective.
I started a course on abstract algebra once, but actually I am still limited to boolean logic. while they mentioned Galois Theory, functions as points in a metric space, graph coloring problems and many things that sound interesting but quickly have me getting lost in details. It's the same effect as with other machine learning ... coff coff.
A picture of a function, its derivative and the notion, that one function shows the other's tangent's slopes, is all that's needed, that should fit in a high-school curriculum especially in physics.
But you are going to hear it anyway if you are going to study.
It's easier if you consider that you and the whole galaxy are moving around the universe at 10% of light speed and that it's not exactly you who moves, but the space bending around us, just like time.
On yet another point, you might imagine time as a projection of the space. We like to think of time as the domain often enough, but perhaps it's the opposite. After all, some event needs to takes place, for a time step to be noticeable.
In other news, it's the Stabile Seitenlage [1] from first aid! https://en.wikipedia.org/wiki/Recovery_position