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Life being out there is a significantly different proposition than encountering it face-to-face (or whatever passes for a face), since that also requires temporal and physical proximity.

I've mentioned this idea before, as a way of producing fish, but it could also fix huge quantities of carbon onto the ocean floor if done at scale. You have a specially designed ship stationed at a very non-productive part of the ocean. ( most of the world oceans are ocean desert ) The ship controls a robotic electrical pump, on the ocean floor. The pump stirrs up sediment, and pumps it to the surface through a thin (but large diameter) polythene tube. When the sediment meets the surface, you get a bloom of algae, which naturally happens whenerver water from the depths upwells. The algae are then the bottom of a food chain, that supports vast clouds of plankton. Besides being fish food, the plankton fix CO2 in their bodies which sinks to the ocean floor when they die, fixing CO2 for thousands of years in a natural way, with no possibility of it getting released in the future. It eventually becomes limestone rock after miliions of years. The money for the pumping could eventually come from fishing licences, taxing the catch that results from the proliferation of fish, in an area where previously there were none. So it could be self financing, once running. So a win-win situation, with carbon being stored and food being harvested from what used to be ocean desert. I realise that this will never happen because of politics and investment problems, but I'm pretty sure it would work. Maybe if the climate really does start giving trouble, it might come into the picture, when the politicians start to panic.

Are they right? Personally I wonder if they haven't already found it in New York https://www.bbc.co.uk/news/av/world-us-canada-66970292

The physicist–philosopher Ernst Mach (1838–1916), who spoke of “the artificial hypothetical atoms of chemistry and physics,” never accepted their existence. As late as 1916, shortly before his death, he declared that “I can accept the theory of relativity as little as I can accept the existence of atoms and other such dogmas.” This goes to show that a scientist can maintain his own principles, bravely holding out against a wide consensus of the scientific establishment, and still be wrong. Weinberg, Steven. Foundations of Modern Physics (p. 58).

I think life outside the Earth has already been found, a new look at old data mixed with new data makes the first Mars landers look for life in a new light. A growing tide of researchers are of a mind that we misinterpreted the data and the landers detected life after all. https://www.space.com/nasa-may-have-unknowingly-found-and-killed-alien-life-on-mars-50-years-ago-scientist-claims

Define head? For instance, a human head is the center of our intelligence, while a squid head is only, roughly, the center of it's body. As for the topic, humanoid alien's are a human concept/conceit; the chance that equivelent intelligent life is our doppelganger, is astronomically (pun intended) small...

Here is the Newton's original drawing, which the banknote artist has copied: How is your Latin? Anyway, the artist has added the background and in it, he placed the Sun exactly in the center of the ellipse, where the major and the minor axes intersect (the point C). This is where the Sun cannot be. By the Kepler's first law, and per Newton as well, the Sun is in one of the foci (the point S). PS. In the earlier hint ("Hint: focus on the geometric drawing.") the word "focus" was the hint.

That photo does seem pretty improbable. Meep meep.

Great summary. I agree with Genady and Markus. Connections are quite independent of metric in general. It's one of the hallmarks of Einstein's GR that the connection is a metric one. Thereby the words "metric connection". Rods haven't been a standard for quite a while. A gauge fibre bundle is an example of a metric-less connection. The gauge field A provides the parallel transport along the manifold, while the gradient of A gives you the parallel tranport on the fibres \( \Psi \), the whole structure is (locally) a product MxF (M=manifold, F=fibres), but with no metric for the \( \Psi \)'s. Sometimes I have a problem understanding what the OP sets out to do. This is one of those times. Before one starts thinking about physics, one should get a clear picture of what needs to be solved. Going back to metric connections in order to try to solve a problem GR doesn't have doesn't look promising. Things that are considered solved are considered solved for a reason or, should I say, for a bundle* of reasons. *

The chance of someone who has no idea about current theories of abiogenesis correctly calculating the "probability of life" is approximately zero.

The main point was that you did not substantiate your claim - a long-standing pattern - and stated a conclusion without actual evidence or eliminating other possible explanations. IOW, not providing any proof and yet claiming that something was proven. No links, not even to the infographic you pisted.