Genady

AFAIK, Riemann surfaces are not related to the Riemann hypothesis. Greeks were fascinated with numbers philosophically. As opposed to Romans, who built cities. As for the other questions, I'd like to know the answers, too.

Why not? In fact, the original version of the puzzle was a multiple-choice, and the choices were: I.e., originally, "Teresa's daughter" was the only correct answer.

Yes, of course.

What they can do is given. 5 ly in the planetary systems FoR.

The numbers I find are: 38 000 mph for Voyager 1, 196 000 mph for Oumuamua. What are your numbers?

A tribe of nomadic aliens is located in a planetary system that can supply them with sufficient resources to get to the next resource rich system. The next such system is 8 ly away, and there is only empty space in between. They can carry enough resources, a "load", to go 5 ly. They can make storages of any size on the way. What is the minimum amount of loads they will need to get to the next system? Is there a limit to the distance between systems that they can cross?

Oh, I see now what you mean. No, I don't think they would be interested to drop in and visit their "mines", i.e., planets. And I don't think that any aliens have been sighted on Earth. They would rather use robots. Like we do.

This was fun. Same to you.

A being adapted to low-g would have difficulty existing in higher-g environments. For a being adapted to much higher than 1 g, they might not have developed space travel at all, owing to the energy required to lift payloads into space. I was talking about evolution that occurs during the nomadic lifestyle.

And if they maintained this lifestyle for several thousand years, they might biologically evolve to better fit it, e.g., no need for gravity, radiation tolerance, boredom tolerance, etc.

I don't think it was a possibility, technically, financially, and logistically. Too fast, too short, too far, too late, too expensive ...

How obvious is that? Picking on Plastics | Smithsonian Science Education Center (si.edu)

Perhaps the "low metabolism" idea was bad. Let's drop it. The "nomadic aliens" idea still stands.

There are many kinds of Riemann stuff, pretty much everywhere in math. This specific stuff directly relates to Riemann geometry, and I don't know of a connection between this and prime numbers.

On one hand, we have only one data point for life. It does not mean much. OTOH, I've just added above,

I did not mean an analogy to trees at all. Just an example of long living organisms. (I don't use analogies and metaphors usually.) Even slow metabolism is not necessary, just a possibility. Another possibility is their natural ability for long hibernations. I'm sure there are many more.

I don't see why biological evolution would be correlated to the age of the universe. Constrained, yes, but correlated? I don't say that it happened, but I don't know why it couldn't happen (unlike the c problem.)

What do you mean "developed as us"?

Sure. To start with, I guess such aliens wouldn't be biologically anything like us, but rather organisms with an extremely slow metabolism. More like trees that live for thousands of years.

z should be equal to y+w rather than greater than. I don't have any idea how to calculate these dynamics, but thinking about an infinitesimal step in the process: A body rising by some small distance allows a small amount of fluid to move down, which releases some energy. It also creates a pressure difference on the wall causing it to move a bit, but this motion is not free as it works to move the water. The energy is somehow split between a small rise in the fluid column on the right and the kinetic energy of the moving fluid, but the wall can move only so that the sum of the latter two is equal to the former. As this equality holds at each infinitesimal step, it will hold at the end after all the steps are summed up.

Your solution is a bit different from the one mentioned before, but it seems to be the same in principle and will work as well. +1

Unless they are wandering aliens, without a mother planet, not sent from somewhere, but rather living in their ships, generation after generation, while moving from place to place. Nomadic aliens.

You can safely ignore W. It can be, in this ideal experiment, equal zero, because the wall mass doesn't play any role and can be equal 0. OTOH, the mass of the fluid cannot be zero, because in that case the body would not rise.

You're right, of course, +1 But what kind of trouble... At first, its answer was very impressive: "If Teresa's daughter is your daughter's mother, then Teresa is your daughter's grandmother. Therefore, you are Teresa's son-in-law or daughter-in-law, depending on your gender." Isn't it smart? Doesn't it demonstrate logical thinking abilities? To see if it in fact does, I've substituted Teresa->John, daughter->son, and mother->father, and asked the same question in this form: "If John's son is my son's father, then what is my relationship to John?" And the ChatGPT's answer was: "If John's son is your son's father, then John is your spouse or partner." Why? What happened to the logic? Of course, logic was never there. The "Teresa" form of the puzzle, verbatim, has been very popular on Internet several years ago. The search returns hundreds of thousands of links. So, it has been included in the ChatGPT training data. While for the "John" version all it could find was something about son, father, relationship... and all it could come up with was the stupid answer. Yes, stochastic parrot is a correct definition.