Genady

I think that Right and Wrong, including their application to torture in general or in specific cases, is a matter of personal taste. The latter develops under effects of individual, social, and environmental factors.

do you formulate a rational explanation? - no, because there are many rational explanations possible Do you ignore it? - no, I do not Do you look up research on such occurrences? - not anymore Do you talk to somebody about it? - yes, sometimes Do you accept it as paranormal? - no, because I don't know what it means. When all these and more of this kind occur most of the time, it's a terrible medical condition. I happened to have a very personal experience of this with my close family. Very tragic. She flew more than 3000 miles once to warn me personally of a danger, because all other means of communication were already affected...

Then, why do you need to change the Newton's law at all rather than hold it as it is, i.e. GMm/r2? See what the consequences are and change something else if needed.

Agreed. "From the initial assumption" is a key phrase. We can make ANY physical assumption about a 2D universe. What would stop us? I wonder, why 2 dimensions in space. Wouldn't it be much more exciting to consider a universe with 2 dimensions of time?

Why is this in Biology forum?

I didn't say anything about proof being required or offered. The above sentence has nothing to do with my claims.

No, the G.M.m.ln(x) is NOT a solution for the Newton's law. The -G.M.m/x is. My question is, what is wrong with it? In 2D, I mean. This is what I mean by "the idea that the Newton's law holds as is."

Our ability or inability to prove something or to construct something in math doesn't affect its existence. The same with ethics. I am not religious. Just logical. The existence of a "chart" mentioned by @Peterkin above, as a list, set of rules, result of a procedure, ..., is "Genady's conjecture." I don't think it is OT. It is my answer to the OP question.

I don't care about Plato. Mathematical sense is not the same as philosophical sense, whatever that could mean (as I said, I don't care.) It is very specific. For example, the number pi has a one billionth digit. That digit exists. It is unique. It doesn't matter if we have it calculated already or not. Being or not being a human creation also doesn't matter for the existence. An equation, for example, might be a human creation. Nevertheless, it has or it doesn't have a solution, regardless of humans. Same with ethics. A Platonic ideal is not required. Isolation is not required.

And, answering my question would be nice, too. Here it is again: what is 'wrong' when you try to integrate the Newton's gravitational force? it seems to obey all your conditions.

None of the above. It exists in mathematical sense. Like a solution of an equation exists. Regardless we know it or not.

No, I don't have such a chart. I claim that such a chart exists.

The concept is not movable. A set of torture cases is large. Some of them fall into the constant concept of Wrong, the others fall into the constant concept of Right.

I consider myself, in this respect, a theoretical ethicist. And torture in my fixed, non-negotiable notion of Right and Wrong, is not always wrong.

This looks like an opinion survey rather than a discussion. Then, I have an opinion, too: Yes, it is not always wrong / unethical / not-right / immoral.

What is wrong when we try to integrate?

in this case, for your 4 statements to hold, you have proved that the idea of field "dilution" can't hold. But what is wrong with the idea that the Newton's law holds as is?

But, as you and @joigus said, Newton did it from the Kepler's law, not from the idea of field "dilution" that you've described in the OP. If you want to do it like Newton did, you need to start with a 2D version of the Kepler's law.

How many solutions like this do you want? Here is one, for example, -G.M.m/(ex-1). Or, -G.M.m/x4

This is incorrect. Force is a gradient of potential energy and its direction is the direction of the gradient. Does not matter what a sign or even the value of the potential energy is, only its gradient. Again, this is incorrect. Since the force is a gradient it would change direction only if the gradient changes direction. Changing the sign of the potential energy doesn't change the direction of force.

In my response above I refer to the OP "fantasized" gravitational force that is inversely proportional to distance rather than to distance squared. Not to the Newtonian gravity.

It will take an infinite amount of energy to remove a body from any given position to infinity.

I thought you got the answer, even more than one. Maybe you have missed this one, for example:

Not necessarily. The 2D world doesn't have to be flat.

Not necessarily. Imagine a 3D sphere with the gravitating mass in the center and the gravitational field lines going from there. The force goes inversely proportional to the distance squared. Now cut the sphere in the middle and look at the cross section. This gives you the 2D image of the field. The force still goes inversely proportional to the distance squared.