Genady

Everything you have mentioned is not difficult to imagine. If anything, it is too easy to imagine. Also, it is not difficult to imagine hundreds of other, unmentioned possibilities. This is what makes it idle for me. Regarding an intelligence of some form with the ability to do so with us having no means of controlling their/its decision or the outcome, what difference does it make if its name is HAL 9000 or Putin?

50 years ago? 1973? IBM360 and others? Oh, you are so wrong! Yes, my answers above apply to these abilities in today's machines. But you don't need that much to kill us.

To me, to you, to any healthy human being I've ever met. Yes, I don't think that any machine of today is capable of acquiring such intelligence. They can very well imitate some aspects of it, though, and even can be better in them than the original. "Machines" of the future? I have no idea.

What's even more interesting to me that it is so not only with science studying reality -- whatever that is -- but rather it is the only modus operandi we use to deal with reality, throughout our lives.

If you mean a human-like intelligence, no. Because I know how computers work.

To ignorant people today, it is also magic and beyond understanding. To knowledgeable people 100 years ago, no.

He was a good professor. It was not a topic of that class, but I'd add that: Rational numbers, integers, or natural numbers are in no way more real than real or imaginary numbers.

In respect to scenarios considered in the OP, yes.

a3) One of my professors once said something to this effect (I don't remember exact words): Imaginary numbers are in no ways less real than real numbers.

This is art. There is much more to artist's expression than how the world looks or how brain recognizes patterns. Another example to enjoy: o'keeffe art - Bing images

When I was a teen and science fiction literature was in bloom, all these and other scenarios were considered. As to me, humans in 1000 years from now are as interesting as humans 100000 years ago. Very limited personal relation.

I don't understand it either, as shown by my example of zooming in to the "surface" to see a cloud of molecules leaving the water and evaporating into the air. There is no well-defined surface of a body of water. Now perhaps you are thinking of surface tension, but still, the analogy is strained. If you zoom in, you see molecules bouncing around. You can never point to any one collection of molecules and say, "That's the surface." Before you're done speaking, some of those molecules have evaporated into the air. I didn't mention molecules or atoms and I didn't mean to relate to a physical structure of water surface in any way. I could talk about a table surface or a mirror surface as well. The point was purely geometrical: to consider a relation between two-dimensional surface and three-dimensional layer. Thought it might be easier to visualize. But, if analogy doesn't work, ignore it.

That is a perfect analogy. Removing 1 from [0, 1] is just like moving the top layer of water as well as its surface. That is why this does not make sense to me geometrically. The numbers/objects are like the H2O molecules. Remove the top layer and there should be a next layer of molecules, but there isn't. I am sorry you don't understand my analogy.

No. In fact, the mass isn't a component in the Einstein field equation. There are densities of energy and momentum, and their various derivatives.

The wrong is that you switched from discussing the post to discussing the poster.

I think they will not be identical. I don't think reducing them to single numbers for comparison would make sense. In any way, the effects are not linear, so I don't think the effect of the mass can be separated from the effect of the motion.

No revenge, but it is wrong that to my completely neutral comment with quotes from a dictionary you've responded with a judgement of me, personally:

In scenario B, the curvature is static. In A, the curvature changes in time. The moving object will affect the curvature in some non-linear ways.

Reimann spacetime curvature is tensor. Its individual components are frame dependent, but they transform all together in a consistent way. So, the tensor is frame independent.

The answers to these questions should be independent of reference frame. Perhaps it would be easier to consider the scenarios in reference frame of one of the objects, i.e., where one of them is at rest.

One example of all three is thermal equilibrium.

Removing a boundary point is akin removing surface from water. It is possible to remove a very thin layer of water from the surface, but it is not possible to remove the surface and to leave the water without a surface.

But we are fine with loosely defined categories in real life.

I think, the no. 1.

OK, let's explore it. Let's assume that a line segment always has an end number. What happens when we remove that number? There are two possibilities: 1. It is impossible to remove a number from a segment. It is only possible to remove some open range of numbers, however small it is, but not one number only. One individual number is not removable. Or, 2. If one number is removed from a segment, what's left is not a segment anymore, but some other kind of object.