Strange

Dimensions are the number of pieces of information you need to uniquely locate a point. For example, if you want to meet someone, then you will need to specify three spatial dimensions (e.g. latitude, longitude and altitude) plus the time = 4 dimensions. Dimensions above these (as far as we know) only exist as mathematical abstractions. The mathematics of string theory requires 10 (or more?) dimensions and there are various reasons (excuses ) why we can't see them: the most common being that they are wound up really small.

It might be that there is nothing to decode. It might just be a work of art and/or clever joke. People do create completely artificial languages, though. There are people (conlangers) who do this as a hobby. https://en.wikipedia.org/wiki/Constructed_language

https://en.wikipedia.org/wiki/Biomimetics No one is saying that you can't use analogies for inspiration. Just that they are of limited value, beyond getting you started. The same could be said about taking a shower: that is where many people get their ideas, but you can't replace science with showering (or analogies).

I think that is kind of the point.

XKCD is (as always) ahead of you. I hadn't seen this one before: I'm not sure how you can relate this analogy to science, though.

But it highlights one of the problems with Mike's approach (and one that we often see on fourms), where people take an analogy like the "rubber sheet" and then extrapolate wildly from it, as if it were the actual model. So people ask things like "what is space-time made of" or "can you tear space-time" or "what is pulling things down on the rubber sheet of not gravity" (and sometimes, "therefore GR is a circular argument and must be wrong").

I assume that is a result of the angular momentum of the black holes (kinda like a gyroscopic effect but even more complicated).

This is similar to the idea of "code talkers" - using people with a really obscure language for secret communications. https://en.wikipedia.org/wiki/Code_talker You could do this with a completely invented language but it has the problem that it relies on "security through obscurity". And the problem with that is that it is always crackable somehow. Because the two people (at least) who are communicating have to know the language, there is the chance someone else will know it. In the case of a made-up language, for example, there is a danger that one of the users might keep a written dictionary because they can't remember all the new words. If I wanted to write a story where someone countered Artemis Fowl's invention, I would plant a baby spy with them, as babies are really good at learning new languages with relatively little exposure! Actually, maybe using a completely made-up language like this is closer to the idea of a one-time pad than code talking ... https://en.wikipedia.org/wiki/One-time_pad https://en.wikipedia.org/wiki/Security_through_obscurity (BTW I have never read any Artemis Fowl books - I'm waaaay too old - but from what I have seen, I wish they had been around when I was young!)

I don't know if you can treat it as a wave for each BH. It is a result of the entire system; I guess the results for a binary black hole are quite different from a single black hole going in a circle (which is physically impossible, so no one will have simulated it!) The barycentre is not a real thing. It is a result of the interaction of the bodies, not a cause of anything. In some models, the barycentre might be used as a reference point and so can't move, by definition. The first video on this page shows a system with a large amount of precession, it is not clear if that causes the barycentre to shift. http://www.black-holes.org/explore/movies

Kekulé said that he dreamed of a snake swallowing its own tail (ourobouros) and that this "analogy" allowed him to solve the problem of the structure of the benzene molecule. There may be a few other examples where an idea ("analogy") has stimulated the development of an idea or solved a problem. But they seem to be very much in the minority.

Yes. That is what "visible universe" (more commonly, "observable universe") means. Remember my suggestion before? When you feel like saying "Is it correct" stop yourself and remember that it almost certainly isn't. It is just some nonsense you have made up. Because it might not be. The fact that all this was explained a few posts previously. And, from what I remember, about 100 times before that. Does the phase "finite but unbounded" ring any bells? No? http://www.bartleby.com/173/31.html

There is absolutely no reason to think you wouldn't see exactly the same sort of thing we see from here: gas, dust, stars, galaxies, galaxy clusters, large scale structure...

What does it mean for expansion to move in a loop? How can multiplying all distance by a constant factor "move in a loop"? You are talking nonsense. This has been explained to you so many times already. Do you really need to be told again? You appear to be incapable of learning anything. Please show the mathematics to support this claim. All I see is meaningless nonsense from someone with zero knowledge.

In reality, I don't think things have changed.

It does. Why do you think it doesn't. We don't. It is just arbitrarily added in. It is measured (as you have been told but have chosen to ignore). Unlike you, science doesn't just make stuff up. It uses the evidence.

And you are wrong. There are centuries of mathematics behind this which you need to catch up on. You cannot describe the curvature of space-time in terms of a radius. https://en.wikipedia.org/wiki/Riemann_curvature_tensor https://en.wikipedia.org/wiki/Curvature#Higher_dimensions:_Curvature_of_space http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity/

It is because gravity is caused by the curvature of space-time. At the "surface" (event horizon) space is so curved that there is no path that leads out of the black hole. Note that the "escape velocity" description is quite popular. But it doesn't quite work. For example, you can throw a rock from the surface of the Earth at less than escape velocity and it will go some way and then fall down again. So that suggest that light could temporarily escape a black hole before being pulled back. It can't.

It doesn't. So, for example, if the Sun suddenly turned into a black hole nothing would change; we would continue to orbit it in the same way. (Well, it would get very dark and cold ...) The difference is that you can get much closer to a black hole than you can an "ordinary" object of the same mass.

I don't think it would. Adding more parameters (spin, more than one black hole, etc) will make a difference but I don't think it will make a very great difference if the masses are the same or not.

How do you work out if it is a good idea or not? Analogies might give you a seed, a germ of an idea. But to turn that into a testable hypothesis and maybe into new science you have to rapidly move beyond the analogy. (Until you come to describe the idea to the popular press.)

The they are no longer analogies. Perhaps you are not using analogies in the usual sense. Perhaps you need to define what you mean by "analogy".

Does that help? I don't think you can describe that in terms of intrinsic curvature; it needs to be embedded in a higher dimensional space.

These may be animations of black holes of equal mass. Does it say they are not? There is one (on the black-holes.org site) that shows two black holes with very different mass and that clearly shows the smaller one flying around the larger one (which wobbles slightly). And, please, you are not seeing errors. You cannot tell me that your "gut feel" about what these simulations should look like trumps thousands of hours of programming work by experts and further thousands of hours of supercomputer time.

Where does that say anything about 3 dimensions? (Note that all the equations for the 2D curve are in terms of x and y, not z.) BTW: I assume you are referring to this page: http://mathworld.wolfram.com/GaussianCurvature.html Because it is talking about curvature, not plane surfaces.

Although genetic algorithms were devised by analogy to the way evolution works (+1 for analogies) the process you describe above has nothing to do with analogies. The solutions have to be calculated (mathematically) and then scored (mathematically) to work out if they should survive the next round, etc. This is just another example of things you can't do by using analogies (you can't program a computer using analogies).