I thought these were great. It's true that they aren't really understandable without their titles, but I don't think that is an overly negative facet. It is still the case that so much is done with so few ingredients.

Thank you so much for the explanation and link. And nice work on a great visualization.

Ah, that may be so; I never did the full calc myself. The plot above is only including the gravitational and centripetal terms, according to the author's code. Like you say, velocity dependence is missing. What frame of reference makes all this clear?

That's the usual wisdom, and what I had always thought. But I've seen a number of reports on phenomena suggesting otherwise. The thing that comes to mind at the moment is photosynthesis:

Bam, a little research clears this up. According to Wikipedia, L4 and L5 are only stable if the ratio of the two masses is at least 25 (roughly). That's true for the Sun/Earth and Earth/Moon system but not true for the values the author used in the plot (according to the code posted in the original article). So I…

I see now that the original author mentions that the two points to the sides (in the reddish areas) are L4 and L5. I still can't for the life of me tell from the graph that they are stable, though.

I just noticed that this article is a little sloppy in its use of the word "stable." All of the Lagrangian points are equilibrium points but they are not all stable. The term equilibrium point means that a particle placed there will not deviate unless pushed away. Stable means that even if it's pushed away, the…

Yeah, I know the physics, I'm just saying I'm finding it hard to read the graph. Which of the black dots are L4 and L5? Because I can't discern any bowl shaped regions.

I think you are confusing a stable equilibrium with a general equilibrium. All five of those black dots are equilibria, meaning something you put there will stay. A stable equilibrium means not only will the particle stay if exactly at the equilibrium point, but also that if you displace it slightly, it will move back…

You can do it that way if you want. All you really need to do is find the minima of the effective potential (potential energy plus a term that encompasses the centripetal acceleration). If you look at the full article, he has a link at the bottom that includes his Mathematica code. That might give you a better idea of…

Visually, it's hard (for me, at least) to tell that any of the equilibria are stable.

Yeah, I had a bit of deja-vu there as well. To be fair, it's not unreasonable that some as-yet undiscovered mesoscopic quantum phenomenon occurs in our brains. It seems that such phenomena are being found to be more common than first suspected. But that said, it doesn't really add any deep meaning to consciousness if…

I starred your comment assuming the use of "frack" was deliberate.

I opened the comments precisely to see if someone made this joke.

Anyone who thinks the idea of evolution is "functionally atheistic" has very little confidence in their god's capabilities or very little idea of what the theory of evolution is.

Often the first refuge, too. Depends on the kind of scoundrel.

A rule of thumb: if you don't have a degree in physics or a closely related discipline then you probably shouldn't use quantum mechanics to explain anything. Even if you do have such a degree you should be quite cautious in your discussion, because you probably still don't understand it all that well.

Efficiency is usually defined as the ratio of output divided by input. You can increase efficiency by holding output fixed but lowering input.

Did anyone else notice the icons on right labeled as "Goal" and "Way to Goal" when you're in the turbolift? This is supposed to be a work in progress so maybe there will be objectives and interactivity added at some point?

Cool, thanks for the recommendations.