anvay could not have downvoted you, as your comment was a reply to them, so no, they didn't downvote you for that.

And then in reply to what you said:

  >> It is locally convex in the sense
  >> that it has no loops

  > Of course it has loops. But in the
  > scale of the drawing, the loops are
  > lost due to the vast distance from
  > Earth/Moon system to Sun.

By my way of thinking, this is wrong. Looking at this from the Sun-centric point of view, thinking of the Moon's path in space in the Sun's frame of reference, the path is convex. Take any finite straight line (no, I'm not going to go into General Relativity) whose endpoints are both, at some point, between the Moon and the Sun, then every point on that line is such that it is at some point between the Moon and the Sun.

In other words, the path of the Moon is convex. By any common usage of the language, that means it has no loops.

I can't downvote anything yet, I am new :)

Yes the wired article is a better explanation(which btw I posted in a comment below). I was however struck by just the no loops part which you rightfully mentioned. It is so counterintuitive. But later I found that the moon is slower around earth than I had assumed(~27days), that was causing the problem for me.