[raattgift]

> slinging general relativity equations

I'm sorry this instantly turned you off.

The only equation in my comment is the Minkowski metric which is the metric for Special Relativity, and should be familiar to everyone who has done any SR at all.

Moreover, it's just a a generalization of the Euclidean metric as follows:

The Euclidean interval for

  spatial
  dimension equation for Cartesian coordinates in flat space
  0         dS^2 = 0
  1         dS^2 = dx^2
  2         dS^2 = dx^2 + dy^2
  3         dS^2 = dx^2 + dy^2 + dz^2

What we do differently in spacetime is add in a term with the opposite sign:

  (mostly-plusses, flat spacetime)
  spacetime
  dimension equation for Cartesian coordinates 
  2         dS^2 = dx^2 - cdt^2
  3         dS^2 = dx^2 + dy^2 - cdt^2
  4         dS^2 = dx^2 + dy^2 + dz^2 - cdt^2

Which shouldn't really scare anyone who has done Euclidean geometry.

The interesting difference is this: in Euclidean space, straight paths are shorter than curved paths, but in flat spacetime, it is curved paths that are shorter.

If you prefer wikipedia, https://en.wikipedia.org/wiki/Spacetime#Spacetime_interval which you can edit, or perhaps you can add to the Spacetime page on the simple English wikipedia.

[ldp01]

gnaritas is being pretty hard on you and shouldn't resort to ad-hominem, e.g. saying you are terrible at x. I think you obviously care a lot about this topic and actually have a lot to offer.

I will offer a perspective on this exchange...

I think people who have survived many-many math based courses often have an immediate and aggressive response to diving into the minutae of a quantitative topic before they have grokked the intuition behind it. This is a defence mechanism built up from hours and hours of wasted time in lectures where the topic has moved on before the student/s have really developed the basics and are ready for the detailed stuff.

Hours and hours of wasted life.

When a person with this defence mechanism sees a noobie about to fall into the same horrible cycle, this will trigger some aggression. For example: downvoting your post- they are trying to protect the noobs.

So if you are interested in reaching as many people as possible, please don't give up. I think your teaching effectiveness could be improved by finding ways to engage people at their (lower) level of understanding and trying to help then incrementally improve their mental models.

[raattgift]

Thanks. That is an interesting perspective, and I understand it.

I hope you don't mind if I pick up your comment as an invitation to go even more meta than you. :-)

> if you are interested in reaching as many people as possible

I'm not sure I am, even if it's "as many people as possible on HN who open this discussion". I'm guessing that most people who will read down a thread on a topic like this have some interest in it, and probably have a little math, or some search-fu, or perhaps even a little physics, but little exposure to General Relativity (one can earn a Ph.D. in physics without ever having to walk through a comma-goes-to-semicolon exercise let alone deal with exceptions to that procedure, but I'm not writing for e.g. solid state physics Ph.D.s here and hopefully they already know how to look beyond an HN thread or Nature News link if they want to know more about SN-BH or similar stellar collisions).

However, I don't want to alienate people on either side of that -- neither the experts nor the enthusiastic-but-allergic-to-mathematical-physics readers.

> please don't give up

Thank you again. If you have any concrete suggestions (now or in some future thread) about how to help engage the latter group, I'll gladly read them.

However,

> before they have grokked the intuition behind it

the problem is that intuitions like "the shortest path between two points is a straight line" are based on Euclidean geometry, which is probably much more often taught rather than discovered by a student sua sponte, although once taught experimental validation is easy. But in Euclidean (well, Minkowski) spacetime, curved paths are shorter. I think that pretty much nobody would have any chance of discovering that feature of spacetime on her or his own, or intuiting it from planar geometry. However, it's easy enough to teach by explaining what a line element is, and what the line element of Minkowski spacetime is. Once that is absorbed and is familiar enough that reading and drawing spacetime diagrams isn't a chore, then one might expect intuitions like "one can resolve the twin paradox by observing that the travelling twin takes a more-curved path through spacetime than the non-travelling twin". But even there, people sometimes stumble on understanding that that statement is demonstrably true under any choice of coordinates, not just ones which hold the non-travelling twin at the spacelike origin (from which the traveller departs and to which the traveller returns) throughout. And even then, where does one's intuition take one when one or both twins experiences significant real gravity?

One option of course is to shrug off opportunities to try to write into words what one would normally describe using a formula. I'm sure that's not what you're suggesting (but others in this topic seem to).

Another is to give a reply that is neither correct nor detailed but which is at least more correct. Maybe that helps a little, but I doubt it advances anyone's understanding rather than be memorized as a slogan or factoid.

Yet another might be a pointer to a standard textbook. Since they tend to be chunky and expensive (and I can't even guess about availability at a local public library rather than a major reference library open to the general public), I'm not sure that's so helpful either, unless the pointer is to a pirate scan. :-)

Penultimately, this is unpaid pseudonomymous fun. I think ELIx (FSVO x) is a good challenge for the explainer too, especially for extremely abstract topics, otherwise why bother? From this perspective, what's a decent choice for "x" on HN? (We surely can agree that it will be different than "x" on e.g. physics.stackexchange.com; in fact I think that is close to your central point.)

Finally, in comparison to the previous paragraph other models exist, e.g. http://backreaction.blogspot.com/p/talk-to-physicist_27.html - I am reasonably sure Sabine Hossenfelder would be happy to negotiate on publishing a transcript or summary of a conversation on her blog or elsewhere (perhaps even as a comment on HN :) ) and I am even more sure the quality of her or her associates' answers will be better than mine.