I found it on a Discovery Magazine blog. Right next to the equation that graphs out a snazzy looking heart and under the brain scans showing brain areas deactivated by love (comparing maternal and romantic).

Roses are red.
Violets are approximately blue.
A paracompact manifold with a Lorentzian metric,
can be a spacetime, if it has dimension greater than or equal to two.

I’m going to google/wiki the individual words, but I’m not sure that’s going to tell me what’s going on. Is this Valentine’s Day oriented, like the rest of the article? Or is it just there because it’s an editing of a well known romantic poem?

The last two lines of the poem are a reference to general relativity, which has nothing whatsoever to do with physiology, psychology, neurology, endocrinology, or anything else related to love. And even at that, the “dimension greater than or equal to two” bit is redundant, since you couldn’t fit a Lorentzian metric onto anything less.

To go into more detail, a manifold is a continuous space. Basically, any set of points that you can describe via coordinates, where the coordinates are real numbers (as opposed to, say, just integers) is a manifold. “Paracompact” is just a way of saying that it has certain qualities, without which it’d be pretty pathological-- Physicists don’t even actually bother with qualifiers like that, since we always just ignore the pathological cases.

A metric is a way of defining distances within a manifold. For instance, in flat three-dimensional space, you could define the distance between two points as sqrt((deltaX)^2 + (deltaY)^2 + (deltaZ)^2), where deltaX is the difference in X coordinate values between the two points, and so on. A Lorentzian metric is a metric on a space of at least two dimensions, where you call one of the dimensions “time” and all the rest “space”, and where to get the distance, you add all the space parts together like in the Euclidean metric above, but where you subtract the time part. Metrics like this turn out to be very useful in describing spaces in relativity.

A spacetime is just what it sounds like: A manifold that has a space part and a time part. Which is pretty much implied by it having a Lorentzian metric.

[moderating]
I changed the thread title from “What does this mean?” to “What does this mean? [interpreting science poem].”
Please try to keep titles descriptive.
Thanks!
[/moderating]

Perhaps some would consider a Lorentzian metric to be possible on a manifold of one dimension, that being the time dimension and all (zero) of the other dimensions being the space dimensions? In that case, the last lines of the bit needn’t be redundant (although they do impute “spacetime” with the connotation that space has a positive number of dimensions, the very same connotation they would no longer require from a Lorentzian metric)…

Whenever I begin to start feeling ever so slightly smug about my ratio of correct answers (questions) to Jeopardy questions (answers), or a bit too proud about how well the joints in my newly-built greenhouse fit together (thanks, Pythagorus), all I have to do is read one of Chronos’ posts, and I am more than sufficiently humbled.

I wonder if neuroscientists have ever quantified or located where in the brain the "Say, wha…! response originates.

Whereas, all it takes for me to be humbled while watching Jeopardy is for them to get to one of the pop culture categories that they have every single round. I’m not omniscient, just specialized.

I’m probably as much in the “target audience” as you are, Chronos, and I thought it was kinda lame. Perhaps it’s meta-humor about how scientists can’t “do” love and poetry.