Tag Archives: 2D space

Flat Space of the Torus

Flat Earth!

To describe how space could be flat, finite, and yet unbounded, science writers sometimes use an analogy involving the surface of a torus (the mathematical abstraction of the doughnut shape). Such a surface has no boundary — no edge.  And despite being embedded in three-dimensional space, the torus surface, if seen in terms of compensating surface metric, is indeed flat.

Yet a natural issue people have is that the three-dimensional embedding is clearly curved, not flat. It’s easy to see how wrapping a flat 2D sheet into a cylinder doesn’t distort it, but hard to see why wrapping a cylinder around a torus doesn’t stretch the outside and compress the inside.

In fact it does, but there are ways to eat our cake (doughnut).

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Expanding the Middle

My blog has such low engagement that it’s hard to tell, but I get the sense the last three posts about configuration space were only slightly more interesting than my baseball posts (which, apparently, are one of the least interesting things I do here (tough; I love baseball; gotta talk about it sometimes)).

So I’m thinking: fair enough; rather than go on about it at length, wrap it up. It’ll be enough to use as a reference when I mention configuration space in the future. (There have been blog posts where I couldn’t use the metaphor due to not having a decent reference for it. Now the idea is out there for use.)

And, at the least, I should record where the whole idea started.

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SF or Fantasy, Pick One?

It’s Science Fiction Saturday, so today I want to consider a fairly common question a fan might encounter: “Science Fiction or Fantasy?” The implication is that one tends to exclude the other. In these polarized times, it can amount to a declaration of your tribe.

One problem is there’s a spectrum from hard SF to pure fantasy with everything in between. But let’s take them as two legitimate poles and consider the question in terms of configuration space. (See posts #1 and #2 if you need to catch up.)

I think you’ll see that using a space give us a new take on the question.

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