Annoying science fiction device detected

[jwgh]

I started reading John Brunner's Meeting at Infinity. Early on in the book we encounter that hoary old bit of science fiction nonsense, the inconstant π:

Pi, it seemed, was invariant. However, certain deductions from curved-space mathematics indicated conditions under with it would assume values different from the familiar 3.1416. It would remain an irrational number of course. But the physical conditions for altering its value could be described.

So the guy creates a machine that creates an area where the value of π is different, and this turns out to be a way to reach alternative universes whose history differs from Earth's proportionately to the difference between its value of π and ours.

I think that this sort of thing comes from a misunderstanding of noneuclidean geometry (or, I suppose, a desire to annoy mathematicians). There are geometries where if you measure the circumference of a circle and divide it by the diameter you'll get a number other than 3.14159265... This doesn't change the value of the number π, though, and it has nothing to do with π's irrationality. It makes about as much sense to posit a universe where 2 has a different value.

Anyway!

Comments

[sunburn.livejournal.com]

In _Eon_ by an author I can't recall (Greg Bear? Dunno) some of the characters enter The Way, an apparently infinite passage that extends into another dimension, or something, from inside an Earth-orbiting asteroid. At one point, I recall that the characters encountered a sort of dimple in their path, and, entering it, found that their instruments were reporting a different value for pi. Okay, we get it, as if an infinited tunnel extending out of a finite asteroid isn't odd enough, something's deforming space or something. Here's my question:

I don't know about the unanticipated transdimension journeys you go on, but what're the odds anyone bothered to invent, much less pack along, a pi-o-meter? I'm thinking we've got the tricorder syndrome.

[mmcirvin.livejournal.com]

Also, in a curved space the ratio of circumference to diameter depends on the size of the circle. In the limit of a small circle it converges to pi.

One case I can think of where that doesn't happen is in a space with a conical singularity, like a cosmic string. Then it just depends on whether the singularity is inside the circle.

um, spoiler warning

[pobig.livejournal.com]

A gee-whiz science book I read ages ago had a bit about how a fly landing in a circle the size of Trafalgar square or something exerts enough gravity to change the 30-somethingth decimal place of pi.

I'm also reminded of Greg Egan's story "Luminous", about some mathematicians who discover a 'defect' in mathematics, away out in the realm of very very large numbers, and find ways to manipulate the border between standard and nonstandard mathematics, and of course soon discover that there are concerned parties on the other side...