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

different golden ratio

[vardissakheli.livejournal.com]

Hmmmm, for some reason changing the golden section makes my brain hurt much faster than changing pi. It must have to do with the way the golden section shows up even when all you're talking about is adding whole numbers (as in Fibonacci series). I guess it's easier for me to deal with the thought of impossible twists lurking in a big, squishy, multidimensional space than in a few poor little discrete integers.

This also reminds me of a crackpot paper posted down in the physics labs about Planck's constant varying with wavelength that I remember reading, and realizing after poking through the guy's equations that there was a much simpler way to state his premise that he somehow never got around to saying: Photons have rest mass. That would certainly be a tidy explanation for why the sky is dark, wouldn't it

Re: different golden ratio

[jwgh]

Well, the thing is that you can define π in ways that don't have anything (at least on the surface) to do with geometry. For instance, the normal (Gaussian) distribution is:



and you could use that define π if you really wanted to.

(Now that I think of it, I think that the book about the guy who finds out he's God also has him change the normal distribution at one point, with the result that people start suffocating when all of the air in a room suddenly collects in one corner, etc.)

Alternatively (if somewhat artificially) you could define pi as follows:

π = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...

You can also take the route of defining the sine function from looking at e^x for complex x, then finding its period (2π), which again has nothing obvious to do with geometry. (If some alien civilization did this, I imagine that some mathematician might have been surprised to discover that half the period of the sine function turns out to be exactly the ratio of a circle's circumference to its diameter!)

It's unclear to me whether these things are also supposed to change when people talk about changing π. I would expect not and that what's being talked about is the ratio of a circle's circumference to its diameter. Things like Brunner's mentioning that even if π has a different value it has to be irrational make it clear to me, though, that in at least some cases there's some confusion about what's what.

I'm interested in reading that Egan story.