Logic/metaphysics question

[Prozac the Robert]

Is it possible to imagine a consistant universe where the rules of mathmatics are different?

Could pi for example be 3.14167 or something like that?

Could right angles be 89.7 degrees?

The resulting universe doesn't have to be anything like ours, it just has to be consistant.

[Ariphaos]

A sufficiently warped universe (elliptic or hyperbolic) might have some funky geometry to it (what effect that would cause on small scales I don't think I could say), but playing with math itself is a bit more difficult.

Pi itself is the result of things like the Viete formula, Leibniz formula, Wallis product, and other approximations. To whit, our Universe makes a certain morbid amount of sense as it is. The same is true for other mathematical items.

You would have to somehow build a self-consistant set of rules that did not describe our Universe. Euclid's Postulates for planar geometry and Peano's axioms for arithmetic. I don't know if there's a good, easily readable source for every axiom out there.

My gut feeling is that it's impossible, it'd be like an Escher universe or something, defying modern logic.[/url]

[Ariphaos]

Err, meant to mean, there are more than just Euclid's and Paeno's for various mathematical systems, and both are initially incomplete.

[Master of Ossus]

Is it possible to imagine a consistant universe where the rules of mathmatics are different?

Could pi for example be 3.14167 or something like that?

Could right angles be 89.7 degrees?

Degrees are merely arbitrary measures of angles defined by convention. You can also measure angles in radians, or make up your own units. For that matter, numbers themselves are defined by convention. However, pi must be an irrational number--there's proof for that.

[wolveraptor]

Could right angles be 89.7 degrees?

Then, according to humans, it's not a right angle by definition. Unless in their system of measurement, 89.7 "degrees" is the angle between two perpendicular lines. So essentially, no.

[drachefly]

Pi is an artifact of the metric. If you start working in the Taxi metric, suddenly the ratio of the circumference of a circle to its diameter is 4. You could call that pi.

That said, if someone in that universe began doing mind-games and decided to consider the euclidean metric (what we consider normal), then they'd get the same Pi we do.

[Kuroneko]

Is it possible to imagine a consistant universe where the rules of mathmatics are different?

Not consistently. Mathematics should be able to deal with your proposals below.

Could pi for example be 3.14167 or something like that? Could right angles be 89.7 degrees?

Sure, but mathematics doesn't need to change--it would just be a different mathematical system. If π is defined via the the taxicab metric, then π = 4. But for a general metric (since it's implicit in the question that π is not defined specifically in regards to Euclidean geometry), there is nothing to guarantee that the ratio of circle circumference to radius is even a constant, much less the familiar π.
[Edit: taxicab circumference]

[Sriad]

It's easy, just get near a black hole or other big object and space-time will be wonky enough that the value of pi will change significantly. Of course, tidal stress will rip you apart, but sacrifices must be made for science!

You can also (hypothetically) get space curvature the other way with exotic matter, but this mini-post is just about observable phenomena.

[dworkin]

Ian Stewart (English maths prof) seems to have no difficulty doing this in Flatterland. Come to think of it niether did Edwin A Abbot.