Heh. So, I've been playing with a physics problem (among others) for the last few months, and came to an answer just today. The answer, you see, is... 2 Heh. This is the type of thing that physicists find outrageously funny. OK, the question, that's going to take some time, but I'll give it a go. It has to do with hyperspace -- the theory of other dimensions besides our four of space and time. The game I'm playing is to try to come up with a geometric theory of everything. My strategy is to begin with Einstein's Geometrodynamics -- the exquisitely beautiful theory of spacetime curvature that so well describes gravity -- and extend it, in substance but not in form, to account for all other physical laws; in particular, the laws and particle zoo of the phenomenally successful Standard Model and Quantum Field Theory. So, I've got a lot of the pieces worked out so far. But for now I'll describe the one with the 2. It has to do with the five fundamental forces: gravity, electromagnetism, the weak force, and the strong force. Each of these forces is described by a set of vector fields -- each of which you can visualize as an infinite set of arrows, one at each point of spacetime. Now, to measure anything in curved spacetime, you need a standard by which to measure these arrows. So, for a space with N dimensions, one defines a collection of N arrows at each point to be the N unit length arrows all perpendicular to each other. This construction is called the "vielbein," which means "many legs" in German (according to Hop). These fields of N arrows, orthogonal and perpendicular, completely describe the intrinsic geometry of the space. So, for example, in four dimensional spacetime, the way these arrows stretch and squeeze together around a massive body completely describes the gravitational field, and thus how a freely falling body will move in the nearby spacetime. And Einstein's equations tell you what set of arrows are allowed, i.e. what partial differential equations the components of these arrows must satisfy. Now, really neat stuff happens when you consider spacetimes with more than four dimensions. Lets say, five. We assume that the fifth dimension is wrapped up on itself, so we don't see it without looking down smaller than we are able -- just like a garden hose looks like a one dimensional object, until we get up close and see that the surface is really more of a cylinder. So, to describe the five dimensional geometry, with one wrapped up, we need a fifth standard arrow. And, quite astoundingly, when we work out what Einstein's equations are for the four components of the fifth arrow that point along four dimensional spacetime, we recognize them as identical to Maxwell's equations for electromagnetism. :) So that's the magic of hyperspace -- we get the existence and equations of motion for all the existing force fields by assuming Einstein's equations and the existence of several extra wrapped up dimensions. Ah, but what exactly is the shape of these wrapped up dimensions, such that they produce not only electromagnetism, but the funny weak and strong forces as well? Well, since we're sticking by Al, they're going to have to satisfy his equations -- which takes work to check. But, it turns out, that all the forces appear if one assumes the wrapped up surface to be the product of a five dimensional sphere and a three dimensional sphere, with a circle divided out of it. Here "product" is meant as in "the product of a line and a circle is a cylinder." And the tricky part was figuring out just how to frickin divide by the circle. Now, this surface, S5xS3/S1 will satisfy Einstein's equations if and only if the radius of the five dimensional sphere divided by the radius of the three dimensional sphere is... 2

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