3 ms·

Best argument for 𝛕 – when we meet aliens, they'll laugh at us if we're still using C/d. "No no, we were transmitting on hydrogen * 𝛕!"

gizmo686 13y ago
I don't think so. The stupid thing about pi is that it is the only place in math that you ever talk about the diameter of the circle, everything else is expressed in terms of the radius. Admittedly, the radius does feel like the natural way to define a circle (all points r away from the center), however that is not the only way to define a circle, and we have no other intelligent species to use a reference for how objectively natural that way is.
- schiffern 13y ago
  We're saying the same thing. I'm using that as an example of why it seems like radius is the right one. Of course we have no examples, but we do know that an alien intelligence would be free from the historical accidents of humanity. "Mathematics is the only truly universal language", as Sagan would say. Here's a similar argument: In mathematics, do we measure angles in radians or diameterans? Why is that? >that is not the only way to define a circle Ok, let's hear 'em! What rigorous definition of a circle is more simply expressed in terms of diameter? The only one I can think of is, "the smallest volume shape that can contain a length D line segment at any angle", but that seems contrived to me. I shutter at using the solution to optimization problem as a definition, except when there is no other choice. What's worst, it seems like a trivial derivative of the radial definition, just with extraneous concepts tacked on.
  - gizmo686 13y ago
    The most natural, diameter based, definition I can think of is, for any given point on the circle, the distance to the farthest point is a constant, D. You probably need to add additional restrictions to make this rigorous (such as requiring the circle to be form a continuous, closed loop). You could also imagine rotating a line segment about its center. This has a nice sense of symmetry, as we are rotating about the center, not an arbitrary end. This also implies a generalization to off center rotations.

gizmo686 13y ago

I don't think so. The stupid thing about pi is that it is the only place in math that you ever talk about the diameter of the circle, everything else is expressed in terms of the radius. Admittedly, the radius does feel like the natural way to define a circle (all points r away from the center), however that is not the only way to define a circle, and we have no other intelligent species to use a reference for how objectively natural that way is.

schiffern 13y ago
We're saying the same thing. I'm using that as an example of why it seems like radius is the right one. Of course we have no examples, but we do know that an alien intelligence would be free from the historical accidents of humanity. "Mathematics is the only truly universal language", as Sagan would say. Here's a similar argument: In mathematics, do we measure angles in radians or diameterans? Why is that? >that is not the only way to define a circle Ok, let's hear 'em! What rigorous definition of a circle is more simply expressed in terms of diameter? The only one I can think of is, "the smallest volume shape that can contain a length D line segment at any angle", but that seems contrived to me. I shutter at using the solution to optimization problem as a definition, except when there is no other choice. What's worst, it seems like a trivial derivative of the radial definition, just with extraneous concepts tacked on.
- gizmo686 13y ago
  The most natural, diameter based, definition I can think of is, for any given point on the circle, the distance to the farthest point is a constant, D. You probably need to add additional restrictions to make this rigorous (such as requiring the circle to be form a continuous, closed loop). You could also imagine rotating a line segment about its center. This has a nice sense of symmetry, as we are rotating about the center, not an arbitrary end. This also implies a generalization to off center rotations.