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> (If you can't see that tau is conceptually a more fundamental quantity than pi, then you actually don't understand the point!) Well then I guess I don't unde

> (If you can't see that tau is conceptually a more fundamental quantity than pi, then you actually don't understand the point!) Well then I guess I don't understand the point. That claim is essentially equivalent saying that circumference is more fundamental than area. You may accept such a strong claim, but I certainly do not.

jessriedel 10y ago
It's not equivalent, but it's connected: circumference is "more fundamental" than area simply in the sense that 1 dimension is more fundamental than 2. In particular, when we build things up in higher dimensions, it's much more clearly done using a 1D primative than a 2D one, e.g., for the Fourier transform, there are powers of 2pi=Tau in any dimensions.
- nercht12 10y ago
  >> it's much more clearly done using a 1D primative than a 2D one Or you could just tell people that pi is the edge length of half of a circle. Pi and Tau are both 1-dimensional numbers that happen to be related to these things, so the argument really is silly. The reality is, we're going to have to pay some kind of intellectual debt in learning anything. So we keep teaching Pi. Suppose everyone switched to Tau. That would make all kinds of older documents inaccessible and harder to grasp, and we would be paying intellectual debt that way.
  - jessriedel 10y ago
    > Or you could just tell people that pi is the edge length of half of a circle. You can certainly tell them that, and they may even find it easier to remember, but it won't actually be the reason that one convention is better than another. > The reality is, we're going to have to pay some kind of... Whether pi or Tau is preferable a priori is logically distinct from whether it makes sense to change conventions once one is established.
    - nercht12 10y ago
      > You can certainly tell them that, and they may even find it easier to remember, but it won't actually be the reason that one convention is better than another. Indeed. But it was arguing against the logic of the parent post, which argued that it was a reason for one convention being better than the other. Not to be rude, but please read the parent post before responding to a response. It tends to make more sense. > Whether pi or Tau is preferable a priori is logically distinct from whether it makes sense to change conventions once one is established. Agreed. But that's not what I was arguing. I was arguing that we have to pay some kind of intellectual debt regardless. I could have used a different example, such as cases where it makes more sense to use pi than tau, and in such cases, we would be paying some intellectual debt. But please, please try to see how the idea applies beyond the initial example. Don't just take the argument at face value.
- fjdlwlv 10y ago
  Math operates in all dimensions. Choosing a prefered vocabulary from one dimension is not helpful. If you hate the number 2, then circumference of a circle is pi times diameter. Problem solved.

jessriedel 10y ago

It's not equivalent, but it's connected: circumference is "more fundamental" than area simply in the sense that 1 dimension is more fundamental than 2. In particular, when we build things up in higher dimensions, it's much more clearly done using a 1D primative than a 2D one, e.g., for the Fourier transform, there are powers of 2pi=Tau in any dimensions.

nercht12 10y ago
>> it's much more clearly done using a 1D primative than a 2D one Or you could just tell people that pi is the edge length of half of a circle. Pi and Tau are both 1-dimensional numbers that happen to be related to these things, so the argument really is silly. The reality is, we're going to have to pay some kind of intellectual debt in learning anything. So we keep teaching Pi. Suppose everyone switched to Tau. That would make all kinds of older documents inaccessible and harder to grasp, and we would be paying intellectual debt that way.
- jessriedel 10y ago
  > Or you could just tell people that pi is the edge length of half of a circle. You can certainly tell them that, and they may even find it easier to remember, but it won't actually be the reason that one convention is better than another. > The reality is, we're going to have to pay some kind of... Whether pi or Tau is preferable a priori is logically distinct from whether it makes sense to change conventions once one is established.
  - nercht12 10y ago
    > You can certainly tell them that, and they may even find it easier to remember, but it won't actually be the reason that one convention is better than another. Indeed. But it was arguing against the logic of the parent post, which argued that it was a reason for one convention being better than the other. Not to be rude, but please read the parent post before responding to a response. It tends to make more sense. > Whether pi or Tau is preferable a priori is logically distinct from whether it makes sense to change conventions once one is established. Agreed. But that's not what I was arguing. I was arguing that we have to pay some kind of intellectual debt regardless. I could have used a different example, such as cases where it makes more sense to use pi than tau, and in such cases, we would be paying some intellectual debt. But please, please try to see how the idea applies beyond the initial example. Don't just take the argument at face value.
fjdlwlv 10y ago
Math operates in all dimensions. Choosing a prefered vocabulary from one dimension is not helpful. If you hate the number 2, then circumference of a circle is pi times diameter. Problem solved.