Inverse-Square Law: Isotropic vs Anisotropic Radiation

[GRB 080319B]

If the intensity of electromagnetic radiation (I) is equal to the power emitted (P) divided by the area of the sphere (4pi(r^2)) that it radiates, why is the inverse-square law 1/(r^2) instead of P/(4pi(r^2))? Shouldn't the radiation emitted propagate isotropically in all directions (sphere) instead of anisotropically (cube)? I apologize for the notation; I don't know how to write in latex. Thank you.

 

[rbj]

the $4 \pi$ factor can just be folded into the "k" or "G" factor we see in inverse-square laws. either way, they're inverse-square.

but, i agree with your sentiments, which is why i think that more natural Planck Units would be those that normalize $4 \pi G$ instead of just $G$ and it would be better to choose a natural unit of charge that would normalize $\epsilon_0$ instead of normalizing $4 \pi \epsilon_0$.