> To the first point, I think that the KL divergence is indeed symmetric in this case, 0.4 * ln(0.4 / 0.6) + 0.6 * ln(0.6 / 0.4) no matter which direction you go.

But my argument also works for any other probability distribution, e.g. P(heads)=0.5 vs Q(heads)=0.99.

> Still, there's no avoiding the inherent asymmetry in KL divergence.

I wasn't suggesting otherwise, I was talking about his interpretation.