@JohnRennie @NeuroFuzzy I still not very satisfied for the no progress (nor even concrete ruling out of) wormholes, transdimensional drives, backward time travel and FTL propulsion. However back in undergrad I do find the feeling of liberation as described by daniel e.g. knowing what entropy really is have caused me to understand the second law better as if I have finally resolved most resentment with a person I knew a long time ago, and find that the real life thing (instead of the popsci notion of entropy as disorder) is actually more interesting

I find it quite interesting that downvotes are positively correlated to effort. Shouldn't logically it should be anticorrelated instead?

Asking others whether it is correct is positively correlated with downvotes might be a reflection of what daniel and other said that we don't like askers who ask us to do the work for them

The ask for a detailed calculation being positively correlted suggest a similar reason above

It is also interesting how the conceptualness of a questiono is anticorrelated to downvotes. I am not sure how to interpret that

@0celo7 @ACuriousMind

Spherical coordinates:
\begin{align}
& \hat{x}=\sin \theta \cos \phi \hat{r} + \cos \theta \cos \phi \hat{\theta} - \sin \phi \hat{\phi}\\
& \hat{y}=\sin \theta \sin \phi \hat{r} + \cos \theta \sin \phi \hat{\theta} + \cos \phi \hat{\phi}\\
& \hat{x}=\cos \theta \hat{r} - \sin \phi \hat{\theta}
\end{align}

Hence

$$\begin{pmatrix}\hat{x} \\ \hat{y} \\ \hat{z}\end{pmatrix}=\begin{pmatrix}\sin\theta \cos\phi & \cos\theta \cos \phi & -\sin\phi \\ \sin\theta \sin\phi & \cos\theta \sin \phi & \cos\phi \\ \cos\theta & -\sin\theta & 0 \end{pmatrix}\begin{pmatrix}\hat{r} \…