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Can math.atan2 return INF?

(sorry for the premature previous post)

Random832 <random832 at fastmail.com>:
> All objects, not just black holes, have those properties. The point
> here is that we are in fact observing those properties of an object
> that is not yet (and never will be) a black hole in our frame of
> reference.

A physicist once clarified to me that an almost-black-hole is
practically identical with a black hole because all information about
anything falling in is very quickly red-shifted to oblivion.

However, there is some information that (to my knowledge) is not
affected by the red shift. Here's a thought experiment:

      /          \
     /  (almost)  \               N
    |    black     |              |
    |     hole     |              S
     \            /
      \          /

We have a stationary, uncharged (almost) black hole in our vicinity and
decide to send in a probe. We first align the probe so it is perfectly
still wrt the black hole and let it fall in. Inside the probe, we have a
powerful electrical magnet that our compass can detect from a safe
distance away. The probe is also sending us a steady ping over the

As the probe approaches the event horizon, the ping frequency falls
drastically and the signal frequency is red-shifted below our ability to
receive. However, our compass still points to the magnet and notices
that it "floats" on top of the event horizon:

      /          \
     /  (almost)  \ N
    |    black     ||
    |     hole     |S
     \            /
      \          /

          / compass needle

The compass needle shows that the probe is "frozen" and won't budge no
matter how long we wait.