It sounds like you’re conflating time dilation with the concept of light being unable to escape once it crosses an event horizon.

Nothing is actually “frozen” around a black hole, but if you accept that light cannot escape once it passes an event horizon then it follows that there must have been one final moment when light still could escape. The light that was able to escape in that final moment would reach your eyes as a “frozen” image of the object where it previously was the exact moment before gravity became too much to overcome.

What's mind bending to me is that a second object just short of that point _also_ sees the first object frozen. It doesn't matter how close you get to the horizon, the image of an object that got there first is still infinitely far in your future.

Yeah, that really is so neat to visualize. That there’s a hard line when the escape velocity reaches exactly the speed of light, and poof. Frozen image of the past right in front of your eyes.

And think… once we crossed the event horizon as observers ourselves (leaving a frozen image for observers behind to see), wouldn’t we see the “tracers” of images the person before us left behind every moment we move closer to the singularity? Edit: no… we never would see any light (in front of us) again by definition when crossing the horizon, duh lol.

When referring to black holes, "falling in" means going past the event horizon. For all practical purposes for us on the outside of the singularity, this is "having fallen into the black hole" as any object is gone to us forever once having done so. We don't use falling in to mean touching the singularity, which as you noted, does indeed take infinite time. Using the definition this way isn't particularly useful.

I don't think that's right.

This is my understanding: It takes an infinite time to cross the event horizon from the perspective of a distant, stationary observer, but a finite time from the perspective of the object that is actually falling towards the black hole. Once past the event horizon, reaching the singularity takes a finite amount of time from the perspective of the falling object. From the point of view of a distant external observer, time from event horizon to singularity is a meaningless question because the events inside the event horizon are causaully disconnected from the events outside of the event horizon.

Guys uh, I don't think we have a lot of empirical evidence from people who've gone near black holes and returned.

Your explanation is wrong. For an outside observer, time dilation approaches infinity at the event horizon. Singularities don't even exist for an outside observer, they have yet to happen in the infinite future.

Is that kind of the same as the idea that if you are approaching a wall but each step is only 50% of the rest of the way to the wall, so you would never reach the wall no matter how close you got?

That's Zeno's paradox and is not the same, because the sum of that is finite.

Here each step takes longer than the one before it and the series does not converge, taking instead infinite time.

Ah, ok. I appreciate you distinguishing between the two for me.