Everyone loves black holes. Immense gravity, a one-way space-time membrane, the possibility of links to other universes. All lovely stuff.
A little trawl of the internets reveals an awful lot of web pages discussing black holes, and discussions about spaghettification, firewalls, lost information, and many other things. Actually, a lot of the stuff out there on the web is nonsense, hand-waving, partly informed guesswork. And one of the questions that gets asked is "What would you see looking out into the universe?"
Some (incorrectly) say that you would never cross the event horizon, a significant mis-understanding of the coordinates of relativity. Other (incorrectly) conclude from this that you actually see the entire future history of the universe play out in front of your eyes.
What we have to remember, of course, is that relativity is a mathematical theory, and instead of hand waving, we can use mathematics to work out what we will see. And that's what I did.
Proton: a life story by Geraint F. Lewis 1035 years: I’ve lived a long and eventful life, but I
know that death is almost upon me. Around me, my kind are slowly melting into
the darkness that is now the universe, and my time will eventually come. I’ve lived a long and
10-43 seconds: A time of unbelievable light, unbelievable
heat! I don’t remember the time before I was born, but I was there,
disembodied, ethereal, part of the swirling, roaring fires of the universe coming
in to being. But the universe cooled. From the featureless
inferno, its character crystalized into a seething sea of particles and forces.
Electrons and quarks tore about, smashing and crashing into photons and
neutrinos. The universe continued to cool. 1 second: The intensity of the heat steadily died away, and I was born. In
truth, there was no precise moment of my birth, but as the universe cooled my
innards, free quarks, bound together, and I was suddenly there! A proton! But my existence seemed fleet…
The German tank problem is a fav of mine. The wikipedia page on it is a little long winded, but I think it can be looked at a lot faster with a little numerical mucking about.
The problem is quite simple. The enemy are producing tanks, and each has a sequential serial number (for simplicity, let's assume that the numbers are reset every month). You encounter this scene on the battle field;
and we see that this is tank number, say, 15 of a particular months production. How many tanks were produced in that month? Can we even answer the question?
This is the problem that faced the Allies in WWII; you really wanted to know how many panzers are out there. Intelligence officers were reporting productions of more than a 1000 tanks per month, but based on statistics, the predicted number was significantly fewer than that, in the hundreds. After the war, the numbers were checked against records and the statistical answer was amazingly correct (read the wikipedia page for more details).