A while back I promised to write this. It has taken some time.

Well the short answer is nobody knows. In principle. Let me explain…

But seeing as this is not QI and I am not the curly haired loon Alan Davis I’d best try to explain why…

There are questions that are unanswered and there are the unanswerable.

Magic don’t exist. Science does and it is a kinda magic (or is that Queen?). Robert Oppenheimer certainly proved that. Well, with his pencil he certainly wielded more power than Dumbledore did with a twig. Real science is magic and it is magic beyond anything these sort of numpties could dream of.

In 1995 at Nottingham University a geezer dressed in a manner that would make Arch-Chancellor Ridcully look under-dressed handed me a piece of paper that was the official recognition of my getting the keys to the Universe. It was emotional, I can tell you. It was a BSc in Physics.

So what I am getting at in this preamble is that magic is real and it’s magic because it doesn’t always make “common sense”.

So, to the point!

Black-holes are essentially collapsed stars that have all their mass within their Schwarzchild radius. This is the radius which even classically, light can’t escape from because as you know Neil, Buzz and Mike had to go rather fast to get off this rock but seeing as the speed of light is a cosmic speed limit once the gravity of a collapsed star gets to that having an escape velocity above that of light then you are in it for the duration. By the way I’m sticking with the non-charged, non-rotational solutions here. Hence Schwarzchild will suffice.

If you really want to muck about with Kerr-Newman metric then knock yourselves out. We’ll keep it without angular velocity (or charge). Now I appreciate the revolutions of Beyonce’s twerking her fundamental singularity as much as the next person but for the current porpoise the entertainer on the stage might as well be Noel Coward in a dinner-suit singing some old nonsense that the late Queen Ma would like.

Because the simple truth is black holes have a property which is awesome. It brings information theory (one of the grandest achievements of C20 maths) into a kind of conflict with one of the grandest achievements of C20th physics. And it’s dead simple. By which I mean it lacks complexity. Now, modeling weather is complicated because modeling multiple processes is. This is a different kind of hard. It does not involve the kind of recursive computation that gets a Julia Set on screen. It is conceptually hard rather than computationally so. Hold that thought – it will matter. There are incredible complicated things that are hard and there are simple things that are hard. Things can be hard in qualitatively different ways.

Now, in the 1930s Alan Turing came up with a theoretical model for computers. I’m typing on one now. Now Turing proved (as did Alonzo Church) by a different route (and Kurt Gödel had a look in too) proved this. Now some of this was purely formal such as the disproof of Peano Arithmetic which set out to prove essentially that the mathematics of integers can be based on a single finite and logically consistent axiom-set. That this was a bit of an embuggeration (especially to David Hilbert) is to say the least. Hilbert had proposed a program in which he hoped all mathematics could be reduced to a single axiom set. Peano Arithmetic was a jolly good punt at that. Essentially he’d proposed an idea to develop something much like the characteristica universalis of Leibniz. Essentially an attempt to reduce everything to rule-following. The idea was this…

When the Peano axioms were first proposed, Bertrand Russell and others agreed that these axioms implicitly defined what we mean by a “natural number”. Henri Poincaré was more cautious, saying they only defined natural numbers if they were consistent; if there is a proof that starts from just these axioms and derives a contradiction such as 0 = 1, then the axioms are inconsistent, and don’t define anything. In 1900, David Hilbert posed the problem of proving their consistency using only **finitistic methods** as the second of his twenty-three problems. In 1931, Kurt Gödel proved his second incompleteness theorem, which shows that such a consistency proof cannot be formalized within Peano arithmetic itself

That’s from wikipedia

So it is entirely a bust flush. Or is it?

Anyway, I realized I’m hundreds of words in and haven’t answered the question! Sorry, but I had to foreground and the essential problem is to do with words like “definable”, “consistent” and especially “infinite”. Now the final one is the impenetrable. Now way back when Galileo realized infinity was a tough nut to crack when he put as an aside the idea (which is true) that the set of Naturals had exactly the same cardinality as the set of Perfect Squares. Now the first set is {1,2,3…} and the second starts {1,4,9…} but both have the same number of members. Huh? You might be thinking there are more of the first because of the gaps in the second? But as Galileo argued and Cantor proved the cardinality (the size of the sets – sort of) can be proven to be the identical for both because both can be put in an exact 1-1 bijection – essentially for each member of the first set there is a one on the other side – kinda like the perfect tea-dance – with integers He (Cantor) called this number Aleph-null. The first of the transfinite cardinals (there are many more cardinals – more than they have in Rome – and some are *fucking enormous* – a technical term I owe to a Leeds University number theorist). I am getting a bit OT here but I must mention a collection known (and I know this sounds rather “Father Ted” but there are, amongst many others, ineffable cardinals. Please read this because it conveys the total Woo-Woo.

Yes, there are numbers that are infinite in ways that can’t be uttered but must exist, logically. Yes this sounds mystic and it is but it is provable. This is *not* homeopathy. This is reality.

What was that paragraph about? Well it was really about trying to say (and this is relevant) that there. In an arguably similar way General Relativity contains solutions (such as those due to Kurt Gödel which include the possibility of time-travel but whilst mathematically impeccable do not pertain to our Universe, but could in principle, just don’t). Now that is interesting. So interesting I wrote an MSc thesis on it. What was dear old Gödel up to? Fuck knows! I don’t know fuck so I don’t. It is all a piggy-rotten mystery and no mistake. It’s like Windows 8. No bastard groks that one.

Anyway Blackholes are simpler. Once you cross the event horizon you is doomed and I mean proper Frazer *doomed*. Not only are you not getting out but you can’t really communicate out either. Because nothing can get out of an event horizon. It’s kinda like dropping car keys down a toilet. Now I’m on my uppers here (but promised to write this piece) but my understanding is that in the vicinity of an event horizon time slows as seen by an external observer but seems the same for the subject falling in. They also get gravitationally red-shifted and dim into the IR. So if you chuck your mate into a blackhole and they wave back at you it seems ever slower and ever redder until you can see nothing of them. Now this time dilation is kinda like working a 36hr day and then a 48hr day and then a 72hr day so you get more done. Essentially any computable problem accelerates (i.e. breaking a code and not whether Miley Cyrus ought to wear pants) because the effective time the Turing machine’s rate of knots has becomes asymptotic because time has slowed for it – though not for the observer at a safe distance. So it can actually solve or get round the likes of the Entsheidungsproblem

Except. As the Turing machine (and if you are reading this – you have one – just not a local blackhole – I hope) hits max and goes infinite it is going beyond the event horizon so you never get to know the results. I know. It sucks. Of course you could leap in after it but you’d never be able to get the data out so what is the point?

Now I have no idea whatsoever where my trash goes. But if it were to be chucked in a blackhole then nothing of it would remain to the external observer other than mass, electric charge and angular momentum. This applies to anything. This applies to pork bellies, gold ingots, the works of Shakespeare and your Aunty Gladys. All meaningful information is lost to the Universe. In a very real sense that is why blackholes are something else. And that is why a Turing machine can achieve infinite speed (even that dreadful Acer you bought five years ago) but anyone outside the hole can do nothing with it. And if you are past the event horizon neither can you.

And for my next trick I have this cat and this box

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