Well in string theory the universe really is very skinny in those directions, and the particles go all the way around: imagine a book sandwiched between two boards: There's three dimensions but the book can only move in two. I'm really not sure what Pratchett and co were getting at.

Oh, and I have another note on Type I multiverses: The Big Bang isn't actually localized to a point. It's infinite density and infinite crinkliness but not necessarily zero volume so it's perfectly possible that the universe is spacially infinite. Everything in the observable universe, however, came from a single point.

Here's a note on Wednesday's video that I only came up with on Thursday:

There's actually another system of infinite numbers. If you think of numbers as the size of sets, you get cantor's infinities. But, if you think of 3 as what you get after going 0, 1, 2 and 7 as what you get after going 0, 1, 2, 3, 4, 5, 6, then what do you get if you go 0, 1, 2, 3 ...? This is omega, the first ordinal infinity. Note that unlike aleph null, you can get w + 1, because that's just the set 0, 1, 2, .... , w. There's an w + 2, w + umpty, w + w, 1000 * w, w ^2 , w ^ w, and so on and so forth. There are actually so many of these ordinal numbers that they actually can't fit into a set.

There's actually another system of infinite numbers. If you think of numbers as the size of sets, you get cantor's infinities. But, if you think of 3 as what you get after going 0, 1, 2 and 7 as what you get after going 0, 1, 2, 3, 4, 5, 6, then what do you get if you go 0, 1, 2, 3 ...? This is omega, the first ordinal infinity. Note that unlike aleph null, you can get w + 1, because that's just the set 0, 1, 2, .... , w. There's an w + 2, w + umpty, w + w, 1000 * w, w ^2 , w ^ w, and so on and so forth. There are actually so many of these ordinal numbers that they actually can't fit into a set.

You can actually extend this to the reals and so forth, and these are John Conway's surreal numbers, which are a weird and wonderful world of their own.

As for collapsing all the way and stuff: It really depends on what you define as now. In Schwarzschild coordinates, which has nice time translation properties, but does weird stuff at the horizon, anything takes forever to fall in, just getting exponentially closer and closer to the horizon. But since this is an exponential decay, after waiting a couple times the amount of time for light to cross the hole, it has effectively fallen in.

And also, the light reflected or emitted would be exponentially redshifted, losing energy and frequency, so after some point it's completely undetectable, which is after the point where the object is less than one period from the horizon in proper time. When it gets near the planck length it probably can't be counted as outside at all.

So you wouldn't see that effect in the picture, which shows the light emitted by the accretion disk, distorted in various ways by the gravity of the black hole.

Black holes:
The mathematically simplest solution for a black hole is the eternal black hole, which includes a wormhole. However, this wormhole isn't traversable, as anything that tries to get through just will hit the singularity instead. And worse, an actual collapsing star doesn't even have the wormhole part at all. And for real rotating black holes, the inner event horizon actually is the point where any fluctuation or light or whatever piles up and get energy dumped into it, so instead of making a wormhole, it makes a very powerful shredder. Ah well.

White holes:
As likely as finding or making a broken egg that spontaneously reassembles itself.

CTC machines.
As far as I can tell, each of these proposed solutions has some fatal flaw or just plain doesn't work.
Anything with negative energy has problems, even with the casimir effect. With the casimir effect, it requires lots of positive energy stuff to be nearby, and i think QFT makes it so you can't get the negative to outweigh the positive.

The levi civita magnetic wormhole isn't an actual wormhole according to this paper https://www.researchgate.net/publication/28965261...

And the light ring seems to be a tipler cylinder in disguise, with a tipler cylinder being an infinite unbuildable sort of thing. (If you tried to build it without infinite length, it would simply collapse into a black hole)

Ah, but that's coordinate dependent. If you use something like kruskal coordinates, spacelike and timelike axes don't swap.

Well, actually...

One thing to note is that changing observers in relativity doesn't violate causality, so anything that is spacelike separated, like the points of constant time in a specific observer's frame, will stay spacelike separated in all frames. What this means is that if you are actually simulating stuff, you would pick a frame and time step forwards just like in newtonian mechanics, so relativity doesn't really force any sort of timelessness.

Also, I feel that Barbour's theories are confusing because they are bunk. In quantum mechanics there are two approaches to quantum mechanics. Schrodinger's approach and the Heisenberg approach. In Schrodinger's approach the state of the system evolves while the value of observables remain constant and and in Heisenberg's method the state is constant while observables change. It's sort of like a clock that is forward or late. You can describe it as turning a specific amount in a specific time or you can just record how late it is and predict where its hands are currently. Even though the description of the system in the second approach is unchanging in time, that doesn't mean that clock's movement is an illusion.

The reason it is possible to have an unchanging description is because if you knew the state, then you could evolve it forwards or backwards as much as you want, but you can't know the state because if you tried to remove entropy from the rest of the universe, it would build up in the measuring device, and then the device would eventually melt or burn up or something. So the thermodynamic arrow of time prevails.

String theory is a rather mathematically nice theory for incorporating in the curved space-time gravity of general relativity into the quantum field theory, which has everything but gravity, The catch is that it unfortunately only works in 10, or possibly 11 dimensions. The 11 dimensional case corresponding to M theory, which, as far as I can tell, hasn't been pinned down yet, but by all rights ought to exist.

Initially, the required number of dimensions came out to 26, but any more than 11 would just be silly, wouldn't it?

Well, nobody _means_ to spend their day procrastinating. Or eating junk food while on a diet. Or all sorts of things.