AKM sama: Would you say a multiverse that is a timeline consisting of 12 Low 2-C universes is sufficient evidence for it to be Low 1-C?
Me: No.
Allow me to explain.
We have three dimensions of space, which we could (in a simplified version) model as RxRxR, that is the cartesian product of three infinite real number lines.
Time we could model as a single infinite real numbers line R.
A timeline is then (RxRxR)xR i.e. space x time.
Now, for multiple timelines, we need to operate in a 5-dimensional space. In the 5th dimension, they would all lay beside each other. Let's say we have 12 timelines, with their positions in the 5th dimensions being 1,2,3,4,..., 12. {1,2,3,4,...,12} is the set of those positions.
The multiverse consisting of 12 timelines would then be described by {1,2,3,4,...,12}x(RxRxR)xR.
In other words the cartesian product of the locations of each timeline, with one timeline.
Let's compare this to a timeline consisting of 12 universes. One universe is again RxRxR.
Those universes are in a multiverse. We again model their positions as {1,2,3,4,...,12}, just that this time those positions wouldn't be across the 5th dimensional axis, but the 4th one. (Which is really just arbitrary numbering)
So the multiverse is {1,2,3,4,..,12}x(RxRxR), in other words, a universe for each of the 12 positions.
Now let's make a timeline out of that. How do we do that? We again multiply (take the cartesian product) with the time axis. The same way we previously went from universe to timeline. The time axis is again modelled as R.
What we get is Rx{1,2,3,4,...,12}x(RxRxR). That is in mathematical terms a timeline consisting of 12 universes.
Let's make sure we got that right: We wanted Low 2-C universes, i.e. entire spacetimes. Are those entire spacetimes? Yes! Because the time dimension we added is equally applied to all universes. We, for example, have a point that is 5 seconds in the future of universe 3 at the coordinates (0,1,15). That point is in the construction above {5}x{3}x(0,1,15).
So those construction meets all demands. A timeline consisting of multiple universal spacetimes.
Let's compare those two constructs now.
Multiverse from 12 timelines was: {1,2,3,4,...,12}x(RxRxR)xR
Timeline of 12 Universes was: Rx{1,2,3,4,...,12}x(RxRxR)
Notice how those look almost the same? That's because they are! They are in fact only a rotation away from each other. The way the are rotated has no particular meaning, though. It's only result of how we happened to construct it. It's a difference equivalent to having north up on the map or having east up on the map.
If we rotate the constructs so that their time and space dimensions each fit to each other and do the same with their position in the multiverse we get that they are exactly the same. I.e. just write the universes number first, then write space and lastly write which time it is and you get exactly the same constructs.
Sooo... yeah, the two constructs are in fact exactly the same thing. So the object in question is just a regular 2-C Multiverse.
