topology_notes

Vincent

V.W. 04/12/04 (Top.)

People¹ often ask, “what is the topology of the universe?” I would often respond, “How much time do you have?”

The short answer is, R^3. We have 3 dimensions, and can move an arbitrary distance in them.

The medium answer is, R^4. One can move ana or kata to arrive in another plane², the distance one travels determining which plane one arrives at.

The long answer is, we don’t know. Our planet is a sphere³, we can’t walk off it and enter space to check if topology functions differently there. Maybe the stars mark the end of space, the great dome. Maybe it loops, and we’re instead⁴ in R x S^2. Maybe going ana enough brings you kata, and we’re on S^3. Also, we have no idea what’s going on with dreams, there might be a separate dream axis. And there’s some evidence to suggest you can move another dimension when moving between planes, so maybe it’s R^5. We’re looking into it.

The long line answer⁵ is, the world is R^(3 + ε) dimensional, where 0 < ε < 2, for certain definitions of ‘dimensional’. I won’t go too in depth here, but the Holstramic view is, one only very rarely actually travels across a nonstandard axis, and what is usually seen as another dimension is just part of the original, after the initial transfer. One such reading of that is, going ana or kata doesn’t actually flip you 4D, it just teleports you far into space. Another such reading, is that flipping yourself 4D is actually what makes the ana/kata bridge 4D. Though, I’m looking into the level before this, this is past even my head. I can recommend some books.

When one initially goes ana or kata, assuming they survive, they are usually greeted by a flat plane filled with fog. The air is breathable, and there is an ambient light from some source, probably background magic passing through a weaker aether⁶. One should not go ana or kata, though. I’ve done it before, and survived, but we don’t know what unknown dangers there could be out there. And, if you can’t get enough thaums together to get out, you could be stuck.

Now, we assume the world is real, rather than rational, but is it? If distances can be discretized…

¹ That is, I. And hopefully some of you, after this lecture

² Hyperplane, technically, as we pass through an R to arrive at another R^3, but better that it colloquially be called ‘another plane’ than ‘another dimension’.

³ We’ve known this for a long time. One can measure shadows cast by two objects at the same time in different locations, and compare their differences. It’d be difficult to do so in Brune, but the Hemotites have done it on multiple occasions.

⁴ Superscript earlier to not confuse for exponentiation. S, of course, being the topology of a circle, a real line looped back and stuck to itself. S^2 would then be a sphere, and R x S^2 would have you pick a point along a real line and a point on the sphere.

⁵ Uncountable copies of [0, 1). Very, very long. We’ll see more of this in lecture 15.

⁶ Like lightning passing through a thin piece of metal, versus a thick. The thin will light up and melt, the thick will be fine.