Wizard proposes turning map of the universe inside-out (web.archive.org)

If an unambiguous centre point did exist, then flipping the coordinate system from (distance to centre point, point on a n-1 dimensional hypersphere) to (1 / distance to centre point, point on a n-1 dimensional hypersphere) would be a trivial and uninteresting transformation. In other words, turning the universe inside out does nothing to decrease (or increase) the difficulty of choosing a centre point.

This transformation is its own inverse. Applying it to the coordinate system in the article we find that the author has chosen the centre of the planet Earth as their centre point; that is what makes their coordinate system possible. This is totally arbitrary and does not solve any deep mysteries. The stuff about turning the universe inside out is just waffle on top of that.

I love this kind of thing. I often wonder how densities would map under such a transformation. What would the density be of the "core" of the inside out earth? What is the density of the universe sphere-reflected about the geospheric surface of the earth? How does this change as you reflect about different layers of the earth? How about sphere reflecting the universe about the surface of a star? Or a black hole?

If anyone is curious, I made some experiments years ago to play with this kind of perspective shifts. Make sure you check out the horse:

https://hyperspectives.wondering.xyz

I also made a blender modifier that does Moebius transformations... There is a patch on the hyperspectives page. But also this fork:

https://github.com/micahscopes/Hyperspectives/tree/hyperblen...

Lately I've gotten into using Clifford algebra (conformal geometric algebra) to do the same stuff. I'm slowly building tools for this... Stay tuned!