One thing that has always fascinated me about the universe is the enormous range of scales, from elementary particles to galaxies and the largest known cosmic structures.

That led me to a purely conceptual question. We usually think of scale as just a numerical parameter describing size. But I began wondering whether it could instead be viewed as an abstract geometric coordinate belonging to its own mathematical space.

If ordinary spatial coordinates can have different topologies, could an abstract "space of scales" also possess a topology of its own—perhaps even a closed one, where continuously moving toward smaller and smaller scales would eventually return to the largest scales?

I'm not suggesting that this describes our universe or that microscopic and cosmological scales are physically connected. I'm treating it only as a mathematical thought experiment inspired by the way nature spans such an extraordinary range of scales.

I'm curious whether ideas remotely resembling this have ever appeared in cosmology, quantum gravity, topology, differential geometry, or any other area of mathematics or theoretical physics. If not, I'd be equally interested in understanding what makes such a construction mathematically impossible or physically meaningless.

The Zoo Hypothesis claims aliens are keeping us in a strict nature reserve. But sociology tells us no society has 100% compliance. If there is a massive galactic community, where are the alien political dissidents, corporate prospectors or religious crusaders? Why hasn’t a single rogue group leaked their existence to us?