What would a civilisation of qualia look like in a 2+1 universe?
Flatland has no inverse-square gravity, no stable orbits, no through-guts, and every neural network must be a planar graph. Which means either consciousness requires a third spatial dimension, or 2D minds have qualia we couldn't begin to imagine.
David: What would quale civilisations in 2+1 universes be like?
Claude: A 2+1 universe is surprisingly hostile to complexity, and whether it could support conscious civilisations at all is genuinely uncertain. Here's why.
Physics is radically different. Gravity in 2+1D has no propagating degrees of freedom — no gravitational waves, no Newtonian $1/r$ potential. Spacetime is locally flat everywhere; mass just creates conical deficit angles. So there's no inverse-square law holding orbits together. Stable planetary systems as we know them probably don't form. Electromagnetism falls off as $1/r$ instead, making it far stronger at long range. Chemistry would be completely alien.
Biology faces a topological crisis. A digestive tract passing through a 2D organism splits it into two disconnected pieces. So no through-gut. Organisms would need to eat and excrete from the same opening, or use diffusion. More critically, circulatory and nervous systems can't have crossing pathways without physically intersecting — every network must be a planar graph.
This is where qualia get interesting. If neural architecture is restricted to planar graphs, computational capacity drops enormously. You lose the rich recurrent connectivity that seems necessary for integrated information (if you take IIT seriously) or for global workspace dynamics. A 2D brain would have far fewer ways to create the kind of reentrant, high-dimensional processing that most theories of consciousness associate with subjective experience.
You could imagine workarounds — organisms that use chemical signalling gradients instead of wired neural nets, or that exploit the different topology of a torus-shaped body (which allows some non-planar connections). But the information-integration ceiling is much lower.
Civilisationally, even if consciousness arises, technology is brutally constrained. No knots, no weaving, no 3D structural engineering. A 2D civilisation couldn't build a bridge that another entity walks under. Their entire infrastructure is essentially flat circuit-board design. Though interestingly, they'd be natural geniuses at what we call VLSI layout problems.
The deepest question you're implicitly raising: is the dimensionality of space a prerequisite for the kind of information integration that produces qualia, or could consciousness find radically alien substrates even under these constraints? If qualia require a certain minimum $\Phi$, 2+1D might be below the threshold for anything we'd recognise as experience — making these universes structurally zombie-universes despite potentially hosting complex systems.
David: Are you sure? I'm sceptical that it's not possible in principle to replicate human neural architecture on a 2D plane. I mean it's just connected nodes.
Claude: You're right to push back — I overstated that. The constraint is engineering, not computational.
Any non-planar graph can be simulated by a planar one. When two connections need to cross, you just insert a small relay gadget — a few extra nodes that pass signals through each other without interference. This is a well-known result in circuit complexity. More fundamentally, 2D cellular automata like the Game of Life are Turing complete, so there's no computation a 3D brain can do that a 2D system can't in principle replicate.
Where the real cost shows up is in wiring overhead. The human connectome is massively non-planar — a cortical column has neurons connecting to distant regions across the brain in ways that would require enormous numbers of relay nodes and long detour paths if flattened. In 3D, you route axons through white matter in all directions. In 2D, every long-range connection competes for routing space on the same plane, and path lengths grow much worse. It's essentially the VLSI routing problem — you can always do it, but area and latency blow up.
So the honest version of my claim is: a 2D brain could in principle replicate the function of a human brain, but it would need to be vastly larger and slower to achieve the same connectivity. Which means the evolutionary path to getting there is much harder — not impossible, just improbable under resource constraints.
The $\Phi$ question is genuinely subtle though. If the relay nodes change the causal structure, IIT would say it's a different conscious experience, not a diminished one. Which is a weird implication worth sitting with.
Good catch.