amazedsaint

I’m waiting to get some patents through for a new type of computing paradigm we are building - but would like to share few learnings and insights anyway

Can a computer compute any algorithm in this universe? Is that even true once we remember the universe has a finite memory and every irreversible bit flip turns into heat?

I take the abstract claim of universality as a guiding ideal, then ask what survives contact with Landauer and Bekenstein. Only computations that fit the energy and memory budget actually happen, so the winning style must squeeze meaning per bit and minimize erasure.

That pushed me to a simple lens. Computation rides on connectivity, not on coordinates. If I draw a circuit on a rubber sheet and stretch or crumple the sheet without cutting a wire, the program does not change. Only rewiring changes behavior. In other words, logic lives in topological classes of the wiring, while geometry is costume.

Once constraints are encoded as topological invariants, energy based model predictive flows on graphs beat stepwise generation.

Think a ball rolling on a landscape carved by the network itself. The search does not waste bits exploring directions the wiring already forbids. Guidance replaces guesswork, so you move less entropy to reach the same answer.

Thermodynamics also agrees. Coz we only pay when we erase information, so I organize computations to be mostly reversible, push entropy to the boundary, and erase only when learning truly demands forgetting. Throughput then scales with boundary more than with bulk, echoing holography.

With a finite cosmic memory, the smart move is to store structure rather than raw state, compressing meaning into invariants that a boundary can carry.

Message passing turns out to be gauge transport in plain clothes. Treat edges as connections and cycles as holonomy loops. The accumulated phase around a loop enforces global consistency without a global overseer. Small perturbations do not matter unless they jump the system to a different topological class, which is why robustness emerges from the wiring itself.

So can a computer compute any algorithm in this universe? In the abstract sense yes. In the physical sense it can compute the subclass that fits within time, energy, and memory, and it does best when it leans on topology. I now see useful computation as homotopy search - start in the right class, deform within it, and rewire only when you choose a different class.

That respects the information limit of the universe and trades costly bits for conserved structure, which is why I believe it is true.

I keep circling back to two facts that seem incompatible until you squint just right.

1- Turing says: any discrete procedure can be emulated on a tape that grows as needed. Irreversibility—and therefore information loss—is baked in.

2- David Deutsch: the physical world is fundamentally reversible; no bit of history is ever truly deleted.

Now to add in something I’ve only recently wrapped my head around: there’s a universal bound—a Bekenstein-style ceiling—on how much information any bounded region can hold. Past that, additional bits aren’t stored; they’re smeared into geometry, energy, and curvature. In other words, the universe enforces a topological limit on computation: you can keep calculating forever, but you must keep folding state back into the same finite fabric.

So, I think the right mental model isn’t “bigger tape, bigger RAM.” It’s topological transformations: moves that twist, braid, and refold the same patch of memory without tearing or gluing anything new. Every legal operation must be invertible, because tearing (irreversibility) would leak information past the bound.

I have a toy implementation of an O(1) VM—where the active cell set never exceeds a fixed small constant, no matter how many steps I run. Round-trip tests pass, and the tape stays sparse. It’s slow and fragile, so I wouldn’t ship it till I perfect it a bit more, but the geometry feels right and I can rewrite quite few algorithms from O(N) to O(1) trading memory for a bit of compute

Why share this? Because the idea reframes practicality - maybe we shouldn’t ask “how do we scale memory?” but “how do we braid computation inside the universal limit nature already imposes?” If that framing holds water, Turing gave us the floor, Deutsch gave us the ceiling, and I think I’m starting to stare towards the center

Curious if anyone else thinks this is more than philosophical exercise. Anyone else familiar with anything like this?