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You cannot transform a mathematical structure. The only thing you can do is find another structure with linked properties. But both structures are immutable. I
by thriftwy 3y ago
You cannot transform a mathematical structure. The only thing you can do is find another structure with linked properties. But both structures are immutable.
It is not possible to transform a sphere so that it turns into a cube and no spheres can be reasoned about anymore.
- naasking 3y ago> You cannot transform a mathematical structure. The only thing you can do is find another structure with linked properties. But both structures are immutable. I think you're conflating the structures that describes mathematical structure with the structure itself. Like I said, mathematics is the study of structure, so the syntactic elements you're used to interacting with are themselves structures that describe other structures. These syntactic descriptions have isomorphisms to the underlying structures they're describing, but they are not the structures themselves (map is not the territory, etc.). Mathematics is larger than this immutable descriptive layer IMO. Edit: as a more concrete example, consider how we model mutable data structures and stateful session protocols in programming languages. One way is to project these into an immutable trace, as an immutable description of the object's state changes, but that trace is not the underlying structure. The underlying structure itself is still mathematical, but mutable, eg. cellular automata.
- thriftwy 3y agoThe idea here is that deterministic computations neither exist nor don't; regardless of whether they are being simulated. A Life pattern does not xare whether you simulate it or not. It will not become conscious in any way after your decision to simulate it.
- naasking 3y ago> A Life pattern does not xare whether you simulate it or not. It will not become conscious in any way after your decision to simulate it. Where's the proof of this? The game of Life is Turing complete. We have every indication that human beings can be modelled by Turing machines.