With what does a number interact? Nothing. If you allow interventions from outside the Matrix, I could interact with humans that are causally separated from my past and future. But even that power will not allow me to interact with the number 2; I cannot affect it, or it me, in any sense.
The post you link to talks about controlling a computer program by making decisions, in particular the decision to one-box. I think that this would sound rather less impressive if it were converted to talking about controlling an FPS by moving the mouse and pressing the space bar, which is functionally equivalent.
Those devices take in inputs. The post is talking about controlling programs that take no inputs. In other words, they are fixed mathematical structures.
Just because the input is a fixed simulation of the agent’s decision doesn’t mean the calculation as a whole has no inputs! In particular, it has whatever inputs are decisive for the agent itself. An agent that gets whacked with a stick every time it one-boxes is quite likely to make a different decision from one with the same algorithm but working on data that doesn’t include stick-whackings. It’s not sufficient to specify the laws of physics, you have to know the boundary conditions as well.
The decision-theory people on LW talk about agents controlling abstract mathematical entities in a way that I cannot so easily dismiss.
The post you link to talks about controlling a computer program by making decisions, in particular the decision to one-box. I think that this would sound rather less impressive if it were converted to talking about controlling an FPS by moving the mouse and pressing the space bar, which is functionally equivalent.
Those devices take in inputs. The post is talking about controlling programs that take no inputs. In other words, they are fixed mathematical structures.
Just because the input is a fixed simulation of the agent’s decision doesn’t mean the calculation as a whole has no inputs! In particular, it has whatever inputs are decisive for the agent itself. An agent that gets whacked with a stick every time it one-boxes is quite likely to make a different decision from one with the same algorithm but working on data that doesn’t include stick-whackings. It’s not sufficient to specify the laws of physics, you have to know the boundary conditions as well.