Hmm there was a bunch of back and forth on this point even before the first version of the post, with @Michael Oesterle and @metasemi arguing what you are arguing. My motivation for calling the token the state is that A) the math gets easier/cleaner that way and B) it matches my geometric intuitions. In particular, if I have a first-order dynamical system 0=F(xt,˙xt) then x is the state, not the trajectory of states (x1,…,xt). In this situation, the dynamics of the system only depend on the current state (that’s because it’s a first-order system). When we move to higher-order systems, 0=F(xt,˙xt,¨xt), then the state is still just x, but the dynamics of the system but also the “direction from which we entered it”. That’s the first derivative (in a time-continuous system) or the previous state (in a time-discrete system).
At least I think that’s what’s going on. If someone makes a compelling argument that defuses my argument then I’m happy to concede!
Hmm there was a bunch of back and forth on this point even before the first version of the post, with @Michael Oesterle and @metasemi arguing what you are arguing. My motivation for calling the token the state is that A) the math gets easier/cleaner that way and B) it matches my geometric intuitions. In particular, if I have a first-order dynamical system 0=F(xt,˙xt) then x is the state, not the trajectory of states (x1,…,xt). In this situation, the dynamics of the system only depend on the current state (that’s because it’s a first-order system). When we move to higher-order systems, 0=F(xt,˙xt,¨xt), then the state is still just x, but the dynamics of the system but also the “direction from which we entered it”. That’s the first derivative (in a time-continuous system) or the previous state (in a time-discrete system).
At least I think that’s what’s going on. If someone makes a compelling argument that defuses my argument then I’m happy to concede!