Re: Newton's states

[Howard Pattee <***>]

Tim asks:
> I can't really speak to your other examples. Does either one of them take us
> outside of the state-based paradigm?

The issue of whether a model is state-determined cannot be resolved without defining how 
time is interpreted in the definition of state. Rosen discusses many ways in which time 
enters models in chapter 4 of Anticipatory Systems (pp. 221-275), and there are other 
ways he does not discuss. Clearly, if you allow a long enough time interval to enter 
enough information into the state description then everything becomes state-determined, 
the limiting case being a synchronic, purely relational, non-dynamic model, or Spinoza?s 
sub specie aeternitatis, a model under the aspect of eternity.

Several philosophers and theologians have used this model, and even some physicists 
(e.g., Julian Barbour, The End of Time, Oxford UP, 1999), but it does not yield easily to 
empirical test.
Boethius (~480~524) gives my favorite definition of ultimate state-determinism:

?Since God hath always an eternal and present state, His knowledge, surpassing time's 
notions, remaineth in the simplicity of his presence and, comprehending the infinite of 
what is past and to come, considereth all things as though they were in a state of being 
accomplished.?

My point is that there are all lengths of time intervals that can be used in state 
definitions in between Newton?s infinitesimal dx/dt and Boethius?s infinity. Rosen?s 
concept of the Newtonian paradigm (pp. 225-232) defines state time as dx/dt where the dt 
is ?instantaneous,? (but not so instantaneous that higher derivatives can?t be defined), 
and where t itself is Newton?s absolute time where simultaneity can be uniquely defined. 
Later in AS Rosen defines time for general dynamical systems that allows a scaling of 
time so that Hamiltonians with different time scales can be compared. This requires what 
amounts to coherence of the time scales and must be expressed by exact differentials. In 
any case, his discussion of state in LI uses Newtonian instantaneous states.

For both conceptual and practical purposes, finite time interval states are usually 
separated out from the dynamics and called memory states. These are usually not coherent 
in the sense of Rosen?s general dynamics. That is what ?random access? means. Typical 
computer architectures have as many as 3 or 4 levels of memory depending on the time 
intervals involved. The brain has at least that many.

In this sense, modern physics has many examples of non-Newtonian states, such as 
hysteresis, delayed potentials, sum-over-histories, and many others. The fact that these 
might in principle be rewritten as state-determined does not make them Newtonian models.

Howard