Re: Form

[Howard Pattee <***>]

Steve,

I normally use ?form? in the sense of shape or configuration. However, the essential 
aspect of form as used in physics, mathematics, and much philosophy is that it can be 
conceived of as synchronic or timeless, and consequently independent of any dynamics that 
maybe imposed on form. Technically, physicists speak of ?configuration space? in which 
forms are defined independent of the dynamical laws. Logical and mathematical forms are 
also considered as timeless structures. That is why they are called ?formal.? This is 
somewhat like the Platonic concept of forms that were considered as timeless or eternal.

Synchronic and diachronic models are complementary. Physical laws can be described by 
state-determined models that change in time, or equivalently by synchronic forms like 
symmetry principles or extremum principles (least action). In quantum theory there is the 
?sum over histories? approach that is somewhere in between. The Ghorbanzadeh paper is 
interesting because his model is also somewhere in between. I think he is chunking normal 
state descriptions into ?short-timeless? forms that he defines as a new kind of state. (I 
haven?t followed the math.)

Relational models as described by Rosen are timeless forms. They do not imply a dynamics. 
Rosen was well aware of the complementary nature of formal and dynamical models. Here is 
a short discussion from the 70s when he was using automata models. We were discussing von 
Neumann?s point that formal timeless systems can produce paradoxes whereas real systems 
that depend on time cannot. 

Rosen: In physics you [usually] take the state description as primitive, and what you are 
interested in is the way the system changes state. . . In automata theory one of the 
things you can do is to define states in terms of equivalence classes of histories. The 
state becomes an equivalence class of all possible histories going back to minus 
infinity, as it were, which put the system into the same state.

Pattee: It eliminates time, the order in time of the system.

Rosen: That?s right. So you have an alternative way of describing what?s going on, either 
in terms of equivalence classes of histories . . . or the state description which physics 
takes as primitive. Also, the fact that we are dealing with complex systems which admit 
many descriptions, each of which is only partially true, gets rid of many of the logical 
difficulties that have been raised here, while at the same time raising still others. 
[A Question of Physics: Conversations in Physics and Biology, Paul Buckley and David 
Peat, eds. Univ. of Toronto Press, 1979, p. 106]


Howard