30 September 2009

Some Thoughts on Phase Space

Filed under: Ktismata, Psychology — ktismatics @ 8:10 am

Hey, it’s just a blog, right?

Citing my favorite source, Wikipedia, phase space is

“a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space.”

A particular system might occupy only a fraction of its possible states during its existence. The phase space can be described as an array of probabilities that the system will actually occupy any particular state. So if an object is to include the entirety of its phase space, then the object contains not just its actual state in a given moment in time, nor even all the states it occupies during its lifetime, but all the possible states it could, with probability > 0, achieve during its lifetime.

This is a rather abstract description of an object, including a whole array of potentialities that are never actualized. So, e.g., the chair I’m sitting in would include in its objecthood all the possible physical places it could occupy in the universe. The probabilities are highest for its someday occupying some other space in the living room, but the probability is greater than zero that someday it might find itself sitting someplace in upstate New York. The chair’s potential to be pretty much anywhere on earth at some point during its lifetime could be regarded as an important aspect of the chair that doesn’t participate in its interactions with me or with the other stuff in the room it currently occupies. But I don’t see how the chair’s potential to be elsewhere is withdrawn from its current interactions here and now. The chair is indifferent to being moved; it resists only in a purely mechanical sense of being stationary and, as an inanimate object, incapable of autonomous movement. But if the moving men came and put the chair in a truck, the chair will cooperate. Potential doesn’t withdraw from its own actualization. Rather it’s a matter of probabilities, which seem neutral rather than withdrawn.

The quarter sitting on my nightstand is currently in the heads-up position, but it contains within itself the potential to be tails-up. If I flip the quarter it’s not going to resist coming up tails.

The probability approaches 100% that I will still be an embodied living human being when I post these thoughts on the blog. The probability approaches 100% that I won’t still be an ELHB 60 years from now. The possible trajectories I could have taken in the past are withdrawn save for one: the actual path that I took. The further into the future I project my potential existence, the greater the likelihood that one day I will visit Ulan Bator or  any other remote location on earth that’s part of my low-probability geographical phase space. Some day though, all my futures will join my pasts in being fully used up, fully withdrawn from actualization.



  1. If you are going to accept a “phase space” defintion of the quarter on your night stand, it would have to include an absolute entropic distribution of all its elements such that “nothing” of what you would otherwise call “a quarter” (perhaps a mush of molecules or partical plamsa) remains (not just whether it is heads or tails). Surely this is not the retreating “object” behind the quarter’s identity. In fact, given such an imaginary defintion, a lump of clay taken as a system, and the pot it is molded into, would have to have the same “retreating” object (phase space). The problem with phase space, at least as a solution of identity is that it actually pertains to very specific things, closed systems, and Levi wants to pertain to anything we can see or think of. In other words, anything we can put or “mind’s eye” on.

    When you are talking about the chair you are not talking about a closed system.

    Comment by kvond — 30 September 2009 @ 8:13 am

  2. I added a bit about my own entropization at the end of the post, which wasn’t there when you originally wrote this comment, kvond. So I’m attuned to the issue of entropy which you explored on your prior post about phase space.

    I think that “phase space” can include the ontological space within which some thing or force or event can be regarded as existing. It too is a set of probabilistic contours. How far does the quarter have to degrade before it’s no longer still a quarter? Is its ontological existence a property intrinsic to the quarter itself, or is it a relational, intentional, pragmatic property; e.g., I could still use it to pay for a fraction of a chicken sandwich? Either way, the structural integrity of a thing seems to depend both on the rigidity/flexibility of the informational pattern defining the structure and on the structural integrity of the pattern’s physical manifestation.

    The chair and the quarter are relatively closed systems: both can degrade. The movement of the chair in the world is a relational property of the chair interacting with the world. This was one of my earlier thoughts on phase space: it’s mostly a description of interactive properties. So, e.g., the phase space of a marble rolling downhill from the lip to the center of an inverted conical space: its shape is identical to the cone itself; the probabilities gradually increase from just above zero to 100% at the pointed end of the cone. Interaction of objects with realities is made evident when considering phase space.

    Comment by john doyle — 30 September 2009 @ 8:42 am

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