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"The Concept of State"



From "Life, Itself", page 69, in the chapter called "The Concept of State", under the sub-heading 4B: "Chronicles":
 
Robert Rosen wrote:
"I will begin by stepping back a bit, by supposing that we do not yet have a notion of state at our disposal. In effect, I will retreat to the level of percepts and perceptions and treat the self as a pure observer. The idea of state, being a concept and not a percept, thus does not yet enter the picture at all. Thus, all we have is the self looking out at its ambience. What does it see?
 
All the self can see is a sequence of percepts, ordered by its subjective sense of time. We suppose that the self can choose which percepts it will look at (in more sophisticated language, which variables it will measure) and whether it will look continuously or sample at discrete intervals. (Subjective) time is itself a complicated concept (see AS), but it is a primitive that we can take for granted at this level. Thus, the result of the self looking at its ambience is only a tabulation; a list of what is seen, indexed by when it is seen. Such a list we shall call a chronicle.
 
Chronicles can thus be completely arbitrary things, at least insofar as what is tabulated in them is concerned. Weather bureaus, stock exchanges, census takers, and a host of other familiar institutions provide endless streams of them. In the scientific realm, they are data. To the historian, entirely concerned with what happened when, they are the very stuff of existence.
 
To the (applied) mathematician, and to the statistician, a chronicle is simply a time series. It is thus a way of associating events, or attributes of events, with numbers (instants of time). It is even an effective way of associating events with numbers; all we need to do is wait for the appropriate instant to occur and then tabulate the corresponding event. In formal terms, then, a chronicle or time series is simply a mapping from numbers to events or their attributes; for simplicity, we can even suppose it to be a completely formal mapping from numbers to numbers.
 
But the self is not merely an observer. Doubtless the self has heard of Natural Law, and hence, does not believe in sequences of events that are entirely arbitrary. Further, the self may be impatient and unwilling to wait for the unfolding of time to reveal events to come; it would like to extend its chronicle into the future before the sequence of events does so for it. Likewise, in addition to being impatient, it may be curious about what its time series was like before the self actually started looking at it or tabulating it.
 
So, along with any time series (which we shall think of henceforth as a piece of a mapping from numbers to numbers) comes the urge to extend it into the future and into the past, to extrapolate it, to predict and to post-dict.
 
The most elementary thing we can do in these directions is attempt extrapolation on the basis of the fragment at our disposal, our data. At this level, we do not know or care what the individual entries in our tabulation mean; we try to use the data as the basis for extrapolation into the future or into the past. This is, of course, itself a very syntactic approach; it presupposes that what we need inheres somehow in the very structure of the list or chronicle itself, apart from all other considerations and all other chronicles. Put another way, we seek to extract from the structure of the list itself something that will already entail those entries that are yet to come or those that have come before.
 
Thus, for instance, if the self is a statistician, it will look for correlations which it may or may not find; but in any case, all it can find this way are properties of the list, and not in general of what the list represents. Clearly, Natural Law does not operate at this level. It is not a law that in general favors statisticians, though this has not inhibited their activities.
[A good one-liner there, Dad!]
 
Indeed, the enterprise of trying to find the operation of Natural Law from the contemplation of arbitrary chronicles or lists of data is precisely the dilemma of experimental science itself. At root, of course, the problem is one of induction, which I have already briefly discussed above (see section 2K); it is a problem of extrapolating from a sample of a universe to the entire universe from which the sample was drawn. In the present case, we are sampling in too many ways; we are obviously sampling over an extremely limited time frame, but we are also sampling what we do observe and tabulate from the universe of what we could observe and tabulate. As always, these sampling processes corrupt us in two ways; they lose information precisely because they are samples, and they also add irrelevant information (noise), which pertains to the sampling process itself.
 
As we have seen, the problem of induction is generally hopeless, because arbitrary properties, simply by virtue of being arbitrary, do not reveal themselves in samples. Stated otherwise, no sample entails anything about a non-sampled instance. Hence, the problem of extrapolating arbitrary time series is likewise hopeless.
 
There are two strategies we can adopt to cope with this hopeless situation. The first of these is to retain the idea of sampling but simply sample more and different attributes. Each of these will, of course, just give us other, a new time series, more data. The hope here is that multiple series will do what one alone generally cannot, namely, entail, on the basis of the internal structure of the set of chronicles, what unsampled entries must be (and especially, of course, particularly those entries that are yet unsampled) [future samples].
 
The other strategy is to be more judicious in the attributes we are sampling. Although the arbitrary induction problem is hopeless, there are those properties that do admit sampling and extrapolation. As we saw earlier, these are properties for which entailment already exists between the entries in the sample or chronicle.
 
The concept of state embodies both of these strategies; more chronicles, more judiciously chosen. We will consider what is involved in the subsequent sections."
 
[The next section, 4C, entitled "Recursive Chronicles", has a lot of mathematical illustration, but the final paragraph, which is all prose, sums up what he was illustrating quite well...]:
 
"In general, whenever we isolate something, either in the ambience or in the internal world of the self, and ask "why?" about it, we are treating it as an effect and inquiring about its causes. One way to cope with such questions  is precisely to produce a recursive chronicle, a history, which starts from some convenient initial condition and takes us to the effect we inquired about, through a chain of successive entailments (i.e., a trajectory) arising from a mapping and its iterates. In the circle of ideas we are in the process of developing [that describes what contemporary physics "believes"], which will culminate in the concept of state, causality manifests itself only through a sequence of state transitions, entailing an effect that is again a state. Although, as we shall see, a number of important tactical details intervene, this is the basic picture that permeates all of contemporary science. If there is something wrong with the picture, or especially if there is something missing from it, then the root of the trouble lies already here."