hull@hao.UUCP (Howard Hull) (12/29/84)
I wish to approach the matter of Causality, Determinability, and Determinacy
by placing before you the following "strawman" model, derived largely from the
techniques used in Weinberg's "An Introduction to General Systems Thinking"
(Wiley 1975).
Suppose that a creator makes a 21-dimensional universe. The 21 dimensions are
perhaps different in character, in that some of them are time-like, some are
space like, some are momentum-like, and some are gravitational/mass-like. The
thing that defines the notion of dimensionality is that each dimension is an
"orthogonal regime", that is, apriori, it does not couple to any other regime
except by means of a transform expression (I will, for the present, place no
restrictions on the description of the transform expression).
Now suppose that the 21-dimensional universe is further segmented into 3 groups
of 7 dimensions each, and that these 3 groups have a superimposable symmetry.
Each is a *statistically* similar system full of "billyions and billyions" of
objects. As an aside, please note that a multi-dimensional object has many
descriptions; these may be merely regarded as descriptions of the object from
many different "viewing angles". Often such objects are labeled by that viewing
angle which, to a particular set of observers, produces the most distinctive
projection of the object. However, please note that the character of an object
is not dependent upon which angle the observers agree is the one that defines
its "name".
In the beginning, we make the rule that the transform expression allows no
commutation of any property from one of these 3 groups to any other of the 3
groups. At an appropriate point in the ensuing presentation we will want to
change this rule in some specific ways. We also make the rule that we have
various classes of observers; some can couple to only one group. Others can
couple to two groups. The creator not withstanding, no observer is sensitive
to all three groups (the creator is not a "traditional" observer). We require
that all observers must perturb (i.e. influence, even if microscopically) a
group in order to gain knowledge about its state. The creator is the only
observer capable of knowledge of the universe without perturbation. We are
perhaps also, for the purposes of this discussion, forced to require that those
observers who have the capacity to "see" more than one group do not couple a
perturbation from group to group. At the start, we declare that each group
is absolutely deterministic in the sense that the sequence of events, observer
perturbations and all, can be replayed from start to end.
At this point, we could say that each of the 3 groups, although similar to the
others, is an independent object. These are the assumptions of the model. To
appreciate the model, we will have to be critical of the sensitivity of the
behavior of the model and the state of knowledge of the observers (both in
quality and in quantity) to these assumptions. In a way, it must be realized
that each batch of observers is a part of the respective group to which it is
coupled.
The creator gets the universe running by assigning (randomly) 7-dimensional
magnitudes to each of the objects in each of the 3 groups (remember, there are
"billyions and billyions" of objects in each group). When everything has run
until the creator becomes bored with it all, he stops the thing and then he
gathers all of the observers together and asks them to discuss whatever they
observed. Now, for the sake of brevity, I will state what I think shall be
the case. Each group of observers should be capable of agreement concerning
the interpretation of what they saw. If not told that there were 3 separate
groups, the observers will, as grouped classes, argue until hell freezes over
concerning the group-separated details of what happened. However, they should
be able, even as separate groups, to agree concerning rules of the universe,
and the statistical behavior of objects in a universe of this sort. The
resultant statement concerning Causality, Determinability, and Determined
behavior will be: 1). Things in a universe have causal relationships as long
as it is me and thee (our group) that observes them. Everyone else has seen
things queerly. 2). There were some things that thee and me could not have
found determinable. The others have the same problem, but concerning their
particularly queer set of observations. 3). Only the creator will know for
sure that the universe was Determined.
Now the creator runs the universe again, in a manner similar to the preceding,
except that he allows the transform expression to be responsible for the
transportation of *some* quantities from one group to another. For the sake
of limiting the net discussion to four or five gigabytes, we can assume that
the commutative properties are expressed the same group to group, and are
essentially non-random in character. Again the creator becomes bored with it
all, and gathers the observers together for a discussion. As above, I will
put my tender pink body on the line by stating what I think the conclusions
will be: 1). Things in a universe have causal relationships no matter who
observes them. Not only are those other creeps more like me and thee, but
we all are more completely aligned to the creator's image. 2). There were
*still* some things that thee and me could not have found determinable, and
those other creeps had trouble determining closely related things that seem
suspiciously connected to what we were doing. 3). Only the creator will
know for sure that the universe was Determined. To wit: The importance of
the transform coupling is that it makes us all more "competent" as observers,
but it doesn't eliminate our temporal/spatial incapacity.
We can continue along these lines, varying the properties of the transform
and the intentions of the creator. Things will not entirely make sense to the
observers until it is set up so that the observers all know what he knows.
In particular, as Ken Arndt points out, the fact that the observers can see
only one isolated property for each measurement they make is crucial to the
development of a sensation of random behavior. The data are undersampled.
This results in a horrible aliasing of otherwise depictable and deterministic
situations. Under these circumstances, the description of things becomes
non-absolute, and mostly statistical in character.
Howard Hull
{ucbvax!hplabs | allegra!nbires | harpo!seismo } !hao!hullfderavi@cybavax.UUCP (F. Deravi) (01/10/85)
The statement in H. Hull's article attributed to K. Arndt > ... , the fact that the observers can see > only one isolated property for each measurement they make is crucial to the > developmnent of a sensation of random behaviour. may be criticized on several fronts. If an observer *could* observe two *isolated* properties in the one observation, taking each property to be resident in one of the sets of seven ( why seven ? ) dimentional space, the observer must simultaneously interact with set 1 space and set 2 space. But nothing in set 1 can interact with set 2 which places the observer in a rather odd position. If a perturbation in the observer due to set 1 and a perturbation in the observer due to set 2 could NOT interact, which would be necessary for no interaction between set 1 and set 2, then the poor observer would be formally regarded as two individual non-interacting observers. Ken Arndt's point then has no real meaning in the physical sense. There is a similar problem with H. Hull's examples. His 3 sets of seven dimensions could only be completely independent if an observer could see, at most, those properties in the one set if some kind of "superspace" ( which includes the divine intervention of Hull's examples ) was then made available to an observer in one set to argue with an observer from another set, any points of agreement, disagreement or ability to communicate in general would be entirely a function of that superspace. Andrew Mackay, edited by F. Deravi. - - - - - - - - - - - - - - - - - - - - - - F. Deravi, | UUCP : {UK}!ukc!ru-cs44!cybavax!fderavi | EE, University College, | JANET : fderavi@swxa/234207920018 | Swansea, SA2 8PP, U.K. | phone : +44 792 205678 Ext. 4565 | - - - - - - - - - - - - - - - - - - - - - -