[ExI] "The Empirical Object", by Dr. Sunny Auyang

[Lee Corbin]

This is an excerpt from Sunny Auyang's book, "How is Quantum
Field Theory Possible?".  The section is "The Empirical Object"
and begins on p.99.  One purpose served here is that anyone
curious about the book can see a sample page of her writing,
(which I happen to consider to be extraordinarily clear, although
difficult to get through because of the difficulty of the material).

I will intersperse my own comments and summary from time to time.


"The Empirical Object"  (by Sunny Auyang)

"Object" is used in two senses in the following. The narrower sense is the *physical object* whose state is represented by x in Fig. 
5.1.[in a typical differential geometry type diagram, where x is a point in an abstract manifold]. The broader sense is the 
*empirical object*, the topic of knowledge. "Empirical" here includes only the conceptual aspect of experiences, which are 
recognized as a kind of representation; it does not include the sensual aspect, which was considered in section 12. An empirical 
object is an object-variously-representable-but-independent-of-representations. The concept of empirical objects is represented by 
the full structure in Fig. 5.1; it includes the physical object as a conceptual element.

   Okay, the most of this may not be making much
   sense to you if you have not been reading the book.
   It should become clearer, however:

The introduction of the physical object whose state is x not only adds an element in our conceptual structure; it enriches the 
elements discussed earlier. For the first time [in the book], the idea of representation *of* something is made explicit. The 
physical object reinforces the common-sense notion of things that are independent of our representations. On the other hand, since 
representations are associated with observations of things, the idea of phenomena becomes more weighty. The multiplicity of 
representations of the same object forces us to acknowledge the idiosyncrasies of particular representations; hence it clarifies the 
meaning of conventionality.

   Here x is an element of a "manifold", which in this
   case is an abstract state space of all the *possible*
   states that the thing (ordinary object) could be in.
   In differential geometry, x is a point in the manifold
   M introduces the possibility of "coordinate functions"
   So picture M as a two or three dimensional space
   residing "above" one or more coordinate spaces (that
   is, ones composed of ordinary Euclidean coordinate
   systems.

   The functions fa and fb are arrows from x into these
   coordinate patches. ("Patch" is really the technical
   term for the one or more N-dimensional coordinate
   spaces just described.) Again, all this is standard
   differential geometry (of manifolds).

   But I can hardly do justice to dozens of preceding
   pages of the book which might make what you are
   reading more understandable.

Since the object x is categorically different from any of its representations, the mean of [the coordinate function a] is no longer 
unanalyzable.  It is now coordinates-of-x equals fa(x),
reading "the value coordinate-of-x for the property type fa", the predicate coordinates-of-x of x in the representation fa(M)", or 
"the appearance of the coordinates-of-x from the perspective fa(M)" Various representations can be drastically different, but they 
represent the same object. The same electromagnetic configuration that is a mess in the Cartesian coordinates can become simplicity 
itself when represented in the spherical coordinates. However, the two representations are equivalent.

   Okay, here is what this is all about. There are real
   things out there ("ding-an-sich") which in scientific
   theories may be represented by a state space. That is,
   each of the supposed states of the object is a point
   in the manifold representation (or theory, or picture).

   x is a point in the state space. So we cannot quite
   say that "x *is* the object", else we run afoul of
   all the problems Korzybski warned about when we use
   the word "is". In a literal sense, x only represents
   a physical object in a particular state. In your
   physical theory.

   This really does soon get back to people and how people
   understand the universe, hang tight!

   fa (the function f-sub-a describes x in one coordinate
   system, say rectangular) and fb (another function that
   takes the point x into a coordinate space) are further
   representations of x, but this time in ordinary coordinate
   systems. Sadly, I cannot find any good pictures on the
   web to illustrate this, but this here isn't too awful:
   http://simple.wikipedia.org/wiki/Manifold, but you
   don't see the arrow functions fa and fb from x into
   ordinary coordinate systems.

   The point is, like she says, that various representations
   of the same object can be quite different.

[The last heavy-duty math paragraph]. Since fa and fb are imbedded in the meaning of coordinate-function-a-of-x and 
coordinate-function-b-of-x, the transformation fb of the inverse of fa connects the two representations in a necessary way dictated 
by the object x.  fb of f-inverse-b is a composite map. It not only pairs the two predicates a-coordinates-of-x and 
b-coordinates-of-x, it identifies them as representations of the *same* object x, to which it refers via the individual maps 
f-inverse-a and fb. Since fb of f-inverse-a always points to an object x, the representations they connect not only enjoy 
intersubjective agreement; they are also objectively valid. To use Kant's words, the representations are no longer connected merely 
by habit; they are united *in the object*.

   I regret for not being able to use the real math symbols
   in this medium, and I also regret that I could not find
   on the web a good picture of an "atlas" with its coordinate
   functions that appears in dozens of books. In fact,
   Auyang's diagrams are excellent, but rather standard.

   The next (math-free) paragraphs make this clearer, I hope.

The objective state x is called coordinate-free or representation-free. This is not an arbitrary designation but an active negative 
concept that signifies a *lack* of representation. The invariant x explicitly articulates the commonsense notion that physical 
objects are independent of our conventions and free from the arbitrariness of our perceptual conditions. A negation is a distinction 
between what is and what is not; for instance, what is given and what is not, what is conventional and what is not. A theory must 
have certain minimum conceptual complexity to internalize a distinction. The negativity, being free from or independent of, drives a 
wedge between the physical state and its representations, which become truly significant in the larger conceptual framework. Since 
modern physical theories have internalized the distinction signifying detachment, they themselves can assert objectivity for their 
objective statements, a task of which older theories are incapable.

The repressentation-transformation-invariance structure can also represent momentary perceptual experiences.

   There is a whole previous section in the book about
   the "representation-transformation-invariance"
   structure. It's quite interesting and important, but
   basically it's really nothing more than this
   same diagram that shows a Manifold, and a couple of
   coordinate functions that take points, or a typical
   point x, in the manifold to coordinate spaces.
   The paragraph continues

The content of an experience is represented by the coordinates of [x in the a or b Euclidean space], for observations are always 
specific. The conceptual complexity of the equation that equates the a-coordinates-of-x to the value of the function fa(x) implies 
that we directly access the object x in our experiences and do not indirectly infer it from some given sense impressions. The object 
is not a transcendent reality but is immanent in experiences. Looking at the other side of the coin, the phenomenon 
"coordinates-of-x" is not a semblance of mere appearance that stands for something else; it is what the object shows itself in 
itself. The idiosyncrasy in coordinates-of-x is ascribed to the conditions of experience. The conceptual complexity implies that our 
experiential content goes beyond mere sensory stimulation. When we observe a particular representation coordinates-of-x, we 
simultaneously observe [or are aware of] the invariance-under-transformations-of-representations [her hyphenated words, not mine]. 
Suppose x represents a round table and [the a-coordinates of x and the b-coordinates of x] various elliptical profiles. When we see 
the table from an angle, we see *in* the particular profile its invariance when seen from alternative angles. This is how we 
distinguish a round table from an ellipse.

   Understand what she's saying here? There is a real
   table out there, and the whole "categorical framework"
   we use when applying common sense allows us to
   understand that the mere appearances (depending
   on angle) are not to be confused with the thing-in-itself.
   The appearances are like coordinates, or the values of
   coordinate functions taking points in the state space
   of the object (table) to appearances.

The categorical framework of objects is a unitary whole. The physical object x is neither posited in advance nor constructed out of 
its representations afterwards. It is defined simultaneously and encoded in all its representations in the integral structure. 
Neither the representation-free x nor the representation a-coordinates-of-x alone is sufficient to characterize the primitive unit 
of empirical knowledge. Both and their interrelation are required; x realizes the general conditions for the possibility of objects 
*and the coordinates the general conditions for the possibility of experiences of objects*. The two arise together in objective 
knowledge, as Kant argued. Representation-transformation-invariance is an integral structure that realizes the general concept of 
empirical objects in physical theories.

Since the concept of empirical objects has enough complexity to endow the content of experiences with meaning beyond what meets the 
eye, it can account for doubts, errors, illusions, and partial knowledge. There are enough elements in the categorical structure so 
that some can be left blank without a total collapse of comprehension. We may know a-coordinates-of-x but not b-coordinates-of-x, or 
we may know both but not the transformation relating them.

   A nice example she gave earlier is that of a desk. "Imagine," she
   wrote on page 92, "two persons seeing something. One says it is
   a sea of electrons in an ionic lattice. The other says "What? It's
   a plain old metal desk," and mutters, "crazy physicist".

   So there is this same object x (or represented by x in the state
   space) and two different coordinate functions on x. What is
   important is that in order to be able to understand each other,
   we require fa of f-inverse-b, or in other words, a way of
   connecting the two descriptions. Our common sense does have
   this ability, though when two people cannot understand each
   other, it is because no such function "fa of f-inverse-b"
   has so far been found.

Philosophically, the importance of the representation-transformation-invariance structure lies in the conceptual complexity of the 
general structure and not in the details of the various elements. It is the adoption of something like it instead of the simplistic 
structure of the given and the conventional that differentiates common sense from phenomenalism, metaphysical realism, and 
conventionism.

   I hadn't even known that there was a doctrine called "conventionism".
   She's saying that these other theories just don't have enough
   conceptual complexity. But common sense does! And her goal is
   to explain how common sense actually works. More about conventionism
   coming up.

[The paragraph continues] The conceptual structure points out the possibilities of various representations and transformations but 
neither prescribes the procedure rules for formulating them nor guarantees they can be successfully formulated. In mathematical 
physics, the representations are rigorous and the transformations explicitly performed. In our everyday thinking, the 
representations are sloppy and often defy exact transformations. However, this does not warrant a lapse to conventionism, which 
denies the general idea of transformations because specific transformations fail. [I have to take her word on this; I don't know 
anything about "conventionism".] On the contrary, the imperfection of specific representations makes the general conceptual 
complexity more important, for it alone allows the thoughts of approximations, idealizations, and improvements in objective 
knowledge.

The representations may be partial in the sense that they characterize only one aspect of the objective state. For instance, the 
momentum representation does not include the spin of an electron. Representations of different aspects cannot be connected by 
transformations. Einstein was dissatisfied with special relativity, saying "what has nature to do with our reference frame?". He 
expanded the theoretical framework so that more representations are included and connected in general relativity.... The world of 
our daily activity is much more complicated than the world of basic physics. Often various "world constructions" highlight various 
aspects and are therefore not mutually translatable. They should not distract from the objectivity of knowledge in general, for the 
important idea is the recognition that they are representations, and representations can be partial.


Conclusion: By "The object is not a transcendent reality but
is immanent in experiences" what is meant is that for the
ordinary object, empirical object, the (our) topic of knowledge.
The rest of this had to do with "object" in the narrower sense,
a piece of Kant's view, evidently.

My favorite line in the book is "I have never seen a sense
impression in my life". In other words, we see objects;
we *perceive* (I suppose) sense impressions. So the realism
of "I see a car coming towards me" is supported, and other
theories that might tempt one to say (when speaking
precisely) "I see the sense impression of a car coming
towards me" are denigrated.

Lee