[ExI] "The Empirical Object", by Dr. Sunny Auyang
lcorbin at rawbw.com
Wed Jul 18 17:31:17 UTC 2007
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
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
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
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
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
[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
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.
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