More on Combinative and Coincident Information Architectures

Posted on Fri 27 August 2010 in Situation Theory

In the interest of exploring Perry and Israel's information architectures further, I will elaborate upon my previous post on the topic, and give a more fine-grained account of some of their ideas.

Suppose that we take as signal the presence of smoke, and its indicated content that there is a fire, relative to the natural constraint that if there is smoke there is fire. Perry and Israel distinguish two kinds of indicated contents, reflexive and incremental:

Reflexive: The fact that smoke is present carries the information that there is a fire which produced the smoke that is present.

Incremental: The fact that smoke is present carries the information that Matt has started the cooking fire.

Reflexive contents are more general or abstract, depending on the properties of the signal to "pick out" the object in question. Reflexive information is characterized by having the carrier of the signal occur in the indicated content of an informational statement. Incremental contents instead rely on connecting facts such as the fact that it is a cooking fire, which Matt would have started, and so on.

Having reviewed reflexive and incremental contents, we consider Perry and Israel's first information architecture, the coincident architecture in which the architectural relationship between indicating properties induces a relationship between their indicated contents.

In the following section I will be following their paper's discussion very closely. Consult their paper for further information.

Coincident Architectures Revisited

We start with Perry and Israel's paradigmatic example of a coincident architecture: a mechanical device that simultaneously measures a person's height and weight. The architectural relationship between the component that measures height and the component that measures weight is such that the person's whose weight is being measured is the same person whose height is being measured; this architectural constraint between indicating facts or signals induces a relationship between their respective indicated informational contents.

Following Perry and Israel, to make this concrete, suppose that a person, Elwood, is at the doctor's office and is standing on the device. Perry and Israel describe possible reflexive and incremental contents of each signal independently (p. 150):

Reflexive indicated contents:

(1a) The fact that the weights on the weight bar are at 100 and at 80 carries the information that the man affecting the weight bar weighs 180 pounds.

(1b) The fact that the height bar is at 5 carries the information that the man whose head it contacts is 5 feet tall.

Incremental indicated contents:

(2a) The fact that the weights on the weight bar are at 100 and at 80 carries the information that Elwood weighs 180 pounds.

(2b) The fact that the height bar is at 5 carries the information that Elwood is 5 feet tall.

The reflexive content would be true of any man weighing 180 pounds with a height of 5' standing on the scale. The incremental content is factual only in case that man is Elwood. The latter relies on a connecting fact, namely that Elwood is the man affecting the weight bar and whose head is in contact with the height bar.

Notice however that the contents (1a) and (2a) make no reference to the height bar, and those in (1b) and (2b) make no reference to the weight bar. In some sense they each stand independent of the architectural relationship existing between the height bar and the weight bar. Perry and Israel contrast these with the following contents (p.150):

Architectural contents:

(3a ) The fact that the height bar is at 5 carries the information that the man affecting the weight bar is 5 feet tall. (emphasis added)

(3b) The fact that the weights on the weight bar are at 100 and at 80 carries the information that the man whose head the height bar contacts weighs 180 pounds. (emphasis added)

These contents are like reflexive contents, except that they rely on a connecting fact and constraint existing between the weight bar and height bar.

Perry and Israel designate these relations, facts, and constraints as follows (p. 150):

With (3a) and (3b) a new sort of connecting fact and a new sort of constraint is involved. The fact is just that the height bar and the weight bar are parts of an apparatus of this sort. We shall call such facts architectural connecting facts, and the relations involved in them architectural relations. The weight bar is the architecturally connected carrier in (3a); it is the height bar in (3b). The constraint reflects the architecture of the apparatus and facts about the shape and size of humans: if a weight bar and height bar are connected that way, the person whose head contacts the height bar is the person who is affecting the weight bar. We call the sort of constraint involved in (3a) and (3b) an architectural constraint and the relation between persons (in our case, identity), the architecturally grounded relation. Information relative to architectural connections and constraints, we call architectural. (p. 150) (note: numbering changed for presentational purposes).

Perry and Israel suggest that an analysis of an information architecture needs to be able to answer the following four questions:

(i ) What are the architectural relations—that is, how are the carriers related?

(ii ) What is the architectural constraint?

(iii ) What relationship among the contents is determined by this architecture? Is this relationship induced or reflected by the architecture?

(iv) How are the constraints and connecting facts in the signal structures related to one another and to the architectural constraints and connections? (p.151)

Regarding the previous example, they answer these questions as follows:

(i ) The doctor’s apparatus is constructed so that the height bar is directly above the platform, force upon which affects the weight bar.

(ii ) This relation, in virtue of facts about the shapes and sizes of human beings, guarantees that the person whose head is in contact with the height bar is the very one whose feet are on the platform, and hence the one whose weight is registered by the position of the weights on the weight bar.

(iii) Thus, the subject matter of the two signal structures is the same; this is induced by the architecture, not merely reflected by it.

(iv) In this case, the original constraints are independent of one another, and of the architectural constraint. If the weight bar is broken, the apparatus can still be used to measure height, and vice-versa. (p. 151).

Combinative Architectures Revisited

In a combinative architecture, the relation between the signals reflects rather than induces the relation between their respected indicated contents. For example, the relationship that exists between several documents may be that they pertain to the same topic, or have the same author. For this reason they may be placed in a folder or file as a signal indicating the relationship that exists between them. In general there will be many relationships; in a designed system, it is the job of the architecture to make the target relationship cognitively relevant.

Perry and Israel use a patient's medical files a paradigmatic example. A dictionary might work as well. A dictionary organizes its text by alphabetizing the words to be defined. It is not by having a dictionary so ordered that their respective words can be alphabetized; rather it is the fact that the spellings of words can be alphabetized that is reflected by the organization of the dictionary. In this latter case, the architectural relation is not one of identity, but of ordering. Another example would be to imagine fingering a quarter and determining through the feeling in your finger-tips which side of the coin is which. Clearly your sensory perceptions reflect rather than induce which side of the coin is which (assuming veridical perception, of course).

Induced Reflections and Reflected Inductions

The last example considered above is good reason to pause and reflect upon the intimate relationship that seems to exist between combinative and coincident architectures, namely that they frequently occur in pairs*.

Consider the reflection on the water of two birds flying south over a lake. The signal carriers are the reflections on the water, the indicating property that they are reflections that appear like birds that are moving in a southerly direction. The indicated contents that they are two birds flying south over the lake. The architectural connecting fact is the reflective surface of the water, the architectural relation that the reflections of two birds are next to each other, the architectural constraint being that when two objects appear to be next to each other in a reflection, the reflected objects are in fact, under normal circumstances, next to each other. Most critically, the architectural relation between the two figures in the reflection does not induce the fact that the two birds are next to each other; rather the reflections in the water reflect the architectural relations between their indicated contents.

But we see that a coincident architecture is discernible in the other direction. The indicating fact that birds are flying south over the reflective surface of a lake carries the information that the reflections of two birds next to each other will appear on the surface of the lake below. Clearly the relationship between the birds in the air (that of being next to each other) induces the architectural relationship between their respective reflected images on the surface of the water, given various constraints related to the lighting conditions and reflectivity of the water, etc.

Coincident-Combinative Architectures

When I look at someone's face, I have no trouble seeing the color of their eyes and the color of their hair and the fact that these features belong to the same face. But this situation should not be taken to be typical. In general the fact that an architectural relationship between two indicating facts induces a relationship between their respective indicated contents may not be obvious to any cognitive agent. Such relationships may have to be discovered.

Let us modify the original example introduced by Perry and Israel. Suppose that when our mechanical device measures the height and weight of Elwood, it sends an insertion query to two separate database tables, one for height and and one for weight, in such a way that the fact that the two measurements are measurements of the same person is lost. So, although the coincident architecture remains intact, the information about its respective indicated contents is lost. Elwood and the doctor have no way of discovering the results of these measurements. It is this potential to lose the architectural relationships induced by a coincident architecture, that such things as labeled folders in doctors offices are necessary.

To remedy this situation, the doctor calls in a database specialist who tells them to take database theory 101: their database tables need primary keys such that each record is uniquely identified, and the relationship between records can be specified. The specialist recommends that each patient be given a unique patient id, and this patient id be used as a primary key, so that when a doctor needs to find both weight and height, records with the common key can be matched**. This key information provides a combinative architectural mechanism by which the original relationships between data can be preserved.

Further Directions

In my next post I will discuss combinative and coincident architectures in relation to programming languages. I would also like to work out an analysis of ritual performance in this vein, inspired in part by Roy Rappaport's information-oriented accounts of ritual outlined in Ritual and Religion in the Making of Humanity. Readers suggestions on this account are most welcome. Also, no discussion is complete without considering flow architectures, which are orthogonal in many ways to the architectures discussed here.


Israel, David, and John Perry. Information and Architecture. In Proceedings of the Second Conference on Situation Theory and Its Applications, edited by Jon Barwise, Jean Mark Gawron, Gordon Plotkin, and Syun Tutiya, 147-160. Vol. 2. Stanford, CA: Center for the Study of Language (CSLI), 1992.

* this is not to say that they must always occur in pairs, or that if they do occur in pairs, the pairing is one is a reversal of the other. A frequent situation in user-interface design is the need to design an interface that reflects the architectural relations of some set of features but where such a relation in the user-interface design is not induced by that architecture. To take an example from Donald Norman's book The Design Of Everyday Things, the control knobs of a stove are ideally arranged so that each knob simply maps (geometrically) to a corresponding burner on the stove: e. g.

B1 --------B2

| / (burners) B3----B4


| / (control knobs) K3----K4

where Bi maps onto Ki one-to-one. But such an arrangement of knobs is hardly required by the arrangement of burners.

** a more practical solution would probably be to also combine these two tables, but that would ruin my example, wouldn't it?