Example of How Meaning Is Attached to Structure

What follows is a detailed example of the thought process followed by a software developer to create a class of data structures and how meaning is attached to those structures.

Consider that the meaning of one data structure may be composed of the collection of meanings of a set of smaller structures which themselves have meaning. Take the following description as the meaning to be represented by a structure:

An employee is a human being or person. Each employee has a unique identity of their own. Each employee has a name, which may be the same as the name of a different person or employee. Being human, each employee has an age, calculated by counting the number of years since they were born up to some other point in time (such as present day).Each person of a certain age may enter into a marriage with another human being, who in turn also has their own identity and other attributes of a person.

To represent this information using data structures (i.e., to project the meaning of this information onto a data structure), we might tie the various concepts about a human being/employee to a computer-based data structure. Recognizing that a human being is an object with many additional characteristics of which we might want to know about, we might choose to project the concept of “human beings” or “people” onto a relational table and the concept of a particular individual onto one of that table’s rows (or a similar record structure).

This table would represent a set of individual human beings, and onto each row of the table would be projected the meaning of a particular human being. Saying this again in a more conventional manner, we would say that each row of the table will reference a singular and particular human being, the all of the rows will represent the set of all human beings we’ve observed in the context of our usage of the computer system.

In a more mathematical vein, we would define a projection Þ from the set of actual human beings Α onto Š, (Þ(Α) |–> Š), the set of data structures such that for any α in Α where α is a human being, there is a record or row σ in Š that represents that human being.

A record data structure being a conglomeration of fields, each of which can symbolically represent some attribute of a larger whole, then we might project additional attributes of the human being, such as their name and identifier, to particular fields within the record. If σ is the particular record structure representing a particular human being, α, then the meaning (values) of the attributes of that person could be associated with the fields, f1..fn, of that record through attribute-level projections, ψ1..ψn for attributes 1 .. n.

To represent a particular person, first we would project the reference to the person to a particular row, Þ(α) |–> σ, then we would also project the attribute facts about that person onto the individual fields of that row:

ψ1(α.1) |–> σ.f1

ψn(α.n) |–> σ.fn

Projection onto Relational Structure

When modeling a domain for incorporation into computer software, the modeler’s task is to define a set of structures which software can be written to manipulate. When that software is to use relational database management systems, then the modeler will first project the domain concepts onto abstract relational structures defined over “tuples”. These abstract structures have a well-defined mathematical nature which if followed provides very powerful manipulations. The developer projects meaning onto relations in a conventional way, such as by defining a relation of attributes to represent “PERSON” – or the set of persons, and another relation of attributes to represent “EMPLOYEE” – or the set of persons who are also employees. Having defined these relational sets, the relational algebra permits various mathematical operations/functions to be applied, such as “JOIN” and “INTERSECTION”. These functions have strictly defined properties and well-defined results over arbitrary tuples. The software developer having projected meaning onto the individual relations, he is also therefore able to project meaning on the outcomes of these operations which can then be used to manipulate large sets of data in an efficient, and semantically correct way.

As the developer creates the software however, they must keep in mind what these functions are doing on two levels, at the level of the set content and at the level of the represented domain (the referent of the sets and manipulations). Thus the intersection of the PERSON and EMPLOYEE relations should produce the subset of tuples (records, etc.) which has its own meaning derived from the initial projected meaning of the original sets. Namely, this intersection represents the set of PERSONS who are also EMPLOYEES, (which is the same, alternatively, as the set of EMPLOYEES who are also PERSONS). This is an important point about software: the meaning is not simply recorded in the data structure but the manipulations of the data by the computer themselves have specific connotations and implications on the meaning of data as it is processed.

Representational Redundancy

As a typical practice in the projection of information onto data structures within the relational model, there will usually be a repetition of the information projected onto more than one symbol. In particular, the reference to the identity of a single person will be represented both by the mere existence of a single row in the table, and also by a subset of fields on the row which the software developers have chosen (and which the software enforces) for this purpose. In other words, under common software development practices, each record/row as a conglomerate entity will represent a single person. In addition, there will be k attributes (1 <= k <= n) on that record structure whose values in combination also represent that same individual. These k attributes make up the “primary key” of the data structure. The software developer will use and repeat these columns on multiple data structures to permit additional concepts regarding the relationship between that person and other ideas also being recorded. For example, a copy of one person record’s primary key could be placed on another person record and be labelled “spouse”. The attributes which make up the primary key often have less mechanical meanings as well (for example, perhaps the primary key for our person includes the name attribute. As part of the primary key, the name value of the person merely helps to reference that person. It also in its own right represents the name of the person.

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Context Shifting Is Easy

Today’s discussion asks that you perform a thought experiment.

Imagine that you are sitting in a room with a bunch of other people. All of your chairs face to the front of the room where there is a large desk. A young woman walks in with a stack of papers and places them on the desk. She picks up a piece of chalk from the desk, then, still standing, she turns to face all of you, smiles and begins to speak.

Right here I’m going to pause the narrative and ask that you consider the situation. Imagine it in your head for a moment. What is the context Ive described?

So what do I mean by context? Well if I were to say that our story so far is a very familiar context for most of us, one we all remember from childhood: an elementary school classroom, then here are some of the things you might expect to happen.

Having now stated a context, you, dear reader, should have images of yourselves sitting quietly in your desks while your teacher imparts some lesson. You also already know many of the basic ground rules of being in a classroom:

  • Pay attention to the teacher
  • Take notes
  • Don’t speak unless the teacher calls on you
  • Raise your hand if you have a question or comment and the teacher will call on you

Do you recognize this context? Feels familiar and confortable, right? Great! Let’s hold this thought now and count slowly to twenty while we let the memories of this context play about in our heads.

Really, start counting, or you won’t get the total effect:

1, 2, 3, 4, 5

6, 7, 8, 9, 10

11, 12, 13, 14, 15

16, 17, 18, 19, 20

Now let me throw you a little curve ball and tell you that you’ve been thinking about this in the wrong way. The situation I described is not really a classroom and that woman is not a teacher. She’s an actress, presenting a one-woman show about a famous teacher. The desk is a set, the papers just props. You are not in a classroom, you are in a theater made to appear as a classroom. This is just a play and you are a member of the audience. In fact, so there’s no doubt in your mind about this, you suddenly remember you put your ticket stub in your front pocket.

Did you feel that grinding sensation in your head as you read these last few sentences? That shifting from the classroom to the theater context – you should actually be able to feel it happen in your mind. The fact that even this little bit of information has allowed you to sense a shift in context is not a trivial matter. Usually, when you switch contexts like this, it is never so palpable or apparent. We humans are switching contexts all of the time, sometimes in the same sentence. It is one of our particular talents to recognize and adjust our conceptualizations at will when the context changes.

We have just completely switched contexts and you didn’t even need to lift a finger, did you? Just by my saying “this is a play” your expectations have completely changed. Now that we’re in the “performance context” what has happened to our mutual expectations. First of all, the roles have shifted, instead of a teacher, our woman is an actress, you, dear reader, are not students you are an audience. As a member of the audience (especially an audience witnessing a play about a teacher) here are some of the different expectations you may now have:

  • If you raise your hand, you may get an usher, but the actress will not respond to you
  • While you will still sit quietly and listen, the expectation is that at the end of the performance, you will clap your hands
  • The actress will provide the audience (hopefully) with an entertainment

So, shifting contexts is easy. And thus, I end this little monologue by pointing out that really, dear reader, we aren’t in a theater either. Instead, we’re sharing a context called “reading a blog entry”. I hope you enjoyed this little exercise!

Bridging Contexts

If it’s true that every human grouping can form its own context, how can communication occur between different groups? If one group defines a set of symbols using some set of concepts and a syntactic media that is different from those of another group, as a practical matter, how can the chasm be spanned? The answer is through the development of bridging contexts.

The following figure depicts several common strategies, each with its particular benefits and drawbacks.

Three Types of Bridging Contexts

Three Types of Bridging Contexts Within One Corporate Organization

There are three basic forms of bridging contexts. First and perhaps the most common in the real world is the creation of a specific, point-to-point bridging context through discussions/negotiations between the representatives of the two specific contexts. Most organizations take this approach because it simplifies, focuses and shortens the discussion, leading to faster turn-around. All application and data interfaces that are custom-built as point-to-point connections, no matter what the actual transmission protocol or language used, fall into this category.

The second form of bridging context occurs when two groups rely on a pre-existing, parent context to act as the bridge. The parent context may push a common context down onto the previously individual contexts, or the two contexts may appeal to the parent to resolve the conflict. In either case, the result can be that the child contexts become absorbed by the parent context, thus eventually what began as a bridging context becomes the entire context. These forms of bridging contexts are often common in such situations as corporate mergers, enterprise architecture initiatives, and business process reengineering projects.

The third form of bridging context is found whenever an organization selects a third-party standard as a communications protocol. In these cases, the organization creates a bridging context between itself and the external standard, including mapping its symbols into those of the standard. Theoretically, once completed, the organization can use such a bridging context to communicate with other organizations that have likewise built bridges to the standard. In practicality, however, it is not uncommon that organizations will bias their bridging context to their own point of view. When this happens, the external standard devolves into mere syntax, and other organizations must create new, subtle bridging contexts (a la form number one) in order to communicate successfully with this organization. This was a common occurrence in the heyday of Electronic Data Interchange (EDI), and still occurs today even with more modern, XML-based standards.

While proponents of standards bodies decry other approaches, it must be stated that the third form of bridging context is also the most complicated to develop, as well as requiring the longest amount of time to establish, and is often the hardest to maintain. The reason for this is that it requires so many more people to define, and for most situations, the key to its success is also its biggest drawback, namely that the context is defined externally to the organization. Thus, the interplay among the membership of the standards body creates the external context. The organization has a business activity establishes the local context. The humans involved in establishing the bridging context must be able to translate from the local context to the external standard. There is always a risk that these individuals will misunderstand the external standard and translate their local context to it incorrectly. In addition, the bridging context must be maintained constantly as changes occur both in the standard and in the internal organization. At least within the local context, it is more likely that a change will be noticed.

In addition to EDI and XML protocols, other examples of the third form of bridging context would include Semantic Web approaches, but also such mundane approaches as the use of ERP systems, or any other packaged application where a fixed syntactic media is presented.

Context As Observer

Consider a context as a reflection of one point of view. As a frame or lense through which the external environment is observed. The “things” that “matter” to the context are the events or features which are both:

  • VISIBLE – or otherwise perceptible, and
  • NAMEABLE – or describable/categorizable

If something is imperceptible, then obviously there will be nothing to notice – no “referent”. In this case, imagined perceptions will be included as “perceptible”. If the thing which could be perceived is not nameable or otherwise describable within the context, then the context hasn’t noticed it and it does not exist.

That is to say, that a reality exists independent of any particular context, but in terms of the point of view of the context, that which the context has no expression for lies outside of the context. If context is the perceiver, then the indescribable reality outside of the context may as well not exist, for all the benefit the context gains from it.

Every context that exists is limited to the perception of  only a subset of reality. Is there a limit to the perception of reality if we take into account the sum total of all contexts in existence today, and all those which existed in the past? Yes, else one would expect that invention and discovery would cease.

Context is a feature of communication. It is not reality, which is the referent of the communication.

An example comes to mind from the physical world. One context may be the one in which the speed of a particle is important. Another context may be the one in which the position of the particle in space and time is important. Then there’s the context of Quantum Mechanics which is the one which first recognized that there were two other contexts (although it did not call them this) and that one interferes with the other. In QM, due to the known limitations of the physical world and our ability to perceive it at a particular level, these two contexts can never observe the same exact phenomenon. An observer in one context that observes one aspect of the particle necessarily changes the condition of the particle so that the other condition is no longer perceptible.

This seems really trivial, until we broaden the idea out to more complex contexts. The world is an analog, continuous place. Even the most complex context however can only perceive and name certain aspects, and is unaware of or finds inexpressible other aspects.

This is the place where poets and artists find creative expression and energy, between the lines of the necessarily constrained contexts of their own ability to communicate.

Out of the whole continuity of experience and phenomena which is the world about us, we are selective about the things we notice and think and speak about. Why one observation is made instead of another is based wholly on the things we find “remarkable”.

We remark on the things that are remarkable to us. By this I mean, the things we wish to convey or communicate are the things we find words to express. This “finding of words” includes inventing words and turns of phrase. After all, we each bring to the human table a uniqueness of vision commensurate to our talents, proclivities and experience.

Those to whom we successfully impart our observations, thru the act of their understanding the message, enter into the context of discourse of those observations. Once in that context, they may corroborate or elaborate on my original observations, broadening and enriching the context. Over time our collective observations become codified and regular, our terminology more richly evocative and concise, such that we may begin to speak in a shorthand.

Where a paragraph once was needed, now a sentence – where once a sentence now a single term…

As we start recognizing more and more examples of a phenomena, we invent a sublanguage which, when used within the context (and with the proper participants – see definition of context – i.e., with other people who share this context) is perfectly understandable.

An extreme example of differences in contexts would be the contrast of elementary school arithmetics versus obscure branches of mathematics research. The concepts which matter in the one are inconceivable in the other, the notation and terminology of the one are indecipherable in the other.

Consider the origin and usage of the term “ponzi scheme”. The original of the type was perpetrated by a man named “Ponzi”. Anyone who has operated a similar scheme since can now be referred to using the name of one notorious example. In recent years, the largest ponzi scheme ever perpetrated was the brainchild of Bernie Madoff. Time will tell if future outrageously immense ponzi schemes will be given a new moniker.

We might ask: “In what sense do we say that a “context” is an “observer”? There are a few ways we can use this analogy. First, a context is the product of communication among indidivual humans. It is the participation in the communication, in sending and receiving message, that creates the scope of the communication. What is communicated is the shared observations of the participant community.

Context Is:

Communication == Community == Communication

Information transfer among a group of individuals who share a common interest.

The language used is necessarily constrained, at first informally but later perhaps more rigidly as communication becomes more focused. Difficult observations require lots of talk. Once the idea has been grasped, however, less and less is needed to evoke the memory of the original idea, until a single term from the original description can be used as a stand-in.

It is not the abstract notion of a context that actually does the observing. Rather it is the community members themselves, the humans, who do the observing. The subject of communication is necessarily the things of interest to the community. But an individual who observes something is not necessarily participating in the context. Only the observations that are shared and received are part of the context.

A second sense in which the context can be described as the observer at an abstract level. While the context is formed from the collective interests and communication of the group of humans, eventually, the context becomes prescriptive. The extent and content of the shared sublanguage then defines the type and content of the observations that can be made by the members of the context. An observation that falls outside of the context’s prescriptive rules for content and structure is likely not to be understood (received). If it is not received, it may as well not have happened, hence such messages fall out of context.  The more constrained and formalized the context, the more explicit and succinct the observations that can be carried by that context, but also the fewer the variety of observations.

Successful study of the constraints and observations within a context occurs in much of the “social sciences”. Much can be deduced about what is important within a community by analysing the rules and limits of the communication that community’s context permits. In particular, a sense of the portion of existence important to the context can be deduced from the study of the observations communicated within that context.

A Concept is Born: Sense Memory and Name Creation

June 24, 1988

Experience is characterized by memory of sensual information in all its detail. Analysis of this data can be retroactively applied. I can remember that:

“Yes, the sky was grey and windy just prior to the tree falling behind me.”

and therefore come to understand a set of events later, in some other context. Using this sensual memory aids abstraction and analysis because it acts as the raw material out of which abstractions can be built. Thus it is possible at a later date to reflect on past events and discover related occurences where before there was unorganized memory.

Learning of patterns is continuous:

“What was that?”

This question initially gets very simplistic answers when asked by toddlers and children. It takes nearly 20 years for humans to talk about philosophy in a formal way. But as slight variations to the simple occurences of events are experienced, the agent (learner) begins to organize subclasses of the same general event, especially if the social world provides him a useful distinction to use to characterize the subclass. In doing so, the subclass name becomes a synonym for the general idea.

Creative research by the agent (learner) is characterized by the creation of new distinguishing marks and the choosing of a class name for those marks. Communication with others regarding the subclass then becomes a matter of describing those marks, providing the short hand name, and obtaining agreement from the others that both the marks and the name are apropos.

And thus a concept is born…

The Origin of a Context

On this blog and in the writings of many other people through history, the idea of “context” as a component of the definition, interpretation and usage of symbols plays a large role. Be it called “situational” or “cultural” or any of a number of sometimes more and sometimes less academic notions, context provides the key (just as a cipher is a key to an encryption code) to interpreting any message. Without knowing the context, many messages will be uninterpretable, or even worse, unrecognizable.

But what is “context” really? Where does it come from? Here is my decidedly informal discription.

 

Two people thinking their own thoughts meet for the first time

A conversation starts and one tells a story.

The other listens, interpreting silently what she hears into her own experiences.

She then responds, reflecting what she thought she heard, but with a variation or two. 

Conversation Begins

Conversation Begins

The first person agrees with some of her response. He hadn’t at first thought of the variation, but now that she’s mentioned it, he knows she’s on to something.

 

Conversation Ends Context Begins

Conversation Ends Context Begins

The two part company, carrying a memory of their conversation.

When they meet again, they will reinforce and reiterate their common perceptions on the matter. This is the origin point of CONTEXT: the set of principles and concepts that the two agree about, and the shared vocabulary they have used to describe them.

NEWS FLASH: Locals Choose Different Terms for Same Thing – Soda versus Pop

In some parts of the US, carbonated beverages are called “sodas”, and in others they are called “pops”. Both terms are contractions of their original “soda pop”.

So what happened here? It begins simply with a handful of people in each location. Different people in each region get tired of using the full phrase “soda pop”. They start speaking in a short hand with their friends or neighbors, and soon everyone around them is doing the same thing. This is how context works: group of people experiencing the same things communicating. Over time, they coin terms and colloquialisms to make their communication faster and more efficient. Some of these are simply contractions of compound terms. Others may start out as names of specific examples, or perhaps descriptive metaphors or euphemisms that suddenly take on a life of their own.

The point is that different contexts end up with different contractions, slang, etc. for the same things. Over time, this usage spreads out among the local population to become a regionalism. Given enough time and geographic separation, I imagine, this is how dialects arise, and how languages split off from dialects.

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