Meaning Over Transformation

This entry is probably ahead of the story, but I wanted to start moving into this subject and I’m not yet organized. It should make more sense later on when I’ve explained such things as the “magical” function M() more thoroughly.

Review: The Magical Function “M()”

As a review for those who may not have seen this function previously on this site, I have invented a mysterious and powerful function over all things used as signs by humans. Named the “M()” function, I can apply it to any symbol or set of symbols of any type and it will return what that symbol represents. I call it the “M() function because it takes something which is a symbol and it returns its meaning (that’s all of its meaning).

How Meaning Carries Over Symbol Transformations

When we move information from one data structure to another, we may or may not use a reversible process. By this I mean that sometimes a transformation is a one-way operation because some of the meaning is lost in the transformation. Sometimes this loss is trivial, but sometimes it is crucial. (Alternatively, there can be transformations which actually add meaning through deductive reasoning and projection. SFAT (story for another time))

Whether a transformation loses information or not, there are some interesting conclusions we can illustrate using my magical, mysterious function M(). Imagine a set β of data structure instances (data) in an anchor state. The full meaning of that data can be expressed as M(β). Now imagine a transformation operation T which maps all of the data in β onto a second set of data Δ.

T : β |–> Δ such that for each symbol σ in β, there is a corresponding symbol δ in Δ that represents the same things, and σ <> δ

By definition, since we have defined T to be an identity function over the meaning of β, then we can conclude that if we apply M() before and after the transformation, we will find ourselves with an equivalence of meaning, as follows:

By definition: T(β) = Δ

Hence: M( T(β) ) ≡ M( Δ )

Also, by definition of T(), then M( β )  ≡ M( T(β) )

Finally, we conclude: M( β ) ≡ M( Δ )

Now, obviously this is a trivial example concocted to show the basic idea of M(). Through the manner by which we have defined our scenario, we get an obvious conclusion. There are many instances where our transformation functions will not produce equivalent sets of symbols. When T() does produce an equivalence, we call it a “loss-less” transformation (borrowing a term from information theory) because no information is lost through its operation.

Another relationship we claim can also be defined in this manner is namely that of semantic equivalence.  This should be obvious as well, from reflection, as I was careful above to refer to “equivalence of meaning”, which is really what I mean when I say two things are semantically equivalent. In this situation, we defined T() as an operation over symbols such that one set of symbols were replaced with a different set of symbols, and the individual pairs of symbols were NOT THE SAME (σ <> δ)! In a most practical sense, what is happening is that we are exchanging one kind of data structure (or sign) with another, such that the two symbols are not syntactically equivalent (they have different signs)  but they remain semantically equivalent. (You can see some of my thoughts on semantic and syntactic equivalence by searching entries tagged and/or categorized “equivalence” and “comparability“.)

A quick example might be a data structure holding a person’s name. Let’s say that within β the name is stored as a string of characters in signature order (first name  middle name  last name) such as “John Everett Doe”. This symbol refers to a person by that name, and so if we apply M() to it, we would recognize the meaning of the symbol to be the thought of that person in our head. Now by applying T() to this symbol, we convert it to a symbol in Δ, also constructed from a string data structure, but this time the name components are listed in phone directory order (last name, first name middle name) such as “Doe, John Everett”. Clearly, while the syntactic presentation of the transformed symbol is completely different, the meaning is exactly the same.

T(“John Everett Doe”) = “Doe, John Everett”

M( T(“John Everett Doe”) ) ≡ M( “Doe, John Everett” )

M( “John Everett Doe” ) ≡ M( T(“John Everett Doe”) )

M( “John Everett Doe” ) ≡ M( “Doe, John Everett” )

“John Everett Doe” <> “Doe, John Everett”

When the transformation is loss less, there is a good chance that it is also reversible, that an inverse transformation T ‘ () can be created. As an inverse transformation, we would expect that T ‘ () will convert symbols in Δ back into symbols in β, and that it will also carry the meaning with complete fidelity back onto the symbols of β. Hence, given this expectation, we can make the following statements about T ‘ ():

T ‘ (Δ) = β

M( T ‘ (Δ) ) ≡ M( β )

By definition of T ‘ (), then M( Δ )  ≡ M( T ‘ (Δ) )

And again: M( Δ ) ≡ M( β )

Extending our example a moment, if we apply T ‘ () to our symbol, “Doe, John Everett”, we will get our original symbol “John Everett Doe”.

Meaning Over “Lossy” Transformation

So what happens when our transformation is not loss-less over meaning? Let’s imagine another transformation which transforms all of the symbols σ in β into symbols ε in Ε. Again, we’ll say that σ <> ε, but we’ll also define T ‘ ‘ () as “lossy over meaning” – which just indicates that as the symbols are transformed, some of the meaning of the original symbol is lost in translation. In our evolving notation, this would be stated as follows:

T ‘ ‘ (β) = Ε

M( T ‘ ‘ (β) ) ≡ M( Ε )

However, by the definition of T ‘ ‘ (), then M( β )  !≡ M( T ‘ ‘ (β) )

Therefore: M( β ) !≡ M( Ε )

In this case, while every symbol in β generates a symbol in Ε, the total information content of Ε is less than that in B. Hence, the symbols of the two sets are no longer semantically equivalent. With transformations such as this, the likelihood that there is an inverse transformation that could restore β from Ε becomes more unlikely. Logically, it would seem there could be no circumstances where β could be reconstituted from Ε alone, since otherwise the information would have been carried completely across the transformation. I don’t outright make this conclusion, however, since it depends on the nature of the information lost.

An example of a reversible, lossy transformation would include the substitution of a primary key value for an entire row of other data which in itself does not carry all of the information for which it is a key, but which can be used in an index fashion to recall the full set of data. For example, if we created a key value symbol consisting of a person’s social security number and last name, we could use that as a reference for that person. This reference symbol could be passed as a marker to another context (from β to Ε, say) where it could be interpreted only partially as a reference to a person. But which person and what other attributes are known about that person in the new context Ε if we define the transformation in such a way that all of the symbols for these other attributes stay in β? Not much, making this transformation one where information is “lost” in Ε.  However, due to its construction from β, the key symbol could still be used on the inverse transformation back to β to reconstitute the missing information (presuming β retains it).

An example of a one-way transformation might be one that drops the middle name and last name components from a string containing a name. Hence, T ‘ ‘ ( “John Everett Doe” ) might be defined to result in a new symbol, “John”. Since many other symbols could map to the same target, creating an inverse transformation without using other information becomes impossible.

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Tension and Intention: Shifting Meaning in Software

If a software system is designed for one particular purpose, the data structures will have one set of intended meanings. These will be the meanings which the software developers anticipated would be needed by the user community for which the software was built. This set of intended meanings and the structure and supported relationships make up the “domain” of the software application.

When the software is actually put to use, the user community may actually redefine the meaning of certain parts of the syntactic media defined by the developers. This often happens at the edges of a system, where there may exist sets of symbols whose content are not critical to the operating logic of the application, but which are of the right syntactic media to support the new meaning. The meaning that the user community projects onto the software’s syntactic media forms the context within which the application is used. (See “Packaged Apps Built in Domains But Used in Contexts“)

Software typically has two equally important components. One is the capture, storage, retreival and presentation of symbols meaningful to a human community. The second is a set of symbol transformation processes (i.e., programming logic) which are built in to systematically change both the structure and possibly the meaning of one set of symbols into another set of symbols.

For a simplistic example, perhaps the software reads a symbol representing a letter of the alphabet and it transforms it into an integer using some regular logic (as opposed to picking something at random). This sort of transformation occurs a lot in encryption applications, and is a kind of transformation which preserves the meaning of the original symbol although changing completely its sign (syntactic medium).

When we push data (symbols) from a different source or context into the software application, especially data defined in a context entirely removed from that in which the software was defined and currently used, there are a number of possible ways to interpret what has happened to the original meaning of the symbols in the application.

What are some of the ways of re-interpretation?

  1. The meaning of the original context has expanded to a new, broader, possibly more abstract level, encompassing the meanings of both the original and the new contexts.
  2. Possibly, the mere fact that the original data and the new data have been able to be mixed into the same syntactic media may indicate that the data from the two contexts are actually the same. How might you tell?
  3. Might it also imply that the syntactic medium is more broadly useful, or that the transformation logic are somewhat generically applicable (and hence more semantically benign)?
  4. Are the data from the two contexts cohabitating the same space easily? Are they therefore examples of special cases of a larger, or broader symbollic phenomenon, or merely a happy coincidence made possibe by loose or incomplete software development practices?
  5. How do the combined populations of data symbols fare as maintenance of the software for one of the contexts using it is applied? Does the other context’s data begin to be corrupted? Or is it easy to make software changes to the shared structures? Do changes in the logic and structure supporting one context force additional changes to be made to disambiguate the symbols from the other context?

These questions come to mind (or should) whenever a community starts thinking about using existing applications in new contexts.

Bridge Contexts: Meaning in the Edgeless Boundary

Previously, I’ve written about the idea of the “edgeless boundary” between semiospheres for someone with knowledge of more than one context. This boundary is “edgeless” because to the person perceiving it, there is little or no obvious boundary.

In software systems, especially in situations where different software applications are in use, the boundary between them, by contrast, can be quite stark and apparent. I’ll describe the reasons for this in other postings at a later time. The nutshell explanation is that each software system must be constrained to a well-defined subset of concepts in order to operate consistently. The subset of reality about which a particular application system can capture data (symbols) is limited by design to those regularly observable conditions and events that are of importance to the performance of some business function.

Often (in an ideal scenario), an organization will select only one application to support one set of business functions at a time. A portfolio of applications will thus be constructed through the acquisition/development of different applications for different sets of business functions. As mentioned elsewhere on this site, sometimes an organization will have acquired more than one application of a particular type (see ERP page). 

In any case, information contained in one application oftentimes needs to be replicated into another application within the organization.  When this happens, regardless of the method by which the information is moved from one application to another, a special kind of context must be created/defined in order for the information to flow. This context is called a “bridging context” or simply a “bridge context”.

As described previously, an application system represents a mechanized perception of reality. If we anthropomorphize the application, briefly, we might say that the application forms a semiosphere consisting of the meaning projected onto its syntactic media by the human developers and its current user community, forming symbols (data) which carry the specifically intended meaning of the context.

Two applications, therefore, would present two different semiospheres. The communication of information from one semiosphere to the other occurs when the symbols of one application are deconstructed and transformed into the symbols of the other application, with or without commensurate changes in meaning. This transformation may be effected by human intervention (as through, for example, the interpretation of outputs from one system and the re-coding/data entry into the other), or by automated transformation processes of any type (i.e., other software).

“Meaning” in a Bridging Context

Bridging Contexts have unique features among the genus of contexts overall. They exist primarily to facilitate the movement of information from one context to another. The meaning contained within any Bridging Context is limited to that of the information passing across the bridge. Some of the concepts and facts of the original contexts will be interpretable (and hence will have meaning) within the bridging context only if they are used or transformed during this flow.  Additional information may exist within the bridge context, but will generally be limited to information required to perform or manage the process of transformation.

Hence, I would consider that the knowledge held or communicated by an individual (or system) operating within a bridging context which is otherwise unrelated to either of the original contexts, or of the process of transference, would existing outside of the bridging context, possibly in a third context. As described previously, the individual may or may not perceive the separation of knowledge in this manner.

Special symbols called “travellers” may flow through untouched by transformation and unrecognized within the bridging context. These symbols represent information important in the origin context which may be returned unmodified to the origin context by additional processes. During the course of their trip across the bridging context(s) and through the target contexttravellers typically will have no interpretation, and will simply be passed along in an unmodified syntactic form until returned to their origin, where they can then be interpreted again. By this definition, a traveller is a symbol that flows across a bridge context but which only has meaning in the originating context.

Given a path P from context A to context B, the subset of concepts of A that are required to fulfill the information flow over path P are meaningful within the bridging context surrounding P. Likewise, the subset of concepts of B which are evoked or generated by the information flowing through path P, is also part of the content of the bridge context.  Finally, the path P may generate or use information in the course of events which are neither part of context A nor B. This information is also contained within the bridge context.

Bridge contexts may contain more than one path, and paths may transfer meaning in any direction between the bridged contexts. For that matter, it is possible that any particular bridging context may connect more than two other contexts (for example, when an automated system called an “Operational Data Store” is constructed, or a messaging interface such as those underlying Service Oriented Architecture (SOA) components are built).

An application system itself can represent a special case of a bridging context. An application system marries the context defined by the data modeller to the context defined by the user interface designer. This is almost a trivial distinction, as the two are generally so closely linked that their divergence should not be considered a sign of separate contexts. In this usage, an application user interface can be thought of as existing in the end user’s context, and the application itself acts to bridge that end user context to the context defining the database.

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