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[XML-DEV Mailing List Archive Home] [By Thread] [By Date] [Recent Entries] [Reply To This Message] RE: XML Technologies: Progress via Simplification or Complexif
 Roger L. Costello wrote: > Approach 1 - Progress via Simplification > Approach 2 - Progress via Complexification His note also makes reference to Wolfram's book in which patterns which have apparently great complexity are discovered to be the result of applying exceptionally simple algorithms. A common measure of the entropy of a system is the "number of bits" needed to encode the algorithm that describes the system... Take a look at any of the pictures in Wolfram's book and consider them to be systems... If you don't know the algorithm that generated the image, you can easily create a very complex and long algorithm to describe the image. Thus, you might think it had high entropy. On the other hand, if you have knowledge of the system, you'll use the simple, short algorithm and decide that the system has low entropy. What often happens when people begin to understand apparently complex systems is that they eventually begin to discover that the actual entropy of the system is vastly less than the system's apparent entropy. Of course, once the entropy is discovered to be less than originally apparent, the newly apparent entropy begins to approximate more closely the actual entropy -- for those that have the understanding. Thus, apparent entropy is relative to the observer even though the actual entropy is independent of viewer. One measure of relative "understanding" or "knowledge" is the difference between observers in their perception of the apparent entropy of a system. To a great extent, the problem of programming is that of building models of real or conceptual systems. If a model is to be accurate, then it must have *at least* the same complexity as the system whose behavior it models. Any additional complexity in the model is simply the result of a failure to understand the modeled system or the result of a failure of either the modeling language or the modeler -- but need not necessarily impact the accuracy or utility of the model. Any model which is less complex then the modeled system will be, must be, inaccurate (even though it might still be useful for some purposes...). In order to arrive at minimally complex models, and thus simple implementations of what might have originally appeared to be complex systems, what we need to do is to first carefully describe and otherwise identify the full behavior of the modeled system. Then, when we have a full description of the system, we can begin to seek the usually simple model that describes it. The "Progress via Complexification" typically results from this cataloging process. i.e. each new bit of complexity in the model (i.e. the program) results from the discovering of and thus the cataloging of another aspect of the modeled system. The "Progress via Simplification" typically comes when the modeler realizes that what initially appeared to be multiple aspects are really just different perspectives on a smaller number of aspects. Thus, while "Progress via Complexification" often results in a model which grows toward being more complex then the modeled system, "Progress via Simplification" more accurately aligns the complexity of the model with that of the modeled system. (Remember, an overly complex model may still be useful -- only an oversimplified model is guaranteed to be inaccurate.) It should be recognized that cycling between "Progress via Complexification" and "Progress via Simplifiation" is, essentially, inevitable. Complexification comes as a result of discovering the apparent complexity of systems, simplification is the result of discovering the actual complexity of the systems. Complexity is the result of discovery. Simplification is the result of knowledge and understanding. First, we must discover -- then we can understand. Ideally, in a software project, one cycles through as many phases of complexifiction->simplification as possible during the "design" phase. It is really unfortunate, although often unavoidable, when these phases involve released code... bob wyman 
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