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Social And Economic Topology

In mathematics topology is the branch of geometry that explores and defines the relationship between various points on and the surrounding boundaries of a shape. Topology study has expanded to include the investigation of relationships between virtually any collection of points that can be viewed as being connected. The broader study of these topology relationships can be explained using terms that may be more familiar as a part of mathematical set theory. It is common to describe computer and communication networks in terms of their topology. The relationship, connectivity, and boundary concepts from the more traditional study of topology also find usage in the social sciences where the fields of social and economic topology focus heavily on role of individual mobility within a network or set of relationships in the case of social topology and the communication of knowledge, especially technological knowledge, within a network or set of relationships in the case of economic topology. Those working in the fields of social and economic topology, which report on the impact of technology on our culture, feel the lag between the output of new technological innovations and the full awareness of the best usage for any new technological innovation. Thus, even today the topic of mobility in social topology refers to the worker alone without considering that the workplace has equal mobility to the that of the worker. In economic topology the study of communication of information appears to be more about simply how the information in the form of technological innovation moves throughout a network rather than taking more specific note of how the network collectively or on a node by node basis works to optimize the usage of any new technological innovation. In short, lateral thinking is not a part of how researchers normally study new technological innovations.

Unfortunately, current social and economic topology study has exceptionally little to offer when looking at the boundaries of social and economic networks and much less on the types of relationships or communication that might either exist or potentially exist beyond the boundaries of a given social and economic network. The concept of a Möbius Strip, which is central to most discussions related to the traditional study of topology, has no real analog or meaning within the existing field of social and economic topology because from their two-dimensional perspective within the boundary of the networks they study there is no readily apparent analog for the Möbius Strip found in traditional topology. In traditional topology the Möbius Strip provides a visible representation of a surface with only one side and a single boundary. At one time or another everyone has either seen or constructed a simple Möbius Strip and visually verified that the construction has only one side because the view is outside the surface and boundary of the Möbius Strip. If the view was from the surface of the Möbius Strip, the experience of walking along the surface would leave no clue that the surface was twisted.

In the fields of social and economic topology it would be possible to view the analog of a Möbius Strip only by stepping beyond the boundary of the networks being studied. Being dynamic systems the networks and space researchers in the fields of social and economic topology view changes over time, and to fully understand how an analog of the Möbius Strip might exist in the realm of social and economic topology systems must define elements in the fields that would represent and analog of either a standard loop or a Möbius Strip. In viewing social and economic topology systems over a long period of time it would be clear that over time the nature of the social and economic systems have shown examples of both a standard loop and a Möbius Strip along with an analog for the boundary found in the paper versions of both the standard loop and the Möbius Strip. From the dawn of time effort within any social or economic group has been divided between family or community and work or production of the things necessary to sustain the family or community. The community role can be shown as the inside track of the standard loop, and the work role can be shown as the outside track of the standard loop. The boundary between the community track and the work track may be shown as the energy or effort required to move from activity in one track to the other track. Technology, mobility and communication are important factors not only in determining the nature of activity on one track or the other but also in the nature of what is required to move across the boundary from one track to the other track. Obviously, the system becomes more efficient when the energy required to move across the boundary is either reduced or completely removed. Where the boundary between the community track and the work track is absent or virtually transparent the result would be the social and economic topology analog for the Möbius Strip. Where there is a clear and perhaps insurmountable boundary between the community track and the work track the result would be the social and economic topology analog for the standard loop. A social and economic topology system where the community track and work track are well integrated and more seamless is more efficient, and such a system could be viewed as more closely resembling the analog of the Möbius Strip. A social and economic topology system where the community track and work track are more clearly divided and a boundary exists between the community track and work track is less efficient, and such a system could be viewed as more closely resembling the analog of a standard loop.

In both the standard loop and Möbius Strip environment technology, mobility, and communication must flow not only along both the work track and the community track but also across any boundary between the work track and the community track. So, the complete social and economic topology system consists of actors, technology, mobility, and communication all flowing along not only both the work track and the community track but also across any boundary between the work track and the community track. Complications arise within the system because innovation is more likely to come from the work track than from the community track. Over time the introduction of innovation will produce expansion for the system, but it is more likely that the work track within the system will expand at a more rapid rate than community track. If the social and economic topology for the system more closely resembles the Möbius Strip environment, the flow of innovation along the community track will more rapidly match the flow along the work track even though there may be intervals where an eddy, which would reflect a lag in flow rate, creates a flow differential impacting the rate of system expansion. If, on the other hand, the social and economic topology for the system more closely resembles the standard loop environment, the flow of innovation along the community track (inside track) will diminish, which will slow the expansion of the community track, while the flow of innovation along the work track (outside track) will increase and generate an expansion differential that would be visible in the form of an expanding boundary between the community track and work track of the system. As the boundary between the community track and the work track increases, there is a proportional increase in the amount of energy required to traverse the boundary, which must come from either the community track or the work track. If the extra energy required to traverse an expanding boundary between the community track and the work track is siphoned from the community track, the expansion of the community track will slow because the extra energy expenditure will show as an increased lag in the ability of the community track expansion to keep up with the expansion of the work track. If the extra energy required to traverse an expanding boundary between the community track and the work track is siphoned from the work track, the expansion of the work track will slow because the extra energy might otherwise be applied to further expansion of the work track. Further expansion of the boundary between the community track and work track not only diminishes the efficiency of the social and economic topology system but also generates what might be irreparable damage to other elements necessary to ensure continued stability for the social and economic topology system environment as a whole within the bounds of its physical environment.

Through most of recorded human history the social and economic topology system could be viewed as following the Möbius Strip model more closely than the standard loop model because the proximity between the community track and work track was virtually zero. The level of technology, mobility, and communication was very low and remained so for extensive lengths of time. Of course throughout recorded human history civilizations were highly structured along class lines, which not only further limited mobility but also communication between classes, but even within the limits of the class structure established by each civilization throughout history there existed a virtually indistinguishable difference between community and work. At the outset of the industrial revolution the transparency between the community track and the work track began to vanish. Through the intervening years and with the introduction of each new piece of technology or innovation the mobility and communication capabilities of the population may have improved, which did contribute to the growth of a middle class, but the cost burden for such progress has been a migration from the standard loop model for the social and economic topology system. With each technological innovation introduced in the work track there has been a transfer of that technological innovation from the work track to the community track, but only at a flow rate that can be fully assimilated at the community track level. As the rate of technological innovation has accelerated over the past fifty years, the boundary between the community track and work track of the social and economic topology system has expanded because the community track has increasing difficulty in matching the expansion of the work track. The resulting increase in the expenditure of energy required to move across the boundary between the community track and work track has created an increasingly unstable environment, which is visible in the form of climate change. An additional cost associated with the expenditure of increased energy to move across the boundary between work track and community track has diminished the flow and expansion rates for both the community track and work track even at a time when the rate of technological innovation introductions has increased. This reduction in expansion is visible in the form of a slowdown in the economies of the world relative to what might otherwise be expected given the potential for productivity boosts that such innovations may have brought to the society.

The move to full implementation of the Community Commerce Center system will produce a change in the structure of the relationship between the community track and the work track that will create once again a social and economic topology system more like the Möbius Strip model. With the Community Commerce Center system the boundary between the community track and the work track is reduced to the point that it is virtually transparent because the community track and work track join to form a single surface with no boundary. The introduction of new technological innovation to the system must still be assimilated within the flow along both the community track and work track, but such assimilation occurs at a flow rate that does not seriously hamper the rate at which the system is able to accept additional innovations. With the boundary between the community track and the work track virtually eliminated there is a tremendous savings in energy beyond what is required to maintain the system. The result is not only a better running system that is more efficient and able to progress without undue lag but also a system that can actually provide the mechanism for repair to the surrounding environment while significantly reducing the demand for energy. In addition, the increased efficiency within the social and economic topology system produces the mechanism to speed the flow of information to segments of society that may have been lagging further behind prior to the implementation of the Community Commerce Center system.

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