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Design Abstraction & Fractals

Take the full course on our site: https://www.systemsinnovation.network... As part of our course on complex systems design and engineering this section, we discuss the use of abstraction as a powerful tool employed in design in order to structure and solve for excessive complexity. In complex systems there is always two fundamentally different levels to the system, the micro and the macro or what we might call the local and the global. This is in contrast to simple linear systems where it is possible to reduce the whole system to one level. So lets first unpack this statement a bit to see why this is so. Firstly complex systems are composed of many parts we may be talking, millions as in the number of inhabitance of a city or billions as in the number of devices connected to the internet. For those of you who aren’t mathematicians a number like a million is a highly abstract things. Trying to relate a number like a billion to our everyday physical experience where we are really dealing with numbers like 5, 10 or possibly 100, should give you an idea of the vast gap or difference in scale difference between any individual node on the local level and the system as an entirety. Secondly, because the components have some degree of autonomy they are adapting to their local environment, these components are often very simple and they do not respond to information on the global level, thus one pattern of order can and often dose develop on the micro level and a second pattern emerges or is imposed on the macro scale as a result of try to design the system to have some form of global coordination. An example of this might be the official use of two different languages in many parts of the world, where we have the local level that has emerged organically and English that has been placed on top of this so as to make the system more interoperable on the global level. Lastly because of the high degree of connectivity within the system we have many interactions, these interactions inevitably lead to elements synchronising which gives rise to macro scale patters, this is what is called emergence. Traffic jams are a good example of emergence as are bank runs. The net result of all this is that we have two qualitatively different levels within complex systems, meaning they can not be reduced to a single level, this makes designing and managing these systems much more difficult. We need to be firstly aware of this multidimensional nature to complex systems and aware that if we try to reduce them to simple mono-dimensional systems there will be unintended and unfortunate consequences, thus we need to learn to design for this multi-dimensional nature to complex systems. In order to do this we have to be able to structure and model the system we are designing according to its different levels of abstraction, but what is abstraction? Abstraction is a powerful tool used in all areas of math, science and engineering, maybe the easiest way to understand it is as the process of removing successive layers of detail from our representation of the system in order to capture its essential features, what we might call its global features, they are common to all the components and are thus on the systems level. This is like zooming in on a satellite map of a city each level will have a certain degree of detail, creating a certain type of structure that will feed into defining the patters on the level bellow. Thus we see how complex engineered systems are what we call systems of systems but unlike mechanistic systems where each level is just a scaled up versions of the components bellow it, what mathematicians call scale invariance, the levels to complex systems can be understood to be scale invariant but they also have their own internal variation and dynamics that can not be fully abstracted away. So you may or may not have heard of things call fractals, they are geometric structures that have this scale invariant property, examples being the arteries in the human body, the structure to snow flakes, the formation of rigid mountains, and sea coastlines. If we make one of these, such as the coastline and zoom in on it the overall structure on each level will be the same but it will not be exactly the same there will be variation and unique differences on each level. To make this more relevant to us as designers and engineers lets take an example of what this means in practical terms for the systems we are developing.