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Andrew Skalet Assignment 4 1. Point 1: Hierarchy is evident in a wide variety of complex systems, nearly all in fact. Point 2: This is because Hierarchy (in particular, near decomposability) provides a huge advantage to the construction or evolution of complex systems. 1.1 Simon's observation that hierarchy provides a huge advantage in complex systems is not an observation of "how things are" but an observation of "why things are the way they are". His examples of this are quite compelling, and indeed large organizations of people, large organizations of molecules, and large symbolic organizations are indeed hierarchical. To me, it seems that the number of interactions between components is the most important element, because hierarchy limits these interactions and makes very complex systems possible. 1.2 These concepts are extremely relevant to my work, because I am interested in complex software systems, and how people understand them and communicate that understanding to one another. Although Simon does not give this example, I find that complex software systems (particularly object-oriented ones) fit almost perfectly simon's characterization of hierarchy. Indeed, some of the most useful conventional wisdom from software engineering supports Simon's claims about the evolution of complex systems and how hierarchy provides an advantage. 2.1 First, I printed out a copy of the diagram so I would have something physical to manipulate. I then tried to think about how to compensate for the missing squares. I decided that something would have to happen in the middle of the grid to compensate for the difference in the corners (some interaction between columns 4 and 5). I then tried to lay out domino blocks, not just in trial and error, but to understand the problem better. I tried many layouts, but I was unable to reconcile the interactions occurring in the middle of the board when I worked inward from the corners in various ways. I decided that I don't think a solution is possible. 2.2 I used pencil, paper, and a printer to print the diagram. 2.3 I used physical tools to manipulate the problem to try to get an intuitive sense of it in my mind, and made a judgement based on my sense of the problem. 2.4 I used the practice of thinking on paper, drawing, and testing hypotheses. 2.5 Sure, a backtracking test type program could be used to evaluate the problem. Perhaps an n-queens program could be modified to solve this problem. Of course, a solution would not be found if there isn't one. 2.6 n/a I did not find a solution 2.7 What I have learned depends somewhat on whether there is a solution to the problem. If so, perhaps I should have collaborated, but I did not plan far enough ahead of time for this particular assignment. If not, I will learn that an intuitive sense I can gain from manipulating the problem can be valuable. If there is a solution, my process of creating a mental model will be shown to be fallible. |
