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Edit nilo.hw4-new here.

Homework Assignment # 4
Nilo Tsung

1. Name two most important things/concepts which you learned from reading the chapter “The Architecture of Complexity” in the book entitled “The Sciences of the Artificial” by Herbert A. Simon.
1.1 Write one paragraph explaining why you think these 2 concepts are important.
(1). A complex system is one made up of a large number of parts that have many interactions. In such systems the whole is more than the sum of the parts in the weak but important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not trivial matter to infer the properties of the whole (p 184).

(2). Many complex systems have a nearly decomposable, hierarchic structure is a major facilitating factor enabling us to understand, describe, and even “see” such systems and their parts (p. 207).

I think the two concepts mentioned above are very important because the second one encourage us to view a complex system into decomposable hierarchical structure so that we can simplify the system, and at least get some general and simplified idea about it. However, the first one warns us that in order to understand the overall behavior of a complex system in great detail, the work may not just sum up the parts and interactions. The first one let us to get started the problem solving process, so that we get some quick and dirty answers. The second one helps us to appreciate the complexity, and possible work involved.

1.2 Are these concepts relevant to your work or to your interest? If yes, explain it in which way they are related to you.
A construction project is a complex problem. In order to control a construction project, it is not a trivial task. Traditionally, we can break the project control into “project cost control” and “project schedule control”. Project cost can be easily decomposed into hierarchical components, and it is usually called cost breakdown structure (CBS). Similarly, project schedule can be easily decomposed into hierarchical components, and it consists of work breakdown structure (WBS) and organizational breakdown structure (OBS).

Although it is not difficult to control project cost and schedule based on CBS, WBS, and OBS, it can only provide limited help since these three ones interact with each other. In construction industry, people have been talking about the integration of these three breakdown structures for the last three decades, but it is very difficult to manage them all together because the complicated interactions among them.

2. The mutilated “88” matrix, the problem:
The next page shows you a multilated “8
8” matrix (the two opposing corners cut out) and a domino block. One domino block covers exactly two fields of the 8: 
8 matrix. (Note: it is straightforward that one can use 32 domino blocks to cover a complete “88” matrix.)

Remarks: span style = ‘font-weight: normal’> the major objective of this assignment is that you spend some effort trying to solve this problem and answering the questions below. It is not so important that you will succeed solving the problem. You can solve the problem with some collaborative efforts.
2.1 Try to find an answer to his problem. Briefly document your thinking process, including all the important intermediate steps and failure attempts (i.e. think aloud protocol).

2.2 Which resources did you use to solve the problem?
I just use several pieces of paper and a pencil.

2.3 Which process did you use?
I first drew a 2
2 matrix, a 3: 
3 matrix, and a 4
4 matrix on the paper. I then drew hatching on alternated squares, so that the matrixes look like regular checkerboards. We can think a pair of hatched and unhatched field as a unit, which can be covered by one domino block. If I cut off (or mutilate) two opposing corners with one field size as stated in the problem, these corners always belong to same type (i.e. either hatched or unhatched). Therefore, I will always have two extra fields belonging to same type. It is not difficult to conclude that we cannot cover the mutilated matrix (regardless its size 7: 
7, 8
8, 35: 
35, or 8585) with exact number of the domino blocks.

2.4 Which practice (of you or others) did you use?
I started with smaller matrixes, such as 2
2 and 3: 
3, and then to 77 and 88. You can see they all follow very similar pattern, i.e. the cut-off corners belong to same type regardless their matrix sizes.

2.5 Could computers be useful to solve this problem?
Computers could help us to solve this problem, but I prefer to solve it in a more intuitive way as described above.

2.6 What have you learned, in general, from this class helping you solve this problem?
I guess the technique required to solve this problem may not have a strong link with the material of this class.

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