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Brock LaMeres

1. Name the two most important things/concepts which you learned from the reading the
chapter “The Architecture of Complexity”

The first concept I learned was that hierarchical systems evolve faster. The watchmaker example was very illustrative to this. This concept also lends itself to human evolution beginning with single-celled organisms to what we are today. The cell had to get itself figured out before it could form a macro-celled structure, and so on.

The second concept I found interesting was “Nearly Decomposable Systems”. We tend to think about hierarchy in the truest sense, that being that each sub block is independent. But this is not always the case. Proximity plays a role in the operation of subsystems due to stronger communication with its closest neighbors. One could make the argument that the proximity causes evolution into a greater subsystem.

1.1. give a one paragraph explanation why you consider these concepts important

They are important because before you design or debug complex systems, you must first understand them. The problem with understanding a complex system is that it is sometimes “too” complex. We can only wrap our brains around smaller pieces to begin with. Once we understand the lower-level blocks, we can put them together and understand the upper level blocks. It’s analogous to trying to understand the Microsoft windows operating system. It seems a daunting task until you learn about subroutines.

1.2. are the concepts relevant to your work, to your interest, …. – if yes, why?

Yes, I currently am a hardware designer for Agilent Technologies, Inc. When I begin the design of a logic analyzer, the system is too complex to comprehend. It is only until I break it down into subsystems that I can begin to grasp what’s going on. In addition, the hierarchical breakdown not only applies to the designing of the subsystems, but also to the partitioning of work amongst employees.

2) The Mutilated “8x8” Matrix
The Problem:
Question: Can one cover the mutilated “8x8” matrix with 31 domino blocks?

Yes, it is possible. However, I used a technique that may or may not be allowed. Without giving it away, at times I placed the domino in a non-vertical, non-horizontal fashion….

Please do the following (please structure your answer accordingly — thanks):
1. try to find an answer to this problem! ‡ document briefly your thinking — including all the
important intermediate steps and failing attempts (i.e., create a “think-aloud protocol”)

I used “trial and error” to find the solution. I got it on the fourth trial.

2. which resources did you use to solve the problem?

Getting very technical, I printed out a bunch of copies of the matrix and then used a pencil to cross off ‘dominos’. The resources I used were paper and pencil.

3. which process did you use?

The method was trial and error. The processes I tried were:

a) Left-to-Right Elimination
b) Clockwise Elimination
c) Reducing the Matrix
d) Corner Shaving to create a straight cube.

4. which practice (of you or others) did you use?

I simply printed out a copy and crossed off dominos.

5. could computers be useful to solve this problem?

Yes, however the computer would only be able to attempt the processes that it was programmed with (left-to-right, clockwise, etc…). This is very nice if larger and larger patterns needed to be solved. However, it does not help if the original problem statement is changed.

6. what have you learned solving the problem: in general and for our course?

Problems can be broken down into smaller subsections. Just as hierarchical systems evolve more quickly, hierarchical solution sets should also follow suit.

7. what have you learned not being able to solve the problem: in general and for our course?

Trial and Error is only as good as the imagination of the person developing the “trials”. A computer will be very efficient at applying the “trials” and determining error, it will NOT be efficient at creating the “trials” themselves.

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