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

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

In my opinion, these concepts are important because they are crucial to the growth of technology. As the author demonstrated, these concepts can be generalized and applied to all "complex systems", though as someone involved in the growth of technology, I can see a lot of value in the concepts that were elaborated. The idea of breaking complex systems into smaller, more managable parts in a hierarchic manner is highly useful for efficiently solving any type of problem. Furthermore, the idea of maintaining "subassemblies" is priceless in all projects. On that comes to mind for me is the open source community. By breaking down major projects into a hierarchic structure and then implementing "subassemblies", much time and resources are saved and the project may proceed much more effectively without developers duplicating each other's work.

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

The analogy of the two watchmakers was appropriate to demonstrate evolution. This theory can also be seen where I work. Obviously, when I encounter a troubleshooting issue, I don't start from scratch. Using knowledge I've gained from my few years of experience, I am able to solve problems faster now than I was my first few weeks. The knowledge I retain are "subassemblies" that I can build from each time rather than needed to recreate, or in this case, re-learn, them. In fact, the team I work with uses several software tools (Mercury Test Director, for example) that help us to maintain subassemblies and increase our efficiency as a group.

Questions about The Importance of Representations in Design — The Mutilated “8x8” Matrix
remark: check the attached PDF file to see the graphical image

The Problem:

The associated PDF file shows you a mutilated “8x8” matrix (the two opposing corners cut out) and a domino block. One domino block covers exactly two fields of the “8x8” matrix.

Note: It is straightforward that one can use 32 domino blocks to cover a complete “8x8” matrix.

Question: Can one cover the mutilated “8x8” matrix with 31 domino blocks?

Remark: 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!

Also: engage in some collaborative efforts solving it

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”)

  • Try orienting all dominos vertically. Fails at the vacant corners.
  • Try orienting all dominos horizontally. Fails at the vacant corners.
  • Eliminate the center 4 rows first (orientation unimportant). Still have a problem at the vacant corners.
  • Eliminate the center 4 rows and center 4 columns (orientation unimportant). Still have a problem at the vacant corners.
  • Beginning at the top-most row, orient the dominos horizontally with the first domino adjacent to the vacant corner. At the end of the first row, you must orient the domino vertically. Continue in "s-like" fashion, orienting the dominos horizontally until reaching the first or last columns, where you turn the dominos vertically. This still fails.

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

Collaborated with others. Searched the Internet. Past knowledge working on geometrical puzzles.

3. which process did you use?

Process of elimination and "trial-and-error". With each attempt, I gained more knowledge/comfortability with the mutilated 8x8 matrix, seeing more clearly what worked and what didn't. I also was able to recognize certain patterns more easily. For example, you learn quickly the problem you're encounter are rows (or columns) with only seven positions which is not divisible by 2 (the number of positions in each domino). You then begin to try rotating the dominos whenever you encounter this problem, and continue from there.

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

I'm not sure what the difference is between "process" and "practice" in this context. To me, "practice" means the method by which you try to solve the problem. In that case, my practice would be the same as above, process of elimination. But to further elaborate, I would say the method of practice also include contacting/collaborating with others, searching for answers on the Internet, and using persistent knowledge to undertake the problem.

5. could computers be useful to solve this problem?

Computers could be very useful because you could write an algorithm to solve this. At best, you could create a complex algorithm that mathematically determines the solution (if there is one). At worst, you could take the brute-force and test every possible combination and orientation of dominos. This worst-case scenario, brute-force method is essentially the method I used in trying to solve the problem myself and the advantage of a computer is that it could simulate my actions, but at a much faster pace.

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

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

There are many ways to try to solve a single problem. Not being able to solve the problem is not necessarily a failure since with each failure, you learn more about the problem. In the end, even without a definite solution, your work will pay off because you will have a much better understanding of the problem which could eventually lead to a solution for the problem, or maybe even another, similar problem in the future.

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