Ryan Coyer, Aaron Schram
HW6

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 our understanding, this paper is basically a thesis on the description of complex systems. By exploiting the fact that most of them exhibit redundancy, you can simplify your explanation of a complex system the way you simplify descriptions of each of a country's citizens by simply saying 'The public of country X.' Since the heirarchy of a complex system allows you to describe the subsystems simulatenously, one can reduce the total amount of intellectual labor involved in representing a complex system. This is important because as systems grow more and more complex (in Engineering, the Physical Sciences, etc.), the effort required to describe their heirarchies grows rapidly.

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

The paper spanned a great variety of subjects... there was only one paragraph which dealt with my area of work: "I could equally well compare it with a computer program....". The author valued breadth rather than depth in her article, describing her thoughts in the contexts of many different fields. Had she stuck to one field and given a deeper explanation of her thoughts, the article would have been much more interesting. The article is relevant to our work as engineers, just because like every engineering or scientific field we have to be able to abstract away the complexity in order to comprehend and improve upon existing designs .

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?
YES! Cut one in half.
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”)

Printed out the matrix, grabbed a pencil, started trying to reason through the solution.
Found that 32 dominoes covered the mutiliated matrix with two dominoes half used.
Problem solved by eliminating one of the dominoes (total of 31 now), cutting one of the 31 dominoes in half and distributing the two halves on the two remaining open squares.

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

Pen, paper, mind.

3. which process did you use?

Trial and error

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

Perhaps a bit of cheating (but there were no instructions prohibiting the cutting in half of a domino)

5. could computers be useful to solve this problem?

Certainly, they could run through the permutations of trial and error far more rapidly than humans. Perhaps they could even find a solution that didn't involve cutting a domino in half.

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

Think outside the box... a phrase from High School keeps coming to mind. Cutting a domino in half may not be the ideal solution, nor an obvious solution, but it is a solution.
Solutions to problems may not always be ideal, but if a solution works, use it.

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

Either prove that the problem is not solvable or solve it. Anything else is not a definitive answer.