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Huda Khan

1) One important concept were that systems which are defined in terms of hierarchies (or groupings and relationships between "stable subsystems") are on the whole more stable than just a random assortment of individual parts. The watchmaker analogy employed by Simon explains this concept. Taking this further was the second important concept which was that the presence of stable intermediate subsystems lends itself to the evolution of complex systems.

1.1. give a one paragraph explanation why you consider these concepts important.
Simon's thesis is that hierarchic structures are common in the architecture of complex systems because by definition they lend themselves to the evolution of complex systems. Engineers and others who are involved in the design process are all interested in how to create stable complex systems which will be able to coevolve with or at least live through our complex dynamic evolving world. If there are fundamental design issues which can be brought to light by examining the nature of complex systems themselves, these ideas and concepts can then be employed in the design of software and other complex architectures.

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

Reading the section about nearly decomposable systems, or systems where intercomponent interaction is present but relatively low compared to the intracomponent interaction of parts, and where intercomponent interaction affects aggregate or overall state of the system, I was immediately reminded of object oriented design methodology, or at the very least the concept of modularity.
In addition to OO, it would be interesting to explore this concept in the context of collaborative systems, where the components are people, processes, events, activities, and resources. Would it be true that nearly decomposable social systems work better? Or would it depend on the situation and the quality of the task?

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”)

2. which resources did you use to solve the problem?
3. which process did you use?
4. which practice (of you or others) did you use?

Answers to 2,3,4:

2. I used an Excel sheet to create visual representations of the grid which I could then color in and try to reproduce various possible domino placement strategies.

3. I defined the problem in terms of the squares that needed to be covered, which were 62 for 31 blocks and then tried to find domino placement configurations which could cover 62 squares.

After trying to see whether I had correctly understood the definition of the problem and there were not alternative definitions, I first tried to explore domino placement with the 8 X 8 grid, trying to use dominos placed both vertically across squares and horizontally across because using all vertically placed or horizontally placed blocks would always leave two squares uncovered (and thus cover only 60 squares and use 30 blocks).

3 and 4. I then switched to using a 4 X 4 grid to see if solving a simpler problem with the same or similar structure could lend any clues, visual or strategic, that would help me in finding the solution to the 8 X 8 grid. The use of simpler problems to find approximations to larger problems is a technique that was mentioned in AI class last semester. Also, Simon in his paper refers to a selective process of trial and error, which is essentially the technique I employed.

Answer to 1. The documentation of thoughts as I progressed as well as a picture file showing some examples of trial and error using the Excel sheet to represent different grids.
Documentation below records some of the thoughts as I was trying to find a solution:

a) Problem definition
The problem states a domino covers exactly two blocks. Are there any instructions saying you can't cover have overlapping domino blocks?

obviously, having overlapping would allow for other than 32 dominos to cover the squares.

If not (no overlapping allowed), there are 8 X 8 - 2 = 64-2 = 62 blocks to cover
Mathematically plausible to have 62 blocks covered by the dominoes
but since adjacent blocks cut out?

b) Alternating horizontal and vertically placed dominos.
I thought that perhaps if there was a way, it would involve overlapping horizontal with vertical domino blocks so that all the squares would be covered. I attempted with an excel sheet to color code various cells to see if it would be possible to try different overlapping techniques. I tried to foresee where domino blocks would not cover the squares completely, since 31 blocks is equal to 62 squares being covered perfectly.

c) Simpler problem

Visually, working outward from the edges, I started to consider the following:

If it's a matter of odd number of domino blocks covering even number of squares, experiment with a smaller grid.
Try a smaller problem and see if that can be solved.
A 4 by 4 grid.
16 squares means 8 domino blocks.
With 2 edges taken off, can we fit 7 domino blocks in?

Vertical domino blocks means there are still two spaces left.

Tried it with a 4 4, trying to alternate horizontal and vertical to cover as many squares within a the dimensions of even numbers (i.e. 2 X 2, 4 4, etc.). Still running into the trouble with having two sqaures that are empty.

5. could computers be useful to solve this problem?
Computers could definitely be useful in solving the problem as they could try out various techniques very fast, and within problems such as this one, random techniques can be pretty efficient.

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?
Sometimes a difficult problem needs a new perspective and to be seen in a different way. Different techniques, such as the conversion of problem into a simpler problem, can be employed.

For our course: After spending some time on this exercise, I thought on how learning is also design, as we have to create a framework within which to view alternative solution strategies as well as give shape to the problem definition.

Note: Was unable to upload file so have included a link to the page where it can be seen.

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