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Genevieve Hudak

1. The first concept thing that I learned from the reading has to do with the evolution of complex systems.

The second concept I learned dealt more specifically with biological evolution.
1.1 The thing about the evolution of complex systems that I think is important is that science (this includes many fields) is utterly dependent on the evolution on systems. And in order for those systems to evolve in any meaningful way, i.e. in a way that furthers our general knowledge about the world; those systems end up being complex. Therefore, in order for these systems to evolve, some evolution of complex systems must take place.
Biological evolution in terms of hierarchies is important for many obvious reasons. Mainly, in order for life to become more evolved, it almost seems that is must necessarily become more complex. And in order for it to evolve efficiently, as was demonstrated in the watch example, that complexity must be based on a hierarchal structure. If we ever hope to truly understand our genes and how they make us who we are, we will have to approach DNA in a hierarchal way.

1.2 The first concept is relevant to my interests/work in that it is important to philosophy of science because it relates to the complexity of theoretical terms. Though it is often attempted to tie theoretical terms to observations, it seems nearly impossible because of the inherent complexity of these theoretical terms. The truth is there is more to them than just observation. It is relative to computer science because high-level languages are complex hierarchies of symbols built to represent more and more low-level computer instructions (going all the way down to assembly language and then binary, finally reducing to voltage) where each higher level of the hierarchy is more complex and built on the level below it.

The biological evolution is an important concept related to my interest work on my senior project that deals with programming search tools for searching for specific patterns in the human, mouse and rat genomes. If there was no hierarchal structure to the complex system of DNA –> RNA –> proteins (the central dogma of MCDB that is obviously hierarchal), then it would be difficult to find a way to search through it. It seems that hierarchy imposes some sort of structure. That or the structure leads to hierarchy. In any case, it is clear that a biological system that wishes to survive must evolve, and therefore some biological evolution must occur. So it is related to my work in that you must understand how it evolves in order to be able to gather any information from it, or search through it efficiently in other words. As the watch and safe examples show, understanding the hierarchal structure underlying complex systems allow you to drastically reduce the search space and thus the time needed to process that, or reach your goal, etc.

1. In first trying to attempt this problem (I remember being presented with it before, and I remember that I don't think it is possible, though it seems as though it should be), I remembered an old way to approach the problem, namely, alternately color each of the square so that it has the appearance of a chess/checker board. From this you see that you remove two black squares. First you must back up and realize that a domino block will always cover up one black square and one white square. Then it is simple to see that if you remove two black squares, you will not be able to properly cover the board. Had the second removed square come from the upper right corner instead of the lower right corner, then it would have worked. But since I have too quickly come to the solution (since I have seen the problem before) I will outline some of the initial thinking I had the first time I had seen this problem.

My first intuition was to just start at a corner and start 'placing' blocks, covering as best I could (leaving no holes) all the way around the board until finally coming into the middle and reaching a point where it was no longer possible to arrange the pieces in any way that worked. I tried this a few times, with different arrangements. None worked.

Next I was convinced that I had missed some trick to the problem, so I went back and asked some questions about how the pieces could be placed. However, this did no good. The problem had been presented straightforwardly, and there was no solution.

2. The resources I used were to look at the diagram and use a pencil to mark the possible position of pieces, and then to mark which square would be black or white.

3. Ultimately I used a process of reducing the complex board to that of a more hierarchal one, where the board was made up of 'subunits' of one black and one white square, adjacent to each other. You can then mark each set of these two pieces as one component, then see if you can fit 31 of them on the board.

4. I used the practice of marking the board to look like a checker board. This is the solution that had been presented to me the first time I saw this problem.

5. A computer might be useful in solving this problem, but it seems as though it is simple enough that you don't need one. Surely if the board had been size 100 X 100 or even 25 X 25, then it would have been less tedious if done on a computer as opposed to by hand.

6. I learned solving the problem that there are many different approaches to problem solving, and sometimes it is not easy for you to come up with all of them on your own.

7. I learned from not being able to solve the problem that for problems that do not have a straightforward solution or have no solution at all, that you cannot know this until you try out several different approaches. I could have just as easily just said that the puzzle was unsolvable by observing that they removed two pieces in diagonal orientation to each other and that if we had relocated them to be adjacent diagonally, that it would have been instantly clear. However, I still had to think about this before I could solve the problem. What I think I'm really trying to say here is that when approached with a complex problem such as this one, it is often necessary to reduce the problem to a simpler hierarchic structure in order to obtain a solution (or at least the notion that there is no solution).

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