This blog is meant for the students of Recreational Mathematics to post about the class.
Wednesday, September 10, 2014
Chapter 8, The Wonders of a Planiverse.
This chapter was very interesting, and thought provoking. Although the topic appears to be mundane to begin with, the ideas towards the middle of this chapter become more and more intriguing. I feel that this chapter stands to show how relevant seemingly irrelevant thoughts can be. To prove this point it is necessary to recap certain parts of the chapter. When the chapter begins, it explains the basics of what is being discussed, which is a two dimensional reality. This is said to be impossible, for it would pose many issues and questions that we simply do not have the answers to. The book says that one issue with studying a two dimensional world is that we have no axioms, and we can only perform gedanken, thought, experiments. Even though the only path to understanding a planiverse that we have is through gedanken experiments, a lot can still be accomplished. Within this chapter, many properties of this planiverse are discussed, and how they relate to our steriverse. There are countless properties of the planiverse that are different than our steriverse. A lot of this has to do with nature and physics. For example, the earth would revolve around the sun, similar to what our earth does, but in the planiverse the path of the earth would be either a perfect circle, or an incomplete ellipse. Another example is that water and wind could not move around objects as they do in our reality. This would change many things, such as the geology of the planiverse, also rain would be way more dangerous there than it is here. The inhabitants of the planiverse is another topic of debate. These inhabitants will need to pass each other at some point, but in order to do so they will need to jump over each other to get by. This reminded me of the older 2D video games such as Mario. Another interesting topic discussed in this chapter was board games. The book said that the inhabitants of the planiverse would be able to enjoy boardgames similar to those played in the steriverse. Although they could play games such as checkers and chess, they were quite simple and usually had a preconceived outcome. But Linear Go could become quite interesting if the number of spaces was extended dramatically. Although these games are possible, they would need different rules and would require a lot of space. The amount of space is another issue that the planiverse would need to solve. Inhabitants of the planiverse would need to live underground to save space for necessary vegetation. This means that roads, houses (above ground), and cities must be kept at a minimum, if at all. The only solution would be to move everything underground. Even though the planiverse comes with many issues, there is a good side to it. Due to the constraints it puts on building machines and simple objects, it gives us a new way of viewing the use of space. An example from the chapter is the lock. We could create a two dimensional, with a very small width, that would save space, and the keys would not have to turn. Even though this is possible, it does not mean it is probable. The lock is a great idea, but is very expensive. So, the planiverse is great at giving us a different outlook on problems, but it does not give us realistic solutions.
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I really like the way you compared it to a video game! that made a visual image in my head that helped me understand better.
ReplyDeleteYour examples were very interesting and helped me understand better. The connection to the video game was very cool, I really enjoyed it. They all made great visuals in my head.
ReplyDeleteYour summary helped me better understand this chapter. I really liked all of the examples that you used like the Earth revolving around the Sun one. The video game comparison was really interesting too.
ReplyDeleteI like your comparisons and the way you made the chapter easier to understand. I agree that it is necessary to recap the chapters.
ReplyDeleteI liked the comparison you made to that of a Mario game to show how difficult it would be to get around in a Plainiverse. There would be less space since it is two-dimensional and this concept is interesting to know about, but it seems to have more cons than pros in a Plainiverse.
ReplyDeleteI like the comparisons you made. You also did a good job summarizing the main points.
ReplyDeleteI find concept of different dimensions very mind blowing however not easy to understand. Your summary shone some light on how on land movement in Planiverse is possible. However, the idea of motion in air still remains vague to me. Especially birds! Unlike projectiles, they have to maintain flight and I don't get how they would maintain flight without wings. Or did I miss a point which mentioned that birds do not exist in Planiverse?
ReplyDeleteLoved the summary of the chapter and how you explained the second dimension. I like how I can use this chapter and the movie we watched on Friday in class to better grasp the Planiverse.
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