Flatland. Flatland 1/16

Transcription

1 Flatland Flatland 1/16

2 The book Flatland was written in 1880 by Edwin Abbott. A copy is available at banchoff/flatland. Flatland is inhabited by 2-dimensional geometric figures. The more sides somebody has the more status they have. Flatland is run by the circles, who can be thought of as figures with infinitely many sides. In the movie a sphere comes to flatland with the hope of educating the population by introducing one flatlander to the third dimension. He then takes Arthur Square into this new dimension. While there Arthur encounters 0-dimensional and 1-dimensional worlds. He has a hard time understanding their limited view of the universe while he has a hard time understanding the third dimension. Flatland 2/16

3 Some Things to Think About How does Arthur Square appear when he goes into a 1-dimensional universe. Is this reasonable? What kind of shape(s) do you get when you cut a three-dimensional shape by a plane? This shows up in the movie. The circles are trying to keep knowledge of the third dimension hidden. Why is this? The sphere opens Arthur Square up to the idea of a higher dimension by taking him to the third dimension. How does the sphere react to Arthur s broadening of his horizons? Flatland 3/16

4 Clicker Question When flatlanders rotate 1/2 turn, their eye always is right side up. Do you think this would happen to actual creatures in a 2-dimensional universe? A Yes B No Flatland 4/16

5 Clicker Question The sphere is trying to open up Arthur s mind to the idea of the third dimension. But, he thinks considering a fourth dimension is a ridiculous idea. Are you surprised by his attitude? A Yes B No Flatland 5/16

6 This is discussed around 19:45. We ll explore this further when we watch the movie Sphereland later in the semester. Flatland 6/16

7 Clicker Question Can the king of Lineland switch left and right? A Yes B No C I don t know Flatland 7/16

8 Arthur Square meets the king around 13:00. The king talks to his queen of the left and the queen of the right. He can t switch left and right; if he could switch left and right then the queens would switch positions. We ll see more about this when we watch Sphereland. In particular, we ll see how he can get left and right switched by existing in flatland rather than just in line land. The idea came up when we discussed reflections earlier in the semester. Flatland 8/16

9 Clicker Question Why do the circles want to keep the knowledge of the third dimension hidden? A Because they don t like cubes B To keep their power C Because they don t understand the third dimension Flatland 9/16

10 Around 19:00 in the movie Spherius says the circles deny because nobody would obey their rules if flatlanders knew about Spaceland. Flatland 10/16

11 Fractals The pictures drawn in the interior of flatlanders and elsewhere are fratals. They made heavy use of them, especially the Mandelbrot set, in the background art. Flatland 11/16

12 Let s watch a YouTube video of Carl Sagan discussing flatland. Cosmos - Carl Sagan - 4th Dimension Flatland 12/16

13 Clicker Question Does Carl Sagan sound like Agent Smith? A Yes B No C I don t know D I don t know who Agent Smith is Flatland 13/16

14 Agent Smith YouTube video Flatland 14/16

15 Next Time We will begin a three week discussion of probability. Next week will focus on a little history of the subject and some of the principal ideas. In particular, we ll conduct some probability experiments to help understand the meaning of probability and to see some common misconceptions. In the second week we ll discuss poker and several aspects of how probability comes up in poker. In the final week we ll discuss various games of the New Mexico Lottery and see how likely it is that you d win when playing those games. Flatland 15/16

16 Assignment 3 The next homework assignment is available. It is about errors and encryption. Flatland 16/16