Fractals & Chaos Assignment for 10/26

The last topic of the first section of the course is to further expand our notion of dimension, but in a different direction: Can there be dimensions in excess of 3?

As we are 3-dimensional creatures, it is challenging for us to conceptualize what a 4-dimension world would be like. It is best understood by analogy: by considering how a 2-dimensional creature would experience the 3-dimensional world. Fortunately, much of this heavy lifting has already been done for us!

In 1884, Edwin Abbott Abbott published Flatland: A Romance of Many Dimensions. It is told from the perspective of A. Square, a denizen of the titular 2-dimensional world, and starts off explaining aspects of their universe in great detail. The second part describes his first encounter with the 3-dimensional Spaceland, and the changes to his world-view as a result.

Abbott wrote the book partly as an exercise in geometry, but also partly as a satire on the regimented Victorian-era social hierarchy. As a result, there are some rather uncomfortable characterizations of women as lower-class citizens, among other shocking commentary.

You can read the full book here (I have paper copies if you’d prefer that), but for Monday please at least read this excerpt.

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