Chapter 8: The Wonder of the Planiverse

Chapter 8 The Wonders of a Planiverse, talks about a universe that exists in only a 2-dimensional plain. This “planiverse” would be completely flat and there is an assumption that no intelligent life would be able to exist on this 2-dimensional plain. The construction of simple machines that we use in everyday life would have to be completely redesigned to accommodate the flat world it was built in. Life forms would be extremely different than anything we know here on Earth, and forces like gravity and the flow of water are rather different than in our 3-dimensional world.  The normal laws of physic that we know and accept here on Earth don’t apply to Arstria, that’s the name given to this flat world by Dewdney. Gravity in the Arstria is the same as on Earth, where “a force between objects that varies directly with the product of their masses, but it varies inversely with the linear distance between them, not with the square of that distance.” (pg. 95) Take water for example, gravity pulls water down a slope after it rains. This water flows normally down this slope as it would on Earth, the difference is when this water makes contact with a rock or any other object it cannot flow around it. The water then gets trapped behind that rock and starts to accumulate until so much water is stuck that it begins to push the rock down the hill. Wind would also have a big effect on Astria because it to cannot go around objects. Life forms would look very different on Astria than they do on Earth. For one we would be able to see all of these organisms internal organs like any being that exists on a 4-dimensional plain would be able to see ours. On page 100 of the Colossal Book of Mathematics there is a diagram depicting how Dewdney and Hilton imagine these creatures to look. Hilton describes the life forms to have one eye and two arms on the same side of this animals body, they will always face the same direction. Dewdney’s Astrians are biologically symmetrical with one eye on each side of its body as well was one arm on either side of its body. The benefit of this creature is that it can see in both directions verses its counter part that can only see in one direction and a largely one-dimensional view of their world. Construction of building, roads, and simple machines would pose a big problem people living on Arstria. Consider building a road, on Earth building a road through fertile farm land would only destroy a very small percentage of its land. Where on Asrtia, the completely flat world, it would destroy 100% of the farm land. This poses a large problem with building builds and homes. The most logical solution to this problem would be building underground to preserve the life-giving plants and animals on the surface. A diagram of a model of one of these underground houses is depicted on page 101, it shows how the tables and chairs would be collapsible to preserve space in the house and the doors would open in both directions. Plumbing would be tricky but not impossible to construct as well “Tubes and pipes must have partitions, to keep their sides in place, and the partitions have to be opened (but never all of them at once) to allow anything to pass through.” (pg. 101).  I think its amazing that we have been able to engineer these models that work even though we do not exist in a purely 2-dimensional universe. G. J. Whitrow believes that intelligence could not evolve in a 2-dimensional space because the nerves needed to operate an intelligent life forms brain would be to complex to form. Dewdney was able to disprove this idea by saying that the neves are allowed to fire nerve impulses through “crossover points” then you would able to develop a nervous system just as complex as any in the steriverse. Although this process would be considerably slower than that of and organism in the steriverse intelligent life would be able to exist in this flat world.        The Planiverse Project: Then and Now brings up topics that were not discussed in the book like stars and planets existing as disks of two-dimensional matter, the orbits of these planets and the inverse square law, and the amount of light that falls on a linear meter from a star. These concepts are very complex and I’m happy they were not included in the reading. The topics about engineering and technology are similar to what is talked about in the book and they also talk about water getting trapped in the soil because of the different kind of gravity that is exerted in this two dimensional plain.
The article Lower Dimensional Gravity touches on how gravity fields act differently in other areas of space and time. Gravity in the third dimension acts as we know it should, but the way gravity works in a two-dimensional plain acts strangely. Take water for example it can only flow down a slope, if anything was to impede its forward progress it would stop there. The water would not flow around the object, and it would start to pool behind that object. Where we know that in our three-dimensional world the water would just rush around the rock and not slow down very much at all.