Back in 2009, after the Tutor.com Book Club read Flatland I wrote a blog post that was deleted after we sold the company. Today I found a copy of that post thanks to the “Wayback Machine” that archives the internet. Here is that post in its unaltered entirety.
This month’s Tutor.com Book Club pick was “Flatland, a Romance of Many Dimensions,” by Edwin Abbott.
It is hard to believe that a book written 125 years ago would lead to our book club discussing quantum entanglement, string theory, multiple universes, and the purpose of life, but I suspect that Mr. Abbott would be very pleased to see it so, were he still alive.
He wrote this book with two obvious goals in mind. One was to satirize the social culture of Victorian culture. The other was to nudge people towards thinking about what a fourth dimension might look like. (Yes, an actual fourth geometrical dimension.) We discussed the folly of Victorian narrowness but spent most of our time discussing the geometry, physics, and metaphysics of the book.
The story of this book takes place nearly entirely in a two-dimensional world called Flatland. The narrator of the book is a square, who describes life in Flatland, where circles are revered, women are line segments, and a man’s standing in society is directly correlated with how many sides his polygon has. (More sides means more prestige: Squares are superior to triangles.)
In a dream, the square character visits a one-dimensional world called “Lineland,” which is inhabited by beings that can not grasp the possibility of a second dimension. The square, standing to the “side” of Lineland, tries to explain to the King of Lineland how to turn his head to the side and see the second dimension. The King can not, to the square’s obvious frustration.
Upon waking, the tables are turned on the square when a three-dimensional sphere visits Flatland in the same way that the square visited Lineland. Now it is the square’s turn to be frustrated as the sphere says “I’m right here, above you.” The square of course knows nothing of “up,” anddoes not have the physical ability to look up, and so is angry and confused.
As the dialogue between the square and the sphere continues, however, the sphere explains how the square can use the math of two dimensions to deduce the existence of a third dimensions.
And of course that leads to our realization that it is quite possible, if not probable, that there is a fourth dimension that we humans can’t see or touch because of our physical limitations, but is nevertheless immensely real.
Just as a square only needs to look “up” to see the third dimension, so it may be that we only need to look in a direction that we have no word for . . . yet . . . to sense the fourth dimension.
As our discussion kicked off, Abel suggested that anyone who reads Flatland or is curious about the idea of additional dimensions should view this excellent video on YouTube of Carl Sagan. In it, Mr. Sagan does a masterful job of introducing the concept of multiple dimensions and the ideas of Flatland.
The conversation then shifted to an interesting “what-if” scenario: What if humans never developed eyes of any kind? If we evolved with only touch, smell, taste, and hearing. Would we be able to deduce “sight” as a sense? Could we prove light existed?
This led to a discussion of whether it could be possible that some animals can somehow sense things through a fourth dimension and then to a discussion of one of the biggest mysteries in science today: What is the force behind quantum entanglement — the phenomenon of subatomic particles somehow being connected to each other in a way that scientists can not yet explain.
Quantum entanglement seems to violate the known laws of physics by allowing particles to communicate with each other far faster than the speed of light. For a quick summary and some good links, here’s a blog post I wrote about “The Age of Entanglement: When Quantum Physics was Reborn.” (For a more detailed explanation of quantum entanglement, consider this wonderful lecture DVD series.)
I suspect that Mr. Abbott would think that there is indeed a fourth dimension, and that it is the medium through which the quantum particles are connected.
Our discussion of quantum entanglement led to a discussion of several theories that could explain it, including multiple universes. That led to a discussion of the laws of physics in our universe and some of us wondering whether these laws have always been the same, have they evolved over time, and what might a universe look like with slightly different physical laws? (For example with stronger gravity but weaker nuclear forces.)
From here we launched into speculation about whether four-dimensional beings may be looking at us the same way that we would look at simple two-dimensional beings. We then wondered whether it might be that, as most intelligent life evolves, it gets to a point where it can “sense” the fourth dimension and then eventually learns to go there? Maybe that is why we have not detected any other life in the universe yet?
That discussion branched to another interesting topic — whether we are about to reach the fascinating (and possibly scary) point in our own evolution when we no longer need to wait hundreds of thousands of years for natural selection to do its thing: Are we about to be able to genetically engineer ourselves into a series of different species? For example, one that is adapted to deep-space exploration? Another with gills, to live underwater? Would this be good or bad? Would it increase our chances of surviving possible apocalypses?
This led to an interesting discussion about ardipithecus and happiness. How do we define happiness? Are we happier now than ardipithecus was more than 4 million years ago? Leisure time? Meaningful interactions with friends and family? (Abel recommended that we check out a book called Cosmicomics, which is a book of metaphysics short stories written in 1974 by Italo Calvino.)
At the end of the discussion, everyone other than Carolann and Lynne said they really liked the book, and everyone felt that the discussion of the book was one of our best ever. Carolann said it felt like a textbook, without any real plot. Jill noted that she was a big naysayer at first but when she got into the book she loved it.
Jen, however, had the comment of the day. Expressing frustration at our collective inability to explain the bizarre paradox of quantum entanglement (which takes place at the at the sub-atomic level), Jen expressed her preference for the macro world as follows: “I can tear a beating heart out of someone’s chest and SEE IT in my hand.”
In addition to serving as a stern warning to anyone who might attempt to steal the stapler from her desk, Jen can take solace in the fact that her words are right in line with many famous physicists, such as:
- Neils Bohr, who said, “Those who are not shocked when they first come across quantum theory cannot possibly have understood it.”
- Albert Einstein, who said, “This quantum question is so uncommonly important and difficult that it should concern everyone.”
- John Wheeler, who said, “If you are not completely confused by quantum mechanics, you do not understand it.”
- Erwin Schrödinger, who said, “I do not like quantum mechanics, and I am sorry I ever had anything to do with it. “
Next up for our book club is The Sex Lives of Cannibals by J. Maarten Troost.