Reflections: Sphere-Land

Sphere-land is the sequel to Abbot's classic book Flatland. I'd been looking forward to read this book and it didn't disappoint me. The two books explore the concept of geometric progression and our conception of the number of possible dimensions in space. In Flatland, Abbot conceptualizes how life would be in two-dimensions, and how completely appalled the two-dimensional creatures would be, if they were told there was a universe bigger and more complex than they knew existed. Abbot hilariously brings out the utter confusion and disbelief of the 2D people in trying to visualize and come to terms with a new dimension, a new direction and completely different species and structures. It's an ultimate satire on how cloistered we 3D folks really are, in assuming that there can't be anymore dimensions, or more complexly developed species other than us. In Sphereland, Burger continues the discussion by adding more layers of geometric complexities that the 2D people toil to solve. He extends Abbot's narration by showing the scientific, societal and cultural evolutions in the land of Flatland. Scientific revolutions were at their hilt, through space and world expeditions to learn more about their world, as well as test their hypotheses on the 3D land. Two scientists who were ahead of their "flatanders" started observing intriguing things that completely altered their basic scientific knowledge - people who traveled straight along the east, somehow started meeting their friends who traveled along the west, there were mind-bogglingly startling triangles, whose angular sum exceed 180 degrees, and it seemed like the distance between their world and other worlds kept increasing for some reason! An expanding spherical universe?!! What does it mean?! With a benevolent 3D sphere paying visits to the Flatlanders every New Years' Eve to offer hints on their perplexing geometric problems, the prime scientists grapple with constantly having to revise their notions of scientific plausibility that go against some of their fundamental concepts!

Yet again, the book reinstates that our beliefs and scientific knowledge are very limited and are subject to constant revision. Just as the Flatlanders brandish the two scientists as being insane trouble-makers who indulge in black-magic with supernatural creatures from the other world, so is our perception on many baffling and inexplicable phenomena in our world. Burger also brings out the sad and frustrating truth about how even the intellectual scientific community ostracizes the two intelligent scientists and refuses to try and comprehend their research and solutions...it goes to show that it takes a lot to be open-minded to consider hypotheses that stretch the limits of one's current imaginations. To a 2D creature, it is unfathomable to visualize or conceive of a third dimension and the meaning of "perpendicular".

The book is well-written and while it may not be as revolutionary in inspiring to think about multiple dimensions, the book yet again hammers in the basic humility that we human beings are probably not the only sophisticated and complexly developed creatures, our current knowledge of science ultimately reduces to a set of plausible hypotheses, and there are definite limits to our mental and cognitive faculties. Just because we cannot understand a phenomenon because of this basic limitation, it doesn't rule out the truth about the phenomenon.