📙 Flatland: Romance of Many Dimensions

Introduction: 💾 #

This is a satirical novel featuring a pentagon flatlander’s revelations and brain-twisting experience of space-land. The author takes us into a fictional world of flatland where all flat-shapes live. Squares, pentagons, hexagons, polygons and circles(very rare) detailing out religion, politics, sex, race etc. The everyday lives, sense of perception of these members, their worldview etc. Here the author introduces the flat-lander pentagon to line-land inhabitants who are just lines of different lengths and can see only dots. Then he brings in a sphere from space land and tries to convince the flat-lander pentagon that higher dimensions exist, and this prophecy is kept secret in higher community members of the churches of flatland. Finally, the author also extrapolates how a sphere encounters a hyper-sphere in space-land.

Highlights: 📊 #

• Experience of Higher-Dimensional entities by lower-dimensional space inhabitants
• The trouble of handing over the prophecy
• The flaw of the higher-dimensional view
• Extrapolation to hyper-dimensions
• Experience of Higher-Dimensional entities by lower-dimensional space inhabitants 🔥

Imagine a circle passing through an x-y plane. When the circle touches the plane, it happens at a particular point, when it is passing through, it cuts a circular section of that plane. But the funny fact is if we see it from the perspective of the plane, a dot appears and it grows to max size and shrinks back and goes out of existence!.

Summary of an Event of Observation of a 3D object in a 2D plane from the perspective of the Plane #

This is the same idea with which physicists are trying to detect the higher dimensional existence by checking the loss of energy of particles in particle collisions in particle colliders. If energy is lost, we can hope that it might be because it has reached higher dimensions of which we have no perspective. This is explained as a dream which our pentagonal flat-lander experiences where he observes line-land population. Then, he experiences a sphere from space-land in his world(flat-land).

The trouble of handing over the prophecy: 🤫 #

The circle tries to convince the pentagon about the existence of higher dimensions which the pentagon presumes to be 🧙 voodoo witchcraft. Then the circle confesses that this secret is kept tight among higher intellectuals of the church of the flat-land, and a law is passed such that anyone who speaks of it will be guillotined publicly. So, the sphere claims o be discreet and promotes the pentagon to be the prophet of such a prophecy. In fact, the circle tries its best to reason and after a few desperate attempts pull the pentagon outside the flat-land and shows the space-land experience. After viewing the space-land with his own eyes(the pentagon), he agrees to teach this to his fellow flat-landers. The sphere also says that it will take another 1000 years for the space-landers to make contact with flat-landers and the pentagon is responsible for scientific development in flat-land.

The Flaw of Higher-Dimensional View: (personal criticism) 🧐 #

I feel that the pentagon, after being brought to the space-land, will still see dots and lines rather than shapes as his eyes have the capacity to perceive only those. A special eye must be provided to even perceive the 3rd dimension. This but will reduce the excitement of the plot and reduce the chances for the flat-lander pentagon to realize the existence of a higher dimension. I stand to a point that the perception has to be granted, it can’t be extrapolated with the limited apparatus.

Extrapolation to Higher-Dimensions: 🧝🪄🪄🪄 #

AI tries to learn Schubert’s composition styles from his previous compositions to attempt to complete his 8th symphony which he left uncompleted. In technical terms, AI is actually extrapolating his 8th Symphony. In reality, it sounded more of pop style(with just 4 chords) and some flavour of Rachmaninoff rather than Schubert himself. The author finally attempts to extrapolate this line-land to flat-land and flat-land to space-land transformations to space-land to hyperspace-land. The extrapolation sounds promising in the fact that the observations of 4-D objects in 3-D would seem similar but the perception of 4-D in a direct sense is a dream. But he also shows the ignorance of the sphere and the knowledge/reasoning gained by the pentagon from the sphere reverts back to the sphere as lessons. But our sphere neglects it in a go. More on this can be found in the last 2 chapters of the book.

Conclusion: 🥱 #

Overall the book trains us to make observations with limitations available in our environment and utilize such observations to interpolate and extrapolate the knowledge in our frontiers of research. A good introductory book inspires readers to see past the limitations. After reading this book, I got an idea to study and understand infinities in a similar fashion, thanks to the author for kindling the spirit.