Preface:

Inspired by the countless imaginative works of science fiction I’ve come across, I decided to engage in some of my own science-based speculation. I wrote the following after pondering about what the Earth would be like in a two-dimensional universe, and I thought it might be an interesting read! This is quite different from my usual posts, in the sense that most of my claims aren’t followed with rigorous equations to back them up; I did, however try to run the equations behind the scenes as accurately as I could. Enjoy!

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Imagine a world where the Sun is the size of a pinprick in the sky, but shines with the same brilliance as ours. A world completely devoid of seasons, but cast into abrupt darkness mid-day every month or so. A world where daytime conjures temperatures soaring beyond Death Valley, and nighttime plunges the air below Antarctica’s most frigid winds. A utopia of unlimited clean energy, but plagued with painful sunburns. What is this world, you may ask? Enter the Flativerse: a two-dimensional universe I built to preserve as many laws of physics as possible.

Many have imagined what a flat world would look like. Perhaps the most famous example is Edwin A. Abbott’s 1884 novella Flatland, which describes a two-dimensional world whose residents are line-segments and polygons. Intuitively, life confined to a plane reveals a myriad of everyday difficulties, but curiosity drove me to wonder what unexpected results could come from considering the physics of such a universe.

I started with everyone’s favorite force: gravity. While transitioning to two dimensions, I chose to preserve one of the most fundamental descriptions of gravity (and many other forces!): Gauss’s divergence theorem. Imagine that every massive object is emitting countless imaginary rays outward in all directions, called field lines. As we go farther from the object, the field lines get sparser, which weakens gravity. In our three-dimensional universe, the field lines get sparse very quickly: doubling one’s distance to a planet will cut gravity fourfold. But our Flativerse has one less dimension for field lines to disperse in, meaning that gravity decays much more slowly: doubling distance only halves gravity!

This may not seem like a big deal, but on Earth’s surface, the difference would be stark: buildings would be crushed to the ground. Making Earth smaller would solve the problem, but even then, Egyptologists would emphasize the difficulties that increased gravity posed to the ancients while constructing the Great Triangle of Giza.

However, the equations behind our Flativerse’s exotic gravity face a roadblock. With the Sun’s current mass, Earth’s orbit (or any orbit, for that matter) would be impossible: Earth would be moving faster than the speed of light! By my calculations, the only solution is to cut the Sun’s mass by at least a factor of 1500. With such a small sun, how would we get enough light to survive?

Fear not, Gauss comes to the rescue: his divergence theorem applies not just to gravity, but to electric charges. Crucially, our Flativerse would have an exotic electric force that’s much weaker at short distances, meaning that the repulsion between atomic nuclei would be much easier to overcome… which means… nuclear fusion! Despite the Sun’s diminished size, it would shine just as brilliantly, owing to the greater ease at which hydrogen would fuse to create sunlight. Back on Earth, humanity would also rejoice as CERN designs the first artificial fusion reactor, solving the energy crisis overnight.

Unfortunately, thermodynamics rears its ugly head, the equipartition theorem. In our 2-D Flativerse, the Earth and its atmosphere (flatmosphere??) would have a much lower heat capacity, meaning they would heat up and cool down much easier than in our world. As a consequence, days would be very hot, and nights very cold. Zeldovich’s antidynamo theorem rubs salt in the wound: geophysicists would lament how Earth’s magnetic field ceased long ago, leaving the Sun’s unimpeded radiation to skyrocket sunburns. Student residence houses would be moved underground, and material-scientists would develop an ultra-powerful sunscreen for surface visits. The New York Subway would join with Tokyo Metro, as all the world’s public transit systems link together into an underground planet-wide loop encircling the Earth.

There are a few upsides to our Flativerse, though. Students at my school would find it much easier to hear professors in large classrooms: just like gravity’s field lines, two-dimensional sound would decay much slower. Seasons would cease to exist without Earth’s axial tilt, and our simpler calendars would be based on the Moon, whose lack of orbital-plane tilt would bring spectacular solar eclipses every new-moon. At each third eclipse, school tradition would bring students to the surface, celebrating the end of each academic quarter under the Moon’s calming shadow. As humans would only be able to see along a line, writing would be confined to one dimension; all the world’s languages would be united as one: Morse code.

Having only scratched the surface of the physics rabbit-hole, I’m looking forward to exploring Earth in our Flativerse, but in the meantime, I’ll be busy stockpiling sunscreen…