How To Scientifically Design A 2-Dimensional World? (I)

Science fiction talks about higher dimensional beings all the time, but how many of us have thought about life in a 2-dimensional world? We live in a 3-dimensional spatial world (4-dimensional, if we consider time as a dimension). We are used to our world and like our lives here. We find it difficult to imagine how higher-dimensional life would fare. Even more difficult (if not, seemingly downright absurd) is to imagine life in a 2-dimensional world.

Really? Life in a 2-dimensional world? Am I talking about a speculative work of fiction?

Well, no. I am talking about a scientifically designed 2-dimensional world with its own laws of physics, astronomy, chemistry, biology, etc. Life in such a 2-dimensional world (3-dimensional, if you consider time as a dimension) seems very restrictive as we are used to our world. But, as you will shortly learn, there is a wealth of knowledge and insight that we can gain from designing a 2-dimensional world! Let us start with a short history behind this concept.

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The Origins of the 2-Dimensional World

It was Edwin Abbott Abbott who first wrote a satirical novel titled “Flatland” in 1884. This book was largely a work of fiction with almost no information about the science and the laws governing the flatland-world. Charles Howard Hinton improved upon this situation in his work “An Episode of Flatland” in 1907. He used cardboard characters and developed the first instances of scientific laws that would govern a 2-dimensional world.

However, Hinton’s book went out of print and eventually lost popularity. Martin Gardner popularized Hinton’s work once again by covering it in a chapter called “Flatlands” in one of his works in 1969. This inspired a computer scientist named Alexander Keewatin Dewdney to approach this topic scientifically. He set to work and published remarkable foundational works on this topic in 1978 and 1979.

His work, “Two-dimensional Science and Technology” was a 97-page masterclass covering a wealth of basic scientific laws that a 2-dimensional world would require. From this point on, Dewdney became the power-house behind the scientific exploration of the topic, while Gardner helped popularize it further among science enthusiasts. Their collective work was so influential, that you are reading about it in 2022 in this essay. As they say, fads may come and go, but great ideas stand the test of time.

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The Principles behind the 2-Dimensional World

Dewdney called his 2-dimensional world Planiverse (and our own world the Steriverse) and imagined it as an analogue world to our own (in terms of scientific laws) and free of contradictions. Such a universe could be truly 2-dimensional or could have a slight thickness and move between frictionless plates.

The planet equivalent to Earth in this world is Astria. Life in Astria is set on the rim of the planet. Living beings (Astrians) can differentiate between east and west and up and down (not north-south).

In order to develop rigorous scientific laws, Dewdney followed two principles:

1. The principle of similarity

2. The principle of modification

According to the principle of similarity, Planiverse-concepts and states must be analogues of the corresponding Streiverse-concepts as much as possible. For example, the circle is the 2-dimensional analogue of the 3-dimensional sphere. This is the reason why Astria is a circle while the Earth is (largely) a sphere.

According to the principle of modification, whenever there occurs a choice between conflicting hypotheses, the more fundamental hypothesis must be chosen while the other one must be modified accordingly. In this context, Dewdney defined a hierarchy of sciences. For instance, he considered physics more fundamental than chemistry, chemistry more fundamental than biology, etc.

Now that we have seen the principles behind the 2-dimensional world, let us explore what they mean in terms of concrete phenomena of the various sciences.

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Physics in the 2-Dimensional World

Dewdney conceived gravity as one of the fundamental elements of the Planiverse. Like in our world (Steriverse), the gravity in the Planiverse is directly proportional to the product of two masses, but it is inversely proportional to the distance (as opposed to the square of the distance in the Steriverse) between bodies. Dewdney made this change so that light (and other objects) in the Planiverse could move in straight lines.

When we consider time, the Planiverse presents itself as a 3-dimensional space-time fabric (continuum) made of fundamental particles and elements that are analogous to the Steriverse. Energy is quantized and propagates as waves. Dewdney spent the time deriving major laws such as the first and second laws of thermodynamics, inertial laws, work, friction, magnetism, elasticity, etc., for the Planiverse.

To get a feel for how these laws might interact, consider the Astrian hoist design that is featured below:

Say that an (Astrian) engineer came up with this design. First, a metallurgist approaches the engineer and tells her that planar materials are more fracture-prone than 3-dimensional materials. So, the engineer thickens the parts appropriately. But later on, a chemist approaches the engineer and tells her that molecular forces are much stronger in the Planiverse compared to the Steriverse. So, the engineer reduces the thickness of the parts accordingly.

Astronomy in the 2-Dimensional World

The Astrian sky appears like a semi-circle. As the planet rotates around the Astrian sun, day-night cycles occur. At the night, stars populate the sky as twinkling light “points”. Dewdney calculated that the only stable orbit possible in the Planiverse is a perfect circle.

The calculation of complex orbits involving multiple bodies is an open challenge. As expected from the principle of similarity, the three-body problem holds in the Planiverse as well.

Chemistry in the 2-Dimensional World

Dewdney took the effort to model plausible chemical elements based on our own world’s laws of chemistry and quantum mechanics. He came up with 16 fundamental elements. In the 2-dimensional world, atoms can combine to form molecules. But intersecting bonds are not allowed. In this sense, bonding can be modelled using planar graphs.

In the Steriverse, 230 distinct crystallographic groups are possible, whereas only 17 are possible in the 2-dimensional Planiverse. Planiversal chemistry could be compared with the behaviour of streriversal monolayers on crystal surfaces.

Geology in the 2-Dimensional World

The Astrian weather is similar to Earth’s own, with exposure to four seasons, sun, wind, clouds, and rains. One notable feature of the rains is that unlike on Earth, the water cannot flow “around” objects in Astria. It can only flow over objects.

This means that rainfall often gets collected between rocks, and exerts forces on these rocks. These forces ensure that the Astrian rim is remarkably smooth and circular. Furthermore, because of the 2-dimensional behaviour, it becomes difficult to distinguish between Astrian rivers and lakes.

Dewdney also posits that if the rainfall is frequent enough, water would become trapped in the Astrian soil, causing large areas of dangerous quicksand. Like water, Wind cannot flow “around” objects in Astria as well. So, we can expect landmasses between mountains to be remarkably still.

Biology in the 2-Dimensional World

In the Planiverse, animals are made of cells, bones, muscles, and connective tissues. Dewdney showed how these elements could work structurally in a 2-dimensional world. All the modes of movement from our Steriverse transfer over to the Planiverse — walking, crawling, flying, swimming, etc.

When it comes to flying, an animal does not need wings. All it needs to fly is an air-foil-shaped body and a tail-like body part to flap around. So, expect air-fishes!

When it comes to 2-legged creatures like us, as long as both the legs are on the ground, the animal would not fall over. Balancing with 2 legs is much easier in the Planiverse than in the Steriverse. As a result of the reduced loads, Astrian animals would feature lower bone densities and muscle strength. Dewdney even went in-depth into modelling nerve connections using the Sterian 2-dimensional network models.

Dewdney depicted Astrians as triangular creatures with two legs, one arm, and one eye on either side (Astrians see in either direction). This is the reason why I chose to go with such triangular creatures in my illustrations for this essay as well.

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Practicalities and Challenges of the 2-Dimensional World

Unlike the Steriverse, the Planiverse is a severely cramped space. Lack of the extra dimension means that populations are likely to be much lower than in the Steriverse. When it comes to space utilisation, Astrians have to be much more efficient than their Earth counterparts.

For instance, cars cannot overtake one another; they need to jump over one another. When we extend this limitation to other aspects of life, housing becomes a major challenge. Consequently, Astrians would live in underground homes with collapsible chairs, tables, etc. To get a feel for this lifestyle, check out the illustration of such a typical underground home below:

Final Remarks

The idea of the science behind a 2-Dimensional world is so vast and full of possibilities that this essay just barely scratches the surface. It is impossible to do justice to the work of Dewdney, Gardner, and co. in just one essay.

Therefore, in a follow-up essay, I will be covering practical tools, technologies, designs, and innovations that would make up a 2-dimensional world. This future essay will also feature applications of such knowledge to our own reality on Earth. So, stay tuned and let your scientific imagination flow!

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References and credit: A.K. Dewdney and Martin Gardner.

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