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

In my first essay on how to scientifically design a 2-dimensional world, I started by touching upon the origins of A.K. Dewdney’s technical work and Martin Gardner’s mainstream work on this topic. Then, I went on to briefly cover Dewdney’s principles and treatment of various scientific laws branching out to physics, astronomy, chemistry, geology, and biology. Finally, I gave a brief introduction to the practicalities and challenges in a hypothetical 2-dimensional world.

In this follow-up essay, I will be covering specific 2-dimensional technologies starting with the most fundamental building blocks to slightly more complex ones. Finally, I will be covering the practical implications of this adventure and how we can benefit in our 3-dimensional world from all this knowledge.

I will be using Dewdney’s terminology throughout this essay. As a short recap, Dewdney referred to his hypothetical 2-dimensional world as Planiverse and our own universe as Steriverse. He further went on to refer to his hypothetical 2-dimensional Earth-equivalent as Astria.

This essay is supported by Generatebg

The Fundamental Technology of the 2-Dimensional World

When it comes to the basic building blocks of technology in the 2-dimensional world, Dewdney’s principle of similarity serves us well. For instance, consider the following illustration of basic mechanical components in the Planiverse:

They are directly analogous to their Steriverse counterparts. Dewdney went on to use these components to design more complicated technology as part of his technical venture (more on that in a bit).

Even though the illustration you see is for mechanical systems, we could extend the principle of similarity to other fields such as electrical circuits and bio-technology.

In fact, even in our real world, we often model complicated technologies as 2-dimensional models first before we proceed with upgrading them for our 3-dimensional world. This is a good way of weeding out dimension-independent errors in design. Multibody Systems (MBD) and 2-dimensional hydraulic circuit designs in mechanical engineering are good examples of this. Similar principles are pretty much industry standards in electrical/electronic engineering as well.

---

Examples of Complex Technologies in the 2-Dimensional World

In the previous essay, I covered how Astrian people (depicted by the Dewdney-styled triangular creatures) would have to construct underground homes due to spatial constraints in a 2-dimensional world. As a recap, check out the illustration of one such typical Astrian home below:

If you observe closely, there are quite a few intricate technologies involved here. Consider the collapsible table/chair, for instance. How are they supposed to be able to collapse? Or consider the doors. How are they supposed to open/close?

Well, Dewdney used some of the fundamental building blocks we just covered to come up with a very practical door design. Below, you can see how a vertical rotary hinge allows the door to swing both ways while a central wedge stabilizes it in the center position. As the door has symmetrical levers on either side, one can open/close the door from either side.

Here is another one: below, you can find an illustration of Dewdney’s 2-dimensional faucet design. It uses a simple 2-dimensional valve made of a spring, a lever, and hinges. When one pushes the lever forward, the valve opens, and water can flow downward (2-dimensional gravity).

Dewdney did not stop there. He went on to illustrate/design more complex technologies such as 2-dimensional engines and lock-key mechanisms.

---

How to Benefit from 2-D Science in our 3-D World?

Following Dewdney’s and Gardner’s works, several researchers from different fields reported that these ideas inspired them to explore novel thinking styles and solution approaches in their respective fields.

J. Richard Gott, a Princeton astrophysicist, reported in 1980 that when he looked into the physics of a 2-dimensional world, he was surprised by how counter-intuitive gravity behaved. In our world, we have 3 spatial dimensions and 1 temporal dimension. This means that the energy-momentum tensor has 10 independent components and the Riemann curvature tensor has 20 independent components.

In Planiverse, the energy-momentum tensor has 6 independent components whereas the Riemann curvature tensor has 6 independent components as well. Gott was surprised when he learnt that in a vacuum, all 6 components of the energy-momentum tensor and the Riemann curvature tensor were zero. Consequently, no gravity waves are allowed!

Some successful equipment manufacturers of the time adopted cardboard designs for prototypes and added appropriate thickness to manufacture the parts for real-world applications. Such designs were turned out to be very space-efficient. If you have ever worked with Computer Aided Design (CAD) based “extrusion”, you can relate to this.

Researchers slowly started embracing the notion of researching 2-dimensional science for the sake of it. Fast forward to today, we have several fields of science that are dedicated to studying planar phenomena.

Final Remarks

In 1984, Dewdney placed the cherry on the cake by publishing his work titled “The Planiverse”. This was a book that was partly technical non-fiction and partly fantasy. This inspired other authors to explore such scientific fantasy worlds.

I am one of those people whose technical career choices were inspired by brilliant works of science fiction that I experienced as a child. I cannot express how satisfying it is when someone manages to marry fiction and science without compromising on scientific thinking.

Not only is such an approach immensely satisfying, but it also inspires the next generation of scientific thinkers and innovators. What do future novel thinkers and innovators have in store for humanity, I wonder!

---

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

If you’d like to get notified when interesting content gets published here, consider subscribing.

Further reading that might interest you: How To Really Solve This Combinatorics Puzzle? and Are We Living In A Simulation?

If you would like to support me as an author, consider contributing on Patreon.