Thursday, April 28, 2022

Four-Dimensional Urban Planning

At the beginning of this month, I came across this Twitter thread describing a city plan by Leonardo da Vinci. They key concept is to make use of altitude to separate essential functions into different planes--essentially, vertical zoning. Residential areas are on top, over pedestrian pathways, then the commercial and transportation district, and bulk shipping canals on the lowest levels. Separation of zones by planes allows keeping the elements of each zone close together with other zones out of sight, but still easily accessible by moving a short distance through another dimension.

While modern cities do make some use of transportation tunnels (subways, car tunnels, underpasses and overpasses) and stacking residential apartments over commercial spaces in multi-story buildings, a combination of gravity and coordination issues (how do you build new stuff on top of, or underneath, another building?) makes the full realization of da Vinci's 3D city rather difficult. However, there are fictional environments in which it makes perfect sense!

Within the confines of our own universe, 3D zoning makes perfect sense for a large space colony in zero-g. But da Vinci's city plan is also ideal for creatures living in a 4-dimensional universe!

Planets in 4 dimensions are hyperspheres with 3-dimensional surfaces. It is thus possible (and indeed, entirely natural) to build a 3-dimensional city in which every building sits directly on the ground, and there is no need to worry about gravity overcoming the structural strength of other buildings "below" you. Just as unplanned human settlements tend to grow in a roughly circular pattern, the "organic" city growth patterns of a 4 dimensional people would most naturally tend towards blobby spheres--and they can be much more compact. High-rise apartment population density is the natural state for early 4D cities, not a result of advanced construction & logistical technologies, with supplies able to brought in to a city and wastes removed over a whole 2D surface rather than a 1D border.

Zoning is not obviously a more obvious concept in 4 dimensions than in our 3, but once someone comes up with it, it becomes far easier to actually implement. Confining each district to a plane makes internal navigation only as difficult as it already is in our two-dimensionally-arranged cities, and density can be recovered if the 4D people simply learn to build upwards, exploiting their 4th dimension as we exploit our third. Thus, planar zones such as da Vinci envisioned can be constructed next to each other, without needing to be stacked on top of each other. And thus, 4D urban planners could achieve a very high degree of logistical efficiency and provision of utility services for a higher standard of living at a very low level of material technology. 

1 comment:

  1. I'll note in passing that, for whatever dimension, roads would take up less space in a hyperbolic geometry.

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