Lower-Dimensional Projection
The Idea
We usually only see a lower-dimensional distortion of reality and the people around us.
In 1884, Edwin A. Abbott created a mathematical thought experiment and published it in a novella called Flatland. In it, he describes the hypothetical world of objects that exists only in two dimensions — circles, triangles, squares, hexagons, and so on. All of these have some length and width, but no height as they live on a flat surface where up and down do not exist.
If we now imagine a 3D object like a sphere passing through this Flatland of lower dimensions, we can see that the only thing appearing of the sphere in two dimensions is an expanding and then contracting circle: As the bottom tip of the sphere touches Flatland, you will see a small cross-section of it in two dimensions. This cross-section grows until it reaches the middle and then shrinks again towards the top of the sphere. The three-dimensional sphere will appear as a pulsating circle in two dimensions.
The gist is this: Higher-dimensional objects will appear very strange and distorted with lower-dimensional perceptions.
While this century-old thought experiment is still being used in math and physics, for example in order to think about how four- or higher-dimensional life forms could be detected, this concept has interesting applications in everyday life when thinking about human and societal behavior in different contexts.
For instance, we perceive and thus interpret our colleague’s actions and demeanor at work based on a set of work-related dimensions: job performance, relationship to management, working style, culture fit, tenure at the company, and so on. However, even a broad set of dimensions in this context will be lower-dimensional compared to everything that makes the human being who happens to be our colleague. As their private life stays hidden from us at least to some degree, we don’t perceive dimensions such as their relationship with their spouse and children, their personal interests, their inner values and core drives, their recent social experiences, and much more.
As a result, who we perceive at work is just a lower-dimensional, distorted projection of a higher-dimensional human. The dimensions we are able to perceive at work just are not enough to adequately represent who the person truly is in their entirety.
The principle of lower-dimensional projection similarly applies to how we look at people in our private life as we usually don’t know everything about them. Likewise, it describes how we perceive societies and other collective dynamics: we typically only perceive a subset of all relevant dimensions, and thus our efforts to understand these dynamics will be down-projected and somewhat distorted.
Resources
A few further resources you might like if you find the above idea interesting:
📚 Edwin A. Abbott’s Flatland: A Romance of Many Dimensions
🎥 This incredible 7-min. video of Carl Sagan explaining the 4th dimension
🎥 This TED-ed explanation video of higher dimensions
📝 MindVault: Systems Theory
📝 MindVault: Maps Aren’t Territories
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