[Recording Start]
Scott Douglas Jacobsen: I’m interested in exploring the relationship between numbers and shapes. Specifically, the connections between anything numerical and shapes of various dimensions, such as 2D, 3D, or 4D. Could you elaborate on the relationship between numerical notation and shapes?
Rick Rosner: Alright, let’s delve into this. Generally speaking, we understand from basic principles that systems, or aspects of systems, tend to exist more readily when they are self-consistent. For instance, a symmetrical five-sided polygon is a simpler and more readily understandable shape than a symmetrical polygon with five and a half sides. To even conceptualize a five and a half sided polygon, one might imagine an eleven-sided figure that loops around itself twice. Similarly, a seven-pointed star, which wraps around twice, can be considered as a three and a half sided shape due to its seven sides.
This preference for simplicity and symmetry is mirrored in nature. For example, in quantum mechanics, it was discovered that electrons orbit a nucleus in stable orbits only when the wavelengths of the electrons fit symmetrically in whole numbers around the nucleus. Although this model has evolved into the concept of electron clouds, where energy levels correspond to these symmetrical wavelengths, these clouds still exhibit symmetry around a nucleus. If you look up electron clouds, you’ll see that stable electron orbitals assume various symmetrical shapes around nuclei.
Now, this symmetry, which is crucial for stability, is often described using numerical values that possess a high degree of self-consistency. Arithmetic, as a system, exemplifies this. While you can have one and a half apples, or an apple cut in half, a system with an indeterminate number of apples (sometimes one, sometimes two) isn’t particularly stable. This instability is less apparent in macro situations, where the number of entities, like apples in a kitchen, is generally known and relevant.
In quantum mechanics, we encounter scenarios like Schrödinger’s cat, where a cat inside a box may be simultaneously alive and dead until observed. This concept extends to the idea of having two apples in a box, where one may or may not be destroyed based on a quantum event. In macro situations, however, such indeterminacy is generally tied to irrelevance. We might not know exactly how many apples our neighbor has, but it’s consistent within their context and only relevant within that specific environment.
In the macro world, objects exhibit self-consistency. They don’t blink in and out of existence; they behave as macro objects typically do. This behavior aligns with the unitary nature of objects and the self-consistency of arithmetic. Countable objects like apples operate within the bounds of arithmetic, allowing for counting and fractional division. This is rooted in the inherently self-consistent nature of arithmetic, a system that lends itself to the existence and understanding of objects and concepts in our world. And I guess that’s the end of my ramble on this topic.
Jacobsen: The end?
Rosner: The end.
[Recording End]
Authors
Rick Rosner
American Television Writer
Scott Douglas Jacobsen
Founder, In-Sight Publishing
In-Sight Publishing
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In-Sight Publishing by Scott Douglas Jacobsen is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Based on a work at http://www.rickrosner.org.
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Rick Rosner 