Applying Pure Mathematics to Daily Life
For those engaged in the intellectual pursuit of writing digital material, such as coding or marketing, this post may offer an educational perspective. It is not uncommon to find oneself exhausted from juggling multiple tasks and dealing with extensive workflows, despite the efforts of a product manager to streamline the process. The various programming languages and writing styles required for each task only add to the complexity. But this is a natural and unspeakable truth that we must acknowledge.
As a generalist engineer by profession and amateur mathematician by hobby, I often explore themes of pure mathematics and attempt to apply them to daily life. Despite the diversity of goals for each task, they all belong to the classification of “things one may execute in a certain manner.” Although we strive to carry out tasks continuously, we are human, and our tasks are inherently discrete and countable, much like apples in a basket. Each task consists of a series of instructions that can be performed in different ways and speeds.
To illustrate this point, consider writing an essay or a letter. Imagine you have a briefcase in front of you with all your favorite pencils, each with its thickness and color. While you would like to use all of them, it would take a considerable amount of time. However, if you were immortal and had an unspeakable number of pencils at your disposal, you could use all of them without concern. This is precisely what the Axiom of Choice dictates in the realm of mathematics.
In mathematical terms, an axiom is a fundamental and general statement that allows mathematicians to understand certain truths about numbers and logic. The Axiom of Choice guarantees the existence of mathematical objects that are obtained through a series of choices, extending the finite process of choosing objects from bins to infinite settings. Although this extension seems obvious and reasonable, it also leads to powerful and unexpected consequences.
The above quotation from the post cited earlier summarizes the idea of the Axiom of Choice. Through this post, I have presented this concept and its potential applications. For those interested in exploring the topic further, I recommend reading “Zermelo’s Axiom of Choice: Its Origins, Development, and Influence.”
