The Advantages & Disadvantages of Working from Home

Note: This post was created using Chat GPT to demonstrate the features of the Dante Astro.js theme functionality.

At some moments, my strong belief that even in chaotic circumstances is occasionally reinforced by previous positive actions and responses to others. In life, you sincerely played stalwart roles for others, so they respond you back with generosity though. How lucky and blessed I was yesterday! Mr. Michael openly shared what he thought I should learn as I asked for suggested books on software engineering.

I, a math enthusiast since high school is now so distant from it. From the time being, it feels like awakening me again to delve into the technical maths behind the software. Even after I could implement some apps in reality, I wish I wasn’t so stupid back again in terms of system-level theories and concepts. Huh! you may wonder why I wanna dig inner abstractions again in the midst of endless underlying ones owing to AI.

Of course, I, too, have been greatly influenced by AI like many of you have. But I think there’s nothing wrong with my own choice unless I simply have big dreams to become an entrepreneur for coins. And frankly saying I’d rather cultivate my farms through systems and theories for a period of time, lol. So let’s talk about category theory. Here, I would just recall what I remembered from a YouTube lecture and a book intro.

Hah, I have committed unnecessary spoiler.

People often struggle encountering new barriers in life, significantly because they cannot easily recognize familiar patterns or structures that relate to their previous experiences. Take a skilled carpenter, for example. When building a large structure like a modern skyscraper, they don’t view it as countless unrelated pieces. Instead, they recognize familiar patterns and abstractions, so help them understand how everything neatly fits together. The same applies for Rubik’s Cubes such like 2×2, 1×3, 3×3 with different colors or shapes, 4×4, 5×5, pyramid ones as they share same underlying patterns. When you catch those abstractions, I guarantee understanding becomes much easier.

Typically, we understand abstraction is as ignoring unnecessary details in order to focus on the underlying structure. In programming, different animals namely dogs, cats, and humans all share same ability to eat as part of their natural behavior. Despite their differences, they can all be grouped under the broader category of Animal as an abstraction. Composition, on the other hand, is the process of combining two or more functions between objects into a single function. Once I capture this idea more clearly, I could finally relate why my math teacher at school always emphasized function composition using f(x) and g(x). Definitely, functions map one object to another, we can compose them repeatedly in between, and even creating more complex transformations from simpler ones.

We often hear the saying, “People who accept their identity are happier.” There is always an essential edge directing themselves to stand out who they are in life. However, what does it mean by identity in category theory, working with configured objects and morphisms? It refers to a special morphism associated with every object. Every object has an identity morphism that maps the object to itself without changing it like below mappings.

idA : A → A idB : B → B

person → number ( → is age morphism ) person → person → number ( first →is identity morphism, second → is age morphism )

Here, the results on right side would be the same. And therefore, composing any morphism with an identity morphism leaves the original morphism unchanged. To be figured out we can follow the given expression.

f ○ id = f id ○ f = f

Here, identity will not make any impact on function. In math, any addition with zero has not changed its default value. The identity morphism is like the natural element of composition.