Ben Myers
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# Wordcast 1 *Feb 4, 2022* Topic: **Wordcast** — Today, I’m going to delve into the world of thought. Blogs are always so well-formatted and predictable. Today, I’m going to write about whatever comes into my mind. I’ll call this type of blog a #wordcast, as indicated by the #tag. I’ll start with a random topic. But before I begin, I want to specify that no sentence *must* always be “connected” to the next (i.e. topics can be changed without warning). With that, I’ll start. I feel like more people should learn proof-based mathematics. I think they, in addition, should be able to understand the logic-based foundations of math (i.e. learn the concepts of set theory, then discover how to formulate set theory from logic). Why? Because it does two things. It helps one learn that *anything can be deconstructed into logically equivalent parts*, and hence be able to manipulate logic in everyday life; and that the study of mathematics is a topic that, while shrouded in beauty, is completely (and satisfyingly) learnable. I mentioned in the previous paragraph the idea of *discovering how to formulate set theory from logic*. This recalls a issue I find very profound: how mathematics (and, in similar ways, all subjects) are taught in the classroom. I think the inherent beauty of mathematics is diminished when it is revealed in lecture or assignment format. Instead, I believe students should learn the concepts through a method of *discovery*. A (surely non-perfect) instance of this could be challenging students to invent their own types of mathematics, then let them see how close they were to the original thing. As a personal recount and an example of this instance, I once created my own type of mathematics. I called it “versatile trigonometry”, and it took the typical trigonometric functions ($\sin$, $\cos$, $\tan$, etc.) and added a new “parameter” with a function input in the form $$ \begin{align} \text{sin}[f(t)](\theta) \\ \text{cos}[f(t)](\theta) \\ \end{align} $$ where $f:\mathbb{R} \rightarrow \mathbb{R} ; t \mapsto f(t)$. To calculate, one would take the proposed $f(t)$ function, “graph” it, then draw a ray with an angle of $\theta$ to the horizontal. The “absolute sine” (as I defined it) would be the x-coordinate(s) of intersections between the ray and $f(t)$, and the “absolute cosine” would be the y-coordinate. I then expanded the definition to $$ \begin{align} \text{sin}[f(t)]^a_b(\theta) \\ \text{cos}[f(t)]^a_b(\theta) \\ \end{align} $$ where the same method is used, but with a ray having a terminal point at $(a, b)$. I then investigated the properties of such an expression, and it was a very interesting and exciting experience to do so. In the process, I discovered characteristics about my own creation, and I learned that mathematics is a lot more enjoyable through means of discovery. Encouraging students to create and learn on their own, in fact, is a skill that (in my opinion) is significantly more valuable than learning topics as-is. For it not only provide students knowledge, but also *ingelligence and critical thinking*. In a world changing with increasingly complex problems, a humanity of critical thinkers is what is strongly needed. There’s a problem with compost bins in (at least) Los Angeles. At UCLA, waste is categorized into three bins: landfill, compost, and recycling. Yet most bins you’ll see contain interspersed, incorrectly-categorized trash. I think that this is a problem. To be honest, however, I am also aware that I have minimal knowledge on the effect of this miscategorical mishap, so I don’t know how big this problem really is. I don’t know how to solve this problem, but I was interested in bringing it up because of the amount of times each day that I am reminded about this issue. Walking through campus every day, I typically encounter 20 to 30 of these cans filled with the wrong types of items. I just wanted to bring some attention to it in hopes that people’s attention is brought to the issue. I find it interesting that people are just people. I used to think that people older, more experienced, more mature, etc. were completely different people. In particular, I didn’t believe I could relate with the people that may be older or seem more mature than me, but now I feel that I have the ability to relate to a person solely by observing them. For instance, I’m writing this at a party. And as I walk around and observe people, I see people trying to blend in. I see a person stand, lean in and make a comment that never gets heard. I see someone reiterate what someone else said, and then do an awkward laugh. And so it makes you realize that the way you act is no different than the way others act. As a result, two things can happen. Either you can continue to act the way you do, which is acceptable. Or you can act however you’d like, which, in the best case, is confidently. Now, keep in mind that I am not trying to be a motivational speaker or anything of the sort. I think, rather, that it’s nice to have the liberty of expression without much regard to the judging of others. After all, one who is too worried about their own actions will have no time to judge that of others’. The exception to this, of course, is others who have realized this. And, in that case, it may be fair to respect that they have come to this point. After realizing this myself (recently), I’ve learned that it’s acceptable to talk about anything. I’ve come to realize that small talk is a tool, not a saving grace for conversations. And if a conversation doesn’t seem to flow, then the person your conversing with doesn’t connect with you well, and, therefore, shouldn’t be a priority; or, at the very least, a source of social anxiety/stress. Wordle has been getting pretty popular recently. It’s rise caught me off guard, but the reason why it grew so quickly doesn’t surprise me. It seems these days, the games that tend to blow up in popularity are the ones that are extremely simple, and hang at least one social aspect about them. Wordle is, of course, a fine example of this. It’s a simple website with *one* puzzle that *everyone* plays daily. One can share their progress as emojis with their friends and group chats. And that is it. It’s interesting to see how games like these blow up. I always wonder whether it is luck or strong game design. I would not be surprised if it was a combination of both. On that note, taking about Wordle reminds me about another problem. When I first got in to Wordle, I searched the App Store for the game, and I found nothing but a ton of Wordle clones. “Wordee”, “Wordles”, “Daily Word Puzzle”, “6 Words”, etc. It’s sad to see these clones copy the original game’s ideas. I wish there was a way for the App Store to verify an app as the original product. This would minimize the exposure of fake apps. Consequently, I believe that this would also ensure that more time is invested in to unique, creative apps. For the time spent creating a clone of a popular game could be used to have a chance to make another great game, and that time shouldn’t be wasted. Speaking of verification, I also believe that Instagram verified accounts should have the ability to designate other accounts as “affiliate”. What I mean by this is a solution to verify sub-accounts related to a main account. For instance, if the UCLA Instagram account had the ability to verify accounts for affiliate status, then students checking out UCLA-related accounts for clubs and/or organizations could rest assured that the account is legitimate and indeed affiliated with UCLA. Just good for thought. And, on that note, this ends my first Wordcast. As I am not the most avid writer, this first one took me about a week over time to complete (keeping in mind I write when I feel like it for these) — Tags: #proofs #mathematics #logic #wordle #set-theory #number-theory #recycling #ucla #social-relationships