January 22, 2024
Mathematics Education
I personally feel that something is fundamentally wrong in the (American) education system for matheamtics. To begin wtih, it doesn't try to help people actually understand concepts; rather, it simply encourages memorization without understanding and regurgitating information on exams. This can be seen even in elementary schools, as concepts are not thoroughly explained. For instance, when schools teach students that the angles in a triangle add up to 180, they simply give the information as it is without offering a proof. Without understanding why things are the way they are, students are left to struggle on their own and end up seeing mathematics as a subject of pure memorization. As a result, many students grow a hatred for mathematics, which only makes them less likely to pay attention, because who would want to learn a subject that they don't like? In order to solve this, I personally think that all mathematical concepts taught in schools should be accompanied by proofs and explanations, so that students can truly understand them. A good example of this form of education working is the Art of Problem Solving website (not affiliated), where students can sign up for online courses or look at problem sets to learn mathematics to understand. As always, however, I am merely a random kid on the internet, so once again take whatever I just wrote with a grain of salt.
January 10, 2024
New Year
Nine days ago, we started a new year (please ignore the fact that I was too lazy to write on this blog on the previous days), and this one seems to be especially interesting. To begin with, if we look back on the events of 2023, one might find that it actually seems like a precursor year to significant world events. In the area of geopolitics, many developments have happened in international wars; furthermore, tensions have increased between different countries as well. Moving over to technology, developments in GPT and DALL-E have been happening, although generally outside of the spotlight except for tech circles. These substantial changes, when combined, make me feel that we are going to be in for a big year for 2024. I personally expect to see many major events in geopolitics; although things might not escalate to all-out wars between superpowers, I feel that certain problems and tensions are bound to be addressed this year. In technology, I think that the exponentially expanding pattern of human advancement will continue; as a result, it seems that generative AI programs will only improve, and their ethics will soon be called into question. Finally, 24 is a multiple of many numbers, which means that in most countries, elections are going to occur for new leaders. This could result in a monumental shift in the way the world runs, but only time will tell. As always, I am just a random kid on the internet, so please take everything I say with a grain of salt.
December 19, 2023
Languages
What attributes make a good language? This is a question that I have pondered for the past few days, and I have a few opinions on what the answer(s) might be. To begin with, let us examine our current natural languages. The first to come to mind for most of you reading will probably be English, which is actually a pretty unique and intersting language. Unlike many other languages that have the majority of their roots from one main family, English posseses Latin, French, and Germanic roots in large amounts while having Greek, Proper Name Derivation, and other roots in lesser (albiet still present, totaling about 16%) ( source ). While these aspects do make English interesting, they can also make it fairly confusing to learn. On top of the diversity of its roots, English also has a myriad of irregular tenses and strange grammar rules to memorize. Because of this, I believe that either Spanish or Italian would be optimal picks from the Indo-European language family. When moving over to the Chinese languages + Japanese, one of the most recognizable features is the usage of a logographic alphabet. In my opinion, the major benefit of a logography is information density in written language, while the major downside is the amount of work that it takes to memorize; thus, I believe that in an optimal language, there could be a small, optional logography to be used for books and related media. Aside from a logography, the Chinese (and some other East / Southeast Asian) languages use tones to have more than one meaning per each syllable sound. This once again is a +1 for information density; but as always, I feel like having such a system to the extent of these languages (4+ tones) can easily result in confusion. While I do think that 2-3 different tones could be possible, having any more would be too difficult for too many people. In order to address the flaws of these natural languages, a bunch of linguistics nerds have created constructed languages, or conlangs. The most well-known example of a conlang would probably be Esperanto; it was designed in the late 1800s to be a language for international communication. My personal opinion on this language is that it was a strong attempt with a respectable goal, but still lacked enough roots from non-European languages to truly be a successful international language. Another notable example of a conlang that I have a more favorable opinion of is toki pona. This language has only 120 (or a few more) words using only 14 unique letters (including an optional logography called "sitelen pona"). This makes it extremely easy for nearly anyone to learn it, allowing people to express a wide variety of ideas with a miniscule learning curve. My single (very small) gripe about this language is that I feel that it could have a bit more words, such as 300-400; however, it is overall a very consistent language which I personally believe to be the closest thing we have to an ideal language. But of course, I am just some kid on the internet, so please take whatever I just said with a grain of salt and do your own research to come up with a conclusion.
December 10, 2023
AIME Qual
YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES!!!!!!!!!!!!!!
December 2, 2023
Motivation
What I didn't have to write today's blog post. Maybe I'll make a better one tomorrow.
December 1, 2023
Stability vs Modernity
There seems to be a debate going on in the the Linux community on whether stable or rolling distros are better. Those on the side of rolling distros believe that modernity is more important than stability and reliability; those on the other side believe the opposite. I personally take the side of stable distributions. My argument lies on one main idea: the extra technology that one gets from rolling release distributions is not worth the risk of a lack of stability. To begin with, do normal users really experience significant detriment by being just one year behind in their available software? Although new advancements happen all the time, one year is usually not enough for significant change in most software programs. Furthermore, if one DOES want the modern version of a specific software, they can download it themselves in the form of a .deb or .tar.gz. By having the bleeding-edge version of all software on one's system, they run a significant risk of at least one program breaking, which has the potential to cause problems across the entire operating system. Because of this, I believe that a stable release distro with modern packages of the user's choice is the best type of Linux desktop setup. (Take that, OE-SAN)
November 29, 2023
Number Systems
Why do we use a base-10 number system anyway? Is it because we have 10 fingers; is there nothing more to it? When talking about other systems, people argue that easy divisibility by 5 is important, but I would argue the contrary: easy divisibility by 3 is more important as it is a lower prime number. Aside from human-made constructs (e.g. packages that come in a multiple of 5), how often do you actually find yourself needing to use the number 5 in daily life? Now think about your usage of the number 3 and its multiples. I would guess that it is much more common when you would need to use it (e.g. dividing amongst 3 people, buying 3 of something) than when you need to use 5. Because of this, I feel that it makes more sense to have the base of a number system be a multiple of 3. Since it is the lowest prime number, we interact with the number 2 a lot as well. Easily telling if numbers are odd or even and easily dividing numbers by 2 are hallmark characteristics of the base-10 number system. However, we also find ourselves interacting with multiples of 4 a lot in our daily lives, begging the question of why we use a base system that only has one 2 in its prime factorization. Factoring this in as well, I believe that an ideal number system should have a base with 2 2s and at least 1 3 in its prime factorization. The minimum size fr this base would be 12; if we choose to add 5 as a factor, than the minimum size would be 60. However, a base that high would be highly unintuitive and very hard to learn for the majority of people; thus, for practical purposes, I think that base-12 is the best number system.
November 28, 2023
Reject Modernity; Embrace 90s.
I honestly hate the trend that web and user interface design has been doing over the past decades. I feel that in the past, the internet used to be much more personalized, and UI was far more utilitarian rather than appearance-focused. On the modern internet, everything follows the same metro design scheme, leaving web designers unable to do much with their webpages. After learning about the old internet, I have decided to start this personal website to bring back that feel. Furthermore, I feel that operating system / desktop environment design has gotten worse with time as well. In the 90s, the mimimalistic gray design had a unique charm to it, and the glossy 2000s aesthetic had a different yet still enjoyable feel. Starting in the 2010s, with the big push for flat, modern OS designs, both details and functionality were taken out of the equation, leading to the generally poor aesthetic that we see today.