"Somerset Maugham once wrote that in each shave lies a philosophy. I couldn't agree more."

–Haruki Murakami

One of my favorite books is *"What I Talk About When I Talk About Running"* by Haruki Murakami. It's not a bestseller or pageturner, but the charm is in the mundaneness of the book, it's an account of his running endeavors as well as musings on life. Murakami writes that "if my life were turned into a movie, this would be the episode that editors would likely leave out. It's not bad, but it's ordinary and doesn't amount to much. But for me, these memories are meaningful and valuable."

It's a fitting theme with the subject of the book, which is running. Such a mundane activity can hold so much meaning for people. I'm not going to get into my philosophy/running journey or anything like that, but I thought posts like this would be a nice place to record my thoughts after running. Which is what Murakami was doing, except he published his thoughts in a book.

I have to say I didn't choose the best time: to me this kind of stuff shoudn't matter too much. But afternoon in Mid-September really beats down on your mental spirit, combined with the monotony of a track, seeing the same pole over and over again. Not like I'm complaining or anything: when times get rough and you want to quit at mile 1, I always think of David Goggins running with four layers of clothes in the desert to train his heat resistance. Then I can always squeeze out another couple hundred meters or two.

When I run or see people run, I always think of the same question. Are you running from something, or are you running toward something? It sounds like a deep philosophical thing, but it's just curiousity— and the answer depends on the day. Seven months ago, I was running toward the finish line in Galveston. Today, I'm running from my pile of homework and reading that I put off over the weekend.

If I were writing a memoir, I would have to think of less fitting ways to end things: all I would have to do is cram the running logs into one, and only write one chapter ending. But alas, this is not the case. Until the next time I run (and write).

]]>
For most people, minimalism starts with humble beginnings, thoughts like "My desk is too messy!", "Why is my closet always full? I never wear 80% of these clothes", and "I would follow my dream and move to X city, but I have so much stuff and moving it all is going to be a huge pain." (I never struggle with these things: it takes about 30 minutes to load everything I own into a car, with plenty of room to spare). The reason why is simple, every object you own takes up mental space in your brain, like a tenant that doesn't pay rent but nags at you all the time. Every time you walk through a cluttered house, each unused object is reminding you of the fact that you paid money for it to sit there and do nothing. This mental fatigue adds up over the hundreds and thousands of times you notice a useless thing^{[1]}.

Another example of what brings someone to minimalism is social media. Companies like Facebook and Google are employing tons and tons of techniques to ensure that all you care about is the next hit of dopamine. For example, for the average city dweller, the last time they immediately started the day by checking their notifications for 10 minutes (or hours) and spent the last hour before sleeping in bed on their phone was probably not too long ago. In a sense, sleep is the intermediary for the phone, always looking for the next "thing" or the "things" they missed (of course, in reality they are never missing out on anything that will significantly impact their life positively, on the contrary, they are missing out by using their phones). This is not their fault. Once again, this is not their fault. Billions of dollars have been invested to have engineers make this outcome inevitable, to turn our society into mindless zombies waiting for the next "thing" to happen, whether it be a like on their posts, a new message from somebody, or simply just new content to be consumed in an infinite scrolling feed ^{[2]}.

Finally, the American Dream. This is the epitome of destructive consumerism: that the ultimate goal in life is to buy cool stuff, a fancy car, a nice house. Then you'll finally be happy and free. After the idea of always wanting more stuff was ingrained by our society, after you get this one thing you'll finally be satisfied, I swear. Why are the jobs we deem successful (CEO's, Businessmen, Financial Analysts, Silicon Valley, Wall Street, etc) all based off stepping on others to increase their ranking in the well-ordering of the set of human beings by net worth? These people who manage corporations propagate and shove consumerism down our throats, for example, brand loyalty. Why would anyone identify themselves with Large Corporation No. 7 because they make cooler stuff than Large Corporation No. 16? (Eg: Apple phones, Branded clothing, Cars). It's because these people have normalized it, for the purpose of also owning more things (money).

These examples gives to a radical reaction that embodies itself in the movement known as minimalism. What's the solution to always being bombarded by notifications and group chats messages? Delete social media. What about my old books that I will never read again but like having on my shelf to show people I'm cultured? Recycle them or donate them (I like giving out old books I've read to friends). The answer to always being told that things are important and life is all about things is to reject things altogether.

How to do this is by radically reducing the amount of "things" you own down to the bare essentials, as a form of rebellion. But honestly, the inconvenience this causes is minimal. For example, not having a browser on my phone has only caused me trouble when I wanted to nagivate somewhere. Throwing away people's well intended presents has strained no relationships. Sentimental items only weigh in on the mental fatigue (as seen in the second paragraph), and only owning 4 T-shirts just means I have to do the laundry twice a week. This shows that minimalists aren't just insane ascetics who hate pleasure, it's just about being intentional about where it comes from. However you will be bored: this is normal, boredom is a sign of mental growth. Without boredom and solitude, there is no outlet for the brain to produce meaningful work (what if Dali spent all day scrolling through Instagram instead of heading the Surrealist movement?) Don't worry about missing out, because to be honest, the next new thing quite frankly is useless and won't make you happy.

References/Further Reading:

1: To read more, check out Fumio Sasaki's Goodbye, Things.

2: Also check out Cal Newport's Digital Minimalism.

I've always an interest toward cycling. After reading Murakami's *"What I Talk About When I Talk About Running"*, the urge to compete in a triathlon was awakened within me: I was so close too! I ran a marathon in February 2020, check. Swam for a couple years, works as a lifeguard: check. The only thing that was left was cycling. Almost like a reminder, my English professor at TAMS last semester was an avid cyclist, always talking about her 60+ mile rides (I listened with a sort of understanding of the "bonk", and envy).

(Also: I enjoyed her musings on Atwoods *"The Handmaid's Tale"*. Is this the best of all possible worlds? ... yes I said yes I will Yes.)

I felt as if the only thing I was missing for me to get into cycling was a decent bike: buying a thousand plus dollar bike just seems like extreme consumerism to me, but there was no way I could ride on a road with my slow bike (that had a basket attached to the front! I liked it for riding around campus, but it just wasn't suitable for racing). Almost as if a miracle, I stumbled upon a very, very old, racing bike.

It comes all the way from Ohio, where my brother purchased it at a yard sale (for $5) and fixed it up a little bit before I took it back to Texas. It's a Schwinn World Sport, I believe my model is from 1968: they say it was a popular powerhouse road bike back in the day. I've spent the last couple of weeks trying to fix up the bike: some of the thing's I've dealt with include

- Bent Derailleur Hanger
- Inner Tube broke
- Tires too wide (chafing on frame)
- Brake Pads out of alignment
- Seat feels like concrete
- Attaching a water bottle holder
- Breaking (removing) the chain

I met with our local bike expert at UT (through a church friend), and once again realize I have a lot to learn about fixing things. Although, this process of stuff constantly breaking and getting your hands dirty fixing it is oddly familiar— it reminds me of when I first installed a Linux distribution, always going through the manual and source code, trying to find the source of all these errors.

In a sense, it's a sign that the thing you're working on is truly yours: as you fix and learn more, you become less reliant on harmful fool-proof software/mechanisms, and more autonomous in general. An example: it took me an hour (with the aid of my brother) to learn to how to change out the engine oil in my car. This one hour of work, that was arguably pretty fun, will save me 30 dollars every 6 months by avoiding the mechanic (and will also make me less dependent on others to fix my stuff).

The bike's still busted, but I'm gonna keep working at it. One day I'll be out there with the cool cyclists, going on triple digit rides and seeing everything under the sun (who knows when this day will be)!

]]>People always told me I was insane for doing so much math. It started back when I was a wee child in 9th grade, who was "insane" for trying to test out of the (oh so horribly formidable) subject of Pre-Calculus over the summer. In fact, my Algebra II teacher said she was "looking forward to seeing me earn a C or possibly fail" in Calculus, which was pretty much my driving force to succeed in 10th grade AP Calculus BC. (I got a B.)

Then I was insane for trying to learn Real Analysis over a summer without having touched proofs before. Sure, I admit I was a little off my rocker when I signed up for this one. But I persevered, wrote a college essay on it, and started my senior year at TAMS in both Abstract Algebra and Real Analysis II (strongly against the recommendations of my Academic Advisor, who is a wonderful person by the way).

After acing both courses, I was out of my mind for trying to take Topology (and Abstract Algebra II). I was advised by many people, some even physicists and math majors, that Topology was the hardest undergraduate course UNT had to offer. I was warned of problem sets that would take 2-3 hours per question (sounds like Harvard's 55a), and horror stories of those who failed or dropped out of TAMS due to the class. (Galois theory was difficult too, but no one had taken it). I was told even graduate students struggled with the class!

Now the courses were non-trivial of course, but nowhere near the level of challenge that others made them out to be. It built up a sort of false confidence, a mentality that "I can do anything! (With a non-trivial but nowhere near back-breaking amount of effort)." Because to be honest, none of these courses required an insane workload: they all built upon each other, clearly defined everything from the beginning, and if one paid attention and did all the homework and readings, weren't very hard to do well in.

This marks the first week of my graduate Algebraic Topology course, and I can safely say it's the hardest thing I've ever attempted in my entire life, and BY FAR. I've spent hours and hours poring over textbook pages, going through a definiton lookup chain, grinding through homework problems, just to stay afloat. It moves at the speed of light: we defined the interval in one minute, and five minutes later, we're talking about the fundamental group of simply connected spaces.

Before class even started, we were assigned a pre-homework that asked five question on Manifolds and CW Complexes each. I've never seen a Manifold or CW Complex in my life before (at that point, I doubted whether I even learned Topology at all)! I worked on it for hours every day, looking up so many definitions and reviewing so many semesters of work, for maybe about 10 hours total, and I managed to solve ... 2.5 problems! Homework 1 was a similar experience. I worked on it for 3-4 hours every day, 6 days of the week, and managed to solve about 6 problems out of 10. It feels like I'm taking Math 55a (looking at the problem sets, they're about similar difficulty) without any of the freshman struggling with me, study groups, and tight community (thanks corona).

I don't really know what I'm trying to say anymore, maybe I'm just ranting. But let this act as a word of caution to qualified undergraduates attempting to register for graduate courses: expect those 3 credit hours to take up 30+ hours of work per week (or equivalently, the same or more as the rest of your undergraduate classes). There's a reason 9 hours is full time for grad students. Of course, I'm going to make it through. I signed up for this course to push my mental boundaries, and now I'm complaining that it's working as intended, isn't that ridiculous? It's going to be a long, very long, hard fight, but in the end I'll stumble out of the ring, face covered in blood, holding up a shaky but triumphant fist.

I was planning on adding a cheesy motivational segment here, but I'm not a good motivational speaker (it would probably have the opposite effect) so I'll leave the reader to find the motivation themselves as an exercise. Or don't, motivation is fickle anyways. Godspeed.

]]>`README`

and make sure you have all the requirements set up on your domain registrar and VPS provider, it's a two minute process to run the script and be on your merry way with a fancy new email server.
However, after setting it up I couldn't send mail for some strange reason. After testing two possibilities (domain on a spam list, postfix configuration issue), my cocky self decided that I didn't mess up anywhere when installing and that my VPS provider, Vultr, had blocked the port that allows me to send email (port 25) so I couldn't use their VPS to send spam emails or something like that. So I sent them a slightly condescending support ticket that went something like this:

Hello Vultr, Can you unblock Port 25? I know y'all are blocking it because you think I'll send spam emails or something, but I promise I wont.

Regards,

Simon

In 57 seconds, a system administrator at Vultr responded with this (not verbatim):

Hello Simon,

[omitted for privacy],

We're not blocking port 25 access. Check your instances firewall rules and listening services, you can do this by running`netstat -uplnt | less`

. Furthermore, also run`iptables -L`

for firewall rules, and`iptables -F`

to flush rules from the chain: to test outbound port 25 access, run`telnet portquiz.net 25`

. Thanks,

Systems Administrator

After spending the last two months learning how to use Linux and setting up my own server, I thought I knew a lot of commands (I have a terminal "cheat sheet" that's 250+ lines long), and a lot about how Linux works in general.

Well, after reading his response, I felt like I knew nothing. It was a good return to reality: Ego is something that creeps into everything (especially when things are going well), and ego leads to complacency. Complacency leads to the slow decline of the quality of work you put out, whether it be personal, academic, or job related. Basically, it's good for us to feel like complete idiots sometimes— it's how we get better.

(After this exchange, I added the three new commands he taught me and some more to a "systems administration" section of my terminal commands cheat sheet).

Anyways, that's it for now. We should all follow along with this motto (spoken by a very wise person):

]]>"I don't know everything, I just know what I know."

–HT

Innocuous questions drastically narrow down targets and provide a lot more personally identifiable information than you think: searching for a local restaurant gives away your location down to a few neighborhoods, your relationship status (depending on the type of restaurant), maybe narrows down the age range. A Chegg query instantly narrows down (almost certainly) the age range to about 16-24 years old. You're probably searching the internet (via Google) about all the hobbies and interests you have, and of course Google knows who you hang out with and what you do with your free time.

How do we privatize search engines to not profile you? An alternative would be DuckDuckGo and/or Startpage, but these services have their flaws: none of them are open source, meaning we just have to take their word on it that they aren't harvesting our data. The only way to be completely sure that you have the blinds down with search engines is the standard solution to everything: host it yourself.

Enter Searx. Searx is a completely *open-source* meta search engine: since it's open source, we know completely what it's up to. The "meta search" part means it anonymously runs your queries through several search engines and aggregates the results (eliminating the need to create your own search algorithm). How they anonymize your queries is by not sending cookies and generating a new browser profile for each session. This way, you can get your results from the sites you love (Google, Reddit, DuckDuckGo) without any of the tracking you hate.

In essence, Searx itself it just a piece of software that is activated and controlled by whoever is hosting it. So the only true way to be completely private is to host your own instance of it. However you could also use a *public instance*, which means you're relying on the administrator to not do anything malicious with your data. I host a public instance of Searx on my server, you can find it here or by clicking on the "search" link below my name on the homepage of this site. Since it's hosted on my server, it doesn't stop *me* from logging all your data. You just have to trust me on this one (just kidding, see the footnote on the main page).

This is what happened— Google was being annoying as usual and sent me my photos with each day having its own directory or something like that, preventing me from using my file manager to quickly live preview the photos. So a lightbulb went off in my head: why not write a script to move every file out of the directories and into the main one! It went something like this:

```
for d a directory; do
cd /. && mv *.* ../
done
```

or something dumb like that (not sure if this was the actual syntax). *Please* don't run this on your home computer.

So it ended up moving **every** file out of its original directory up one level: I didn't realize this at first and ran it again with sudo to get rid of the error messages (big mistake!). As soon as I did this I lost control of my keyboard and it hit me that I was kind of screwed.

The `/boot`

directory was gone, making it extremely difficult for me to go in with `grub`

and rescue at least some files. It makes sense, because everything in a UNIX system is a file. Some of the error messages I got as I attempted to save my system were truly horrific: "`Kernel panic - not syncing: Attemped to kill initf`

", "`Trying to continue (this will most likely fail) ... `

", and my personal favorite,

```
ERROR: Failed to mount the root device.
Bailing out, you are on your own. Good luck.
```

Absolutely terrifying.

I've spent the last two weeks or so offline. After spending the last two months actively installing my system, customizing my dotfiles, getting programs to work with each other, hosting software on my server, writing blog posts, etc, I decided to take a break.

At first I was kind of stressed out: "What about my dotfiles? My LaTeX notes? How will I keep my streak of green on GitHub? What am I going to do in my free time?" It was like quitting social media all over again. It's the fear of missing out: the fear that something online is happening and you're not part of it. It's also the fear of boredom: in a generation of cell phones and constant stimulation, there's no one thing that collectively scares us more than being bored.

In the end, I learned to stop worrying. No matter what your brain says, you really aren't missing out on anything: rather, spending more time online means missing out on more of life. I had a lot of fun doing things like working on my bike, meeting up with friends at parks, learning to write again with the proper grip.

On boredom: Boredom is the driving force that spurs action, without boredom there is no progress. Solitude and boredom are concepts essential to our mental development that have been washed away by the passage of the Internet. As time went on, I slowly began to dread the day I would reinstall Arch and rejoin the virtual world.

As you can see, I've managed to reinstall my system and get access to my server again. It took about a week to get everything working. This time I documented all the commands I ran to set up all the software/fix all the bugs in a text file, so if I ever were to do this again, it would be as painless as 1-2-3. Well, that's about it for now— I've also moved into campus, so if anybody reading this is from UT Austin, let's get in touch. Cheers!

]]>
I just came back from attending the 1052nd AMS (sectional) meeting at Penn State, last weekend, and realized that the Kingdom of Mathematics is dead. Instead we have a **disjoint** union of *narrow specialties*, and people who know everything about nothing, and nothing about anything (except their very narrow acre). Not only do they know nothing besides their narrow expertise, they don't care!

Here's a hot take: all the ideas we describe in math are relatively easy to grasp, but mathematicians make things complicated because of our poor short term memory. To give an example, let's take Calculus— the ideas behind derivatives/integration are really simple (limit of sums, limit of slopes) but we make them difficult by introducing levels of rigor and notation that leave a first year Calculus student behind in the dust.

This applies to higher level concepts as well: I believe that groups, fields, metric spaces, topological spaces, etc are fundamentally simple, but they suddenly aren't because of the level of rigor needed to formally approach these topics.

Rigor arises as a process to justify logical reason, but if our long term memory capacity was higher and we remembered much more of concepts learnt earlier, then there would be no need to obfuscate math with weird symbols and definitions. We add the rigor to remind ourselves that our reasoning related to past subjects is correct, which leads to rigor being required to have further areas of study utilize the current topic.

Of course, without rigor there would be no certainty, which is pretty much the point of math itself. So I guess we wouldn't be studying math, it would just be another branch of science, or maybe even just pseudoscience. On the flip side, solving this issue could possibly lead to the Pre-20th century level of unification in mathematics, one that hasn't been seen since David Hilbert.

Ever since the 20th century, mathematics has become so vast and fractured that specialization is the only way to survive in the field. No one can claim to truly understand more than a couple of hyper-specialized fields anymore due to the immense time and effort it takes to read enough papers to become knowledgable in a field. To quote Doron Zeilberger once again, we no longer have "*mathematicians*", but instead we have "*topological algebraic Lie theorists, algebraic analytic number theorists, pseudo-spectral graph theorists* etc".

This is, of course, not the fault of our mathematicians, but a natural consequence of the direction the field has been going, (and I argue) as well as our natural short term memory capacity. In an ideal world where our brains were constructed differently, we would have mathematicians consulting and working with a plethora of other mathematicians of topics at the highest level, research and developments realidly accessible to the layman that puts in 2 weeks as opposed to 20 years to understand the work, and a rapid flow of major breakthroughs (after all, great proofs like the proof of Fermat's Last Theorem utilized the hyper-specialized work of many many fields).

But of course, this is just wishful thinking and entertaining a fantasy "what-if" situation. Or maybe it's just BS, and if we truly could remember more, mathematics would still end up the way it is to preserve the aspect of exclusivisity and prestige. However, it's something interesting to think about: if we were given a choice between psuedoscience and progress as opposed to rigor and fragmentation, which would mathematicians pick?

References: https://sites.math.rutgers.edu/~zeilberg/Opinion104.html

]]>
Consider the vector space with basis
\[
\mathscr{B} = \{ 1, x, x^2, ... , x^n \}
\]
over $\mathbb{R}.$ This is known as the **vector space of polynomials with real coefficients of degree n or less**, denoted by $\mathbb{R}[x]$ (some texts may use $P_n)$. If it looks familiar, it probably showed up as a frequent example in your Linear Algebra problem sets (and is of extreme importance over an arbitrary field in Galois Theory)!

Note: while in Algebra the PID $\mathbb{F}[x]$ for $\mathbb{F}$ a field contains infinite degree polynomials, in this case we will assume $\mathbb{R}[x]$ to have finite degree polynomials with maximum degree $n$.

We can write an arbitrary element of any vector space as a **linear combination** of the elements of its basis set. In this case, an element of $\mathbb{R}[x]$ looks like a polynomial. A linear combination of the elements of $\mathscr{B}$ is of the form
\[
a + a_1x + a_2x^2 + ... a_nx^n.
\]
We can use $f(x)$ and $g(x)$ to denote such linear combinations with shorthand $\sum_{i=0}^{n} a_ix^i$ for $a_i \in \mathbb{R}$. Note that $x$ *isn't actually a variable:* we haven't defined a way to evaluate $x$ and it doesn't change based off the input. (If you're wondering how we evaluate polynomials in the traditional sense, we use something called the *evaluation homomorphism*).

We can use this vector space to do some cool things, like take ideas from Calculus and express them in the language of Linear Algebra! Remember the **derivative** from Calculus: in this case it's a map
$\frac{d}{dx} : \mathbb{R}[x] \to \mathbb{R}[x]$ such that
\[\frac{d}{dx}\left(a+a_1x+...+a_nx^n\right)=a_1+2a_2x+...+na_nx^{n-1}.\]
In summation notation, it's saying that
\[\frac{d}{dx}\sum_{i=0}^{n} a_ix^i = \sum_{i=0}^{n-1} (i+1)a_{i+1}x^{i}.\]
Using the standard notations for derivatives, we can write $\frac{d}{dx}f(x)=f'(x)$ for $f(x)\in\mathbb{R}[x].$

We can show that the map $\frac{d}{dx} : \mathbb{R}[x] \to \mathbb{R}[x]$ is **linear**. Recall that the conditions for a map $T: V \to V$ to be linear are that
\[
\text{1:}\,\,T(v_1+v_2)=T(v_1)+T(v_2)
\]
\[
\text{2:}\,\,T(\alpha v) = \alpha T(v)
\]
for a vector space $V$ over a field $\mathbb{F}, v_i \in V, \alpha \in \mathbb{F}.$ We know that
\[
\frac{d}{dx}\left(f(x) + g(x)\right) = \frac{d}{dx}f(x) + \frac{d}{dx}g(x)
\]
for $f(x), g(x) \in \mathbb{R}[x],$ satisfying the first condition. Next,
\[
\frac{d}{dx}\left( c f(x) \right) = c \frac{d}{dx}f(x)
\]
for $c \in \mathbb{R}, f(x) \in \mathbb{R}[x],$ so $\frac{d}{dx}$ is linear.

Furthermore, if a map from a vector space onto itself is linear, we can say it's a * linear transformation.* We can represent such transformations with a

To find the first column vector, examine the image of $1$ under $\frac{d}{dx}$: clearly it vanishes since constants don't change. So $ [1]_{\frac{d}{dx}}= \Bigg[\begin{smallmatrix} 0 \\ \vdots \\ 0 \\ \end{smallmatrix}\Bigg] $ Similarly, we have \[ [x]_{\frac{d}{dx}} = \begin{bmatrix} 1 \\ 0 \\ \vdots \\ 0 \\ \end{bmatrix}, \,[x^2]_{\frac{d}{dx}} = \begin{bmatrix} 0 \\ 2 \\ 0 \\ \vdots \\ 0 \\ \end{bmatrix}, \,[x^3]_{\frac{d}{dx}} = \begin{bmatrix} 0 \\ 0 \\ 3 \\ 0 \\ \vdots \\ 0 \\ \end{bmatrix}, \] and so on. Intuitively, this is because $\frac{d}{dx}x=1, \frac{d}{dx}x^2 = 2x, \frac{d}{dx}x^3=3x^2,$ etc, and we represent those values with the vectors above if we write them as a linear transformation of the elements of $\mathscr{B}$ (e.g. $2x=0\cdot 1+2x+0x^2 + \cdots$, $3x^2=0\cdot 1+0x+3x^2+0x^3+ \cdots).$

If we combine all these column vectors, we can find a matrix representation of the derivative! Here it is in all its glory: \[ [\frac{d}{dx}]_{\mathscr{B}} = \begin{pmatrix} 0 & 1 & 0 & 0 & \cdots & 0 \\ 0 & 0 & 2 & 0 & \cdots & 0 \\ 0 & 0 & 0 & 3 & \cdots & 0 \\ 0 & 0 & 0 & 0 & \ddots & \vdots \\ \vdots & \vdots & \vdots & \vdots & \ddots & n \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{pmatrix}, \] where $\dim (\mathbb{R}[x]) = n+1$ (or $\mathbb{R}[x]$ having polynomials of a maximum degree $n$). You can multiply this matrix by some polynomial vectors in your free time to see if this really works.

Furthermore, the derivative matrix has an interesting algebraic property in that it's **nilpotent.** A nilpotent matrix is defined as one that eventually vanishes when multiplied by itself, that is, there exists some $k \in \mathbb{Z}$ such that
\[
A^k = 0,
\]
where $A$ is a matrix and $0$ denotes the zero matrix.

I won't offer a proof, but this is an intuitive result: recall from Analysis that no polynomial of finite degree is infinitely differentiable. So an arbitrary polynomial of degree $n$ will vanish if differentiated $n+1$ times, or in other words, multiplied by the matrix $\frac{d}{dx}^{n+1}$ (in Liebniz notation this would be denoted as $\frac{d^{n+1}}{dx^{n+1}}$). So clearly $\frac{d^{n+1}}{dx^{n+1}}$ corresponds to the zero matrix, and $k=n+1.$

]]>Of course, this isn't a theorem because we have no way to prove this. It's also non-trivial to partition the set of mathematicians by the "algebra" or "analysis" equivalence classes (what of the mathematician that studies algebraic topology?). However, for some reason, this rule seems to hold in most cases. Regarding the mathematicians I talked to in real life, the one who wrote his PhD on Graph Theory eats his corn in rows, whereas the one who does research in Measure Theory eats his corn in spirals.

Personally, I liked my Algebra courses much more than my Analysis ones— I found them much more enlightening, intuitive, and interesting. People rave about the beauty of Analysis proofs, but I just saw them as confusing (perhaps this is due to the fact that Real Analysis was my first proof based course). The strange "theorem" about corn on the cob didn't really click with me until it became personal: after some experimentation, it turns out I eat my corn in rows.

There isn't going to be a definitive answer as to why this happens, but we can guess. Here's my proposition: Algebra is all about analyzing structure, which is why algebraists will see the perfectly laid out rows and follow them. Analysis is about finding patterns, which is why analysts will seek out the spiral patterns and follow those instead.

References: https://bentilly.blogspot.com/2010/08/analysis-vs-algebra-predicts-eating.html

]]>`pacman -Syu`

on your Arch Linux machine. However, the more people you keep up with and the more individual websites you have to visit, the more of a pain this process becomes. Enter RSS feeds.
RSS feeds functions like social media without the bad parts. Rather than having information centralized in one place (and therefore susceptible to being controlled), all you have to do is add a bunch of RSS feeds (urls) to your RSS reader of choice, and it will aggregate the content for you for easy viewing. This way, you don't have to individually check a bunch of sites, all you have to do is refresh your RSS reader and it will pull all the updates to the feeds you've subscribed to automatically.

Of course, it's completely private since all RSS readers do is check for updates to a certain url on someone's page. You can use RSS feeds to replace all sorts of things! For example, you can find RSS feeds for

- Youtube Channels
- Individual Subreddits
- Twitter Feeds
- Public Facebook Pages
- Instagram Feeds
- Github Repository Updates

and of course, blogs! No longer will you have to subject yourself to involuntary surveillance if all you wanted to do was see what someone is up to— which was the original premise of social media anyway, before the mass centralization of internet content.

The RSS reader I'm currently using is Newsboat (terminal based, of course), with vim bindings from Luke Smith's config. I'm currently still working on setting everything up, but you can view my progress on GitHub or my Git server. Note that for Newsboat to start, you'll need to add at least one RSS feed to your `~/.config/newsboat/url`

file.

Of course, if you're not a fan of terminal based applications, there are graphical RSS readers as well. I haven't used any of them, but the popular choices seem to be Newsflow (Windows) and FeedReader (Unix based systems).

]]>
Of course, I am already dead, along with all my descendants, their descendants, and their descendants, all the way down to the $10^{38}$th generation. As you can probably tell by now, the year is not 2157. All $e^{e^{87.5}\ln{(2)}}$ of my descendants are cursing me for the day I decided to pick up a copy of *Infinite Jest* because I heard that David Foster Wallace structured it like the Sierpinski Gasket and included a two-page footnote on the MVT. I reach for the pen— there is no pen. David Foster Wallace is looking into my soul, which is quite easy to do since my body has long since disintegrated away. I too, look into my soul, and see a fine print lightly embroidered along the edges. "Infinite Jest", it reads. Once again, David Foster Wallace reminds me that there is no hope. As I turn of a page of the wall, a small television in the corner of the ceiling flickers and updates. The television is watching my every move. "40%", it reads. I resign myself to my fate and erase another third of the floor.

Welcome to my new series on the many applications of Linear Algebra! I'm not exactly sure which applications I'll cover or how many just yet, but for now I'll just go with the flow. I'm also not much of an applied mathematician, so I'll probably end up writing about the applications of Linear Algebra in other fields of math or something like that.

Linear Algebra pops up seemingly everywhere— if we rephrase "systems of linear equations" as "many equations that seem somewhat straight if you zoom in", it becomes clear why. Here's an inspirational quote:

"Mathematics is about turning difficult problems into Linear Algebra problems."

–Terence Tao

Actually, it probably wasn't Terence Tao who said that. I probably got the quote wrong too. Anywho, you get the point.

Matrix equations will show up all the time if you work in a STEM field, and about half of modern mathematics is built on the theory of vector spaces. It's a fundamental topic everywhere (and should be taught in high schools!) that deserves some special treatment, and so, the birth of this series. Look forward to my first post on image compression with Singular Value Decomposition!

]]>
If you know me in real life, you probably know my cell phone number or someone that has my cell phone number. **The quickest way to contact me is by call.** I won't respond to texts quickly because my phone doesn't alert me if someone texts— **by nature they convey less important information and are more prone to sucking you into a spiral of distraction.** I have many other grievances with text messages that I will not air here. If you do insist on using text, it would be nice if you used Signal though.

The second best way to contact me is by email, which you can find at the top of this post. I've also attached my public GPG key if you want to send me encrypted emails, you can read my posts on RSA Encryption if you don't know what a GPG key is. If you want to contact me for academic purposes, I've listed my UT email address as well. Be aware that Gmail is the email provider for UT, so *don't include anything that you wouldn't put on a Times Square billboard* in any email you send to my UT email address.

If you have the time, I would like you to read Donald Knuth's epic stance on email. I too, make an effort to be on the bottom of things— although I may not be as cool as Knuth, doing mathematics still requires intense concentration for long periods of time. *The average office worker checks their email once every six minutes.* If a mathematician was as easily distracted, **they wouldn't be able to prove a single thing** all day.

Something I do not have is social media of *any* kind, including Facebook, Instagram, Reddit, Linkedin, etc. There are a plethora of reasons not to use these services and the reasons to use them are few and far between. Setting the strongest case for not using social media aside (privacy), **they cause massive damage in other areas of your life** by the concept of instant gratification through dopamine hits.

Everytime you refresh a Facebook page, *you're pulling the lever for a slot machine*, anticipating the possible arrival of a shiny new burst of dopamine. Your phone will light up at every new like, follow, or text message, all bringing successive and random hits of dopamine. **This conditions you to check your phone as often as possible in order to maximize the chance of receiving the next hit sooner.** As expected, this is disastrous for our brains and our ability to concentrate and produce meaningful work. If you want to read more on this topic, I highly suggest reading *Digital Minimalism* by Cal Newport.

My email is at the top of the page, and if you know me you most likely have my phone number. Response times will be slow, but it's not a personal thing— if I respond quickly, I'm probably not doing what I'm supposed to be doing. I don't use social media and you shouldn't either— hating social media isn't a boomer exclusive mindset. Finally, thanks for reading this and have a nice day.

]]>Some people like keeping their blinds open. They roll them all the way down and proudly declare "I have nothing to hide! Why should I keep my blinds down?" They tell me that trying to keep your blinds down is a waste of time, since you've had them open your entire life anyway. Besides, what's the point of lowering the blinds when you're already being watched? They have a point— their house is made of glass. Everything is transparent from the outside, all the way to their bathroom doors on the second floor.

Of course, it is not their fault for buying a transparent house. The three real estate giants, known as Goggle, Pear, and Megasoft have been pushing to make transparent houses an industry standard for years. They market the houses as the "homes of the future", appealing to the consumer using flashy features like "Fingerprint unlock the front door!", "Higher resolution security camera!", and "Better integration with our Smart typewriter and fan!" Of course, they designed the typewriter and fan to fail lest you not have a glass house.

At this point, buying a glass house has been normalized. People are waiving away their right to keep the blinds down left and right, for the sake of faster popcorn delivery by drone and convenience. This is not their fault either— the Big Three real estate companies have made it very difficult to find out what you are actually agreeing to when you sign the contract for your new glass house. On the contrary, it is very easy to sign the contract itself, almost too easy, in fact.

You didn't know about the microphone planted in your car, the cameras in the corners of the rooms. The smart fridge sends a report of your weekly groceries to Megasoft. The chair is analyzing the weight of each person that sits on it and sends it over to Goggle for "analytics". Of course, all the electronics are always on and recording by default. You have the option to turn them off individually, but there are so many of them that this is a gargantuan task. You don't even have the option to remove them from your house completely. Of course, some have tried prying them from the walls, only to see them reinstalled following the next mandatory "maintanence update". You don't choose when the maintanence updates happen either— the mechanics force open the door, kick you out, and make you sit on your front lawn until they're done.

Goggle, Pear, and Megasoft get away with this by not releasing the blueprints to the homes they design. Nobody can really prove the extent that the Big Three spy on us, because their blueprints are private and closely guarded. They have the ability to implement whatever kind of tracking device they want at the drop of a hat, because you don't have the ability to look into the inner workings of your house and decide whether you like what they are doing or not. You signed that right away when you signed up to use the house.

Oh, I almost forgot about the tracking device by Pear that is attached to your person at all times. On average, people will spend 5 hours of their day looking at the device, because Pear designed the device to be addictive. It serves the same purpose as an ankle bracelet attached to prisoners, but it sends a little bit more than just your location. It sends your conversations with friends, sleeping hours, personal library, video game data, everything— it sends it all to Pear. Not only is it virtually impossible to disable the tracking "services", most people actually signed up for this one willingly.

Privacy is a fundamental right, not a privilege. With each subsequent invasion of our privacy, the possibility of an Orwellian totalitarian surveillance state becomes more and more real. The government is very happy that we continue to sign our privacy rights away, and is very upset when we resist— just look at what the NSA did to Snowden, and what they're trying to do to the Tor developers. Our world is truly screwed the day building brick-and-mortar houses and closing your blinds becomes illegal. Join me in living in a house that has an open-source blueprint and closing the blinds to stop the peering eyes of The Big Three. Join me in fighting for the right to digital privacy.

]]>