Wiki Walking

Today, I started here:


and ended up here:


The steps being:

  1. I wanted to download all the images in that manga automatically using JavaScript (or at least open all of them in separate tabs so I can use the “Save image as” context menu easily. As it is, if you right click on the images there, the browser doesn’t register them as images, so you have to use the inspect element thing and hunt for the URL’s manually.)
  2. My first attempt didn’t work because of CORS restrictions
  3. I searched for a workaround on Stack Overflow
  4. There was a trending question about physics in the sidebar
  5. One of the answers mentioned this concept

I think Stack Overflow’s trending questions are getting to be my single biggest cause of distraction lately. Which is only natural I guess, now that I’m programming every day for an internship.

Aristotle, Definitions, and Math, Pt. 1

I’ve been thinking of rebooting my Aristotelian metaphysics series, and I thought I might put this as the preamble or something, so you might also consider this a draft of that.

This stuff is mostly just observations of analogies; I’m not sure if I would consider any of it strictly “proven.”

EDIT: Realized I forgot to add tags.

Aristotelian thought distinguishes two ways in which a given attribute can exist in multiple things: formally and analogically. An attribute exists in two things formally if it is in both of them in exactly the same way; so two red objects both have redness formally, since there are no two ways that something can be red (if we’re specific about what hue we mean by “red”). On the other hand, an attribute exists in two things analogically if it exists in both of them in different ways. For example, both humans and octopuses can be considered to have “hands” in a sense, but obviously a human’s hands are very different from an octopus’s tentacles.

Aristotelian thought also gives us an archetypal form of definition. This form works by considering a genus of things that are assumed to be known to the listener, and delimiting a species from within that genus by means of a specific difference that is common to everything in that species. So for example, a mammal can be defined as a species of animal whose females bear live young and feed their newborns with milk. (Of course, this isn’t technically accurate because platypuses and echidnas lay eggs.) This definition takes a category, animals, that is assumed to be known to the listener, and then delimits the category of mammals by means of their common characteristic of bearing live young and nursing their newborns. Here, the genus is animals, the species is mammals, and the specific difference is bearing live young and nursing their newborns.

Notice that “genus” and “species” are relative terms, since a category can be a genus relative to another, narrower category and a species relative to another, broader category. Further, genera are recursive, since a species within a genus is itself (potentially) a genus; the genus is made up of genera.

Now, math makes a lot of use of things called “sets,” which are rather vaguely defined collections of objects. As you work with them, you gain an intuitive grasp of them, but they’re never really rigorously defined. All you can really say about a set is, as the Wikipedia page says, that it’s a collection of well-defined objects (ironic, considering that the set itself is vaguely defined). Thus a set can contain anything. You can define a set consisting of the numbers 7, 12, 13, 19, and 20, just because you like those numbers. Or you can define a set consisting of red, green, and blue. Or you can refer to the set of all even numbers, or the set of all rational numbers, etc. Or the set of all people who wear their hair in a topknot.

A set can also be broken down into subsets, where every member of the subset is also in the original set (referred to as a superset). So the set containing 2, 4, and 6 is a subset of the even numbers, while the even numbers are a superset of the set containing 2, 4, and 6.

Incidentally, it’s also perfectly acceptable to have a set of sets. In fact, the set of all subsets of a given set is called the power set of that set.

This brings up an interesting question: Is it possible to form a set of all sets? As it turns out, the answer is no, because it results in Russell’s paradox. Every set is either a member of itself or not; for convenience, we can refer to these as self-inclusive sets and self-exclusive sets. The set of all self-exclusive sets would then have to be a subset of the set of all sets. But is the set of all self-exclusive sets a self-exclusive set, or a self-inclusive set? If it’s self-exclusive, then it would have to be a member of itself—which then implies that it must be self-inclusive. By the same token, if it’s self-inclusive, then that means that it’s not a member of itself, which means that it must be self-exclusive. Either way, we get a contradiction. Therefore, the set of all self-exclusive sets can’t possibly exist, and therefore the set of all sets, which must be a superset of the former, also can’t exist.

This leads us to the concept of classes, which is even more vaguely defined than sets. Basically, a class is a group of objects that all have something in common somehow, but that we can’t necessarily represent as a set. “All sets” would then be a class, but not a set.

Now, one interesting point that’s often glossed over in math textbooks is that there’s a very obvious difference between sets like “7, 12, 13, 19, and 20” and sets like “the even numbers.” Formal math doesn’t have a term for distinguishing these two types of sets as far as I know, but for convenience, let’s call the former type of set a scoop (from the action of arbitrarily scooping random things out of a jar) and the latter a proper set. We can then say that a scoop only exists because somebody decided it does, while a proper set actually has a kind of inner coherence. Why is this?

Well, thinking back to Aristotle gives us a clue. The members of a scoop don’t necessarily have anything in common. But the members of a proper set have some common characteristic that they all share formally. And we can take this as a kind of “definition” of proper sets: A proper set is a grouping of objects that all share some common characteristic formally (but see below—I don’t think it’s actually possible to give a rigorous definition of proper sets).

And recalling the Aristotelian contrast of formal vs. analogical and the mathematical contrast of set vs. class immediately brings another connection to mind: A class would just be a grouping of objects that all share some common characteristic analogically.

And now that we’ve gotten ourselves into a math-and-Aristotle-y sort of mood, we might as well go a bit further. Recall how genera and species behave recursively—any species within a genus can potentially be a genus itself, and any genus can potentially be a species of another genus. Well, notice that the relation of supersets and subsets behaves in exactly the same way—any subset can potentially be a superset of another set, and any superset can potentially be a subset of another set. And further notice that a species is delimited by some characteristic that all its members share formally. In other words, a species is a proper set. So a definition is nothing other than a delimitation of one proper set from within another.

And this shows why it’s not possible to define proper sets—we would have to delimit the proper set of all proper sets from some other proper set, which is impossible because, as shown above, there is no proper set of proper sets. But the collection of all sets is a class, which tells us that proper sets are an analogical concept.

Most Secure Credit Card

LOS ANGELES, CA—As of 20 July 2017, First City Credit Union has begun issuing a new credit card which, they claim, is more secure than any yet seen.

“I think we can confidently say that this new card is not only more secure than any other bank’s, but also more secure than any that will be invented in the foreseeable future,” said spokesman David Smith.

“The key insight that led to this new technology is that the number one cause of credit card fraud is the fact that it allows access to the owner’s money. Therefore, the most efficient way to prevent credit-card-related fraud is to prevent all access to the card owner’s account from the outset.”

The new card is set up so that any use of it is immediately flagged as suspicious activity, and the payment it was used for is immediately refused.

First City Credit Union members are elated at this new level of security. “I’m getting one of those new cards as soon as I get time to go to the bank!” said local resident Raphael “Raff” Jones. “It used to be whenever I lost my card, I would have to call the bank, sit on hold for half an hour, answer a bunch of questions, and request a new card to be sent in a week. Now, even if I lose my card, I don’t have to do anything. So convenient!”

Smith added that to encourage card owners to be cautious with their money, reward points will be granted for every month the card owner does not use his card. The reward points in turn are protected by a system whereby every time the account holder uses said points, his points are dropped to zero, the reward request is refused, and his account is placed on lock down. ■

Actual Blogging

I just got a crazy idea.

I think I’ll use this blog for actual blogging.

Up till now, I’ve been using this site as basically a place to publish essays. So I would think of a topic (generally something that annoys me), write an essay on it, and upload it once I had written out the whole thing, read over it many times, and decided that it was completely finished. But then of course, so many of the things I wrote would just rot in my draft box as I either A) got bored of editing it, B) got scared that people would think it was stupid or not worth writing, or C) moved on to the next idea.

So then I got an idea: How about I publish drafts of essays? As in, I’ll write an essay and, even if I think it could be better, publish it with “draft 1” or something in the title, with the understanding that I might re-publish it later as “draft 2” (or 3 or 4 etc.) with heavy modifications. If I actually get something to the point where I think it’s “finished,” then I’ll publish it without “draft” in the title, and maybe link to it on a separate page in the site header. (Or maybe not, because I’m lazy.)

So instead of this site just being a place for finished essays, it’ll be like a log of my writing as it progresses. You know, like an actual web log.

Hopefully, this will also have the psychological effect of helping me see that my writing isn’t something the world revolves around, and it’s perfectly OK for me to put something unfinished on the web.

And for that matter, I could also use this for things other than writing. Like programming or music-writing or whatever.

So I guess I’ll start doing that in the next few days or so. I already have some writing and programming and music related stuff I’m working on, so I guess I’ll put up one of those in the next few days.

And just to make sure I don’t get cold feet, I’m going to publish this the day I wrote it rather than sleep on it.

Random Thoughts

I’m long overdue for a post and I feel like if I try to write something serious then it’ll end up in my draft box for eternity, so I’ll just write some random thoughts. I’m a bit short on sleep at the moment, so sorry if there are spelling or grammar errors.

“Nexus” by ClariS makes me happy. I don’t care if it’s girly or otaku-y or whatever, it’s just fun to listen to. The melody is so catchy, and the rhythmic contrast from the percussion is on point. I would link to a YouTube video, but I couldn’t find one of the original song, just remixes.

The name of my blog is embarrassing. I’m going to change it as soon as I think of something better. Why is it that the first name I think of is always stupid? It’s like this with everything. Even the name of my first Neopet back in grade school was stupid.

Recently, I stumbled across an old post on Yard Sale of the Mind (which is a great blog name, by the way. Why couldn’t I have thought of something like that?) that reads, in part:

“The so-called ‘contemporary’ masses around here are mostly run by and for elderly hippies and wannabe musicians who couldn’t get a gig playing for free at a coffee shop.”


So friggin’ true.

The proof is in the genre of the music at these “young adult” Masses. Genre is like the cultural DNA of music.

What genre even is “Pan de Vida”? “We Come to the Feast”? “Christ Is Our Light”? “Here I Am, Lord”? “Our God Is an Awesome God”? “And He Will Raise You Up on Eagle’s Wings” (or whatever the title of that one is)? I can’t even place them—which just goes to show how culturally out of touch these songs are. The only thing I can think of that remotely resembles these songs is ballad.

By contrast, what are the genres we hear most often nowadays? Personally, I mostly hear alternative rock, pop, and rap, with the occasional 70’s/80’s throwback disco or rock.

Now, does modern Catholic church music sound anything like any of these genres? Of course not. Because it’s not aimed at the people who listen to that kind of music, a.k.a. young adults.

I think probably the biggest lesson I’ve ever learned in life is, “Yes, it really is that simple.” Or rather, the biggest lesson I’ve still only partially learned in life, because I have to re-learn it all the time.

When it comes to composing music, if you can come up with melodies, rhythms, and chord progressions mentally without needing an instrument to hear them on, then yes, composing is just a matter of deciding that the melody will sound like this right here and the accompaniment will sound like this right here.

When it comes to drawing, if your eyes are functional, you can make lines and shading, and you have a sufficient understanding of light, then yes, it’s just a matter of deciding that this line looks like the model so it’s fine, but that line doesn’t look like the model so it needs to be redone, or likewise with shading and color.

When it comes to coding, if you know about variables, scoping, data types, functions, closures, vectors, hash tables, structs, conditional branching, looping, and error handling, then yes, programming is just a matter of deciding that “Yes, the output of this program is what I want it to be” or “No, I want it to output this instead.”

And yet I’m always worrying about whether this or that design choice is “right” or “wrong” in areas where that kind of thinking doesn’t apply.

This is one of several reasons why I think that maybe I should have majored in math rather than comp sci.

I have some on-and-off trouble with scruples, which is a problem recognized in Catholic culture where you keep on feeling like you must have sinned when you haven’t, or like the sins you have committed are mortal when they really aren’t. One of the trains of thought that I always come back to whenever I’m dealing with this is that I’m probably just telling myself that what I did isn’t a mortal sin because I just want to take the easy way out. But then recently it occurred to me…

The right decision is always going to be easier than the scrupulous decision because the scrupulous decision is harsher than it needs to be by definition. So as long as I’m scrupulous, whenever I make the right decision I’m always going to feel like I’m taking the easy way out!!

So I guess that gives me a good diagnostic for when I’m acting scrupulous. If I start worrying about whether I’m taking the easy way out, then I can assume I’m just being scrupulous.

After watching 8-bit Music Theory’s video on nonfunctional harmony in Chrono Trigger, I feel like I finally understand the role of dissonance in composition for the first time.

I went through a pretty long phase where I refused to listen to anything but classical music, so my dad was surprised when I started listening to punk rock and such. But if you look at some of my favorite music from when I was a kid, it’s a pretty natural progression. Here are some of the first songs I remember liking when l was little:

As you can see, I’ve always been fond of fast beats and minor keys. Heck, even my favorite classical pieces are like that:

The horizontal line in this post editor doesn’t always look the same even though the HTML is the same, and it bothers me.