Alex Strinka's Blog

Daylight Saving Time

2025-03-08T17:28:53+00:00

Daylight saving time is upon us.

Personally, I think daylight saving time is unnecessary, and we should just stick to standard time throughout the year. (The American Academy of Sleep Medicine and other organizations agree.)

But, I can't deny that the changing times of sunrise and sunset have all sorts of effects on daily schedules. So, here, I propose two alternatives to daylight saving time that are even more impractical.

Roman timekeeping

For the Romans, every day was twelve hours long, because the length of an hour changed over the course of a year. Daytime hours were longer during the summer and shorter during the winter. There were also twelve hours every night, shorter in the summer and longer in the winter.

In the Roman system, the hours were numbered, so the first hour (hora prima, in Latin) began at dawn, the sixth hour (hora sexta) began at noon and the twelfth hour (hora duodecima) ended at sunset.

If we were to re-adopt this system, what should we do about minutes and seconds? Well, nowadays, seconds are an SI unit, defined in terms as 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom, so I think that should be left as it is, since it's already separate from its historical definition. And Romans never used minutes, so we don't have to either. To refer to something with more precision than an hour, we can just use fractions and decimals, like any other unit.

Post Auroram

This is intended to be a sort of compromise between the Roman way and the modern way. Keep the length of hours the same, 3600 seconds, but change the clocks so that sunrise happens at the same time every day.

I considered setting that time to be 6 AM, but I decided it would be better to just make a different numbering system entirely. Keeping with the Latin theme, I decided to call it post auroram (after sunrise), PA for short.

Sunrise would be 0:00 PA. An hour later, it would be 1:00 PA, and so on. We probably don't want to change date boundary, that is, the time when we rollover from one date to the next date, so to handle time between midnight and sunrise, we'll use negative numbers. That means that an hour before sunrise would be -1:00 PA.

Conclusion

One notable disadvantage of both of these systems is that your local time relies on both your longitude and your latitude, which would likely make time zones much more complicated. Even worse, they completely fail north of the Arctic circle or south of the Antarctic circle. It's hard to base a clock on sunrise when there is no sunrise.

Obviously, no one is going to adopt either of these systems. It's hard enough to switch an established standard, even when the alternative is clearly superior*, and these clearly are not. But I think there's some value in considering them as a thought experiment.

To that end, I've made a converter and clock for these systems. Enter a location, a date and a time, and it will show you the time in all three systems. The clock shows both time and sun position. The red line indicates the entered time. The yellow region is when the sun is up. The blue region is night and the lighter shades of blue indicate civil, nautical and astronomical twilight. Solar noon is indicated by the white line pointed up, and solar midnight by the black line pointed down.

Latitude:
Longitude:

Datetime (in your timezone):

Current time:
Modern —
Roman —
Post Auroram —

Clock Labels

Modern Roman Post Auroram

I used SunCalc.js and tz-lookup to make these tools.

Cosmic Clicker

2024-03-07T02:42:14+00:00

I've made a new game called Cosmic Clicker! The premise is that you're building a colony on an alien planet.

It's inspired by Cookie Clicker and other similar incremental games. It's relatively small and short compared to those other games. I have some ideas about features I can add, but those will have to wait.

There's not really an ending, at least not yet. It's just about making the numbers go up.

On a side note, the background images are AI generated. Most using NightCafe, a few with Bing. There's an ongoing debate at the moment about whether AI art is art and whether it's moral and whether it's plagiarism. That's a topic for another blog post. All I'll say here is that I have no qualms with using those tools.

Since those images are mostly covered up in the game itself, here they are so you can see them fully. Click on them to see the high-res versions.

Free Will

2023-10-22T19:42:02+00:00

The concept of free will, as imagined by AI

There's a common argument that the laws of physics means that free will doesn't exist. That argument is complete nonsense.

Before addressing that argument directly, I'm going to discuss what free will actually is. Free will means that my actions are a consequence of my beliefs and my preferences. Simply put, it's the difference between walking through a door on your own and being pushed through a door by an external force.

I think that this is very clearly a useful distinction to make. There's definitely some gray area where it's not clear if an action is a result of free will or not (for example, when a person with OCD acts on a compulsion). But I think most actions pretty clearly fall into one of those two categories. And that's what I mean when I say that free will exists. It's a useful category.

Some people say that because the laws of physics are deterministic, free will doesn't exist. We are all just billiard balls bouncing around on paths that can't be deviated from. If you set up exactly the same starting condition, then exactly the same things will happen. In my view, this doesn't contradict the existence of free will. In fact, free will requires determinism. My beliefs and preferences are physical things. They're patterns in my brain. I don't know the details, but those physical parts of me interact with my nerves and muscles and other physical parts of me to cause me to act. If my actions were not determined by my physical self, well then, those actions wouldn't really be my choices.

(Tangentially, some people say that determinism contradicts free will, but free will exists because quantum physics isn't deterministic. First of all, whether or not quantum physics is truly non-deterministic is still up for debate. But more importantly, that doesn't actually support free will. If my actions are a result of random chance, then they're not a result of my beliefs and preferences.)

An argument for why determinism negates free will is that of counterfactuals. That is, the idea that you could have acted differently given the same conditions. I agree that, if determinism is true, given exactly the same initial conditions, a person will make exactly the same decisions. But I don't think that's really what people mean when they say you could have acted differently. The thing is, a person's beliefs and preferences change all the time, without changing who they are. For example, if I'm hungry, I want to eat. Then I eat, I'm no longer hungry and I don't want to eat anymore. My preference has changed, but I'm still the same person. So when I say that I could have acted differently given the same conditions, I mean the same external conditions, but my internal state could vary slightly.

There's also an argument that even if your actions are caused by your beliefs and preferences, those actions still aren't a result of free will, because you didn't choose to have those beliefs and preferences. My response is that that doesn't matter. My beliefs and preferences are mine, regardless of where they came from. The molecules that are now in my arm came from food I ate. Those molecules weren't part of my body before but now they are. Likewise, my beliefs and preferences have been influenced by things outside of me, but they're still a part of me now. And it seems to me there's a worthwhile distinction to be made between someone pushing me through a door, and someone convincing me to walk through a door.

I think the real reason people think determinism prohibits free will is an implicit (or explicit) belief in a non-physcial self. The laws of physics as we understand them don't permit physical things to be influenced by non-physical things. If you think your beliefs, your preferences, your self exists as an incorporeal soul, then yeah, physical determinism means that incorporeal soul cannot be responsible for your corporeal actions. My response to that is simply that there is no such non-physical soul. We are physical beings, through and through. Our bodies, our brains, our minds, our thoughts, our feelings, are all physical things, and they are not in any way lessened by that.

Now, a discussion about free will isn't complete without talking morality, if only because everyone else always talks about how the two are related. People say, for example, that free will is required to pass moral judgements, or it's immoral to punish someone if they don't have free will. My thoughts about morality aren't entirely settled, but I'll say this much. If a river floods and destroys some buildings, and then the people who lived there build a levee to reduce the risk of future flooding, that doesn't require those people to make a moral judgement of the river, nor is it a punishment on the river. It's just people acting to prevent future harm. If a person has an epileptic seizure while driving a car, we take away their driver's license. That's not a moral judgement, we don't think a person with epilepsy is evil. It's just acting to prevent future harm. If a person murders another person, we want to act to prevent future harm. Knowing the cause of that killer's behavior is important in figuring out what the best way to prevent future harm is.

Furthermore, if a person acts with free will, then that person can respond to incentives and be negotiated with. You can say, "If you kill someone, then we'll imprison you" and if that person believes you and their preference for not being imprisoned outweighs their preference to kill someone, then they'll act on their beliefs and preferences and not kill someone. There's a lot more that can be said about that, but that deserves it's own post.

Just as my beliefs and preferences have been influenced by things outside of me, my thoughts about free will have been influenced by reading things other people have written about it. The most notable is Eliezer Yudkowsky. The Stanford Encyclopedia of Philosophy is also great if you want a detailed history of every argument about free will.

Dolly Zoom

2022-05-01T17:54:27+00:00

This video shows some good examples of a dolly zoom.

So, how does this work?

Imagine you're standing in one spot, and a person is 10 feet in front of you, a house is visible behind the person 100 feet in front of you, and a mountain is visible behind the house miles away from you.

Now consider what happens if you move 10 feet backwards. The person is now 20 feet away from you, so the distance to the person has doubled. But the distance to the house has only increased by 10%. And the distance to the mountain is negligbly larger than it was before.

That means that, from your point of view, the person now appears to be about half as large as they did before, while the house will only be about 10% smaller, and the mountain will have barely changed at all.

Now, imagine you look at the person through a camera, and you zoom in, so they look twice as large. The zoom affects everything equally, so everything gets twice as large. Now the person looks as large as they did before, but the house looks significantly larger than it did before, and the mountain looks almost twice as large.

Here's an interactive demo of that. There's a small red sphere close to the camera, a larger blue cube farther from the camera, and a very large green triangle very far away from the camera. The top half is a side view, showing the camera and its field of view. (The green triangle isn't visible, because it's ten times farther away from the camera than the blue cube.) The bottom half shows what the camera sees.

Camera position: Zoom: Focus: None Sphere Cube Triangle

The sliders let you adjust the camera's position and zoom. You can see that when you adjust the zoom, the camera's field of view changes, and from the camera's point of view, the sphere, cube and triangle all grow and shrink proportionally. But when you move the camera, the apparent size of the sphere changes much more than the cube, and the triangle barely changes at all.

When you select a focus and move the distance slider, the zoom slider changes simultaneously, to keep the focused object the same size, creating a dolly zoom effect. Notice how, at the position of the focused object, the field of view has the same size, while at points closer and farther away, the field of view gets bigger and smaller.

This is actually closely related to parallax. That post shows what parallax looks like when you move left and right. This is what parallax looks like when you move forward and backward.

Parallax

2022-03-20T15:26:33+00:00

Here's a quick experiment you can do right now. Look at something that's at least a few meters away from you. For the sake of a concrete example, I'll say a lightswitch that's on the far side of the room, but it could be anything. Now, close one eye and hold up your thumb so it covers the thing you're looking at. Then, close your open eye and open your closed eye.

Suddenly, the lightswitch (or whatever) is no longer covered by your thumb! Why?

Your thumb is directly between your first eye and the lightswitch, thus blocking its view of the lightswitch. But your second eye is in a slightly different place, and the line that goes from it to the lightswitch is not blocked by your thumb, so it can see the lightswitch.

This is an example of a phenomenon called parallax. It shows up in many situations and has practical applications too, so let's look into it in more depth.

Let's start with the basics. You know how when an object is close to you, it looks bigger than when it's far away? That's because we don't directly perceive an object's size or distance. We can perceive the direction to an object and the difference between different directions. Here, I'll show you what that means.

Click or tap and drag to move the red circle.

The dot on the left represents your eye, and the circle on the right is an object. The marked angle is the subtended angle, or the angular size of the object. The direction from the eye to the top of the circle is different than the direction from the eye to the bottom of the circle. The closer the circle is to the eye, the bigger that difference is, and hence the bigger the circle appears to be to the eye.

And of course, this works exactly the same when you're looking at the distance between two objects. The direction from the eye to the first object is different than the direction from the eye to the second object. The closer the two object are to the eye, the bigger that difference is, and so the apparent distance between the objects gets larger.

This is also why things that are far away appear to move more slowly. The farther away they are, the smaller the distance they move appears to be, but they still take the same amount of time to move that distance.

You can flip it around so instead of the object moving, you're the one that's moving. It's exactly the same situation, just from the opposite point of view. That's why when you're driving in a car nearby things like houses and trees go by very quickly, but distant things like mountains go by much more slowly.

Instead of one observer that's moving, you can have two observers in different places, or just two eyes. The direction from the first eye to the object is different than the direction from the second eye to the object, and that difference gets bigger the closer the object is to the eyes.

This is one of the ways you can tell how far away something is. When you look at something very far away, your eyes are nearly parallel, but when you look at something very close to you, you have to cross your eyes.

That's how stereograms work. You show one picture to one eye, and a picture that was taken from a slightly different position to the other eye. Here's an example. Cross your eyes until the two images are on top of each other. When they line up, you should be able to see the trees and houses "pop out" in front of the skyscrapers.

This is actually how astronomers can measure the distance to nearby stars. The Earth circles around the Sun, so in six months it will be about 300,000,000 km (186,000,000 miles) from where it is now. That's a very, very large distance, but even then the parallax deviation of the nearest star is less than 0.001 degrees. This was actually used as an argument in favor of geocentrism, because that was too small for anyone to measure until the 1800s. They thought it was more likely that the Earth was stationary than that the stars were millions of times farther away from the Earth than the Sun.

Ask Culture and Guess Culture

2022-01-11T02:50:19+00:00

One source of interpersonal misunderstanding and conflict is the difference between Ask Culture and Guess Culture.

In Ask Culture, you're allowed to ask for just about anything, and you also have to accept that your request might be denied. In Guess Culture, you can only ask for something that you're confident the person you're asking will be willing to provide. When people from Ask Culture and Guess Culture interact with each other, it's easy for both sides to the see the other as rude.

Although the difference is framed in terms of making requests, I think it has more to do with whether or not you're allowed to deny a request.

In Ask Culture, you're allowed to deny a request for any reason. But in Guess Culture, denying a request is considered impolite, unless you've got a really good reason. If someone makes a request that you just don't want to accept, you're forced to either do the thing even though you don't want to, or be impolite by refusing. Which is where the implicit rules about what you can request come from, because you don't want to put someone else in that situation, or for someone else to put you in that situation.

Furthermore, it's not a simple dichotomy. What counts as a really good reason to deny a request will vary from culture to culture, and some cultures will have more or fewer than others.

A related topic is making offers. In some cultures (at least, so I've read) you're expected to turn down an offer. The first offer is only made to be polite. If they really want you to have it, they'll offer it again. It's considered rude to accept the first offer.

This feels to me like a continuation of Guess Culture. Not only are you not allowed to deny a request, you're required to preempt the request by making the offer first. But because you still might not want to actually fulfill the offer, the recipient is expected to turn it down.

Of the cultures I described, I think Ask Culture is the best. And I say that even though I'm more naturally inclined to Guess Culture. But, explicit communication is less prone to misunderstanding than implicit communication. Guessing what another person wants or is willing to do is generally less reliable than asking them.

While I do think we should strive to Ask more, we should also recognize that different people have different expectations and different preferences, and we should strive to be more accepting of those differences.

Five Years of Life Tracking

2021-12-31T20:18:55+00:00

Five years ago, I started tracking my weight and steps per day. I've also tracked things like how many calories I consumed, how much caffeine I consumed, whether I ate animal products that day and what I did that day. Some of those things I stopped tracking after a while, or didn't start until more recently.

I started doing it as part of a New Year's resolution to lose weight and be more productive. I read about the idea on Reddit, and it seemed like a good idea, so decided to give it a try. It's been pretty effective, at least for the things that are straightforward to measure.

Weight and steps are in that straightforward category. Weight is just a matter of stepping on a bathroom scale, and I have a pedometer app on my phone that detects my steps. But other things are much harder to handle. I tried a few different ways of measuring my productive activity. How many to-do list items did I check off? How many minutes did I spend doing various kinds of activity? None of them really worked for me. I think the problem is that the numbers don't capture what I mean by productivity, and I haven't been able to figure out how to define what that in terms of anything objectively measureable.

Doing the tracking is relatively easy. It only takes a few minutes a day. The hardest part is just remembering to do it, which I've done by making it part of my bedtime routine. Though gathering the data can be difficult too, depending on what you're measuring. Counting calories is a pain, but absolutely worth it if you're trying to lose weight.

I've found it to be very motivating to be able to look back and clearly see the progress I've made. And it lets you notice if you're backsliding sooner.

Something I've found is that the very act of tracking changes my behavior. I didn't have any particular goal in regard to the number of steps, but by recording that number, I pay more attention to it, and I end up walking more as a result. Simply being mindful of something can change how you act, and tracking is a regular reminder to be mindful.

It's also pretty easy to set up if you want to do something similar yourself. I use a Google docs form and spreadsheet. You can see an example form here. You can copy that and link the form to a spreadsheet so it adds the data to the spreadsheet automatically when you submit the form.

HexBoggle

2021-10-29T00:44:37+00:00

I've added a new program to my programs page: HexBoggle!

It's basically Boggle, but with a hexagonal grid, instead of a square one. Right now it's just single-player, but I intend to add multiplayer eventually.

Try it out, and let me know what you think! What other features should I add to it? Leave a comment here, or send me an email!

Descriptivism and Prescriptivism

2021-10-20T02:04:41+00:00

In the field of linguistics, there are the concepts of descriptivism and prescriptivism. Descriptivism is about describing how language is used. In contrast, prescriptivism is about prescribing how language should be used.

Linguistics, as a science, must necessarily be descriptivist. You don't learn about something by telling it how you think it should work. To learn about the world, you need to observe the world without judgement.

But that doesn't mean there's no place for prescriptivism. In fact, I would argue that prescriptivism is unavoidable, to a degree. When you speak or write, you have to choose what you're going to say. Many of those decisions happen unconsciously, without deliberate intent, but not all of them. Descriptivism alone can't tell you what words to use.

Where prescriptivism goes wrong is in saying that you should speak a certain way because it is the right way. The problem is that there is no single right way of speaking.

Consider, are people who speak a different language wrong? That seems patently absurd to me, and I think most people would agree. But if using different vocabulary and different grammer isn't wrong when you're speaking a different language, why should it be wrong if you're speaking a different dialect?

Furthermore, there's no clear line between a separate language, and a dialect. Typically, two different ways of speaking would be called separate languages if they're not mutually intelligible and dialects if they are. But consider a case where group A can communicate with group B, group B can communicate with group C, but group A can't communicate with group C. This is called a dialect continuum, and is actually fairly common. Do groups A and C speak different languages, or dialects?

And how do you determine which way of speaking is the correct one, anyway? Historically, it was just whichever dialect the monarch or nobility spoke, but why should their opinion matter more than anyone else's today?

Instead of trying to speak correctly, you should try to speak in a way that maximizes your audience's understanding. (At least if you're trying to communicate, which is usually the came when you speak.)

Can One Infinity be Bigger than Another Infinity?

2021-09-04T02:14:35+00:00

When I was in elementary school, I had a teacher who told us there were fewer even numbers than whole numbers, because half of all whole numbers are even, and the other half are odd. I argued that there must be same amount because there an inifinite amount of whole numbers and an infinite amount of even number, and infinity equals infinity.

Well, it turns out, my conclusion was correct, but my reasoning wasn't.

That probably seems really strange. Surely, if you take the set of all even numbers, and then you add all the odd numbers, it would end up bigger than it started, right?

To answer that, we need to talk about what it means for two sets to be the same size. For finite sets, it's simple; just count how many elements there are. But you can't count to infinity, so that doesn't work for infinite sets.

You can say that if set A contains all the elements of B, but set B doesn't contain all the elements of set A, then set B must be smaller, but that won't work for every pair of sets.

So, mathematicians came up with the concept of cardinality, which works for every set. The way it works is that two sets have the same size if you can come up with a mapping between the two sets, such that every element in each set is associated with exactly one element in the other set.

Here's an example. Let's say you have the two sets {Red, Green, Blue} and {Circle, Square, Triangle}. We can make this mapping:
Red ⇔ Circle
Green ⇔ Square
Blue ⇔ Triangle

Every element in the first set is associated with exaclty one in the second set, and every element in the second set is associated with exactly one in the first, so those two sets have the same cardinality. And, because they're finite, we can also just count them and that works too.

In fact, you could even say that this is actually the same process as counting. You're making a mapping between the set you're counting and the set {1, 2, 3...n}.

And this same concept can be applied to infinite sets. Here's a mapping between all integers and all even integers: For every integer N, N ⇔ 2N

This mapping associated every single integer with exactly one even integer and every single even integer with exactly one integer. Therefore, the two sets have the same cardinality.

You can even make such a mapping between all integers and all positive integers, or between all integers and all rationals, so all of those different sets have the same cardinality too.

Does that mean every infinite set is the same size as every other infinite set?

No!

It turns out that the set of all real numbers is bigger than the set of all integers.

Here's how can show that. First, assume that there is such a mapping, so you can associate every real number with exactly one integer. That means you can put those real numbers in an ordered list, so you can talk about the first number in the list, the second one, and so on.

But there's a real number that's nowhere on the list. To find it, we need to build it, digit by digit, based on the numbers in the list. Here's an example list:
#1: 0.40396...
#2: 0.09714...
#3: 0.73175...
#4: 0.90453...
#5: 0.97491...
⋮

I've bolded some digits, because those are the ones we're looking at. The first digit of the first number, the second digit of the second number, and so on, along the diagonal.

For each digit, we'll add one to it (Or if it's nine, subtract one. What matters is that we get a different number than what's already there.)

By doing that, we'll get a number that starts 0.58262...

This number can't be equal to the first number, because the first digit is different. It can't be equal to the second number, because the second digit is different. And so on, for every single number in the list. And notice that this works for every possible list of real numbers, not just this example.

Since there's a real number that's not in the list, the mapping must not include every single real number, and therefore the sets don't have the same cardinality. This is called Cantor's diagonal argument

So just because two sets are infinite doesn't mean they have the same size.

Spaced Repetition

2021-07-21T04:43:23+00:00

Spaced repetition is great, and everyone should know about it.

Spaced repetition is a technique for memorizing, well, anything. The basic idea is really simple. You learn a thing, and then you review it. You review it frequently at first and then gradually increase the amount of time between each review. In other words, you review it again and again, with each repetition carefully spaced apart, hence the name.

Now, you might be thinking, "Why worry about memorizing things? I can just look things up online." That's true, but I still think it's worth memorizing things. For one, you can look up information in your brain a lot faster than information online. Furthermore, there are many things that you can't easily look up if you don't already know something about the subject.

You might also be thinking, "It's more important to understand fundamental principles than it is to memorize simple facts." Again, that's true, but I would argue that memorizing facts helps to gain that understanding. A large set of examples can help you internalize the patterns that the principles express.

By now, hopefully you're convinced that it's worth memorizing some things, and you're wondering how to do spaced repetition. Typically it's done with flashcards, but you could do it with anything that gets you to actively recall the thing you're trying to memorize.

You can keep track of the timing using the Leitner system. The way it works is you keep your flashcards in numbered boxes. Every day add a few flashcards to box #1. When you review a card and you get it right, you move it to the next box up. When you review a card and you get it wrong, it goes back to box #1. Each box is reviewed half as frequently as the previous, so you review box #1 every day, box #2 every other day, box #3 every fourth day, and so on.

Day	1	2	3	4	5	6	7	8	9
Box #1	✓	✓	✓	✓	✓	✓	✓	✓	✓
Box #2		✓		✓		✓		✓
Box #3			✓				✓
Box #4					✓
Box #5									✓

This table shows which boxes should be review for the first nine days. To state it mathematically, on day N, you should review box X if N+2^X−2−1 is divisible by 2^X−1.

There's also software to help keep track of all the details for you. Personally, I use Anki, but there are lots of other alternatives you can try.

I strongly encourage you to try it, if there's anything you want to learn. If you want more information, here's a fun interactive article and here's an essay written by a teacher about their experience using spaced repetition software in the classroom.

What Does the Equals Sign Mean?

2021-06-16T22:37:09+00:00

When kids are taught arithmetic, they're usually given problems that look like "2 + 3 = __", and they're supposed to write "5" in the blank space. So it's not particularly surprising that many kids (and even some adults) don't actually understand what it means. They think it means something like, "Here's the answer" or "Evaluate this expression".

What it actually means is that whatever is on the left of the equals sign is the same as whatever is on the right.

There's some nuance about what exactly it means for something to be the same as something else, which can vary somewhat depending on the context, but generally it just means that the two things have the same value.

So, 2 + 3 = 5 is a true equation because the expression 2 + 3 has the same value as 5.

But that equation could also be written as 5 = 2 + 3. Since thing on the left is the same as the thing on the right, the thing on the right must be the same as the thing on the left too.

You can even write 2 + 3 = 1 + 4. It might not be immediately obvious why you would want to, but being able to manipulate equations like that is the basis of algebra, which is a very useful thing

Sometimes you'll see someone write something like "2 + 3 = 5 + 4 = 9". This is incorrect. What's meant is "2 + 3 = 5 and 5 + 4 = 9", but the correct interpretation is "2 + 3 = 5 + 4 and 5 + 4 = 9". 2 + 3 doesn't have the same value as 5 + 4, so that's false.

Advice

2021-05-21T01:45:24+00:00

Consider this dialogue:

Alice gets a phone call from her friend Bob.
Bob: My car is broken. Can you tell me how to fix it?
Alice: I guess. What's wrong with it?
Bob: I don't know, it doesn't start.
Alice: Well, you could try jumping it.
Bob: And that will definitely fix it?
Alice: It will if the only problem is a dead battery, but there might be something else wrong with it.

You can't give good advice on how to fix a car, if you don't know what the problem with the car is. You can give advice for the most common problems, and you can give advice about how to troubleshoot it, but whether that advice helps depends on whether the problem with the car is something your advice covers. Unless you can give out a detailed technical manual of every part of the car, some problems won't be covered.

Humans are more complicated than cars, and we haven't figured out the fully detailed technical manuals for them yet.

Therefore, all advice is highly situational. Advice that can help one person could hurt someone else.

Which is not to say that advice is bad or worthless. Advice from someone who knows the situation can be very helpful. And even without context, there are many issues that many people share, and it can be helpful to point out common problems. But, any advice that's given without context (for example, self-help books, or random blog posts) should be carefully considered before being put into action.

That especially applies when it's advice that you agree with, advice that makes you say, "Yeah, that's a great idea!". If you feel like that about some piece of advice, then you probably already believe it, and that belief probably already influences your actions. It won't be in the exact same way that the advice says (otherwise your reaction would have been, "Well, duh.") but it's probably more or less in the same direction. Which implies that the advice is less likely to be the bottleneck to improve whatever it is you're trying to improve.

Stack Of Doom

2021-04-26T14:08:22+00:00

This post is about Civilization IV, a computer game that's over fifteen years old, and has had two director successors. As always, I strive to maintain my reputation for tackling topical issues.

First, a recap of the relevant game mechanics. In Civ IV, different types of military units get various bonuses. For example, a spearman gets a bonus against mounted units, so in a battle between a spearman and a chariot, the spearman will usually win. An axeman gets a bonus against melee units, so in a battle between an axeman and a spearman, the axeman will usually win. And a chariot gets a bonus when attacking axemen, forming a nice rock-paper-scissors setup.

Furthermore, you can stack multiple units on the same tile. Every unit still moves and fights individually though. When you attack a stack of units, the unit that has the highest chance of victory will defend. So, say there's a stack consisting of one spearman and one axeman. If you attack it with a chariot, the spearman will defend. If you attack it with a spearman or an axeman, the axeman will defend. As you can see, well-composed stacks of units are difficult to attack.

And there's no limit to the number of units you can have in a stack, so generally, it's most effective to put all of your troops together in one giant stack, making what's called a "Stack of Doom". Unless there's a significant tech difference, the only way to reliably counter a stack of doom is with another stack of doom. This is understandably frustrating, and it can make combat a little bit uninteresting.

Civ V dealt with this problem by introducting "One Unit Per Tile". You can only have one single military unit in a tile. In my opinion, One Unit Per Tile is far worse than Stacks of Doom, both from a gameplay perspective and from a realism perspective. Here's an article that talks about some of the problems with One Unit Per Tile.

Here are my ideas for how to fix Civ IV's Stack of Doom:

More collateral damage. Typically, when you attack a stack of units, only the one defending unit takes any damage. But some units, like catapults and cannons, and also the Chinese unique unit do collateral damage, which means they can do damage to other units in the stack. My first suggestion is to simply make more units inflict collateral damage, and make collateral damage more harmful.
More targeting. Targeting is a concept that exists in Civ IV, but is only used by a single unit. The Khmer unique unit is the ballista elephant. Like standard war elephants, it gets a bonus against mounted units, but unlike any other unit in the game it targets mounted units, which means that if it attacks a stack with any mounted units, one of the mounted units will be the defender. My second suggestion is to make more units have this ability.
Flanking. This is a new concept that doesn't exist in Civ IV. (There is a concept with the same name, but that's just a special version of collateral damage.) The idea is that if you attack an enemy unit, and there's a friendly unit directly adjacent to the enemy, but not on the same tile as the attacker, then the attacker gets a bonus.
Attacks of Opportunity. This one I'm less confident about. It's another concept that doesn't exist in Civ, but it is related to Zones of Control, a concept that existed in Civ I and II. In those games, if you had a unit that was adjacent to an enemy unit, you could attack or you could retreat, but you couldn't move your unit to another tile that's also adjacent to an enemy unit. It was really restrictive, which I think it why it was removed in later games. My idea here is to reintroduce that, but less restrictively. You can still move around an enemy unit, but doing so would give the enemy an attack of opportunity. In other words, they would get a free shot at your unit, and your unit wouldn't get a shot at them.

All these suggestions are intended to work with Civ IV's existing combat system, but they would require making other changes for balance. The existing units that do collateral damage and targeting would need to be buffed in some way to distinguish them. And since defending a city requires putting a stack of units in it, there would need to be a way of countering these abilities in a city. Perhaps defensive structures like walls and castles could reduce or nullify these abilities. You would probably also need to change the costs, strengths and abilities of various units, and maybe add and remove some.

Sturgeon's Law

2021-04-21T03:07:08+00:00

According to Theodore Sturgeon, "Ninety percent of everything is crap". I think that's worded a bit too strongly. I would say something more like, the majority of everything is low quality. Of course, there's no objective way to evaluate quality, but I think that's true in most cases, by most standards.

Why is this? I think it's because there are far more ways for a work to be bad than for a work to be good, and it takes skill to reliably produce quality work. It's like a dart board. Most throws won't hit the bullseye, unless you're really good at darts.

Some individuals are particularly skilled, and produce mostly high quality work. Ninety percent of plays may be crap, but not ninety percent of plays written by Shakespeare. And more generally, while the majority of everything is low quality, a carefully selected subset of everything doesn't have to be.

I think this is part of the reason some people perceive recent works as being worse than older ones. When you look at old books, movies, music, etc., you typically find the ones that we still read, watch and listen to today. When you look at recent books, movies, songs, etc., you're more likely to see a representative sample. The latter will be worse, but only because it hasn't been winnowed by time.

A seemingly paradoxical implication of this law is that by increasing output, you increase the amount of both low quality work and high quality work. The relative proportion doesn't have to stay constant, though. In fact, it could move in either direction. For example, the proportion of high quality work can increase by an artist getting more skillful through practice. Or it could decrease by removing a selection barrier that had been in place before.

Eclipses

2021-04-11T16:25:58+00:00

There are two kinds of eclipses. A lunar eclipse in when the Earth casts a shadow on the Moon, making the Moon appear dark. A solar eclipse is when the Moon casts a shadow on the Earth. The people who are in the shadow will the see the Moon block the Sun, making the Sun dark. The picture above is one I tookd during a total solar eclipse.

In my previous post, I said that a full moon is when the Earth is between the Sun and the Moon. And as you might expect, a lunar eclipse can only happen during a full moon. But we get a full moon about once a month, and lunar eclipses only happen about twice a year. Why isn't there a lunar eclipse every month?

The explanation requires some 3D geometry, which can be hard to visualize. So, to help, I've made some interactive 3D models. To start, here's a model showing the Earth's orbit around the sun. You can click and drag to rotate it. Note that it's not to scale to make it easier to see. The grid is just to visualize the plane that the orbit lies on.

The Earth moves around the Sun in a circle, with the Sun at the center. (Technically, it's not actually a circle and the Sun isn't quite at the center, but that's a close enough approximation for now.) That circle lies on a plane, called the ecliptic. The ecliptic doesn't move, at least not significantly.

The Moon orbits the Earth on a circle too, but the plane of the Moon's orbit doesn't line up with the plane of the Earth's orbit. This is called the inclination of the Moon's orbit. You can adjust the slider to see how different inclinations look. The actual inclination of the Moon's orbit is about 5 degrees.

You can see how when the Moon is just slightly inclined, it's possible for it to be on the far side of the Earth, but not in Earth's shadow. But now, you might be wondering, how can there ever be an eclipse?

Well, as the Earth moves around the Sun, the plane of the Moon's orbit changes very little. (A process called nodal precession causes the plane to spin around the Earth, but it happens slowly.) This next model shows what the Moon's orbit looks like as the Earth moves around the Sun.

If you adjust both the Earth's and Moon's positions to 90 degrees, you can see the Moon will be in Earth's shadow no matter its inclination. This is why we get about two lunar eclipses per year.

This model also helps demonstrate why solar eclipses are less common than lunar eclipses. Since the Moon is smaller than the Earth, it has to be that much closer to being perfectly lined up. Furthermore, the Moon's shadow can't cover the entire Earth, so only a small portion of the Earth can see a solar eclipse when it does happen.

Because the above models aren't to scale, they might give the wrong impression about the actual sizes and distances of the solar system. So the next model is the same as the last one, except it's to scale. If you can't see anything, zoom in.

Why does the Moon have Phases?

2021-03-12T00:47:57+00:00

Look at the Moon, and you’ll see that it changes over time. It goes through phases, in a regular cycle. New, crescent, half, gibbous, full, gibbous, half, crescent, and back to new.

It's a common misconception that the phases of the moon is caused by the shadow of the Earth. While the shadow of the Earth does sometimes darken the Moon, that's called an eclipse and it only happens a couple times a year.

So, what does cause it? The short answer is that it's our perspective of the illuminated half of the moon as it moves around us. Perfectly clear, right? Let's break that down.

First, the Moon doesn't generate its own light. It's illuminated by the sun. Here's an experiment you can do at home. Take a ball, go into a windowless room, and turn on a single lamp. Notice that the side of the ball that's facing the lamp looks brighter than the half that's facing away. The side that's facing away isn't completely dark, because there's light bouncing off the walls, but there are no walls in space. The Moon is lit up by the Sun in the same way as the ball is lit up by the lamp.

Half of the Moon is lit up, and half is dark. That's always the case, even during the full moon (except during an eclipse). So, why doesn't it always look like it's half lit up?

Go back to the ball in the room. If you stand between the ball and the lamp (but without getting in the way and casting a shadow) and you look at the ball, what do you see? The illuminated half of the ball. You can't see the dark half, because it's on the other side of the ball.

If you stand so that the ball is between you and the lamp, then you can only see the dark side, because now that's the side that's facing you. And if you stand off to the side, you can see part of the ball that's illuminated, and part that's dark.

Here's a diagram of what I just described. The light source is the yellow circle with rays on the right. The half of the ball facing the light is illuminated. The half facing away is dark. There are three observers. A only sees the light half of the ball. B only sees the dark half. C sees half of each.

Of course, the Earth doesn't revolve around the Moon. the Moon revolves around the Earth, but the principle is the same. When the Moon is between the Earth and the Sun, we see the dark half, so it's a new moon. When the Moon is on the other side of the Earth, we see the illuminated half, so it's a full moon. When the Moon is off to the side, we see some of each.

An implication of this is that you can't see any phase at any time of day. You'll never see a crescent moon at midnight, for example. Because in order for the Moon to appear crescent, it has to be closer to the Sun than the Earth, and at midnight, you're facing directly away from the sun. A full moon rises as the Sun sets, and sets as the Sun rises. A new moon rises and sets at about the same time as the Sun.

Is a Hot Dog a Sandwich?

2021-02-23T05:04:48+00:00

Image source

Well, what is a sandwich?

I’m sure you can come up with a reasonable definition, and many people have, but is that definition really what you have in mind when you think of a sandwich? Is that definition the way you first learned to identify a sandwich, or did the definition come later, based on a concept you were already familiar with?

For me personally, I don’t determine if something is a sandwich by checking if it meets a given set of necessary and sufficient conditions. I just check if it’s like a sandwich.

In the philosophy of language, there are two types of definition: intensional and extensional. Intensional definitions are the kind we normally talk about, a concise set of necessary and sufficient conditions that determine whether something is a member of a category. Extensional definitions are given by pointing out specific examples and hoping that you can figure out the connection between the examples.

Intensional definitions are great, because they’re easy to communicate, easy to check and unambiguous. But extensional definitions are what we use for most of the concepts we use daily. What’s the definition of a door, a chair, a car, a cat? You can come up with intensional definitions for those things, but they’ll almost certainly include things that aren’t in the category, exclude things that are, be difficult to apply, or all three.

This is the basic idea behind exemplar theory, which says that we evaluate whether an object belongs to a category by comparing it to known examples of that category. Under this paradigm, you might say that a hot dog is a non-typical member of the sandwich category. Or, depending on your understanding of exemplar sandwiches, maybe you’d say that a hot dog is a somewhat sandwich-like non-sandwich.

But more importantly, what’s the point of the category in the first place? A whale is a mammal, not a fish, and that’s an important distinction to a biologist studying phylogeny. But if you’re a fisherman, maybe all you care about is whether it lives in the ocean, in which case it would make sense to group fish and whales together, both separate from horses. Neither category is wrong, they’re just more or less useful to certain applications.

So, what’s the point of the sandwich category? What are you going to use the answer for?

Inferential Distance

2021-02-02T03:39:25+00:00

If you don’t know algebra, it will be hard to learn calculus. If you don’t know arithmetic, it will be hard to learn algebra, and even harder to learn calculus. That’s because calculus builds on the concepts of algebra and arithmetic, and you can’t build on a concept you’re not already familiar with. This is the basic idea behind inferential distance.

The problem of inferential distance applies to, well, just about everything. Almost everything you know, every idea you have, relies on simpler concepts. Even something simple like “France is a country” relies on simpler concepts, like what the word “country” means and what it means for something to be a country.

This is one of the biggest difficulties of explaining something. In order to explain something to someone, you need to build off the concepts they already have and start with the most basic concepts they don’t already have. To do that, you need to figure out which concepts are which.

That’s not always easy, because some of the concepts you already know might seems so obvious to you that you don’t realize you need to explain them. If you’re trying to explain Newtonian physics to a flat-earther, you might not realize you need to explain what the word “down” means.

It’s even harder when you’re writing a blog on the internet, trying to explain something to a faceless audience. Everyone has a different set of concepts they’re starting with, so no single explanation will work for everyone. If you start with concepts that are too advanced, then you won’t reach people who don’t already know the starting concepts. And if you start with concepts too simple, you’ll come across as boring or condescending to other people.

What’s more, for many topics the foundational concepts might not be straightforward facts, but controversial opinions. For example, utilitarian and deontological ethics are based on two very different ideas of what the words “good” and “right” mean. In such cases, it’s very common for people to talk past each other, because they don’t realize their basic assumptions are different.

Fruitful communication relies on finding and bridging that inferential distance. I don’t know of any reliable way of doing that. My only advice is listen and don’t assume you know what your interlocuter means.

Why Reinvent the Wheel?

2021-01-22T02:52:01+00:00

Image source

“Don’t reinvent the wheel” is the standard advice. And I think that it’s usually good advice. Most of the time, it’s a waste of time and effort to redo something that’s already been done, if you can just reuse the existing thing instead. Most of the time, but not always. As I said in my introduction, sometimes it’s good to reinvent the wheel. Here I'll discuss some of the reasons to do so.

One of the best reasons is for learning. That’s the primary reason I’m doing it with this blog. The best way to learn is by doing. Studying how someone else achieved something is great, but by doing it yourself, you’re forced to engage with it at a deeper level, which gives you a better understanding of what goes into it.

Another reason is if the existing wheel doesn’t do what you want it to do. In this case, it’s still usually better to start with what already exists and figure out how to modify it to fit your needs. But sometimes you just need to restart from the ground up. A good example of this is git. Linus Torvalds created git because none of the existing source control management systems that existed at the time met his needs, so he built his own.

Reinventing the wheel can also mitigate the risks of having a monoculture. In agriculture, it’s common to grow a single species in a field. This is efficient, but also fragile. If there’s a disease, it can easily wipe out the whole field. This idea applies to technology too. For example, if many people use the same operating system, it’s easier to develop software that they can all use. But if that operating system has any vulnerabilities, then everyone who uses it is exposed in the same way. Having multiple co-existing systems can also be beneficial by encouraging competition and enabling cross-pollination of ideas. In this case, the benefit of reinventing the wheel is not just for the person or organization doing it, but for the community as a whole.

All of this is from the perspective of software development, where reusing existing technology is especially easy, but I think these same basic ideas apply to other fields too.

Chance

2021-01-04T02:41:19+00:00

I made this animation a few months ago. To be clear, I just made the animation. The music is Chance by Kai Engel.

I've been interested in geometric art since high school, which is why I made AlDraw. Animated geometric art is a fairly natural step further. It's a step I took a long time making, because animation is complicated and hard.

I decided to make something like this while listening to Daft Punk's Motherboard. I didn't make an animation for that song for reasons of copyright. Fortunately, there's the Free Music Archive, which is where I found Kai Engel's work. I already used that site to find music for my timelapse videos. Fortunately, this song is perfect for this kind of animation.

I made the animation using SVG animation. Most image formats, like PNG, JPG and GIF are raster based, which means they store an image by encoding the information about the color of each pixel. SVG on the other hand is vector based, which means it stores the image by encoding information about geometric objects, for example by specifying the endpoints and thickness of a line. That makes it ideal for the kind of geometric designs you can make with AlDraw, and the kind of geometric shapes this animation uses.

Likewise, most video formats store an animation by storing discrete frames. SVG animation works by letting you specify how a value varies over time. For example, you can say that a line that extends from (x1, y1) to (x2, y2) at time t1 moves to (x3, y3), (x4, y4) at time t2, and between t1 and t2, the values will be interpolated. So, SVG animation is a natural choice for making a geometric animation like this.

Unfortunately, SVG animation isn't widely supported. Most browsers will display them, but they don't include any kind of playback controls. I don't know of any video players that can play SVG animations, and even most SVG editors don't support SVG animation. So, what I wanted to do was write the SVG and then convert it into a more common video format like MP4.

But there's no software that does that. Or at least, there wasn't. So I made my own. That code is pretty bad. It's inelegant, it's inefficient and it doesn't support half of what SVG animation can do. But it's enough to make this video. Someday, I might work on improving and expanding it.

As for actually writing the SVG, and in particular, timing everything just right, that was a lot of hard work. I used an audio-editing application called Audacity to see the exact timing of each note. My wife, Molly, helped too.

You can download the SVG file here.

All told, I spent about five months working on it. About two just on the svg-to-video program, and about three on the animation itself. I didn't keep track of the amount of time I actually spent working on it, but it was probably something around 200 hours.

Why Does Multiplying Two Negative Numbers Make a Positive Number?

2020-12-23T12:00:00+00:00

First, I'm going to illustrate this with some pictures, then I'll explain how the pictures work.

Here’s a typical number line, with 0 in the middle, the positive numbers going to the right, and the negative numbers going to the left.

I’m going to represent numbers as arrows. Here’s the number 2.

And here’s the number -2. Now the arrow is pointing to the left, instead of to the right.

Here is 2*3. We have three arrows, each of which has length 2. The result of 2×3 is at the head of the third arrow, 6.

Here’s -2×3. Now the arrows are pointing left, because they’re negative. So, when you put one after another like before, the end result is -6.

Here’s 2×-3. Now the arrows are pointing right again because the 2 is positive. But the arrows are being laid out backwards, because the 3 is negative. Here, the result is at the tail of the last arrow.

And finally, here’s -2×-3. Following the pattern, the arrows are pointing left and going backward, so the end result is positive.

So, why do these pictures work the way they do? Well, let’s start with addition.

Here’s 3+2. We start with a 3 arrow, and then we put a 2 arrow with its tail on the 3’s head. It should be clear why the head of the second arrow is at 5, the sum of 3 and 2.

Since 2×3 = 2+2+2, it should be clear why it should be represented by the picture above.

Before we get into multiplying negative numbers, let’s do subtraction. Here’s 3–2. This time, instead of putting the 2’s tail on the 3’s head, we put the 2’s head on the 3’s head, keeping the direction the same. Then the result of 3–2 is at the 2’s tail. I put the 2 arrow above so you can clearly see it, instead of overlapping the 3 arrow.

Why lay it out this way? Two reasons. One is to distinguish between subtracting a positive number and adding a negative number. Although the end result is the same, I think this will help when we get to subtracting negative numbers. The other reason is that subtraction is the inverse of addition. What that means is that, if x-y = z, then z+y = x. (For example, 3-2 = 1, 1+2 = 3) You can see how the 2 arrow is the same in the picture showing 3-2 and this picture showing 1+2.

Here’s 3 + (-2). The -2 arrow points left, because it’s a negative number, and because we’re adding it, we put its tail on the 3’s head. And this is why 3 – 2 = 3 + (-2).

And here’s 3 – (-2). Like the previous time we did subtraction, we put the second arrow’s head on the first arrow’s head, and the result is at the second arrow’s tail. And because the second arrow is pointing left, the tail is to the right. In other words, 3 – (-2) = 3 + 2.

Another way of looking at this is that subtraction is the inverse of addition. Since adding a negative number makes the result go down, then subtracting it makes it go up. 3 – (-2) = x. We can rearrange that to be x + (-2) = 3. And adding a negative number is the same as subtracting it’s opposite, x – 2 = 3, which we can transform into 3+2 = x = 5.

What does this have to do with multiplication? Well, multiplying by a positive number is straightforward, it’s just repeated addition. But how can you repeat something a negative number of times? That doesn’t make sense. So, if we want to be able to do that, we need to extend our idea of what multiplication is.

To do that, we look at what properties multiplication has, and figure out how to maintain those properties.

One important property of multiplication is that x×y = y×x. For example, 3×4 = 12 = 4×3. So, if want to keep that property for negative numbers, then 2×-3 must be equal to -3×2. -3×2 can be understood as repeated addition, -3 + -3 = -6. But that doesn’t help if both of the numbers are negative.

Let’s look at another important property. Consider, 2×3 = 6. 2×2 = 4, which is also equal to 6 – 2. 2×1 = 2, which is 4 – 2. In other words, if you know what 2×n is, then 2×(n-1) is equal to 2×n – 2. So, since 2×0 is 0, 2×(-1) must be equal to 0 – 2, which is -2. And 2×(-2) = -2 – 2 = -4. And if you follow that pattern, you’ll get 2×-3 = -6, which is the same answer we got using the last property.

And notice this property works for numbers other than 2. 3×3 = 9, 3×2 = 6 = 9 – 3. 3×1 = 3 = 6 – 3. So, 3×(n–1) = 3×n – 3. And more generally, x×(n–1) = x×n – x. What this means is that multiplying by a negative number can be interpreted as repeated subtraction. Just as 2×3 = 0+2+2+2, 2×-3 = 0–2–2–2. And that’s why in the picture above, I show multiplication by a negative number with the arrows going backward.

Since multiplying by a negative number is repeated subtraction, when we multiply a negative number by a negative number, we repeated subtract it, which means we go up into the positive numbers. -2×-3 = 0 – (-2) – (-2) – (-2) = 0 + 2 + 2 + 2 = 6.

To sum up, the reason that multiplying two negative numbers makes a positive number is that you're going backwards, backwards.

Why Can't You Divide By Zero?

2020-12-16T12:00:00+00:00

A common way of explaining this is to say something along the lines of “Dividing means splitting into groups, and you can’t split something into zero groups.” The problem with that explanation is that it doesn’t really make any sense to divide something into half a group either, but you’re allowed to divide a number by 1/2. You can even divide by negative numbers and complex numbers. Why is zero so special?

Here’s how I think about it. Don’t think of dividing as splitting into groups. Instead, think of division as being the inverse of multiplication. What that means is that if x/y = z, then y*z = x. Here’s a specific example: 12/3 = 4 ⇔ 3*4 = 12

That means, if you try to solve 5/0 = x, then you need to find some number such that 0*x = 5. But there is no such number. 0 times any number is 0.

What about 0/0? 0/0 = x ⇔ 0*x = 0. The problem with this equation is not there is no solution, it's that there are infinitely many solutions. If you say that 0*5 = 0, so 0/0 = 5, you can also say that 0*7 = 0, so 0/0 = 7. But that would mean 0/0 is equal to both 5 and 7, which means 5 and 7 are equal to each other.

The way we handle that is by simply declaring that division by zero is undefined, meaning that you’re not allowed to do it.

Now, if you know what complex numbers are, you might ask why can’t we just define 0/0 to be some new number like i? Well, you can do that, and there are some number systems that do, for example the projectively extended real line and the Riemann sphere. The problem you run into is that when you do this, you end up breaking other useful properties. For example, in the standard number system, addition is defined for every pair of numbers, but not in the projectively extended real numbers.

Introduction

2020-12-15T12:00:00+00:00

This is my new blog. I used to blog here. I gradually stopped blogging because writing is hard, and I didn’t feel like my ideas were worth sharing. I’m re-starting blogging because doing hard things is how you get better, and because my wife and this other blog post convinced me that my ideas are probably more valuable than I gave them credit for.

This new blog doesn't have a title other than "Alex Strinka's Blog". The reason for that is it's not a standalone site, it's just a section of my website, which itself doesn't have a title other than "Alex Strinka". And that seems suiting, since this blog doesn't have a particular subject, other than whatever I happen to want to write about.

I’m changing platforms because, well, because I want to. It seems appropriate that my blog should be on my own personal website. And I’m using my own hand-written platform instead of WordPress or something because sometimes it’s good to reinvent the wheel. The downside, of course, is that it is much more primitive than those other alternatives. I’m still working on adding more features, if there are any features you’d particularly like to see make sure to leave a comment.

Speaking of comments, that’s also hand-written. There’s no user account or login or anything like that. There’s also no formatting. I intend to implement those features and other seventually. Again, if there are any features you want, write a comment or send me an email.