Someone in this thread https://slacker-news.fly.dev/item?id=40401343 linked to a udemy course, then I noticed udemy currently is offerring more than 80% discount on some courses. The discount offer expires in 4 days. I still have some cash with me from the crappy upwork jobs I did a while back, and I want to purchases one or two courses.
Why courses though, I can just read a book. True, for programming, math or anything text-based, articles/books are better for the most part. But for visual, realtime interactive stuffs, watching a video is way better. Things like gamedev, blender, photoshop, and video editing.
What about youtube videos though? Yeah, youtube has tons of content, but it also has a lot of half-baked, low-effort or shallow videos that have terrible pedagogical quality.
Still, I'm not sure udemy would be any better, but it's worth a shot. At the very least, the content is professionally made. Also, udemy offers certificate of completion, so I could use that too when job searching.
That all said, I'm going to try godot courses, since I had no luck finding a comprehensive, good resource for doing godot developement. And maybe some dart+flutter courses.
So I started creating triangles in increasing size. For instance, I have three triangles T1, T2, and T3. T1 has 10 dots in it, T2 has 15, and T3 21.
10 15 21
.
. ..
. .. ...
.. ... ....
... .... .....
.... ..... ......
T1 T2 T3The more interesting part is that I could create squares by combining two consecutive triangles. For instance, combining T1 and T2 creates a square, and combining T2 and T3 also creates a square. By induction, this should hold for triangles of any size.
I wonder what other shapes I can create from rectangles.
Not sure how I could use this for factoring, but it's an interesting self-discovery. The question now is, given a square number, say, 196 = 14*14, how do I get the pair of two consecutive triangle numbers that add up to it. Well, aside from recursion.
Aha, wikipedia cheat to the rescue:
T1 + T2 = [(14**2)/2 + 14/2] + [(14**2)/2 - 14/2]
= 105 + 91
= 196Okay, I've done enough progress on the ant project to the point it's useable now for playing around with squares, specifically for improving the algorithm. Funny, I still haven't implemented the langton's ant, but it should be trivial to add later on since I'm more or less done with preparatory stuffs.
And so, after some playing around, I managed to find a slight tweak in the algorithm to reduces the number of steps by more than half. But, I don't know yet if that change is correct, since I think it's possible to "overstep" and skip over the proper solution.
Okay, I successfully rewrote the initial code to typescript, and I did some refactoring as well. Also, I managed to implement the cell selection and movement, somewhat similar to the dolphin file browser. I copied that behavior since it seems to be more intuitive, and saves me the trouble of trying to define my UI interaction, which may end up being unintuitive.
Uhh, I got a bit distracted and spent way more time trying to scaffold a typescript project with bun I wanted to use bun since it's really fast at compiling/bundling and it comes with all the nice stuffs that lets me skip the trouble of installing a bunch of node dependencies.
The problem is that it doesn't have a built-in feature for hot reloading client code, like what vitejs I really should have opted to go with vite, that kinds of defeat the purpose of using bun, since vite adds tons of dependencies and complexity that I don't need.
What I just need is:
- bundle typescript code
- auto-page reload when any files are changed
- local development server
After some head-scratching and fumbling, I managed to get the setup I want. Now I can go back and continue the ant project for real.
I mostly planned how the UI will behave, I decided to copy somewhat the dolphin file browser behavior. As for cell insertion, I'll add a paint mode, where I can brush or fill new cells. I might consider adding some undo/redo feature too.
The features I listed aren't exactly overscoping, they are at least necessary features for it to be useable, still doable with LOC < 1K.
I'm considering using typescript at this point though, to save me some time debugging or fixing type errors.
So I started a small project recently, against my other plans and priorities, henceforth I will designate as the "ant" project.
As the name implies, it has something to do with ants. Not literal ants though, but as a side note, I recently come across another mycmyrnae, no uh, mcmyrne, myrrnc... Myrmarachne is the word, which is a fancy name for spider-ant mimics, or spiders that pretends to be ants. It's either they are a rare bunch, or just hard to spot. In any case, ant mimics are a nice find when you see them.
The ant project will be primarily be about langton's ant Secondarily, the project will be anything related to cellular automata. The side goal is for me to have a nice UI playground for moving around blocks, for purposes of further developing my factoring algorithm.
Cellular automata are algorithmically straighforward to implement, but the question is which UI framework should I use. After some brief consideration, I just opted to use the web frontend (html+js), firstly because it's what I'm most familiar with, and second, because it's the easiest and cheapest stack to put things out there.
Initially, since I used lua for my static site, I opted to try fengari lua VM so I could still have all of my codebase in lua. This was a mistake though, since after 400 lines of crappy lua code, the web UI would stutter and lag with a grid size of 20x20. That's barely acceptable for me, because cellular automata are better with larger grids.
I thought maybe I was doing something wrong with the canvas API that was causing the lag. But I'm mostly just drawing a bunch of rectangles, surely it can't be that. So my hunch is that fengari is the problem.
I considered using p5js, but it was a large 1MB depedency, plus now I have to learn the p5js API, which would cause me to exceed the planned time budget.
The easiest fix is to try rewriting the lua code directly into javascript. After some mild frustration translating lua eccentricities to javascript, I managed to get it working and fix any weird bugs.
And the result: javascript code was way faster, even with 100x100 grids it performs smoothly. I guess the lesson of the day is that I should have tested how fengari would perform with hot loops.
Oh well, that's that.
Bah, I just spent an hour fixing bugs on my site. The strange thing is, it works fine on my machine, but when it builds on github's runner, a bunch of strange stuffs shows up.
I thought it was because I was using a macOS runner, but same thing happens on ubuntu too.
Of course, the bugs are entirely my own fault, but it would have been ideal if I could reproduce the bugs on my local computer, instead of debugging on github's action logs.
One of the reason I'm using [redbean](https://redbean.dev/) in the first place is that I'm hoping I could get that consistent behaviour across different systems without worrying about special quirks that I have to handle. Oh well, I can't have that too I guess.
Huh, for some reason I'm itching to implement some cellular automata like langton's ant, turmite, or even the classic game of life. Not exactly on the topmost priority, all things considered. But, wouldn't it be cool if I could also create a cellular automaton algorithm myself, maybe something based on factoring or prime numbers.
Well, so much for my plans for today, I mostly just did a bunch of changes on my personal site. I also managed to cut down the build time from 10 seconds to two seconds by caching the filesystem reads.
For reasons or another, I'm starting job search again. Of course, when it comes to reaching out and contacting people, I first need to make myself not too much of an eyesore. And I just realized that my profile picture is already more than a year old. How time flies.
So for tomorrow's agenda:
- take a more recent picture of myself
- update my personal site
- write cover letters
I'm going to put on hold on working on the factoring algorithm. I want to create a tool or app that allows me to play around with grids of rectangles that represent two numbers being multiplied. The purpose of this is to help me get a better intuition and insight, as well as develop or improve the algorithm more visually and playfully.
Playing around with paper is fine at first, but it becomes tedious for grid of size greater than 5x5.
My t440p laptop kept crashing, the exhaust fan was really hot even right after the initial boot. My wireless card also strangely kept failing. This seems to happen more during the middle of a hot day. I unscrewed my laptop open and saw that the exhaust was filled with thick dust. I quickly dusted it off and tapped in on wall to shake rest of the dust inside. That seems to have fixed the problem? Maybe I should replace the thermal paste too, the last one applied was 5 years ago.
Huh, the more features I add to my personal site, the slower the total build time. Adding the tagging feature increased the build time to around 10s. But who cares, I only build the site when I need to deploy, I don't need to build during development and testing.
The codebase has gotten quite a mess though. Anyway, it's mostly temporary, throwaway code that it will change according to my ephemeral whims.
I now have a roughly working algorithm for finding a factor given a number, and by extension, testing whether a given number is prime. It doesn't involve testing against a (possibly large) set of numbers. It's largely a conjecture if it holds for all numbers. I'm still working through examples that I think could be a counter-example, and thus prove the conjecture wrong. Since I'm not a mathematician, it's a long way for me to be able to formulate a mathematical proof. For now, finding counter-examples is easier.
The question is, will it be any better than the current algorithms? I don't know, depends on the complexity of finding the common factors between a number. I think gcd is pretty fast. Fast or not, it doesn't matter, it would be cool enough to create my own algorithm.
Aha, I managed to tag 800 images in one sitting, for about a half an hour. I did with just keybindings using vim and the dolphin file manager. I should just write a script in the future though.
Frieren, Dungeon Meshi and Shanri-la have the most picturesque screenshots. They really do have a good art, I could just take any random screenshots and it would likely look good.
Fu, I actually have a thousand of images to tag, I can't believe I've accumulated that much screenshots already. I should limit the screenshots when I watch anime. Also, lol I can't even remember for the life of me what the names of anime I watched. Even the catchy titles like Solo Leveling.
I have now implemented tagging on my personal site, and current I'm tediously adding tags to each log and image. I kind of wish I did this earlier. Oh well, it's not that bad, it's mostly a repetitive, mechanical work.
Well, it's midday of an early week in a yet another blazing hot day, and I'm lethargic as fuck again. There's lots of things I could do, or rather, I feel like I should do, yet here I am staring blankly at my untrimmed toe. I'm even too lazy to play games.
Maybe I should eat some chocolate. I had a long good sleep last night, yet I feel extra tired when I woke up.
Still, I should just do something, anything, however trivial or useless it is. Does typing all of this counts as doing something?
Actually I'm still working on my notebook, on my futile goal of trying to find other ways to factor a number. I do this before I start my day, while caffeine is still fresh in my biological systems. Why am still even working on it? Because I'm actually slowly making progress, I feel like I'm almost there. My gut feeling, could be wrong, is that there's no reason to resort to brute force when doing primality testing. What so special about prime numbers anyway?
Mathematicians defined a restriction that the factors should be natural numbers, but without that restriction, prime numbers are nothing special. I could also also try changing the unit other than 1. Yes, in my hypothetical universe where people have digit fingers of 1+N~, some (all?) primes become composite, and composite becomes prime.
But that's cheating, a math nerd would say. Yeah, but if my delusions turned out to be true, then prime numbers are mere superficial constraints imposed by our current mathematical system.
I have several algorithms that (at least appears to) work reliably well on small numbers. I could write programs to handle bigger numbers. It remains to be seen whether I could find (or prove) a general solution that works on any number. Or not, I'm just a lowly outsider to the art of mathematics. As always, I'm most likely just wasting my worthless time. No matter, my curiosity is fixated on doing this, I will keep on doing it, until I find something else to do.
No, find a job you stupid hiki-NEET.
Well, another week has gone by. I'm slowly trying to build up my motivation and get back on my feet. Not even sure what to write right now, anything goes I guess. I should take note of positive things for a change.
These days, it's been quite windy. It has also been quite hot, sometimes I'd be constantly sweating throughout the day, especially when I move around a lot. I should increase my usual water intake to avoid dehydration. I don't mind the heat and sweating though, it feels good in fact to have the wind blow and dry my sweat away.
I also finally managed to beat the final-final boss on Ys: Oath in Felghana. I even managed to beat it on first or second try, without too much effort. With 7 HP left, I did it. Maybe I was well-rested and relatively anxiety-free. Or let my mind take a break from something difficult and come back on it with a better insight or skill.
But most likely, it's because I lowered the graphics settings and improved the FPS. Suddenly, deflecting the dark energy ball wasn't so difficult. Maybe it's all of the above.
No it's actually because I've been watching Shangri-La, an anime where the main character is an otaku who likes beating kusoge (diffult, shitty games). I think Ys games qualify as kusoge. I doubt a very attractive, big-breasted young woman is secretly into me, but it's quite easy to imagine myself as a bird-brained freak who fixates on terribly wrong or challenging things.
It's been a while since I last saw this ending. I wonder if Adol ever went back to Felghana to see Elena again. Looking it up, it doesn't look like she appeared anywhere in the later subsequent releases, so it's left for the player's imagination. What I imagine is that Adol never ever came back, and Elena grew old, decreipt and desolate, but still hopeful until the very end.
I also started playing Ys: Origin next. With the blessings of bird-brained sunraku, I've been in girigiri (close-call) situations, where I defeated several bosses with barely HP left. I even defeated the centipede boss with 1 HP left while poisoined. That's almost like Sunraku, except with a serpent instead of a centipede.
I haven't really been doing anything for the past week. No, I didn't lost my way inside the notebook and neglected anything else. I've been doing literally nothing, bar playing games and watching, or other random things to keep myself from being alone with my thoughts, things to distract myself from the cruel reality.
Jung unccrarq vf gung zl uhfxl qbt qvrq. Bs nyy gur guvatf gb qvfnccrne sebz guvf jbeyq, vg unq gb or fbzrbar ernyyl pybfr gb zr, zberfb guna zl snzvyl zrzoref. V'q engure abg guvax nobhg vg zber, abg abj ng yrnfg, juvyr gur cnvashy zrzbel vf fgvyy serfu. V gubhtug V unq n ernyyl fgebat fgbvp nezbe, anviryl guvaxvat gung abguvat pbhyq cbffvoyl uheg zr nalzber. Ohg ab, sngr naq tbq vf n ******* ******* *** ****** ***-******* ******. V pna'g rira oevat zlfrys gb or natel be fnq zber guna V pna, onq sbe zl urnygu. V rira unq n crefvfgrag purfg-cnva naq fubegarff bs oerngu sbe nyzbfg n jrrx.
Fb V'z tbvat gb rdhvc na rira fgebatre fgbvp nezbe guvf gvzr. Va gur raq, abguvat znggref, rirelguvat naq rirelbar qvrf. Jung vf rira gur cbvag bs pelvat, urpx V jvfu V pbhyq onjy zl rlrf bhg naq pel hagvy ab zber. Ng zbfg, zl rlrf trg jngrel. Bayl zl vafvqrf ebgf naq qvrf rira zber.
I'm not going to think about it.
Despite what non-binding nonsense I said yesterday, I'm still stuck on my notebook, slowly chipping away more dirt and mud. Maybe the fun hasn't worn off yet, or maybe I'm just too lazy to do anything else. Mucking around seems quite easy in comparison.
In any case, I should write down something. Not sure where to start, I should list down the seemingly useful formulas and equations that I found or made:
Firstly, I can decrement/increment any factors with any number
For any number n:
xy = (x+n)y - ny
xy = (x-n)y + ny
3(5) = (3+7)5 - 7(5)Another is this one:
x + y + ... = a(xa~ + ya~ + ...)
= a~(xa + ya + ...)Another one is this:
xy~ = 1 + (x-y)y~Also this:
ax + by + cz + ...
= (a + b + c + ...)(x + y + z + ...) - qRelated to this is the following observation (but not yet proven): For (my favorite) example, I have
469 = 7(67)
= 4(10^2) + 6(10) + 9
= 2(2*5)^2 + 2*3(2*5) + 3*3
^--a ^--b ^--cIs it useful? Initially, it thought it could be, but then, the search space is still quite large(r) when going for the brute force method of trying the all the different combination of factors.
So I'm trying the different angle, by looking for alternative or (even more) general ways of factoring, such as
ax + by + cz = (a + b + c)(x + y + z) - qI was going to write what I have been doing for the past 10 days but my mind got lost on fox digging holes. I mentioned Mr. Fox and digging holes because I thought it was an apt metaphor to what I've been doing.
Basically, I've scribbling a lot on my notebook, and it's pretty much what has been on my mind, even on my deep slumber. Unlike Mr. Fox, I wasn't running away from danger. I was just digging out of curiosity. Sure, they were infinitely better and meaningful things to do, but my mind was fixated on digging this hole. For my own detriment, it was almost the only thing I wanted to do for current time being.
My Digging was stupid and useless, and a complete waste of time. The only thing I would get out of this digging is to sink my life further. I was under no illusion that my digging would result into anything I would write home about (which is funny, because I'm always home). There's no glory here, it's all dirt, mud and worms.
Past the initial curiosity, digging turns into obsession, then suffering and borderline insanity. One night awoke in cold sweat three times to the same nightmare, believing I was almost there but there was nothing but a dead end.
In my mind, I was intoxicated with mad curiousity, thinking digging this part would reveal something, or would lead to something mankind has never ventured before. It was a dead end, but then I thought, what about this way, or that way. I could have consulted a pre-made map (by studying number theory), but no, I liked the feeling of ignorance and naivety, thinking there is more to what the eyes can see.
And this is where I am now. Thankfully, my manic episodes has died down a bit, and now I'm ready to go back and do some other projects. I'd say, I can't believe I've just wasted almost ten days digging for no purpose, but then it's completely plausible and in-character for me to do such a thing.
Of course, before I bury and cover up the hole, I should at least charter a map for the dungeons I've made. Which is to say, I should at least write down my own "self-discoveries", however trivial or unnew they are.
Looking at my logs, I realized I haven't written much for almost ten days now. It has been mostly just screenshots, although looking at the screenshots is pretty amusing too. Sometimes I think, hey this anime screenshot actually looks kind of cool. I should probably add some proper attribution though. Alternatively, I'll try noting down when I finished watching a whole season for the anime I watched, maybe throw in some my thoughts whether I like it or meh. But if I finished watching the whole season, it's most likely I liked watching it.
Man, I think my keyboard accumulated too much dust and fur again, some key presses sometimes doesn't work.
Anyways, last sunday I watched the movie Fantasic Mr. Fox. I rarely watch movie nowadays, but recently I read the short book with the same title where the movie was based on. The book was short enough to finish in one or two sittings, and I read it before going to bed. It's not a profound book or anything that gives me new insight or teaches a new knowledge or skill. Still, it was a fun read, it gave me a sense of nostalgic adventure. I used to dig a lot of holes too when I was a kid. The biggest and deepest hole I dug even allowed me to burrow my whole body and peek my head out like a rabbit.
I'm slightly disappointed that the movie changed a lot of things from the book, it's almost a different story, save for the same set of characters. But no big deal, it's still a fun watch too.
Worked on SN, I fixed the datetime so that it server-renders the date with UTC format, then converts that to localtime on the client side. I also added some textbox to easily view HN URLs.
I also looked at the fly logs why my cached json arent' working, it seems that they get deleted before the scheduled time. The logs says it periodically shutdowns the machine when the server is inactive. The fix is to use actual fly.io volumes for persistent storage.
And my quest to devise my own manual long division continues. I tried dividing and factoring several numbers numbers in my notebook, some small and some large-ish. Several observations:
- if I can't get rid of the ~, then it's (likely) not evenly divisible
- I can express larger numbers as a sum of exponential 10s such as: 123 = 1*10^2 + 2*10^1 + 3*10^0
- I should avoid distributing ~ over the sum, since it becomes even harder to solve
- Sometimes I have to add terms together to make them factorable
-
I can further factor these base exponentials to help see some factors:
So here, I could see at a glance that 735 is evenly divisible by 5, without doing full division or factoring.735 = 7*10^2 + 3*10^1 + 5 = 7*5*2*5*2 + 3*5*2 + 5 = 5(7*2*5*2 + 3*2 + 1) - Going further, I could try converting base10 to another baseN to help see the factors at a glance (in theory, I haven't tried)
With that, my division method would then be first to factor out the divisor and the dividend (prime factorization it's called it seems), then cancel out any inverses. To some extent, it works. I managed to do division even for larger numbers like 12345.
Sadly, this doesn't necessarily mean that if I don't see any obvious factors then it's a prime number. Naively I thought that was the case, I quickly ran into counterexamples, most damning of which is the quadruply nice number 469, which is a product of two prime numbers 7 and 67!?! My supposed method broke down, all is lost, god is dead and/or mad, what am I even doing with my life again.
Just kidding (maybe). I'm just missing some important detail.
469
= (2^4)(5^2) + (2^2)(3)(5) + 3(3)
469
= 6(7)Then a thought occured to me: what are real numbers? Do they even exist? Aren't they just an artifact of decimal notation? Of course, some math teacher would bonk me in the head, and point to irrational numbers. But no, what if I want to reject the concept of real numbers, out of uncalled spite, and that irrational numbers can be perfectly expressed as a ratio of two numbers, with some slight tweak in the notation and the base axioms. Maybe these dumb irrationals belong on a separate number line.
Okay, if I'm asking these crazy questions, it's time to take a break. I'll probably answer and disprove my own questions sooner or later as I go along.
To continue from yesterday, to find a way to do factoring and division, I have to ask, what does division mean anyway? What does evenly divisible mean? What's remainder? With some faint recollection of some wikipedia article, after some scribbling, I manage to come up with:
x = ab + cMoving stuffs around:
x = ab + c (1)
x - ab = c (2)
xa~ = b + ca~ (3)
xa~ = b
65 = 2*x + c
Let x = 31
65 = 2*31 + c
65 = 62 + c
65 - 62 = c
c = 3What about if I let Let x = 32
65 = 2*32 + c
65 = 64 + c
c = 1What does this all mean for me? What does a negative remainder mean, and why don't I see it in the wild? Setting that aside for now, from here it's clear that 65 cannot be evenly be divided by 2 (where c = 0). But if I want to divide by 2 anyway, I get 32 with a remainder of 1.
Checking it in python:
>>> 65/2
32.5
xa~ = b + ca~ (3)
65*2~ = 32 + 1*2~
= 32 + 0.5
= 32.5
32.5 = 32 + 5*10~
= 32 + 1*2~Then again, I still don't have a methodical approach of doing long division besides doing trial and error. On the other hand, I could now do fizzbuzz without using the modulo operator. Well, actually I already did that before using a weird alien assembly language , but still.
So today is 11th of March, which means march is practically half-way over, and if I let myself carelessly blink a few more times, it'd be April before I knew it. Time sure is bananas when it comes to flying so fast. I feel like listening again to the song "Heaven" from the game Persona.
What have I been even doing this this March? I said I was going to review my logs this weekend, but I didn't feel like it, too lazy. Most notable I did for the weekend was trying to defeat the final-final boss on Ys, I always die at the last 1000 HP of the boss. I regret going for the hard difficulty, now I can't move on to the other games, and it's a bit stressful trying to push through. I feel I didn't even get to relax this weekend.
As for today, I didn't do much, I've been scribbling away on my notebook like a madman, fixated on finding a way to do long division using my own method of multiplicative inverses. I wasn't toiling on my own volition, I was actually enjoying doing bad arithmetic, I'd make the simplest mistakes that would make a gradeschool teacher laugh. Maybe there's some dopamine hit when I rediscover some trivial mathematical properties on my own. I think to myself, huh so that's why, I can't believe I went through my adult life without knowing this basic fact.
School taught me surface level knowledge how to do arithmetic by mechanically applying algorithms. Or maybe they did teach the underlying insights, just that I wasn't paying attention. I was actually a very distracted student, the world around me would just blur during classroom hours, my mind would wander to a distant fantasy land. To my surprise, I still managed to pass with an average grade on my highschool days. College is different though.
Anyways, back on topic, what I was trying to do was to be able to do "long division" using just multiplicative inverses. So the idea would be:
12345 / 45
= (12345)45~
= (12345)9~5~
(4)(12)(3)(6)4~5~
= (4)(4~)(12)(3)(6)(5~) reorder
= (1)(12)(3)(6)(5~) substitute, 4*4~ = 1
= (12)(3)(6)(5~) remove 1, since 1*x = x
= (12345)45~
= (123(4)(5)45~
= (123(4)(5)4~5~
= (123(4)(5)9~5~
= (123(4)9~There has to be a better way. Applying division with inverses would be very easy if I could just have the form (x1)(x2)(x2)... As it turns out, that's called factoring, so my task shifted to searching how to do factoring by hand. But to do factoring, I have to do division, so what then? I found myself asking a question similar to wondering if a chicken or egg came first. There is another way, which is by trial and error, guessing if a number evenly divides another number.
Well, this log has gotten a bit too long, I'll continue this later. Time for a walk before supper.
Well, for some reason, now I'm trying to come up with my own division algorithm using only addition and multiplication. Partially, because I actually forgot how to do division by hand on paper, but also because of my curiosity to discover things for myself from first principles. Nothing new with what I'm doing, I'm sure someone already thought of these things around a thousand years ago.
I did some changes so that the lua code is compiled and preloaded. Supposedly this should reduce memory usage. And I think the average request time went down too, sort of.
Aha, I managed to deploy slacker news on fly.io surprisingly without much problem, now I can use it on my phone too. I have unused 500 fly.io credits that I got as a bonus for applying for a job at fly.io. Unfortunately, I got rejected, but at least I got free credits in return.
I wonder how long those $500 credit will last with my shitty app though. More importantly, I hope it doesn't get ddos'ed and put me in a massive debt? I recently read something like that, I can't remember the HN thread specifically.
I left an opened pack of pocky sticks in my desk and when I came back just now my desk was filled with tiny itchy-bitey ants. I poured vineger and wiped them away, but they still managed to bite my hands, now it's all itchy. Well, nothing remarkable.
Continued reading FFC, or tried to read. On page 20, I see some very inadequate explanation for finding the derivative for x², at least compared to Keisler's explanation. It's probably more simpler, but now I have more question than answers if this was my first calculus book.
Well, to be fair, I'm not even reading intently that much, but at this point, I'm just looking for something to complain about. I'd be better off reviewing the earlier chapters of Keisler's book again.
Looking at my logs, it has been 14 days now since I started working on SN Err, the lua markdown library I'm using can't handle anchor # inside a link. Oh well.
Look back further, it has been more than a month now since I started logging my daily activites. I think I'll review it this weekend to get an idea what I need to change or improve on. I wasn't actually consistent with logging what I did for a day. What was logged was mostly my time on the computer, and not much else outside that. Well, there's not much else to say when it comes to my daily routine. I live in a tiny hikikomori NEET world.
Worked on SN, fixed some filesystem errors when creating a release build. There's definitely a bunch of added complexity by having a self-contained binary with the assets embedded, not sure if this is worth it. For now, I managed to make it work, I fixed the errors by replacing direct calls to os.Stat with my own fsStat(fs, filename).
I'm more or less almost done with the project, it's quite usable with its current state. I will be using this to read HN from now on.
My original goal was to create an HN clone to test my lua templating library. But creating an HN frontend works as well. I'm convinced using lua as an alternative templating engine works quite well, I might actually use it for more web projects in the future.
I'm still considering whether I should still try creating a full HN clone. It's not actually easy running a forum. For one, I don't have the (financial) resources to maintain it. Second, no one will use it but me. Third, it might get defaced or hacked quite easily. Despite all that, I feel like just doing it anyway. Try reduce server load, I could aggresively just cache everything, and just update the site for one or two times a day. Or not.
For now, I think I'll continue watching that video titled "Godot 4 - Tiled Dungeon Environment From Scratch".
Read a bit of Full Frontal Calculus (FFC), I mostly read and didn't do the exercises. I would have probably been already lost by page 15, but good thing I already have a good intuition of what this all means, so it's easier to follow. Basically, a recap.
Played around with my rocketbook again. I tried answering my own question, how do I express multiplication and division with addition and subtraction.
Multiplication of two numbers x and y is just
xy = x + x + x ... + x
^ y times
xy = y + y + y ... + y
^ x times
x + y = xy(x~ + y~)
xy = (x + y)(x~ + y~)~
xy = (x + y) / (x~ + y~)The sum of inverses sure do come up a lot, maybe there is another way of expressing it? What about
1 = 2~ + 2~
1 = 3~ + 3~ + 3~
1 = 4~ + 4~ + 4~ + 4~
1 = 5~ + 5~ + 5~ + 5~ + 5~
x + y = xy(x~ + y~)
xy(x~ + y~) = x + y
x~ + y~ = (x + y)x~y~
2~ + 2~ = (2 + 2)(2*2)~
2~ + 2~ = 4(4)~
3~ + 3~ + 3~
= (3+3)(3~)(3~) + 3~
= (3+3)[(3)(3)]~ + 3~
= [(3+3)~(3)(3)]~ + 3~
= (_ + 3)[(_)*3]~
= ([(3+3)~(3)(3)] + 3)[[(3+3)~(3)(3)]*3]~What about expressing division in terms of addition or subtraction?
12 / 4
= 12 + -3 + -3 + -3
= 12 + -(3 + 3 + 3 + 3) + 3
= 12 + 3*4 - 3
12(4~) = 3
12(4~) = 3I did plenty of stuffs today with SN, I added showing the comment chain (post context) and top frequent participants in a thread. I also added some cache clearing every 30 minutes, that way, I will only be forced to revisit a thread after half an hour, instead of compulsively checking and rechecking a thread every other minute.
The messiest code is the UI lua/html code, which isn't really unexpected. On the positive side, it's quite easy to modify or add new changes. And it still performs relatively well, less or around 100ms per 100 comments. Sure, text/template might be way, way faster, but it's not as flexible, or even quite painful to use.
The external http request are still by far the slowest though, the filesystem caching is required.
To fill my gaps in my intuition and understanding, I started reading another book called "Full frontal calculus" by Seth Braver. It's surprisingly amusing to read, particularly the writing style of the author, where he uses religiuous analogies to describe the divide between limit-based calculus and infinitesimal calculus. It's certainly a refreshing way of explaining as opposed to the a bit overly dry prose from the other calculus book I was reading. I don't suppose to say that this is better pedagogically speaking, but it's certainly more entertaining.
Well, some way or the other, I managed to make the SN mobile friendly-ish, it's now useable at least. The auto-adjusting font-size is pretty maddening though when on mobile. The rem unit is supposed to make the font-size relative to the root font-size, so why is some texts are still changing and appears smaller than the rest?
As it turns out, there's an exception and I have to explicitly set `text-size-adjust: none` to disable this behaviour. Some say this isn't a CSS best practice, but screw that.
This early afternoon, I also made some changes in the backend, fixed and simplified some problematic code that's causing race conditions. I also added an option to cache loaded lua modules, to speed things a little.
Played around with the notebook, I could more or less get apply the division rule with power rule and product rule. Or really, I only ever need sum rule and product rule. But I can see why there are separate rules for each, since it's not always trivial or obvious, even a bit tedious, to get the directive directly from just the sum and product rule.
But, I'm still not comfortable with the syntax. When it says differential of a dependent variable, it's talking about differential of a function, right? Then, it goes around adding functions together, which is essentially a type error. Likely, it's implied and goes without saying that it's the result of the function that's being added together, not the function themselves.
Nope, my entire being rejects this convention. Where's the fully typed math syntax, I want it.
The hecking fuck, nothing's working. What arcane combination of symbols must I arrange to make media queries work on my phone. Sometime it works, but not actually. The documentation and articles made it sound easy, but the sample codes doesn't even work. Then again, maybe it's just my phone's outdated browser.
I give up, doing calculus suddenly seemed way more easier when trying to make mobile responsive frontend.
There, fixed bugs, and looking good. I want to finish on working on the mobile view so I could test it in the phone before the week ends.
Worked on SN, I fixed several bugs. I also found out that using a field mapped by gopher-luar as a table key causes several seconds of lag. I'm not really why is that, but it's a massive wtf. The fix is to cast the ID first to string before using it as an index.
Also another blocker is the mouseover event. It seems that just moving my mouse inside an element causes the mouseout to emit repeatedly.
Aha, nevermind, fixed it. The bug seems to happen when I nest small elem inside a link: | <a><small>...</small></a> Removing the small fixes the bug. Once again, not sure why would that be a bug in the first place.
Oh well, this is one buggy friday.
So the book did actually and directly used product and power rule for the quotient rule. The approach I did was to start with y = uv~ and get the derivative. But then I wondered, what variable is ∆u and ∆v dependent on? The book used the following notation:
| y = uv | y + ∆y = (u + ∆u)(v + ∆v)
If I let u = w~, how would that affect ∆u? Will it be ∆u~?
Once again, I see and hated the implicit handwavy notations that mathematicians use. I tried explicity converting dependent variables to functions, but then I didn't do any better, it's actually more verbose:
let Y(x) = U(x)V(x)
let ∆Y(x, ∆x) = U(x + ∆x)V(x + ∆x) - U(x)V(x)
= [U(x) + U(∆x)][V(x) + V(∆x)] - U(x)V(x)
= (u + ∆u)(v + ∆v) - uv
where
u = U(x)
v = V(x)
∆u = U(∆x)
∆v = V(∆x)
let Y(x) = U(x)V(x)~
let ∆Y(x) = (u + ∆u)(v~ + ∆v~) - uv~Argh, it's really quite difficult for me when it comes to mobile responsiveness. Things like making sure the text size is right, and all the words and spaces wrap properly. I should properly learn how to do this the right way.
For now, it works enough for me on the desktop. Not on the phone though, it's barely useable with a tiny screen.
Aha, I managed to almost copy the exact popup behaviour of 4chan. Well, almost, then I saw literal some edge case that needs fixing. Oh well, but for the most part, it's looking pretty good. I might actually use this custom HN frontend from now on.
I unproductively tried to imitate the post popup on hover feature on 4chan. The popup works fine, except the positioning is quite tricky to get it right.
Well, it's supposed to be covered by power rule and the product rule, but I'll check tomorrow. Anyways, I found stuffs on HN that could also fun to learn: geometric algebra.
This tutorial seems to be readable for me https://mattferraro.dev/posts/geometric-algebra only highschool algebra is required.
I'm getting too distracted again though, the last thing I want to surfacely jump from one subject to another without actually ever learning anything. I wonder at what point I will stop reading the calculus book I'm reading right now. It's actually almost a thousand pages long. I could probably stop right until integral calculus, then maybe come to it later in the future.
I'm still reading the book "calculus: an infinitesimal approach". I'm on page 60, and briefly went over the rules for deriving rational functions. Nothing surprising so far, I can still follow along without problem. I should probably frequently go back to these pages and commit these rules into memory.
My eye twitched a bit on the quotient rule though. Isn't division just multiplication with inverses (a/b = ab^-1)? So there shouldn't be a special rule for this, it's covered by the power rule, right?
I'll check just to be sure.
Urgh, I can't believe I spent almost an hour finding out what's causing the
<i>100%!&(MISSING)lt;/i>
bug. I though encoding/json was escaping %, but no. I thought gopher-lua was doing some weird string escaping, no again. I thought gopher-luar was doing some weird string escaping, nope.
Then I thought of printing the text right before writing the response back. Curl was showing the broken text, but the printed text shows the text properly.
Aha, by process of elimination, the source of bug was the code writing the response back:
fmt.Fprintf(w, ret.String())I tried googling for %!&(MISSING) but it shows me an FBI kidnappings and missing person list, lots of kids too. Uh-oh. Damn, look at all the unresolved cases, some dating back all the way to 2010.
I'm reminded that the world is a scary place, you'll never know what sick fuck is lurking around the corner.
Still mostly worked on making the UI look like *chan forum. I found a bug where some tags wouldn't close and end up like `<i>100%!&(MISSING)lt;/i>`. It doesn't happen with direct curl to HN API, so the problem is most likely my escaping function, or the json parser.
Did some "studying" on my rocketbook with calculus notations. I tried writing it in a lua notation so it would be clear what scope each variable is, and are the dependent variables.
One thing I did realize is that Δx is not locally scoped inside the derivative, and that ε isn't really an independent variable as the book suggests.
So once I again, I will try to start from scratch, and write all the functions and equations:
let ∆x be any infinitesimal
let dx = ∆x
let f: func(x: *R)
let derivative = f => x => st{ [f(x + ∆x) - f(x)]∆x~ }
let differential = f => x => derivative(f)(x) * dx
let x be any infinitesimal
let y = f(x)
let slope = derivative(f)(x)
let dy = differential(f)(x)I found an HN post linking to a page of cool stuffs that applies math with programming. In particular, there's Differential equations and calculus from scratch which is highly relevant to what I'm doing.
https://news.ycombinator.com/item?id=39511714 I should add some /now on my shitty personal site as well. Not sure about /ideas though, I sure don't have shortage of them, but they are mostly dumb or uninteresting.
I've been wondering too if I should submit my site to aboutideasnow.com, kagi or marginalia. I don't really have any interesting content though. Maybe some time in the future.
So I noticed that the posts have non-deterministing sorting. I thought, fuck concurrency, I'll just do it without any goroutines, it'll be one http request at a time.
I tried rewriting it, and the code certainly looked simpler. But, it's so, slow. The heck, I thought it would only be a little bit slower, but no, it's about ten times slower on some HN threads.
I undid the rewrite, and just used a map to sort posts by insert order.
Seeing my changes also takes a couple of seconds, so I added some caching to filesystem too, to prevent execessive requests while testing.
I more or less now have a working basic HN frontend. I think I'll make the UI linear like lainchan/4chan, instead of the usual tree view like reddit and HN. Neovim's lspconfig with gopls is giving me some error though, pretty annoying, not even sure how to fix this.
Wrote some code to handle concurrent http requests. It's never easy to write multi-threaded code, as I'm never sure if there's no deadlock lurking somewhere, or some unexpected race condition will happen. For now, it's working as expected, and it "looks" correct.
I reviewed the notations for derivatives and differentials. I understand it now, but somehow I don't feel all too comfortable with it, maybe it's the concept or the notation. Perhaps I could think of an alternative notation for expressing differentials and derivatives, preferrably something close to a programming language syntax.
Next time I'll be reading the rules for differentiating rational terms. These rules are what are usually taught in schools to be rote memorized I think.
I decided to use the official HN api while creating the frontend first. That way, it's easier to create a compatible backend later on.
Aha, I think I understand now. ∆y/∆x ≈ f'(x) does actually makes sense. I had an imprecise definition of derivative in my head. More precisely, the derivative f'(x) is
f'(x) = st(∆y/∆x)
f'(x) - (∆y/∆x)
= st(∆y/∆x) - ∆y/∆x
= ε
∆y/∆x ≈ f'(x)
∆y/∆x - f'(x) = ε // by definition of infinitesimal
∆y/∆x = f'(x) + ε
∆y = f'(x)∆x + ε∆xI did consider and downloaded other books about infinitesimal calculus, but I didn't find any mention of the increment theorem. It would probably be better if I skim through at least one of them, to further solidify my understanding. In the end the wikipedia page was enough to clear up my understanding. Or maybe, a weekend break, consisting of turning my brain off.
I'll spend more time getting used to the notation shown on page 56, and I'll need to have a very intuitive understanding of increment theorem, because it seems important to gloss over.
Worked on the website using the lua templating. On my filesystem, I tentatively named the project folder as goom-temple, which actually sounds inappropriate since goom jokingly refers something specific for a certain shark fanbase, but it doesn't matter, it's just a temporary name. For brevity, I'll refer to this project as SN (slacker news) for now.
As expected, I haven't done much for today, most of which are scaffolding stuffs for the overall project structure. I also properly configured my neovim lsp this time, both for lua and go.
Okay, I think I am infinitely close to understanding what the heck increment theorem is supposed to mean.
- I have a shitty curve f(x)
- derivative of f(x) is f'(x), which just maps x to a slope
- I can use the slope f'(x) to create a straight ass linear curve l(x)
Then at point [x, f(x)] and another point [x+∆x, f(x+∆x)] The change in y (f(x+∆x) - f(x)) along the f(x) is called "increment of y"?, notated as ∆y The change in y (l(x+∆x) - l(x)) along the l(x) is called "differential of y, notated as dy
The increment theorem says that the distance between ∆y and dy is εΔx, not that it helps why that matters.
Then somewhere in the book says that
∆y/∆x ≈ f'(x) (squiggly equal lines) and
dy/dx = f'(x)Well technically, any number x ≈ x since x-x = 0 + ε, so it could be that both ∆y/∆x ≈ f'(x) and ∆y/∆x = f'(x) is true.
Oh well, I may need to consult an alternative resource for a different explanation. At least for the increment theorem. I understood well what derivative and differential means. I should probably reviews the definitions for infinitesimal as well.
I wiped my most of my rocketbook pages, so I could have more space for weird symbols to scribble on.
There fixed the __tostring problem by using L.CallByParam. I also had to create my own version of dofile since the one provided by gopher-lua doesn't allow setting the chunk name, and seeing chunk name is important when debugging.
I considered using htmz, but since hacker news doesn't have a lot of UI interactivity, it's not needed for this toy project.
I was wondering why I keep getting a nil pointer dereference, as it turns out, I'm closing L.close() before I could even use L. Now my problem is why the __tostring metamethod isn't being called from the go code. I'm currently looking for code examples how to do that, or just examples how to better use the gopher-lua API.
Worked on getting the lua environment to work with gopher-lua. The custom loader solution works fine, now I just to figure out a way to structure the web application. For demostration purposes, I'll just create a simple HN clone.
Oh, I see I what's going on here:
l(x) - b = f'(a)(x - a)
l(x) = f'(a)(x - a) + bWhat I want:
- scoping of variable for each functions
- dependent variables should be clear whose variable it's depending on
- still have the freedom of doing algebraic manipulations (or equational reasoning? as the FP guys say)
lol, I didn't realize my computer crashed, all input was unresponsive, but it was still playing the same tune 3 second tune in a loop. Oddly enough, it still quite catchy, so I didn't notice until I tried moving my mouse.
Anyway, I was on my notebook wondering what the geometric interpretation of negative exponents. n^m makes sense, it just multiplication. But what about n^-m, it's not apparent at first, but it's just equal division. What about n^(m^-1)? n^0.5 is square root, but what does that mean? Isn't that division as well? Maybe unequal division?
As it turns out, I don't really understand the basic, fundamentals of math. But why stop at multiplication and division. Maybe there's a weird arithmetic operator that has useful properties. Base-2 has `xor`, `nand` and other operators.
What if xor and others was generalized to arbitrary base? So instead of bit-wise pairing, on decimal, it would be digit pairing. What properties woud those operator have?
Can I define some weird operators too? Programmers after all do that all the time, well, haskell programmers do at least.
I will set aside these thoughts for now, I have a calculus book to read.
So I decided to try making a web application with go and the lua template. After all, that was the original reason why I made moon-temple: so I could have an alternative templating engine text/template that comes with golang.
I've done some playing around with gopher-lua, and I managed to run html.lua. There's one problem though: I want the binaries self-contained as usual, so I needed to use embed.FS. Naturally, gopher-lua doesn't know how to load files from my embedded filesystem, and skimming through the docs, it appears there's no built-in support for doing that.
The first workaround I tried is to just extract the embedded files into the current directory if they are newer or doesn't exist. But strangely, running Stat() on the embedded files always return a 0 timestamp.
The second workaround I'm considering is writing a custom package.loader for lua. I found an example that I could use. Crazy enough, that example shows how I could even extend lua's syntax!? Imagine I could even go further with my DSL madness AHAHA. Or not, the editor LSP would start cussing at me if I did that. Pretty neat stuffs though.
Right now, I'm wondering if I should do some maintenance work on moon temple. Tasks like refactoring, cleaning up, add do some proper releases, that kind of stuffs.
Or I could start a new project. I want to try html.lua with a golang backend, and webui as the frontend. Then try htmz for general frontend/backend interaction.
Or not, I should invest more time creating stuffs with godot and blender.
This early afternoon, I gave the six younger puppies, and the 2 adult puppies, a bath. Not much else to say about it, except that it's quite tiring to do, so I really should avoid doing it all at once.
There, I finished my shitty youtube UI. Basically, it's just a youtube player but with a countdown timer. The purpose of this is so I could listen to longer youtube videos without draining my phone battery.
I always listen to youtube before going to sleep, it really helps me fall asleep faster, it keeps me from thinking a bunch of things that keep me awake.
I continued reading "calculus: an infinitesimal approach". I'm still following so far, but I don't quite get the increment theorem. For starters, why would ∆y be infinitesimal? If the book is referring to ∆y in the equation
∆y = f(x+∆x) - f(x)Of course, it's actually referring to a different(?) ∆y, the book is saying the ∆y in the equation
∆y = f'(x)∆x + ε∆xWhat I've learned just now:
- tagential line defined as l(x) - b = f'(a)(x - a) which is a line that intersects the point(a,b) with slope f'(a)
- change in y along the curve = f(x + ∆x) - f(x) change in y along the tangent line = f'(a)∆x
- differential of y and differential of x
- the change in y along the tangent line is called the differential of y, and is notated as dy, as opposed to ∆y, which is the changed in y along the curve
- dx and ∆x is the same, but dx is also used for notation consistency it seems
(x + y)~ = x~y~(x~ + y~)~
x + y = xy(x~ + y~)
x00~
(x^2)~ = x~2
x~^2 = x~2
x^(y~)
sqrt(x) = x^0.5 = x^2~
cbrt(x) = x^0.333.. = x^3~
(x^a)x~ = (x^a)(x^-1) = x^(a-1)
(x^a)^b = x^(ab)
(x^a)(x^b) = x^(a+b)
x^(n^-1)
x^(n^m) =? (x^n)^m
x^(2^3) =? (x^2)^3
x^8 =? (xx)^3
x^8 =? xx xx xxOh well, for today's morning, I've thought about why 0~ is undefined. Wikipedia gives me a lot of answers, but for some reason it still doesn't sit right with me. I should continue on with the calculus book, anyway, until I find another equation that seems difficult to solve with exponential notation.
I'll probably want to explore logarithms as well later.
= [(x+y)~ + -x~]y~
= [(x+y)~-x~(x+y + -x)]y~
= (x+y)~-x~yy~
= -(x+y)~x~Here's the list of theorems that I may find useful in my tedious journey of purely using exponential notations:
xy = (x~y~)~
x + y = x(1 + x~y) = y(1 + xy~)
x + y = xy(x~ + y~)
(x + y)~ = x~y~(x~ + y~)~
a(x+y)~ = [a~x+a~y]~I will set aside that thought, and I will continue forth. Uhh, why am I writing like this? I have a bloody headache right now, mostly because of I ran out of coffee, and caffeine withdrawal gives me a really bad headache.
Continuing from last friday, I found about multiplicative inverses conforming to de morgan's law:
xy~ = (x~y)~
x~y = (xy~)~
xy = (x~y~)~
[1/(x+y) - 1/x]/y
= [(x+y)~ - x~]y~
= (x+y)~y~ - x~y~
= [(x+y)y]~ - x~y~
= [xy+yy]~ - x~y~ // how do I go from this...
= ...
= -(x+y)~x~ // to this
(x+y)~ = ~x + ~y
(x+y)~ + -x~
= -y(x+y)~x~
= -(x+y)~x~y
(x+y)~ + x~
= (x+y)~yx~
-------------------------
= (x+y)~ + -x~
= (x+y)~xx~ + -x~(x+y)(x+y)~
= (x+y)~xx~ + -x~(x+y)(x+y)~
= [ xx~ + -x~(x+y) ](x+y)~
= [ x + -(x+y) ](x+y)~x~
= [ x + -x -y) ](x+y)~x~
= -y(x+y)~x~
x + y
= xyy~ + yxx~
= xy(y~ + x~)
x~ + y~
= x~yy~ + y~xx~
= x~(yy~ + y~x)
= x~y~(y + x)
x~ + y
= x~yy~ + yxx~
= yx~(y~ + x)
x + y~
= xyy~ + y~xx~
= y~x(y + x)
x~ + 0~
= x~0~(0 + x)
(x+y)~
= xy(x~ + y~)~
= [x~y~(x~ + y~)]~
= [(x~x~y~ + x~y~y~)]~
= [(x~2y~ + x~y~2)]~
= [(x~2 + x~2)y~]~
= (x~2 + x~2)~y
= (2x~2)~yLet me try again:
(x+y)
= xy(x~ + y~)
(x+y)~
= x~y~(x~ + y~)~
(x+y)~
= x~y~(x~ + y~)~
(x+y)~
= [ xy(x~ + y~) ]~
= [ xyx~ + xyy~ ]~
(x+y)~
= [xy(x~ + y~)]~
= xy(x~ + y~)]
1/(x+y) - 1/x
= (x+y)~ + -x~ // (A)
= (x+y)~xx~ + -x~(x+y)(x+y)~
= (x+y)~xx~ + -x~(x+y)(x+y)~ // common: x~,(x+y)~
= [ xx~ + -x~(x+y) ](x+y)~
= [ x + -(x+y) ](x+y)~x~
= [ x + -x -y) ](x+y)~x~
= -y(x+y)~x~
= -(x+y)~x~y // (B)Welp, this sucks, I feel like I'm going in circles. I should write and separate the equations that are shown to be true first.
I just finished breakfast, which is quite late for a reason. Around hour ago, my husky dog went through a hole in the wall, and was set free in the swampy wilderness. I didn't realize though until I saw two people in the swap yelling to me about our dog attacking their ducklings. I said, that can't be, all of our dogs are in the house. Then I went around and noticed I don't see the big ole furry dog anywhere. Oh fuck, I thought.
I didn't really have any choice though, but to go out and search for my dog. I screencaped a google map and annotated it to make it easier to explain.
- In the image, the husky dog went through a hole on (B) I really don't want to wade through the swamp if possible, so I went through the front gate first (F) - I walked around neighbourhood street first (1) and (2) and didn't see any husky dog - I checked out the aggrived duckling owners, went through their lot (3) and walked through the swampy terrain. I didn't see or hear anything. - At this point, I went back inside and put some long pants and boots, because the swamp likely consists of various nasty household gooey waste, not to mention the possible snakes. - It's hard to see anything because of the really, realy tall grasses, so went to the discontinued road for a better view of the surroundings (4) - Walking through the abandoned road wasn't any easier, but at least it was dry. It had a lot of sharp tall grasses (wild sugarcane I think they are called), so I only tried walking on the edges. (5) - My mother was on a tricycle yelling, searching for me and the dog (C) - While I was on the way to (6), I heard a splash in the swamp, followed by chickens flying. From point (C) looking at point (A), I finally found the the husky dog - I slowly trudged back to point (A), hoping the husky dog didn't run off to somewhere. Thankfully, the husky was still there standing, waiting for chickens to munch on. I put him on a leash, and made our way back to the dry lands. (7) - I saw a dead orange tabby cat (A), which suspiciously looked like our cat, but I'm not sure. I didn't check further though, because the husky might actually try eating it.
And there, it was quite a terrible morning to start a day with, but I'm just glad I found the husky safe. Worse case scenario, my dog went further out, in the neighbouring streets, never to be found again. I admit, I did kind of enjoy walking in the swamps, just the like old days.
Around 18:30, there's was a traffic incident just across the street from my house. A tricycle and a motorcyle crashed into each other. Me and my mother curiously watched from the front gate. It appears no one was seriously injured. There was an ambulance, but I didn't see any stretchers, or anyone gravely injured that needed immediate medical attention. It was for the most part, a nothingburger, for anyone not directly involved in the incident. Maybe. It's hard to see anything from where I stood.
In my whole life, I strangely don't think I've ever seen a serious traffic accident in person, and I say this as someone who used to walk home alongside the highways a lot back in the old days. Or maybe there was, and I just can't remember.
I'm wondering now, why do I need to add the two fractions together before I could simplify it. Isn't there another way? That does sounds like a math trick that I must do without knowing why. That's what I tried before, but I couldn't get any further:
[1/(x+y) - 1/x]/y
= [(x+y)~ - x~]y~
= (x+y)~y~ - x~y~
= [(x+y)y]~ - x~y~
= [xy+yy]~ - x~y~ // how do I go from this...
...
= -(x+y)~x~ // to this
x~ + y~ = (x+y)x~y~
x~ + y~ = [(x+y)~x]~y~
x~ + y~ = [(x+y)~x]~y~ // TODO:
xy~ = (x~y)~ // ooh, this is actually true
x~y = (xy~)~ // woah, this holds as well
xy = (x~y~)~ // this too!?!?
xyz = (x~y~z~)~ // cool, it generalizes to arbitrary number of terms
// actually ~ behaves a like de morgan's law
x~ + y~
= (x + y)/(x*y)
x numerator
-----
y denominatorTo solve `1/x + 1/y`, I just need to make them have the same denominator:
1/x + 1/y
= (1/x)(y/y) + (1/y)(x/x)
= y/xy + x/xy
= (x+y)/xyNow I just need to translate this to exponential notation:
x~ + y~
= x~yy~ + y~xx~
= (yy~ + y~x)x~
= (x+y)x~y~----
Back to the previous problem, I need to simplify `(1/(x+y) - 1/x)/y`:
Simplify the numerator first
1/(x+y) - 1/x
= (x+y)~ + -x~ // (A)
= (x+y)~xx~ + -x~(x+y)(x+y)~
= (x+y)~xx~ + -x~(x+y)(x+y)~ // common: x~,(x+y)~
= [ xx~ + -x~(x+y) ](x+y)~
= [ x + -(x+y) ](x+y)~x~
= [ x + -x -y) ](x+y)~x~
= -y(x+y)~x~ // (B)
(1/(x+y) - 1/x)/y
= [ (x+y)~ + -x~ ]y~ // (A) times y~
= [ -y(x+y)~x~ ]y~ // replaced (A) with (B)
= -(x+y)~x~ // yy~ are inverses, so yy~ = 1
= -1/(x+y)*x----
I'm still not sure if avoiding fractional notation is better, but at least so far I've managed to avoid relying on special rules to do algebraic simplifications. I still don't know how the book was able to get `-1/(x+y)*x`, it just seems "magic" for me. Well actually, looking closer, the book did use the same trick by making both terms use the same denominator. It only just skipped lots of steps in between.
Added some markdown library, so my logs would look well formatted. The markdown library is actually using the older spec, so triple ``` isn't event supported. It's good enough for now, but ideally, I should just avoid markdown and just put longer notes on a separate lua page.
I also gave myself a haircut today. By haircut, I mean I trimmed excess hair so the hair would stop poking my eyes, and I could save some soap and shampoo. Cutting my own hair saved me about $2, and importantly saves me the anxiety of having to go outside. Needless to say, my hair looks like shit, before and after.
But as the saying goes, even stinkiest fart eventually goes away. I'm sure in the whole history of mankind someone said that, surely. I just remembered a certain shark saying "fart in the wind", which is identical in meaning.
I skimmed over the book of abstract algebra last night, I didn't find anything I could use.
Played around more with equations, on paper, vim, and with python/sympy.
What I just realized is that, 1/(x+y) - 1/x can no longer be simplified. The book actually does simplification with (1/(x+y) - 1/x)/y
Second realization is that sympy does not automatically simplify when comparing equality between expressions. I seriously started questioning and doubting myself when it returns false with (a*b)*x == a*x + b*x.
I actually need to do simplify((a*b)*x) == simplify(a*x + b*x)
That said, the furthest simplification I got was
(1/(x+y) - 1/x)/y
= (x+y)^-1*(y^-1) + (-x^-1)*(y^-1)
(1/(x+y) - 1/x)/y
= (x+y)~y~ + -x~y~
(1/(x+y) - 1/x)/y
= (x+y)~y~ + -x~y~
= [(x+y)y]~ + (-xy)~
(1/(x+y) - 1/x)/y
= -1/(x*(x + y))
x~ + y~
= (x + y)/(x*y)
= (x + y)(x*y)~Ultimately, my goal is to show (to myself) that I can do algebraic manipulations without using fractions. It's a hill I'm willing to die on, probably. Or at least, lose a leg.
Aha, I found what I'm looking for:
(ab)^-1 = (a^-1)(b^-1)Now, I'm trying to follow an example of how to get the derivative of 1/x. Once again, whenever I see I fractions, I frequently scratch my head how did the book go from this to that. I should probably learn the basics how to combine fractions together, but I am weirdly fixed on notational purity, so I want to see could I solve this just in terms of exponents.
First, consider the equation:
1/(x+y) - 1/x
= 1/(x+y) + -1/x
= (x+y)^-1 + x^-1
(x+y)^-1 =? (x+y)1^-1
x^n = (x^a)(x^b) where n = a+bNope, it's even more complicated now, I've further strayed away from the light, the opposite of simplifying.
Oh well, I think I'll read the book of abstract algebra first.
Modified the build action so that local links with filename parameters will be included in the build files. I also updated converted the .gif files to mp4, which reduced the overall size from ~100MB to 20MB. Even though I only worked for about an hour or two, I feel like I got a lot of things done. Useless stuffs to be sure, but at least I felt productive. Also, the owl has just finished singing.
Finished the pagination. In my previous site generator, I used query parameters for the page numbers, but this time I used a custom file parameters, such as:
/page[page=1,param=2,xyz=foo].html
This way, the local links will be the same on dev server, and on the html build files. I also discovered that I can lazy load images by doing `<img loading="lazy" ... />.` This should at least reduce page load time and bandwidth usage. It's a nice work-around for not being able to generate thumbnails for the mean time.
I started implementing pagination for the logs page, this is too avoid loading too many images in one page. The ideal, alternative solution would be to generate thumbnails for my screenshots, but for now I want moon-temple to be fully cross-platform without any dependencies, and for that, I can't rely on external image libraries to resize images. It's possible to write a pure lua implementation of png resizing, but that's not going to be an easy task.
Didn't do much this morning, aside from cleaning and walking around. I also spent some time answering a questionnaire for a job assessment. I got an email back this weekend from a job application that I sent months ago, either I completely forgot about or just gave up on it. I'm not expecting much, I don't have strong feelings one way or the other, rejected or not, life carries on as usual.
So I spent about 30 minutes scrolling through bluesky, mostly on discover and video game feeds. Among the hot takes and content shilling, I didn't really see anything of interest, except for some nice drawings I saw. I want to see less of people giving hot takes or promoting their own content, and more people just talking about what they did or create, boring or uninteresting as it may be.
It all comes down to curating my own feed and following the right people. I'm following one person who sort of talks about boring mundane things, and that person is a voice actor learning software engineering. What a weird combination of interest, I don't see that much often. I'll lurk and see what sort of things he create.
Didn't really do much on this weekend, which how it should be. Relax, and don't think about anything, so that when Monday comes in, my mind will be fresh anew.
The week is almost over, but what did I even do this week? Luckily, with notes and screenshots, I should have a fairly good idea of what I did. Let's see... Watch anime, watch vtubers, programming, study, and ad infinitum. Basically routine stuffs I do everyday on my computer.
As to the specifics, I mostly worked on improving moon-temple and adding stuffs on my personal site. And oh yeah, bluesky. It hasn't become a habit to regularly scroll bluesky like I do with HN and reddit. Which is understandable, as I also find it hard to get into twitter-type of content.
I do kind of what to use bluesky more, since it's one way of becoming more social. I should get out of my comfort zone and make it a habit of interacting with people online, and not just lurking. Maybe, that's one step towards getting rid of my social anxiety.
...
I should remind myself that I'm uploading this text onto a public site. I don't think I should be writing down my personal problems here. But if I filter that much thought, what is there left to write? Not that anyone would even bother reading this shit. Although there's always the problem of potential employers sniffing through my possibly inciminating writings. Then again, I'm just being myself, and if being myself is grounds for disqualification, then so be it.
I finally defeated the dragon chicken boss on Ys. It was quite the rush, I barely have any health left, but I managed to defeat the chicken. Has that boss part always been that hard?
I checked out sympy, a computer algebra system in python. sqrt(x)/x does indeed simplify to 1/sqrt(x). ... It took me too long to realize that sqrt(x) is not x^-2, but actually x^0.5
Nah, fuck this shit, I'm undoing all the changes I made today to moon-temple, I just added a bunch of pasta spaghetti monstrosity just to save me save keystrokes when reloading my changes.
On an unrelated note, I think I want to create a mini-simple computer algebra system, like an interactive math equation builder. That way, I'll have more fun manipulating equation with a keyboard. It'll be simple, just a symbolic modifier.
Something like this:
repl:
> expr = createExpression()
> expr // (nothing)
> expr.add(sym.x) // x
> expr.add(sym.x) // x + x
> expr.mul(sym.y) // (x + x)y
> expr.distribute() // xy + xy
> expr.factor(sym.x) // x(y + y)
> expr[1].combine() // x2y
> expr.swap(1,2) // 2yxI've been trying to run a file watcher using neovim lua scripts using like nvim -l script.lua, but nothing is working so far, even the official examples. I'm guessing libuv doesn't work well with -l.
Or not, I should ask reddit or other neovim support channels.
Still reading the neovim docs, I'm looking for function that I can use. I'm thinking of creating a side-by-side table showing comparing lua and vimscript. But then again, I really don't know much vimscript. I guess I could just copy the code snippet from the docs.
Worked on the neovim guide, I didn't get to do much, mostly read the neovim docs. I'm not even sure how I should organize the document, or if this is even worth spending my time on.
I continued reading the calculus book. I got stuck while following an example problem where sqrt(∆x)/∆x = 1/sqrt(∆x) and ∆x is a positive infinitesimal.
I can only get sqrt(∆x)/∆x = ∆x⁻²/∆x = 1/∆x∆x² = 1/∆x³ There's no way x³ = x⁻²
Oh well, maybe just a typographic error, or I'm just dumb. Not important anyway. Moving on.
I'm going drive my humor a little more. Previously I said my pronouns would: he/huh/potato/orc, but that's barely sufficient if I'm aiming to optimal political prowess. Asking my pronouns should be akin to navigating a deeply intricate labrynith of recursive state machines, each pronoun infinitely contingent on a random, ambiguous state. This way, no mortal sentient being could possibly get my pronouns right, ever, under any circumstances. Asking for my pronouns is a guaranteed zero-sum, losing game: the only winning move is not to play (or kicking me in the nuts works too).
... The "joke" isn't as funny as I thought it would be.
I started creating an outline for some guides/tutorial that I'm planning to write. My motativation for this is that writing might help me get a foot in the technical writing. If that fails, I could also try selling the guide on gumroad or something. Worst case scenario is that no one gives a fuck about it, but that doesn't sound too bad since I learned something myself.
Cleaned up my code yesterday. I tried using `loadfile` instead of `dofile` to run page script, so that I could avoid problems with messing up page state when there are concurrent page requests. I reverted my changes though since `require` behaves strangely when inside a loadfile env, the globals couldn't be resolved anymore.
Not a problem I guess. Oh wait, I do think this is definitely not a problem because redbean forks a new subprocess for each page request, so each page request state is isolated.
As usual, I scrolled through HN with my mind on autopilot while sipping coffee. Also, I see bluesky is now open for public. In my own inaccurate description, bluesky is a social network for the purpose of competing and luring existing dissatisfied twitter users.
I don't really use twitter or any social network, but out of curiosity I signed up for bluesky anyway last night on my phone, in the middle of the night.
This morning I scrolled over the "Video game" feeds on bluesky. And... I barely see anything remotely related to video games. For a second, I thought I mistakenly signed up for an esoteric dating site. Of course, the reason for that is because there's an influx of new users coming in, so most of posts are "re-introduction" posts that consists of the following name, pronouns, location, hobbies.
I know when a I see a pronoun preference listed, there's bound to be eggshells scattered everywhere[*]. I've heard of tales where blood filled the streets because a pronoun was mistaken (okay, I made that up). But I will refrain from making any direct remarks with regards to how these people look.
Still, I will note down some (probably wrong) cursory observation. And that is, a lot of those who listed she/her as their pronoun will likely include "gay" in their hobbies/interest, and their strong muscular facial structure indicates a biological male gender. In contrast, people who listed he/him actually look like a normal male person, and not who transcended. My question is, why is that? Or not, I'm too distracted to even make a objective observation. Trying to infer gender based on facial structure is exactly the kind of thing that would pour gasoline over the eggshells, so I don't know why I'm still writing.
Anyways, I noticed some dude listed lemon as his pronoun, and a girl used fae/faer as the pronoun. That's cool, I didn't know you could use any word as a pronoun. Okay, I've decided then, if anyone asks for my pronouns, it would be: he/huh/potato/orc
[*] https://www.collinsdictionary.com/dictionary/english/walk-on-eggshells
What did I even do today...
I played some YS this late morning, I still can't beat the dragon chicken boss though. I was supposed to continue reading that calculus book, but my mother was being (extra) disruptive today, basically telling me to get a job.
This evening I watched some anime while on coffee break usual. Then, I worked on moon-temple to add autoreload when a file has changed. It doesn't look like redbean has built-in filesystem monitoring, probably because there's no easy way of doing cross-platform filesystem monitoring. So I had to resort in creating my own in lua, using polling+stat. It looks very hacky, but surprisingly works just fine.
Autoreload is not even an important, I just feel like doing it.
Neat, github actions is actually pretty handy. I used to commit the generated html files before, but with github actions, the site is automatically rebuilt when I push new commits, and I only need to commit the lua source files.
Yeah, I like this setup. I like the moon-temple too, it's the best static site generator I've made so far. The whole dependency for building the site is a single cross-platform 2MB executable file.
I also like the DSL I've made with lua. It's really expressive, it's inpired by JSX, dare I say, even more so. I like writing code with it.
There, I modified the code for the daily logs page so the screenshots and log content are grouped by day, and by hour for each day. Well, it's a slow day, that's about the only programming I did for today.
I should do a test deploy on github pages and see how it long it loads with a bunch of images in it.
Okay, I finally understood now what differential calculus is. Or at least, I have a high-level intuitive understanding of what it means to differentiate a function. It's not actually a difficult concept, it's just a higher-order function that returns the slope of f at point x with an infinitesimal change ε, to state it loosely and imprecisely.
It's not like I could now compute the derivatives of any function I could find in the wild, but at least I know how it works or what it means, which was my original goal: not to become a mathematician, but to learn how to apply math with programming.
Too lazy to write anything today. I did the minimum physical chores, I didn't give the other 7 adult dogs a bath today, maybe tomorrow. At least, I least I took some screenshots of some of the things I'm watching or playing. It's not like I need to accurately keep track of the time for each things I did, just something I need to give me an idea what I did, or look back on.
Sometimes I do forget to screenshot though or take note of what I'm doing. I wrote a tool before that periodically takes screenshot of my screen, but that it became quickly a chore to sort through the dozens of screenshots.
A better way is just to have a notification that asks me what I'm doing every hour or two.
I gave the six puppies a bath, which took me around two hours to do.
I played oath in felghana for about an hour or two. Not sure if I should even write these down, oh well, I'll see if it becomes a habit, or I'll just quickly get tired of writing inconsequential things down.
I got up from bed around 9:30, I cleaned up a lot of dog poop, then cooked me some omelette. As usual, I browsed HN, reddit and youtube while sipping coffee.
I also modified the screenshot script a little so I could take screenshot of the entire app window, in addition to being able to select a region of the screen.
I've now wrote some code to automatically embed the screenshots on my log page. Look at the disgustingly horrible code. Oh well, it works for now, I'll modify it a month later once it starts running too slow.
Also listening to some ragnarok online BGM. I never got to play the game, but I still remember my highschool buddies talking about it back in the day. I kind of want to play the offline version of the game though. The art style sort of looks like trails in the sky.
Uhh, I just spend almost an hour adding a vim abbreviation to insert the current date time. So I would type cdt in insert mode, and a date gets inserted.
Not exactly what was I planning on doing this early evening of friday...
It's not like I have better things to do though.
I took a nap after my last log, and I just finished watching two anime episodes while drinking coffee.
I got up from my computer around 13:00. So in three hours, I did the following in order:
- walk around
- give husky a bath
- give myself a bath
- eat
- feed the doggies and cats
- clean
I got distracted and looked up how to insert ≈ and ≉ in vim. Vim has default digraph entry for ≈ (ctrl+k ?2), but not ≉. So I made a brief visit to the vim docs to figure out how to add digraphs. I did the following:
:digraph /2 2249
:digraph /2 8777
vim.cmd.digraph("/2", 8777)Math nerds and their silly symbols. And oh yeah, a ≈ b means a is infinitely close to b, or that a -b is an infinitesimal. Otherwise a ≉ b.
I'm currently reading "Elementary calculus: An infinitesimal approach". I've been slowly reading for about an hour each day. But just a random thought, I should make a simple youtube web frontend, so that I could listen to longer videos while I sleep. I want the videos to stop playing automatically after 30 minutes, so it doesn't waste my phone batteries when I'm already deep slumber to listen.
I spent about a 0.5 hour browsing HN and reddit while sipping some coffee and munching on some bananas. I briefly went over the "Who's hiring thread" and scanned for jobs that I might qualify. As usual, most posts are US/EU constrained by time or location. I basically have abysmal chances of getting even an interview, so I'm not even going to bother applying this time.
Okay, now I added some bash script using the scrot tool to easily screenshot my current questionable decisions in life. I just now need to modify the log.page.html page to automatically embed the screenshots I did for each hour.
Also, I didn't realize how much bigger PNG images are compared to JPEG. I know JPEG is a lossy format, but to think how much disk space it saves, the JPEG screenshot I just took is about 1/10 the size of the same PNG image.
Anyway, that's enough coding for the day. My chest is starting to ache a bit from the coffee+adrenaline and sitting for too long.
Following up on my prior disbelief of flying time bananas, I will now make a habit of making a log of what I'm doing. Right now, I'm still working on my personal site/blog. The logs I'm writing here will be automatically added in the site, which reduces the friction of writing some stupid shit.
I'm also digging up my random notes and add it to my crappy site.
I should also add a script to make it easier to add screenshots of what I'm doing.
I was using lua to generate a new page using the redbean runtime, but I noticed the local time returned by os.time() was off by -16 hours. I thought this was just a quirk of lua library (lua does have a lot). But then, I tried it again with the official lua interpreter, and it returns the correct time. This isn't documented anywhere, so I guess it's a redbean bug.
More importantly, I felt like the year was also off by one, it's shows 2024, but it's only 2023 right?
No, it's already 2024. The fuck...?