As you may know, I’m now participating in compulsory slave labour for the country. If you didn’t, now you know. I don’t like the experience there.

Let’s see. I’m not supposed to talk about what goes on in there. Oh wait, I’m not even supposed to divulge that I’m not supposed to talk about what goes on in there. In other words, no :blogging: about that shit. How boring, except I don’t really have much to say about that.

Recently (okay, this news is rather outdated now because of my permanent temporary chronic acute blogging hiatus), Katawa Shoujo was released. Despite the obviously Japanese name, it’s a visual novel / dating sim made by weeaboos, where the premise is that the protagonist goes to a school for disabled people.

That’s pretty much exactly like where I’m at in the slave labour camp. Except there’s a significant proportion of aspies which don’t exist in Katawa Shoujo, and there are only males. How utterly boring.

THIS BLOG POST BROUGHT TO YOU BY TEN INTERRUPTIONS OVER THE SPAN OF TIME I TRIED TO WRITE IT. I HATE EVERYBODY I LIVE WITH.

I’d like to point out a certain flaw about the word “want” as used in common speech. At the very basic level you have the “I want to do this because it makes me happy” kind of “want”. That’s a “want” I believe everybody can consider a real “want”. The ambiguity comes in at somewhat more complex types of “want”s, like a “doing this lets me not suffer” kind of “want”. It’s debatable whether that counts as a “need” or a “want”. And then you have a “doing this makes me suffer now but is better in the long run” kind of “want”. Is that a “want”? A “need”?

And then, by necessity any action that has already been done was “wanted”, even if they’re now undesirable (with new information, or simply bipolarity). If it weren’t wanted, that means there wasn’t a “want” to do the action, ergo the action would not have been done.

You have varying levels of “want”. There’s a “I want this, but only if I don’t have to pay for it”, and then there’s an attachment to the amount to pay (“I want this, only if I have to pay less than “), and the next step up is “I want this and I’ll use whatever I can to get it”. Note that what’s being paid might not necessarily be money, but other things human subjects attach value to (those with sentimental value, for example). And while the latter two “want”s are quite clearly true “want”s in the layman (read: inexact) definition of “want”, they’d fall under the third type of “want” in the second paragraph. Which is highly debatable.

Anyway back to main topic which is ranting about my life and why I hate everything (except you, I love you guys (maximum homo if you’re male, maximum hetero if you’re female)).

Ever since I learnt of the concept of not consuming dinner at the dining table, I’ve had a habit of taking my bowl to wherever else to consume the stuff inside the bowl (which I hesitate to call food at times). Or well, not so much a habit as something I had the capability of doing and actually did. The “adults” I live with (I realise I can’t use that to refer to everybody else anymore because I’m legal now, but screw that) seem to have a pretty gigantic issue with that though, especially recently. Well yes of course I can’t tell them I’m busy putting subtitles on Japanese cartoons (illegally, even) and expect them to be fine with it, but it’s not like I take my bowl off to my room every day.

Heck, I don’t think I’ve even been doing that the past few days before today.

I’ve had plans to an hero for some time already (months, at least, don’t remember exactly how long) but kept procrastinating. I think I’m still undecided over how I’ll proceed with this. Ideally I’d want a pain-free method since I’m really pain-averse, but I guess there aren’t alternatives for things like this.

I had some coffee about an hour ago. It did not have much effect. It’s not really keeping me awake or making me feel sleepy. It’s just… like that. Nothing.

And then on a whim I just decided to bust out my notepad/notebook (these things are actually pretty handy even though I never bother flipping back and reading past pages because my thoughts are always highly context-dependent and there’s just about no way to figure out what I’m writing unless I pen down everything that’s conspiring around me when I write) and work on that no loop problem. Remember from 2009 when I said I made a program (HTML+JS, but still!) to check if a given configuration had loops? Yeah, I still have that. On my previous laptop. Which I haven’t touched in more than a year. Screw that. Also programming is boring. Anyway. I managed to work out huge portions of what I’ve worked out before (just to confirm, because mistakes are possible, and also because I lost much of the work I had before).

A brief (re)introduction to the no loop problem would be in order. Given a graph, of all the induced subgraphs that are forests, determine the order of the largest such subgraph (and also the number of vertices “removed”, the “no-loop number”, which is more of interest due to the way the problem was originally stated). Of particular interest are square grid graphs, because they’re easy to work with (and were also part of the original problem formulation). I did a short write-up (short by my own standards, which would be “extremely short” by just about anybody else’s) about this applied to hypercube graphs, but I didn’t get far because of bugs in code which left results unreliable. (I could probably redo the code, but it’s :effort: and I’m too uninspired to do anything requiring thinking.)

Q₂: 1 removed (trivial)
Q₃: 3 removed (almost trivial)
Q₄: 6 removed
Q₅: between 12 and 14, inclusive (14 assuming the program was correct)
for : no results beyond what’s trivially implied by the above (lower bound of , or assuming the program was correct), although intuitively (and very roughly) speaking an upper bound of seems possible to prove easily. Think removing vertices by parity, then plugging back vertices where possible. Not sure how far a greedy algorithm would go with this. These bounds aren’t very tight though, which sucks. (Also lol suddenly TeX.)

Now back to square grids. (“back to” would be inappropriate here actually since I didn’t even begin with that, but whatever. Deciphering this blog’s content is part of the fun of reading it, no? >implying reading this blog is fun) Because they’re great fun. I wonder how many hours I’ve spent working on them by hand. The trivial result that a 1×1 board (oh yeah, we’ll also ignore treating the grid as a graph), or slightly more generally board requires no squares removed is kind of useless. The next step up is 2×2, which happens to be , and it’s pretty obvious that the NLN (hooray abbreviations) for this is 1, since the whole graph is a cycle. It’s not hard to extend this further, to give the result that the NLN for boards is .

That illustrates the usefulness of a lemma I omitted earlier because it was kinda obvious. For any two disjoint subgraphs of a graph, the NLN of the larger graph is at least the sum of the NLNs of the subgraphs. This readily generalises to more than two disjoint subgraphs. In the square lattice case, it allows splitting grids into smaller grids to easily obtain lower bounds.

Moving on to larger boards, we’ll skip first, and proceed to . If is even, by splitting the grid into 2×2 blocks, a lower bound of is obtained; otherwise is odd, and a lower bound of is obtained. There exists a 4×2 grid that tiles horizontally (assuming height-by-width notation like matrices (contrast the more sane and commonly used width-by-height notation used about everywhere else)) with two squares removed, leading to an upper bound of for even ; for odd half of the tile can be appended to the right end of a , with a total of squares removed, and an upper bound of . It’s effectively solved for even now, but odd still needs more work, and it’s going to be even more awkward trying to type out a proof without diagrams, but I’m too lazy to pull up diagrams, so you’ll have to trust me on this: the NLN for a grid is , regardless of parity.

As a side note I used to have a bunch of text files with nicely ASCII art illustrated proofs (for with , 5×5, 6×6, 7×7, and maybe more) hosted somewhere which is (un)fortunately no longer accessible. Oh, a complete list of all 4-removed 4×4 grids too (40 of them, 6 not counting symmetric equivalents, iirc). They’re also all on the old laptop, which is no longer accessible either. Sometimes it’s just unhelpable.

Now going back to , which is going to be easier. If is less than 4 you can easily work the NLNs out (0, 1 and 2 for respectively). That, combined with the knowledge that , leads to the lower bound , which also happens to be tight because of the existence of a 3×4 horizontal tile (“horizontal tile” meaning that it tiles horizontally, not that it is landscape, which it incidentally happens to be) with 3 squares removed, and some other things.

Now is about the right time to introduce the concept of removal density: the ratio of the number of squares removed to the total number of squares in a grid. In the above examples, for all had removal density 1/4 in the limit of . This doesn’t hold when , since (proof omitted) and . The asymptotic removal density for can be shown to be 5/18 with some effort, but the asymptotic removal density for is as yet uncertain, bounded by 19/70 (from ) and 11/40 (from existence of a 5×8 tile with 11 removed). I’m guessing that , which would conclusively answer this as 11/40, but unfortunately there’s no obvious way to prove this short of a massive brute force-like approach. I don’t feel like doing that now (hint hint read the second paragraph of this post). 11/40. Larger seem completely out-of-reach for now.

As for general upper bounds, as , the best I managed to come up with is still 1/3. It’s kind of frustrating; two of the three methods I have of covering with 1/3 removal density seem to leave few gaps, and are generally hard to improve on. (The third method is a 2×3 tile, which sucks compared to the other two because it doesn’t exploit the finiteness of ; they’re all asymptotically equivalent (in terms of density).)

Anyway, enough of pointless exposition. I know nobody’s going to read that. Not even myself. Number dump, because that’s marginally more useful. (If I do fail with my planned an heroism, these numbers are likely to be more useful than pointless exposition.)

for various values of :
5: 6
6: 8
7: 9
8: 10
9: 11 (assuming I didn’t make any wrong assumptions, the only two 5×9 grids with 11 squares removed are mirrors of each other)
10: 13
11: 14
12: 16
13: 17
14: 19
15: 20
16: 21-22 22
17: 22
18: 24
19: 25
20: 27
21: 28
22: 29-30 30
23: 30-31 31
24: 32-33 33
25: 33
26: 35
27: 36
28: 38
29: 39
30: 40-41 41

Update: After some fiddling with numbers. Only applies if , if that’s not the case, then well, the numbers are above. If or mod 8, , otherwise \rfloor.

if ; in particular, . Density is clearly 5/18 here; a similar upper bound for the density can be derived for even , but how tight it is for is unsure because the amount of effort required to prove shit grows exponentially with both and , making overall effort growth rate superexponential.

for small (because extending this is much effort):
2: 3
3: 5
4: 7
5: 9
6: 11
7: 13 (notice a pattern here?)
8: 14-15 15
9: 16-17 17
10: 18-19
:

Density is clearly bounded between 13/49 17/63 and 2/7. This one is more frustrating because it’s guaranteed that the density will never hit 2/7, but a way of removing squares with lower asymptotic density has not been found (and probably doesn’t exist).

On to …

2: 4
3: 6
4: 8
5: 10
6: 13
7: 14-15 15
8: 18 (not verified recently, but it better be correct)
9: 19-21
10: 22
11: 24-25
12: 26-27

And squares ( meaning , of course):

1²: 0
2²: 1
3²: 2
4²: 4
5²: 6
6²: 10
7²: 13
8²: 18
9²: 22
10²: 27-28 (old blog says it’s definitely 28, haven’t verified because I recall it being much effort)
11²: 32-34
12²: 40-42
13²: 45-49
14²: 54-58
15²: 62-67
16²: 72-76

The upper bounds for 10² onwards appear to be the best I can get. It doesn’t seem trivial to lower them (if that’s even possible). On the other hand the lower bounds can be considered to be “trivial” since they’re all derived from smaller rectangular boards directly. (That’s also true of all the lower bounds listed above.) It’s possible and not hard to brute force through all 4×4 4-removed grids, but the larger grids tend to have a lot of solutions.

Previously, previously. (I would search for more links but WordPress.com is seriously lagging for me.)

I recently torrented TAOCP (feeling guilt, will buy the book another time), just for volume 2 actually, because Seminumerical Algorithms. Which contains a chapter on pseudorandom number generators. It’s fairly interesting, but the age of the book precludes inclusion of more recent (but still rather dated) algorithms like ISAAC, but I’m pretty fine with just studying about simpler RNGs (by which I actually mean PRNG, but that’s an extra letter) if that means I get more solid (instead of empirical) results.

Summarising from the book, a sequence can be defined as random if every string of every length appears with the same probability. Hold on, this sounds just like the definition of normality… yeah. There’s actually a hardly-known RNG that uses the digits of a proven-to-be-normal-in-binary number, with the seed being where the digit reading starts. But there are simpler normal numbers. Considering for now just normality in base 2, a binary analogue of the Champernowne constant, could theoretically function as a perfect random number generator, but the obvious flaw is obvious:

The seed is essentially the random number itself. In other words, this is effectively like using a very large random number table. Sure, it’s random, but only asymptotically; it’s impossible to have a uniform distribution over the nonnegative integers, so there’ll inherently be some bias, and therefore predictability given sufficiently many digits of output, by autocorrelating and stuff.

(Last edited on February 24, 2011 at 2:08 pm. DRAFT QUEUE CLEARING.)

I currently can’t be arsed to find the old post, and I don’t really remember what’s in it because it’s been so damn long since I wrote it, so I’ll just go by memory. Currently, if you’re trying to log in to a web site you’ll have to give the web site your password. HTTPS provides authentication and encryption, so there isn’t much problem, until you realise that many sites also require your email address to sign up, and if you’re a lazy piece of shit you’ll probably be using the same password for both accounts, and the site you just signed up for can use that password to access your email.

Of course, being lazy, you want to use the same password everywhere, or something to that effect. What do you do? One way is to keep a file with proper cryptographically random passwords, and encrypt that with your favourite insecure password. Programs exist that do this for you. It’s still a suboptimal solution though, because you have to keep that file. It’s kind of like the issue I have with Bitcoins. Generally I don’t bother with backups (hurr durr), but these are actually worth something more valuable than my time. Also, those crypto-random passwords are completely unrelated to the master password, so if you lose the file somehow you lose everything.

Currently passwords are usually stored salted and hashed on the server (note: depending on how not-retarded the person coding the server is, this may or may not be the case)

(Last edited on July 19, 2011 at 12:10 pm. DRAFT QUEUE CLEARING.)

I find it pretty ridiculous. Archive Team, of all people, suggesting plain text, and PNG and SVG on the same page? Along with Ogg (presumably Vorbis) and AVI? I call bullshit. Plain text is an understandable choice, because even if a file was sent to an alien civilisation, with reference to real written/printed text, it’s very possible (and not hard) to decipher it using frequency analysis. (Assuming English, of course.) As for pictures, Windows bitmap and PNM look like the best candidates, for obvious reasons; these are again easily reverse engineered. (Well, BMP not so much because of all the random headers, but generally they’re unimportant.)

Now, Gzip (and compression formats in general) is something that cannot be reverse engineered easily. How many compression formats are in common use today? There’s Gzip, Bzip2, Zip, 7z, Xz, RAR and maybe a bunch of slightly more niche formats. There’s no way to define the “best” one to use for everything: Gzip has low encode/decode requirements, but isn’t supported by default on Windows (lol). Bzip2 compresses well, but isn’t supported on Windows either. Xz has even better compression, but again isn’t supported on Windows, not to mention Xz is actually pretty niche and apart from a certain free software distributor (lolgnu) nobody ever seems to use it. Zip is supported almost everywhere, and is kind of the de facto standard, except that this standard magically evolves over time. Support for encryption and non-Deflate compression algorithms (including Wavpack, even) were just added in relatively recently. 7z is… well, some people use it. As for RAR, lolderp.

The only time-proof compression format is to have none at all. This is feasible for text, pictures and audio, but video… that’s hard. One hour of 24 fps 1920×1080 4:2:0 8-bit video already takes up ~75 MB per second, or ~268 GB per hour.

(Last edited on September 9, 2011 at 8:53 pm. DRAFT QUEUE CLEARING. Also this post is at least partially factually inaccurate, iirc, which was the reason I didn’t finish it.)

It’s not too uncommon to encounter a situation where multiple people are trying to use a resource that can only be used by at most one person at any time, and normally different people will hog the resource for a differing amounts of times (but assume it’s constant regardless of whatever position in the queue they’re in). Now suppose how pissed off (because everyone wants to be first) a person is roughly proportional to the ratio of the waiting time to the execution time, and you want to minimise the overall pissed-off-ness of everybody. (Theoretically, optimising this would be roughly equivalent to having the wait:execution ratio the same for everybody.)

First-come-first-serve is the general strategy used in real life. It also sucks. Without a context regarding the order, this isn’t any different from a random ordering.

Another one that comes to mind is to just sort, and have people with faster tasks be earlier in the queue. This unfortunately leads to a problem where if more people with fast tasks join the queue as the resource is being used, the slowest task never gets done. It also violates the

(Last edited on September 17, 2011 at 1:45 am. DRAFT QUEUE CLEARING. I also have no idea how I was going to finish that sentence.)

Chrome’s is somewhat derpy. The way downloads are initiated is stupid, to begin with, and while that’s not technically part of the download manager, it affects the downloading process, so I shall describe it. Apparently, what Chrome does is if it encounters something with an unknown type (using MIME, presumably), it’ll treat that file as something to be downloaded, and automatically download it unless you change some setting. It’s dumb, because this can also happen when a server running PHP momentarily derps up and doesn’t set the MIME type or something, leaving the browser to extrapolate type information from the extension (which for the purposes of this example is assumed to be “.php”). And then it leads to magical clutter of the downloads folder with random HTML files with a .php extension that seemingly came out of nowhere, from the point of view of the user. Of course, that’s not the only cause; generally, random server derps can cause Chrome to download all sorts of things. And I believe it should even be possible for a (malicious) server to force Chrome to download random junk, with the only indication being the download bar at the bottom (which is pretty obvious, unless such an attack uses small files that download quickly, but that wouldn’t do much harm).

Now on to the actual download manager. Like the rest of the main Chrome interface, it’s rather minimalistic. But it’s an actual manager in the sense that it can handle more than one download in the same interface. And it even allows pausing and resuming downloads (depending on whether the server allows it, of course)! Yeah, but that’s all there is to it. Now, if you try to cancel a partial download, it’ll delete the file. It makes sense, given that Chrome is retarded enough to automatically download everything. With Firefox this is different, but wait for that.

If I remember correctly the last time Firefox’s download manager interface changed significantly was from the 2.0 → 3.0 transition. (And that was a long time ago.) Unlike Chrome, Firefox’s download manager goes in a separate window.

And then at this point I got sufficiently distracted while writing this post. To be continued. (Posting it publicly first to prevent it from getting stuck in the draft queue (23 posts and counting) forever.)

(Last edited on October 9, 2011 at 2:06 am. DRAFT QUEUE CLEARING.)

Anyway, just going to rant about something (else).

Gigantic TV screens are a dumb idea. For that matter, I also hate the standard 16:9 aspect ratio. It’s unnecessarily complicated; while 9 and 16 are both nice square numbers, the ratio deviates too much from being square, or even √2. (Lol HTML sqrt tags, haven’t done those in a while.) I don’t see any benefits to using 16:9 (in landscape) over 8:5 (also known as 16:10 by people too stupid to divide by two).

(Last edited on October 26, 2011 at 7:47 pm. DRAFT QUEUE CLEARING.)

Web browsers shipped with operating systems should never have plugins enabled by default. Especially with badly written plugins. Okay, it’s 2011 already, and all browsers worth their shit have some form of plugin sandboxing. That’s fine and all, but it doesn’t really limit the damage plugins can do. You know, shit like nuking the home directory. To my knowledge most Gnome-based Linux distros ship with a certain retarded media player also known as Totem. Totem is shit, partly because it made by Gnome devs. And also partly because Gstreamer is shit. Seriously, why do people even use Gstreamer? FFmpeg Libav is a much better library to use; you lose extensibility, but that’s only important for people who care about trivial shit like using an MP3 decoder legally. And somewhat less trivial shit like separating the working and non-working decoders… except, why would you even be using a non-working decoder? Anyway, Gstreamer sucks and so does Totem. And Totem comes with a plugin (NPAPI, I believe) that’s by extension also shit and likely a security risk just for existing. I also find no use in having a media player extension embedded into the browser when its interface is that horrible. You know, these guys are the same people who think that pressing the left and right arrow keys should seek in different amounts. You can’t trust them to make a sane UI. Even Firefox’s internal video player has a better interface (except it uses pixmaps instead of vector graphics and doesn’t scale, durr). Then there’s also the more common (on Windows) Java, Flash, Adobe Reader, etc. plugins… let’s just say they don’t really have a good reputation for being secure.

Of course, plebs exist. The same kind of people who would install fifty different antivirus programs, all running in the background simultaneously, along with twenty toolbars in IE, wonder why their computer is running slow, and install even more antivirus programs. Honestly, these people shouldn’t be touching computers. My Firefox/Minefield/Nightly UI has been minimalistic ever since about 2009, and some people just cannot resist ricing their UIs, but it’s just so ugly. It’s understandable to have toolbars installed if they provide useful functionality. But they usually don’t. The same probably applies to IE, except its UI is already ugly and so it can’t be helped. Actually that explains a lot. IE users have no sense of aesthetic.

And about people touching computers. I really don’t like how everybody’s trying to make UIs more intuitive. Naively, this seems like a good idea. Unfortunately the only thing I’ve seen coming out of this is people refusing to learn more about how computers work, which leads to retardation everywhere. You might claim I’m being elitist, and I’m not going to deny that. The way users are treating computers as black boxes that do what they want to do is disturbing. A lack of knowledge about software/hardware workings also harm advocacy movements, such as the free software movement. Yeah, four years on and I still believe in that crap. But it’s almost funny how Stallman’s whining about the evils proprietary software can inflict have somehow managed to come true, even though back then people just thought he was exaggerating.