In response to Popisfizzy
The great river of life flows north.
Been playing around with Pixi.js and DroidScript trying to make some stuff for android. Nothing spectacular so far, but fun to play with.
I took Popisfizzy's advice and split my world map into two: political and geographic. Here is the result:

I've also written a lot more lore on this place: 1cTWY_WwHTdFfnAjKdcPTQfSLEo00TtWx1JMWZaUvjPY/ edit?usp=sharing
In response to Doohl
That's definitely a lot clearer. It looks like you normalized the fonts as well, which Lummox'd brought up.
I'm now here to announce the first ROM-capable build of ClassicVCom HD. In fact, it is the first executable program made for ClassicVCom HD (though it is still incomplete). The link below has been provided before, but it is updated with the ROM.

Link: Test%20Releases/

Try to run it without the ROM and it will now show an error message. Since the ROM is incomplete, a lot of the capabilities are still inside the virtual machine. There is a good possibility I may turn ClassicVDOS into a hard drive install. This also makes it possible to create a working BIOS.
As far as the names go, there's one map in particular that I always use as a what-not-to-do reference. It's basically every blatantly cliche naming convention that's been used in high fantasy.

That's not to say that cliche names or places is a bad thing, but it can certainly help break up the insert-different-name-of-same-fantasy-town-here vibe that I get with way too many fantasy names.
I barely even notice the names of areas in games.

I can name you all Pokemans in the first 2 generations but I can't even tell you 5 town names off the top of my head. Names like "Goldenrod" and "Pallet Town" come to mind instantly but that's about it. I could probably name more but I'd need a few minutes.
In response to Doohl
How'd you go about deciding what the map would look like?
Updated Status on ClassicVCom HD: First stages of mounting virtual hard drives is now supported. Hard drive creation will likely be allowed soon. That way, y'all can create multiple virtual hard drives.

Not only that, virtual disk image creation will be supported. This form of virtual disk image uses a rather basic and very similar header to ClassicVCom HD's Hard Drive specifications (with the exception of no hard drive size limit for disk images). They will work similar to archive files, though without any compression. Compression solutions can be provided for files stored inside of these virtual disk images though considering the nature of the virtual machine.

Like I said before, I might make ClassicVDOS hard drive installable. The command system still works from the C++ code. However, this will change in the future hopefully by a brand new command system based on what was used on various OSes. Think of the system that a BYOND game called "Console" that also used such a system for adding new commands. :P
I've been too busy to do a whole lot of anything lately, largely because of work but also because of some other things. It's been annoying and I've been feeling very unproductive. To mitigate this, I've slowly been working through John M. Lee's Introduction to Topological Manifolds both to get back into doing math stuff and to get a better understanding of topology, and extremely important field and one of the three fields you're supposed to have a good understanding of before you go to grad school (along with abstract algebra and analysis).

While working on the exercises in the book, I ended up working on the proposition below as I thought I would need it to prove one of those exercises. Turns out, it was a lot of work for nought because when I sat down to prove the exercise in earnest, I figured it out within ten minutes not needing this result. Still, it was a couple days well spent thinking about it while I was at work and scribbling stuff down, and the proof itself is pretty nice I think. So I'm gonna ~~~share~~~ it, because sharing is caring, and explain all the terminology. Proposition first, and then I'll explain everything, though I'm going to assume there's at least some familiarity with what things like sets are. If you have any questions, go ahead and ask.

Proposition. Let A be a non-empty and possibly infinite set. Let LR+ be indexed by A. Let SM—where (M, d) is a metric space—be defined as S = ∪αA Brα(c) for some cM. Then S = BsupL(c).

Now for the plain English version (with some simplification): Imagine you're drawing a bunch of circles centered at the same point, and considering all the stuff inside the circle, not considering the edge as being part of it. Intuitively, all of those circles should be inside the largest one. This is pretty simple to see if you have finitely many circles, but what if there are infinitely many circles? And what if their radii are (just choosing some arbitrary example) L = {1/2, 3/4, 7/8, 15/16, 31/32, ...}? Then things become a little more complicated.

The first two sentences are what allow for the possibility of the radii being finite or infinite. A is what's called an indexing set, and basically it says that for every αA (read as "for every alpha in A") there is exactly one corresponding rαL (generally read as "exactly one corresponding r-sub-alpha in L). If A is finite, then L is finite; if it's infinite, then so is L, whether A is as infinite as the natural numbers or as infinite as the real numbers.

L is also a subset of R+, the positive real numbers (and this is what LR+ means). Thus, we don't have to worry about awkward notions of negative or zero radii, only radii that are strictly positive.

Next, S (the set we're concerned with) is a subset of some larger set M. The notation "(M, d)" means that the set M together with another mathematical object d is a metric space, which is an important mathematical concept. The object d is a binary function from M to the non-negative real numbers (denoted R≥0) called a metric—binary meaning that it takes two arguments. If x, y, zM are arbitrary (meaning that we don't pick x, y, or z in any particular manner), then d is a metric if it has the four following properties:

  1. d(x, y) ≥ 0. That is, the distance between two objects in M is always positive or 0.
  2. d(x, y) = 0 if and only if x = y. That is, the distance between two objects is 0 when they are the same object and only when they are the same object.
  3. d(x, y) = d(y, x). That is, the distance from x to y is the same as the distance from y to x.
  4. d(x, y) + d(y, z) ≥ d(x, z). This is the triangle inequality, and basically states that "detours should not be shortcuts". That is, if I go from x to y and then from y to z, it should not be a shorter path than if I go from x directly to z.

These generalize what we intuitively think of when we talk about notions of "distance" between two objects (though some particular metrics are weird and unintuitive, even though they satisfy the above criteria). Most people are familiar with, at the very least, the Euclidean metric: d(x, y) = √(x - y)2. Metric spaces are important because they tell us what it means to talk about distance, and give a lot of structure to an otherwise-structureless set.

Once we're able to consider distances, we are then able to talk about open balls. Go ahead and laugh now, since non-math people love to laugh at that terminology.

Done? Okay, moving on.

An open ball is basically what I mean by saying "everything inside the circle without the circle itself": it's the set of all points less than a certain distance away from a central point. More formally, the notion Br(c) for a positive real number r and a center point cM is define as: Br(c) := {pM : d(p, c) < r} ("the set of all points p in M such that the distance between p and the center point c is less than r"). A sort of analogy is that if you have a basketball, from a mathematical viewpoint the ball is gonna be the air inside but not the rubber and leather at the edge of it. This notion is often quite useful, even though the distinction probably doesn't seem very important to a non-mathematician.

And now we can move on to the definition of what this set S that we talked about five or so paragraphs ago is. Remember that S is a subset of M (SM). Specifically, it's defined as the union of every open ball of a given radius rαL with an arbitrary center point cM. That is, using the notation from the statement of the proposition: S = ∪αA Brα(c) ("S is the union of all open balls of radius rα centered at c for every αA").

To make it clear, this is what the proposition assumes that S is defined as. So far, I have not yet covered the thing that we're actually trying to prove. Mathematical notion and terminology is very dense.

So, what I'm actually trying to prove is that, given all the preceding things, is that assuming S is defined as above, then S = BsupL(c). That is, S is just an open ball centered at c with a radius equal to supL. A simple notion (assuming you were able to follow all the preceding paragraphs), except that we just have to explain what supL is. Quite plainly, supL (in this case) captures the idea of the "largest circle" from the plain English statement of the proposition. In particular, supL is the supremum of the set L. Supremums are sort of like a slight generalization of the notion of a maximum element. For example, let's say you have some set T = {1, 2, 3, 4, 5}. The maximum element in T is simply the largest element in T: maxT = 5. If, for a given set, the maximum element exists, then the supremum is equal to it. Thus, supT = 5.

But, there are some sets without a maximum. Recall the example choice of L from earlier? L = {1/2, 3/4, 7/8, 15/16, 31/32, ...}. This is an infinite set, whose elements are all numbers (2n - 1)/2n for all positive natural numbers (i.e., n = 1, 2, 3, 4, 5, ...). This set has infinitely many elements, but with two important properties:

  1. For any element of the set, there is another element larger than it.
  2. No element of the set is greater than or equal to 1.

This first property clearly shows it can't have a maximum: there is no element in the list that is larger than every other element. But, the second property is suggestive. Clearly, 1 is an upper bound on the set: every element in the set is less than 1. But, there are infinitely many upper bounds: 37, 149, π, 6/5, and so forth. 1 is special, though: it is the least upper bound. No other upper bound is smaller than 1, meaning that if you choose any number smaller than 1, you'll find an element in the set larger than that element. The supremum is exactly this: the least upper bound. Thus, for our example choice of L we have that supL = 1.

An extremely important property of the real numbers is that every set of real numbers with an upper bound has a supremum (a property called Dedekind completeness).

So, by saying that S = BsupL(c), we're basically saying that in the way we defined S (as the union of those particular open balls), we can show that S is actually just the open ball with the smallest radius possible so that it's still at least as larger as anything in the open ball. While this sounds obvious, actually proving it is another matter.

We're basically ready to move on to trying to prove this. All that we need is the following: for consistency's sake, I will define B(c) = M for any cM. Basically, an 'infinitely large' open ball in any metric space is just going to be every point in the metric space (i.e., the space itself).

With that, we can begin!

Proof. I shall break the proof into two parts. First, I'll assume that L is unbounded, and then I'll assume that L is bounded (I'll explain these notions in the relevant portion). For any subset of the real numbers (which L is), the set is either bounded or unbounded. Thus, we can consider these two disjoint cases on their own, and the assumptions are valid.

First, let us assume that L is unbounded. That is, the elements of L get 'arbitrarily large' (e.g., L = {1, 2, 3, 4, 5, ...} is unbounded). Formally, this means that for any arbitrary ρR ("any arbitrary rho in the real numbers") there exists some αA such that ρ < rα, where rαL. In plainer language: pick any number, and I can find a larger one in L.

Let pM be arbitrary. Because we can pick ρ to be any number, we can also pick ρ = d(p, c). From the definition of d, it is a real number and so a valid choice. But, by assumption we know that L is unbounded meaning that there is some rαL with ρ = d(p, c) < rα, and so p is in some open ball that was contained in S and therefore pS. Because p can be any point in M, this result must be true of all points in M, and so all points of M are in S, which is to say that MS. But, we know from the proposition that SM. If two sets are subsets of one another, we say they are equal and thus S = M.

Next, when a set is unbounded we say that its supremum is infinite, and therefore supL = ∞. But this means that S = M = B(c) = BsupL(c), that is S = BsupL(c), as we were to show. Thus, the result holds when L is unbounded.

Now, assume that L is bounded. Then, as stated before, supL must exist. Let us consider some set Σ = BsupL(c). Because it's true for every pS that d(p, c) < supL, then it must be that pΣ. That is, SΣ.

Let us now assume that there is some qΣ such that qS. That is, we assume that S and Σ are, in fact, different. Then we know that for every αA, the inequality rαd(p, c) < supL must hold.

It is at this point we will use an equivalent definition of supremum to make some progress. Earlier, I mentioned that the supremum is the number such that if you choose any number smaller than it, you'll find a number in the set larger than the number you chose. There's a way to make this notion precise, and it is as follows: For every positive number ε (that is, every ε > 0) there exists some rαL such that supL - rα < ε. In plain English: pick any positive number, no matter how small, and I can find a number in L closer to supL than the number you chose. This definition is equivalent to the one that I mentioned earlier, about the supremum being the smallest upper bound (equivalent here meaning that if you assume one is true, you can prove the other and vice-versa).

Thus, not only is the above inequality satisfied (rαd(p, c) < supL) but it is also satisfied that for every ε > 0 there exists some βA with supL - rβ < ε. Because we can choose ε to be any positive real number, we can also make a particular choice: let ε = supL - d(p, c), recalling that p is the point we assume is in the set Σ but not in S. Because we know that d(p, c) < supL, supL - d(p, c) > 0 and is then a valid choice. We then require that for every βA that supL - rβ < ε = supL - d(p, c) ⇒ -rβ < -d(p, c) ⇒ rβ > d(p, c).

Thus, for every βA we have that rβ > d(p, c). But, from the previous inequality we also had that rαd(p, c) for every αA, including the particular choice of α = β. This is a contradiction! Going back, every step we made was logically justified, until we reach the step where we assume that p exists, that is where we assume that there is some element in Σ that is not in S. Therefore, this step must be false, and it must actually be the case that S = Σ, but Σ = BsupL(c) and therefore we have that S = BsupL(c) and the result holds when L is bounded.

Thus, we have that for any indexed set of positive real numbers L, S = BsupL(c), as was to be shown. ∎

And there you have it, a proof of the proposition! Even though I ended up not needing the proof, I feel it was a very nice proof and wanted to share. If any of you are mathematically-inclined or simply curious, here is a "homework" problem of a point I sort of glossed over in the proof. See if you can work out why it's true:

  • I stated that the inequality rαd(p, c) < supL must hold. Why?

If anyone has any questions, I'll do my best to answer them.
I seem to be the only one who really uses this thread. Oh well.

For the past several weeks, I've swung back into worldbuilding with full force. I quit my last job because it was stressful and filled with bullshit, and tinkering away with my world is always something that can keep me occupied for long stretches.

One big focus I've had lately on this round of worldbuilding is expanding articles and giving them some real content, rather than just being (to use Wikipedia's terminology) stubs that I plan on expanding in full later. There's still quite a lot of those. Some are simply because I haven't expanded them with all the details from my notes, while others are because they are really just in need of a little focus because my notes and plans for them are fairly slim.

The first article I'd focused on expanding was the timeline of the Heartland—the Heartland being the region (as well as culture, nation, and empire) that my focus has been on. It covers a period of about 3,000 years. If I want to be extremely specific, based on current assumptions that will likely later be revised, it covers a period of 3,028 years and a few months. The most detailed portion is a period of around 410 years from c. PFK 400 up until c. FK 133, covering several important periods in the region.
  • The Occupation Period, when the Heartland (or at least some portions of it) were under control by the Empire of the Far Jungles, the first major power in the larger region (the Southeastern Interior) following the Cataclysm. They rolled in c. PFK 400 and lorded around for about 110 years before they fell into civil war in their homeland and collapsed.
  • The Warring Kingdoms Period, which followed the sudden collapse of EFJ power structures in the Heartland, especially their military power. Dozens of warlords sprung in the chaos, carving out their own pieces of the Heartland to rule. Feudal-like structures developed to cope with the inability of these new kingdoms to effectively centralize power and authority. This was a very violent period in the Heartland's history, and only calmed down as larger kingdoms absorbed smaller ones and borders began to stabilize, at least to some extent.
  • The Period of the First Kingdom, which occurred when the Kingdom of the Lower Cólþạrc succeeded in conquering the Heartland in full. These campaigns lasted for decades, supported by Kingdom being the most prosperous in the region.
  • The Civil War of the First Kingdom, which initially began as a rebellion lead by the eastern nobility.
  • The Second Kingdom, during which the absolute monarchy of the First Kingdom was thrown out in the wake of the civil war, and in its place was put an elective monarchy, where the nobility had oversight and authority.
  • The Early Imperial Period. Strictly speaking, the Second Kingdom and the Empire were the same government, but over time the system of government evolved to meet the needs of a growing empire, giving good reason to distinguish the two.

Expanding the timeline was a good choice, in my opinion, as it provides many seeds to work and expand from. I do think, though, I need to revise the timeline a bit; it feels that some periods are rushed relative to all the events that take place in them. While a bit annoying, lots of worldbuilding is revising, revising, revising.

The next article I expanded on was one of a very different flavor, prompted by asking someone simply to pick what article I should focus on. They ended up choosing ant-crustaceans. Ant-crustaceans are a clade of animals that are agriculturally and economically important, as they're raised in many regions with plenty of access to water (along lakes, rivers, and shorelines mainly) for their eggs, honey-jam, larvae, meat, and carapaces. Though their exact appearance varies depending on the species and subspecies, in general they have a lobster-like appearance, but with a eusocial structure dominated by a king.

The article I'm working on right now is one the Old Heartland Religion, a religion practiced in the Heartland for nearly a thousand years. It experienced serious decline over time, and for the last 500 years or so of its existence, it was only practiced in very remote villages or by a very small minority of practitioners elsewhere, a sharp contrast to its height where it was the primary religion and practiced by nearly all the Heartland's denizens to some extent. It was polytheistic, animistic, and had a great deal of ancestor worship. In most areas, the main focus was on the Luþojëmíx, or Great Spirits/Great Gods/High Gods, who held authority over all other spirits and deities. The religion lost dominance over time to the New Heartland Religion, a significantly-revised form of the practice introduced by Teša Aqīre, a philosopher and prophet born in the homeland of the Empire of the Far Jungles, and popularized by his sons.

Those were the big projects I've done, though there's been numerous other small projects in the interim, done on-and-off while I took a break from the big ones. For example, I've been working on other language stuff (as I love to do). Most recently, I have been working the Vasilic language, which is a working name. This language was spoken prior to the Cataclysm (a major historical catastrophe in my setting), and is the ancestor of a number of languages in the region. Right now, I have three sentences I worked up just to figure out some grammar details.
  • Luähifroën ilhaşe àrre Muçoke. meaning, "We (strongly/vigorously) profess the truths of the High God." This sentence is actually an anachronism. It's an abbreviation of the Oath of Belief, and affiliated with the New Heartland Religion. This would not come about until nearly 1,700 years after the Cataclysm.
  • Àmmehipall etl saërre pińculh? meaning, "Have you eaten (some food)?"
  • Şeŕ àmmeyenarr. meaning, "The boy is eating."

So, yeah, been keeping myself busy.
In response to Popisfizzy
Popisfizzy wrote:
I quit my last job because it was stressful and filled with bullshit,

If you're talking about the job that required you to cut your hair, I mean, I could've told you that job was going to be bullshit. That was red flag #1.
In response to EmpirezTeam
Yes, but I was also in dire need of money and it was the only job offer I had.
Been a while since I participated in this thread. If I have anything to talk about, it's my virtual machine again. Been working on plans for new system calls.
Learning UE4, Blender, and material construction. Gifs really dont work well for this, but...
Looks very nice Flick. I only have some basic grasps of UE4 and Blender myself.
In response to Bandock
Bandock wrote:
Looks very nice Flick.

You could say he's a... hexcellent game developer!

How long have you dabbled in the Unreals, gramps?
In response to EmpirezTeam
EmpirezTeam wrote:
You could say he's a... hexcellent game developer!
About a week a few months ago and about a week now. Its interesting. I kind of like the blueprint stuff. Makes my code look nice even if its a mess :P
The blueprint system is definitely awesome. Heck, that sort of system is starting to get more common in games that support modding. Space Engineers being one recent example.

If I ever work on a UE4 game, I would definitely use C++ and blueprints together (since the former can provide support for the latter). I was supposed to be working on a game with someone who used to be on BYOND, but haven't done anything yet (due to like being caught up on my own projects).
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