Jex

Hope I didn't come across as rudely shutting you down—it's not so much that I didn't want to continue the discussion; it's just that it seemed off topic for this thread and I was afraid we were annoying the other participants. If you want to continue the mathematical discussions, I'd be fine with doing so in the Alastor's Skull Inn forum, since that seems to be the more anything-goes, off-topic forum; I just was uncomfortable doing it here and derailing the thread. And speaking of not derailing the thread, I guess I should post something relevant here now, except that I'm still new enough to RuneQuest that I don't really know that I have any dumb theories interesting enough to be worth sharing yet, or rather that I probably do but I don't know enough to realize how dumb they are. But I'm almost done reading through the Guide to Glorantha, and I'm learning, and I'm sure soon I'll have no shortage of really stupid theories.

Apologies if I'm misunderstanding the question and this isn't helpful, but in case you weren't aware, the adventure "Defending Apple Lane" in the Adventure Book included with the RuneQuest Gamemaster Screen Pack involves an attack by a band of Tusk Riders, and has full statistics for all eight Tusk Riders and their mounts. It's not a squad sheet, but if you just need some Tusk Rider stat blocks, you can yoink those for use in your own adventure. There's also some advice about the Tusk Riders' combat tactics, though those are tailored to the specific scenario and may not be as useful for you.

So, I'd originally posted about this in the Alastor's Inn forum, but as @g33k pointed out, I probably should have just made the post here. (I didn't do that initially because in some other forums necroing old posts/subfora is strongly discouraged, but apparently that's not the case here... sorry.) Anyway, I was wondering if there existed anywhere an archive of the information about the SharedWorld? Some of the information is available in this forum, but browsing the forum posts I get the impression that there's a lot of additional information that was only in a now-defunct wiki... and while the overall page on the SharedWorld setting is available on the Wayback Machine, it seems the subpages with further details are not. Did anyone keep an archive of the SharedWorld information, or know if there's another place it can be found? (@Trifletraxor, you seem to have been the main driver of the project, so I'm assuming you'd be the most likely to know about such a thing?) It seems like quite a bit of thought and work went into this, and it would be a pity if the whole thing was lost forever with the old wiki. [EDIT: Guess it might be a good idea to also ping @Atgxtg, since it looks like you were also involved with the SharedWorld project and you've been active on the forum more recently than Trifletraxor...]

Apologies; I didn't post there because there had been no posts there in over a decade, and in a lot of forums it's considered very bad etiquette (or even explicitly against forum rules) to resurrect old threads or subfora. It does seem, though, that that sort of thing isn't frowned upon here as it is elsewhere; had I realized that at the time, I agree that that would have been the better place for my post. Sorry about that.

@Scotty: Oh, I think I just ran across one more. Currently reading the section on Umathela, and there's a description of a port city called Gargulla, but I couldn't find any city by that name on the map, either in the Guide to Glorantha or in the Argan Argar Atlas. There's a city called Govgulla on the Jarasan Gulf, but that's a different city with its own separate description in the Guide. There's also a Garguna in Fonrit, but, again, that's a different city. I can't find any city on the map called Gargulla. Apparently I'm not the first person to notice its absence; a web search turned up a relevant post from a few years ago, but with no apparent followup or resolution. Seems like an interesting city, with its own Gnostic-flavored sect of Malkionism, and it would be nice to know where it is. (Also, FWIW, since the topic of this thread seems to have broadened, I changed the thread title; hope that's okay.)

Oh, wait, one more, though this one's maybe a bit more obscure. The entry for Hornilio says that the goblin Queendom is "a few hundred miles south along the coast from the Cliff of the Agankar Wind", but there's no other mention of the Cliff of the Agankar Wind and I couldn't find any indication of its location. (For that matter, a few hundred miles is a long way, and it would be nice to get a more specific location for the goblin Queendom—though of course that's not really important since it's not a place many PCs are ever likely to be going.)

Oh, wow, thanks! To be completely honest, I wasn't necessarily expecting to be told the exact location; I would have settled for getting confirmation that it wasn't there and that I hadn't just missed it. But of course actually finding out the location is much better! Oh, I did find more entries that were missing from the maps, but I didn't ask about those because I'd either found them in other sources or found a post by someone else asking about them that confirmed they weren't on the map. But if you want to know about them for the Q&A page, let me try to remember... As I said in a previous post, Manelarpanan in Kothar isn't labeled in the Guide, though it is labeled in the Argan Argar Atlas. The section on Fonrit describes Benestros, but it doesn't appear to be labeled on the map. (I found a forum post speculating that it was synonymous with or included within Gargosganda, which seems plausible but doesn't seem to be confirmed.) The cannibal island of Motumobabi in the East Isles does not appear to be labeled on the map. In the section of Maniria, Troll Mountain and the Haunted Fields are not labeled on the map. I did find an older source that showed they were next to Ice Peak, but this isn't clear just from the Guide. (Granted, the description of Ice Peak does mention "a nearby troll stronghold", and it's reasonable to guess that might refer to Troll Mountain, and certainly it makes sense for a troll hunting ground to be near the troll stronghold too, but the Guide doesn't explicitly say so. As a matter of fact, until I found the older source confirming their location, I'd guessed that Troll Mountain and Haunted Fields might have been in that area, but dismissed that idea because I thought it was unlikely that the Haunted Fields would be so near the Temple of Peace, but it turns out they were there after all.) Those are the ones I remember off the top of my head, but there might have been more. If I remember any others, I'll let you know.

How are you "cutting" the shape without removing points? If there's a discontinuity in the shape, which there must be if you can't pass from one side to the other without leaving it, then there are missing points. In everyday colloquial language, "infinitesimal" might be used to just mean very small, but in mathematics it has a more precise meaning. "Infinitesimal" literally means infinitely small. Sure, there's no problem with two different shapes having a boundary in common. Two shapes can share some of the same points. You can have two different shapes overlap each other as much as you want. But a shape can't meaningfully overlap itself—a shape can't share points with itself; a point is either in the shape or it's not. There's no meaningful sense in which a shape can share a boundary with itself and still include the boundary. You can't just draw a line through the middle of a shape and declare that it's included in the shape but also a boundary. That doesn't mean anything. Sure, you can just declare by fiat that the red circle can't pass through that line, but in that case you're not changing anything about the shape itself; you're just setting rules about what the red circle can do. Note that a shape doesn't have to include its boundary. A square that includes its boundary and a square that excludes its boundary are both validly defined shapes, but they're different shapes. (For that matter, there's no reason a shape can't include only part of its boundary, though that's not particularly relevant here.) So if you want that line partway through C to be a boundary, well, is it included in the shape or not? If not, then the points on that line are in A but not in C, and the two shapes don't have the same points. If it is, then shape C is continuous across it and there's nothing special about that line, so in what sense is it a boundary? Well, sure, if you just want to write a nonsensical argument between intoxicated gods, then mission accomplished, I guess. [EDITED TO ADD: Look, I seriously would rather not keep getting into mathematical discussions in this thread; I feel like we're really derailing the thread and probably annoying its other participants. (Yes, I know I could just not reply, but I keep feeling compelled to respond against my better judgment due to Somebody Is Wrong On The Internet syndrome.) Some of the points you bring up touch on some fairly deep mathematics, and I don't want to discourage your interest, but if you really want to discuss these things, might I suggest you take it to somewhere like math.stackexchange.com? That's a site all about discussing mathematical questions, and you may find people there who have a lot more experience explaining these things and may be able to give better explanations than I do.]

Oh, heck, we're back to math again. Are you trying to get a contradiction out of the idea that a plane figure is defined by the points it contains? Because it seems unlikely that you're going to successfully undermine the foundations of geometry. In this case, the problem with your argument is that A and C clearly do not contain exactly the same points. You've removed a line segment from the middle, so the points on that line segment are in A but not in C. Yes, the line segment is infinitely thin, and doesn't affect the area; A and C do have the same area. But they don't have all the same points, and so they aren't the same shape. It may seem counterintuitive that removing an infinitely thin line of points can make a meaningful difference, but it does. (Again, there's a lot in math that's counterintuitive.) Even removing a single point from a shape makes it a different shape. Again, it doesn't change the area, and it may not seem like a single infinitesimal point should make any difference, but a plane with a single point missing and a fully intact plane have some very different properties. (Among other things, one is an open set and one is a closed set. I'm not going to go into exactly what that means, but it's a mathematically significant distinction.) [EDIT: Oops, more accurately, one is an open set, and the other is both open and closed.]

Whoops, yes, you're right, of course; I meant Tarien, not Kothar. Got the sides of Pamaltela mixed up. Still, though, yeah, I couldn't find it on the map and couldn't find any information about it online so I was wondering if anyone knew where it was or if it hadn't been specified. (I think the reason I had Kothar on the mind was that there had been a different location in Kothar I couldn't find in the maps in the Guide to Glorantha: Manelarpanan. But in that case I checked the Argan Argar Atlas, and it turned out that while for some reason Manelarpanan wasn't labeled in the maps in the Guide, it was marked in the Atlas. But I checked the Argan Argar Atlas for Lath Eskan, and no luck.)

So, I'm in the process of reading through the Guide to Glorantha from cover to cover. It's been slow going, because as I read the entry for each site I've been trying to find it on the map, and that's not always easy particularly for the sections, like Fronela and Fonrit, that cover large areas split over multiple maps, and it sometimes takes time to find the location. A few times I was unable to find a site on a map, but in each case a web search turned up a post by someone else asking about the site in question, and it turned out that either (a) the location was specified in an older book, or (b) at least there was confirmation that its location wasn't specified on the map and I hadn't missed it. But now I just finished the section on Kothar, and there's a site that's got me stumped. I can't find Lath Eskan on the map, and this time a web search didn't help. All the Guide to Glorantha says about the site is "This oasis is where Pamalt broke the mask of Trickster and freed him from his own worst trick." So it's apparently somewhere in Kothar, but Kothar is a big place, and it doesn't seem to be on the map; I was wondering if anyone has any idea where it was (or, conversely, could set my mind at rest by confirming that its exact location hasn't been established). I suppose this isn't really particularly important, given that I don't anticipate running or writing an adventure set in Kothar any time soon, but I'm trying to learn as much as I can about Glorantha, and it bothers me a bit not to know where something is, though again it'd bother me considerably less to have confirmation and know for sure that its location isn't defined and that I haven't just missed it.

Originally I'd tacked this on to the end of my post about the ruins by the Stream, out of reluctance to start two separate threads so close together, but it was unrelated enough I figured I probably should make a separate thread for this question after all. Anyway, I know that in the events of the Lismelder campaign, the Lismelder King Thanos of Swordvale died in 1616, and was succeeded by the Poss chieftain Harvald the Hairy (who would later be devoured in the Dragonrise and succeeded by the Greydog Branduan Greatblade). However, I haven't found any information about how King Thanos died. Was that something that was established? It's not terribly important, but I'd like to mention his cause of death in the Lismelder King List in the Marshedge project I'm working on.

So, I'm still working on my Marshedge adventure and gazetteer, and I've started making maps of both the Lismelder territory and the Marshedge clan territory specifically. I want to include a brief description of each location on the maps, similar to the descriptions of the locations near Jonstown in the Starter Set. However, there are two ruins near the Lismelder lands that appear on several maps but that I can't find any descriptions of anywhere. I've circled them below on an excerpt from a map from the Starter Set: Does anyone know if there's any information anywhere about these two ruins? If not, of course, I have no problem with making something up myself, but I wanted to check first to see if there's already been something established about them that I shouldn't contradict.

Oh, I figured that, but I figured I may as well explain it anyway in case anyone was interested. No, while it's true that there is a radius that can be drawn through any point on the circle, that wasn't the main point; that was just a step in the proof. The point was that it can be proven that adding together the rotated lines gets you all the points in the filled circle. It's not something you have to "swallow"; it's something that's mathematically provably true even if it's counterintuitive. (There are a lot of things in math that are counterintuitive but true.) As for adding up all the points getting you the area... well, yes, if something includes all the points in a filled-in circle, then it includes that filled-in circle; a shape by definition is the sum of all the points in it. Every finite (or infinite!) shape is made up of infinitely many (dimensionless) points; it's routine in geometry to define a shape by specifying the points in it. For instance, a disk—a filled-in circle—can be defined by the formula x²+y²≤r². But what that formula is really defining directly is the points in the disk—it's saying that every point (x, y) that satisfies the inequality is included in the disk. That infinitely many zero-area points can make up a shape with finite (or infinite) area is kind of fundamental to geometry. But anyway, I feel like I've kind of been hijacking this thread to ramble about math; sorry. Unless there are any related questions anyone really wants to know the answer to, I'll shut up now and let people get back to dumb theories about Glorantha. [EDIT: Okay, I said I'd shut up, but I just thought of another explanation that may help... or may just make things worse; I don't know. Anyway, I think the crux of the issue here is that when we're asking what's the area of infinitely many dimensionless points, we're multiplying zero times infinity. Now, zero times any finite number is zero; infinity times any finite (nonzero) number is infinity. So what's zero times infinity? It's undefined. It doesn't have a unique value—at least without more context. Zero times infinity isn't necessarily zero, or infinity; depending on exactly how you get the zero and the infinity, it can be zero, or it can be infinity... or it can be one, or fifteen, or π. So how could you get a value for zero times infinity in a given situation? Well, one way is to use limits. You let one value get larger and larger, and one get smaller and smaller, in such a way that the bigger the one value gets, and the smaller the other value gets, their product gets closer and closer to a given value. And that's one way we can define area! We can approximate the area of an object by covering it in squares. For the purposes of this argument, let's take for granted that we know the area of a square of side length L is L². So okay, let's take a circle of radius 2, and we'll take a bunch of squares of side length 1 and use them to cover it. Each square has an area of 1, and it takes 16 squares to completely cover the circle. So the total area of the squares is 16 times 1, or just 16. But of course this overstates the area of the circle, because some of the squares extend beyond the edge. We can come closer using smaller squares. Let's use squares of side length 1/2, so the area of each square is 1/4. Now it takes 60 squares to cover the circle, so their total area is 60 times 1/4, or 15. Of course, there are still a few squares that extend beyond the edges, so this is still an overestimate. What if we make the squares even smaller? Let's use squares of side length 1/4, so the area of each square is 1/16. Hm, now it takes 224 squares, so the squares' total area is 224 * 1/16 = 14. But there are still some squares overlapping the edge. As we use smaller and smaller squares, the area of each square gets smaller and smaller—tending toward zero—but the number of squares we need gets larger and larger—tending toward infinity. But if we look at their total area, while it does decrease the more squares we use (because we're lowering the amount that extends outside the circle), it doesn't decrease at the same rate; the rate of decrease gets smaller and smaller, as the total area of the squares—the area of each square times the number of squares—approaches a particular value that it never drops below no matter how small the squares get. Specifically, in this case, it approaches 4π, or about 12.56637... We can take this to be the limit of the sequence as the area of each square approaches zero, and as the number of squares approaches infinity—and we can take this limit to be the area of the circle. (In fact, one very common way to find the area of a shape, integration in two dimensions, essentially is doing just this, finding the limit as the shape is divided into infinitely many infinitesimal bits.) Now, if at the limit the squares have zero width and zero area, what's the difference between a zero-area square and a point? We've effectively just divided the circle into infinitely many points, and in this case their total area—infinity times zero, the infinity of the number of points times the zero area of each point—came out to 4π. But of course while that value holds for that circle, if we used the same procedure for other shapes with different areas we'd get different limiting values. So, like I said, infinity times zero can be... pretty much anything. But, in particular, it certainly isn't necessarily zero. The TLDR takeaway here is just that infinity is really weird, and doesn't always behave how you'd expect, and infinity times zero is especially weird. And now I really will shut up unless there's some mathematical question someone really wants addressed.]

You can't put together finitely many zero-area line segments to get something with nonzero area, but you can do it with infinitely many zero-area line segments. Infinities are weird, and things can happen at infinity that are qualitatively different from what happens with any finite number, no matter how big. (Here's one way to think of this: So, we're looking at a disk of radius D/2, centered on point O. Pick any point P on that disk (besides the center). There is a line segment of length D/2 centered at point O that passes through that point. (How do we know this? Because two points determine a line, so we know there's a unique line passing through those points, and we can just chop out the length we need. That line segment is at some angle from the x axis, and it's not too hard to show that it's the only line segment (of length D/2 centered at point O) at that angle from the x axis. So as we rotate the line segment 360 degrees, it must pass through point P. Since point P was an arbitrary point on the disk, that means this is true of every point on the disk. (Well, we did specify that point P wasn't the center—that was to assure the uniqueness criterion—but of course all the line segments pass through the center.) So since the line segments pass through every point on the disk, if you put together all the rotated segments you do indeed get the full, filled-in disk. In fact, not only can you get a nonzero area from adding together infinitely many zero-area line segments, you can even get an infinite area. The entire plane can be composed from infinitely many lines.) That's not an "antifractal"; that's just a (kind of) regular fractal—in fact, that's one kind of fractal I had in mind. For some famous fractals that work this way, see Cantor dust or the Sierpiński gasket. (Those fractals of course don't meet the Kakeya/Besicovitch criteria, but they're examples of fractals that work subtractively.)