coppro
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Well, its time for me to post my ramblings about the DROD canon here, so here goes a theory that might actuall explain part of the Eighth's very strange physics, not to mention how the Fegundo actually makes it to the center of the sun without bumping into 14 other mating Fegundos.

Here goes:

As we all know, the Eighth as a world is in fact one-eighth of a pie (a circular shape). When drawn on maps, it looks like one-eighth of a circle. The Eighth exists eight times, each right next to each other, forming a complete circle. An untrained observer may think that the Eighth is a cone, because traveling off one side deposits you right at the same point on the other side, but actually the effect is caused by one merely traveling into a "different" Eighth, while 7 other yous do the same thing, resulting in one per Eighth. Now, I think the big question we've all been asking is "Why?".

I beleive I have come up with a solution that follows the standard rules of physics, but plays with many a variable that could result in some of these occurances. The most simple thing to remember is that while the Eighth is a completely different universe, there must be a way of traveling between them, so they clearly have some sort of similar laws to us. Strange to us, but the idea of a spherical planet would almost definitely seem foreign to Beethro and Halph.

Now, I shall start by laying forth the idea of quantum superposition, a quirk in physics that allows a particle to display two different values for the same property at the same time, most notably position. This has been proven using the infamous double-slit experiment, where light is shone through two slits in a sheet, and the resulting shadow is banded due to the interference cause by the photons. When single photons are fired one by one, the pattern still occurs, leading to the only possible conclusion that the photons are interfering with themselves. However, on a larger scale, this effect does not occur. One theory is that observing a particle causes it to settle into one state, but that is not logical. Another theory states that the gravity of the particles forces settlement, which, due to Occam's Razor, seems much more likely.

Now, what does this have to do with the Eighth? You see, the most likely explanation for the eight copies is in fact quantum superposition. But how can that occur? With gravity settling the particles into singular states, how can octuples of everything exist in the Eighth? The answer is simple. The Eighth lacks lateral gravity. The Eighth evidently has vertical and radial gravity, but lacks gravity that would hold particles around the circles. In addition, this explains the Fegundo's behavior: the mating ritual is clearly a method of artificially inducing a gravity well, settling the multiple Fegundoes into one long enough for the Fegundo to explode over the edge (which is a completely different phenomenon in and of itself).


Now we see what Erik has to say, but I still like my theory because it displays the quirks that the Eighth possess, while allowing my scientific brain to properly sort things out. Although, if anyone can provide a better explanation, please do so.

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[Last edited by coppro at 07-06-2006 04:56 AM]

Chaco
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It's Eighth or eight, not Eigth.

Anyway, sorry to hijack your thread, but I have another duplication-related scenario that also needs evaluation:

Say that Branthro Budkin has been working out for years. He's a very strong man, able to lift his own weight and a little more.

If the eight Branthros go to the North axis, grab each others' legs, and all lift upwards, would they form a circular elevator around the North axis?

Ahem. Having read your essay now, your points seem valid. Clarification would be good.

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[Last edited by Chaco at 07-05-2006 10:09 PM]

ErikH2000
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Chaco wrote:
If the eight Branthros go to the North axis, grab each others' legs, and all lift upwards, would they form a circular elevator around the North axis?

I've tried lifting myself before, but with only limited success. No matter which way I push or pull, it seems parts of my body are attached in such a way that the effort is defeated. The best I've been able to accomplish was the time I propelled myself up onto the kitchen counter. I claimed it was a form of levitation, but Brittany said it looked more like I just jumped off the ground about 6 inches. She's wrong--it was at least 11 inches of self-powered vertical movement. And then I got bread crumbs and sugar-free boisenberry jam all over a new shirt. So I don't recommend it.

I think Branthro would have a similar problems. Of course, he sounds a lot stronger than me, so maybe not.

-Erik

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ErikH2000
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coppro wrote:
Now we see what Erik has to say, but I still like my theory because it displays the quirks that the Eighth possess, while allowing my scientific brain to properly sort things out. Although, if anyone can provide a better explanation, please do so.

You have to find Agaricus and check this stuff with him. He's got a much better handle on the Eighth physics than I do. At first glance, I would say your explanation is not nearly complicated enough because I myself can almost understand it.

-Erik

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coppro
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ErikH2000 wrote:

coppro wrote:
Now we see what Erik has to say, but I still like my theory because it displays the quirks that the Eighth possess, while allowing my scientific brain to properly sort things out. Although, if anyone can provide a better explanation, please do so.

You have to find Agaricus and check this stuff with him. He's got a much better handle on the Eighth physics than I do. At first glance, I would say your explanation is not nearly complicated enough because I myself can almost understand it.

-Erik

It's quite complicated because it implies the following: the Eighth has four dimensions: vertical, lateral, radial, and time. Each follows its own laws. This alone makes the physics extremely complicated and difficult to deal with. The best part is that it doesn't explain the radial explosion/implosion, thus making it a perfectly viable reason as to why the eighth works that way. And I haven't seen Agaricus in a while, and is he the official physics guy, or just the unofficial official physics guy?

gamer_extreme_101
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I think he's generally just the "Guy who knows more about the Eighth than anyone else dare tries". Seriously, you ask that guy a question about the Eighth, and he'll either give you an answer or logically formate an answer that fits in with everything else.

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coppro
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Aah. But, as I said, he's not around anymore.

That said, how come he gets to make up the physics while we have to listen to illogical explanations from mike rimer (it's his fault I cannot think of puppies without thinking of ketchup (on an unrelated note, I lost The Game))?

gamer_extreme_101
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Yeah, he isn't around anymore. It's truely sad, but I think that it has something to do with his Cambridge University acceptance post a while back.

As for that, I can't help you there - my DROD history isn't as deeply rooted as Erik or Wesley's.

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silver
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"canon" - you say that a lot. I do not think that word means what you think it means.

It's "an attempt to explain the physics of the Eighth" when you post it. Or maybe it's "a story set in the Eighth" or somesuch.

It's "canon" when Erik blesses it and makes it "canonical". He is the author, and it's his world, ergo he decides what is official.

Minus your mis-assertion that you were writing canon (when I believe you meant something "potentially canonical, if Erik likes it"), I enjoyed your post. Keep at it.



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coppro
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Well, since Erik just told me that he's the guy to talk to, I think that makes it canon, as long as it remains consistent with everything said so far.

gamer_extreme_101
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coppro wrote:
...as long as it remains consistent with everything said so far.

Not just consistent, but flawlessly consistent!

If I hadn't said it, someone else would have.

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Chaco
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gamer_extreme_101 wrote:

coppro wrote:
...as long as it remains consistent with everything said so far.

Not just consistent, but flawlessly consistent!

Really? I always thought it was supposed to be flawlessly consistant!

EDIT:

Bah, you're right. A quick spell-check in the dictionary proved it. flawlessly consistent! it is then.

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[Last edited by Chaco at 07-06-2006 04:50 PM]

ErikH2000
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coppro wrote:
Well, since Erik just told me that he's the guy to talk to, I think that makes it canon, as long as it remains consistent with everything said so far.

Nope. Despite the coolness of your description, it's not part of canon. It has neither been accepted nor rejected.

Practically speaking, the only way to get something into the canon is to make it part of the story used in an official release, i.e. DROD: The City Beneath or one of the Smitemaster's Selections. I want the canon to serve the releases and not visa-versa. Plus there's just not enough time to review everything. I've actually got 4 pieces that Patrick sent me that have been waiting months for a thumbs up.

Wesley (Agaricus5) isn't really an official Eighth physics guy. I just joke about him doing something like that because he was really deep into explaining the Eighth ideas I came up with at one point. It is too bad he's busy with school or something. I miss having him around.

-Erik

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Syntax
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For what it's worth, Agaricus5 taught me a lot of goblin manip skills. Unfortunately I never got to know him well, but I have the utmost respect for a player such as him who can somehow put structure in chaos. As such, I'm certain his views of the Eighth physics were sound, and although not canonical, certainly physically viable. I've certainly missed him.

Chard
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This is all very interesting. Incidentally I'm pretty new to the forums in general so bear with me if I make any terrible mistakes. Anyway I have some questions/ideas which might be worth attention. I'm coming from a fairly solid background in mathematics and the actaul topology (that's maths speak for "shape and then some") of the Eighth is what's interesting me here. Anyway,

It was asserted that the Eighth has four dimensions:
1) Time isn't really that interesting here as it would seem by all accounts to behave as we would expect.
2) The lateral dimension is the most interesting one, it is finite, of course, indeed we can measure how broad the Eighth is but there is a twist, that the closer to the "point" you are, the narrower it becomes. Is it possible therefore to actually reach this "point"? There are examples of spaces which exhibit the opposite, ie. that as you approach a certain "pole" which is not actually part of your space, the space itself is somehow "denser" and you will never actually reach said "pole".
3) The radial dimension also raises questions (apart from the above ones) in that the Eighth has an "edge". What is at this edge? Can you throw stones over it? Is there in fact an infinite expanse of void?
4) Finally the vertical dimension. Again, how far does it go? Is it infinite? In both directions?

Now for my topology bit. I've read what I can regarding the Eighth and I can picture in my mind what the world should look like if I were in it and it would have various nice properties that bizarrer topologies would lack. It can for example exhibit properties such as distances and angles, and almost anywhere I stand the bit of it around me looks just like a pit of a plane (as in a flat sheet, not the big metal tubes with wings).

But despite my mental picture there is a nagging issue. I will imagine the Eighth in the most natural way I can, ie. that it's a big piece of pie in empty space. Thus any dimensional convolution like the questions above reduce to a simple change of cordinate system (in this case 3-dimensional cartesian to 2-dimensional radial and 1-dimensional cartesian). But there is no reason for it to be anything like so simple.

I suppose what I'd like to know is (perhaps just because I haven't been able to find it) how much of this has been settled? How much of that is set in stone?

Okay, no more essays, over to someone else now.

Mattcrampy
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Chard wrote:
2) The lateral dimension is the most interesting one, it is finite, of course, indeed we can measure how broad the Eighth is but there is a twist, that the closer to the "point" you are, the narrower it becomes. Is it possible therefore to actually reach this "point"? There are examples of spaces which exhibit the opposite, ie. that as you approach a certain "pole" which is not actually part of your space, the space itself is somehow "denser" and you will never actually reach said "pole".

A good question, but I'm guessing from the canon that we have (that the sun moves vertically, centered on the pole) either it has special rules or that the space near the pole is as dense as anywhere else on the Eighth.

3) The radial dimension also raises questions (apart from the above ones) in that the Eighth has an "edge". What is at this edge? Can you throw stones over it? Is there in fact an infinite expanse of void?

Nope: it has an edge, but it's somewhat hard to determine what that edge is experimentally as when anything crosses it, it comes out on the other side. This gives the Eighth an appearance from the air as a disc that repeats eight times. (I believe Clayton's made an image of what that looks like.)

Everything else, I believe, hasn't been settled. Erik has been reluctant to talk about the vertical dimension because it's considered spoilers, and I don't recall how much discussion there's been regarding the coordinate system or how dense the Eighth is at the edges (although high amounts of oxygen would probably help explain the Zealot's Plague), or even if an explorer moving towards the pole stays a constant size.

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MartianInvader
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Chard-

I think the point you've missed is that the world wraps around in both non-vertical directions. Not only can you go around the sides, but if you go off the "round" edge in the south, you get compressed to a point at the north, and if you somehow go through the point at the north, you are spread out evenly along the edge in the south. I think it's more or less safe to say that the vertical direction extends infinitely upwards. As for downwards, well, that's been a secret (though I think there may be some sort of "City" down there, and some kind of Empire )

WARNING: Crazy math/topology talk ahead

So topologically speaking (it sounds like you've got enough background to understand this), the Eighth is NOT a 3-manifold, nor is its surface a 2-manifold, because of the odd behavior at the north pole. If you removed a closed neighborhood of the north pole, then the surface would be a 2-manifold. Topologically, I think you could, roughly, get the underlying space of the Eighth if you took a closed unit square in 2-space, identified the x and -x sides, identified everything where y = 1 and y = -1 to a point, and then took the product with the real line. But the geometry is a little weird, in that as you approach the "sqaushed" point (aka north pole) from the positive y direction, the lateral geodesics shrink down to a length of zero (in particular the length of a lateral geodesic is pi/4 times your distance from the north pole since the angle is pi/4), while if you approach from the negative y direction, the lateral geodesics stay roughly constant. In fact, they grow a little, approaching pi/4 * the distance from the north pole down to the south edge.

Well, I hope someone can understand that. To quote Professor Frink... "This should be obvious to even the most dim-witted individual... with an advanced degree in hyperbolic topology, mm-hey"

One last thing... It seems to me that it would be impossible for an average denizen of the Eighth to go through the north pole point. If you started walking there, as you got close you would see seven copies of yourself heading to the same point. When you tried to walk through it you would bump shoulders before you could get there. Stick your finger out to the point, and it will bump into seven other fingers. So there's no real way to push past yourself and go through to the other side.

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[Last edited by MartianInvader at 11-17-2006 08:26 PM]

BeefontheBone
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Wish I'd taken more topology and less set theory and logic, now - if I'dve known it'd come in handy when discussing DROD that would've made it much more attractive

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Chard
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Okay, so I started thinking about it as a disc with all 8 Eighths around it and tried to imagine how that would work (shape-wise).

What we have is a disc where the circumference is identified as a single point and that point identified with the pole. The first identification gives us a sphere. and the second identification gives us a sphere where the two poles are pinched together in the middle which is a fairly odd shape to imagine. Now the maths:

<maths>This is not a 2-manifold no becuase the centre is too crazy. What concerns me even more though is that even before doing the second identification, while it was a 2-manifold, it was not Riemannian in any sensible way. This is obvious when you think about what you would see if you looked over the South edge. The other pole would be spread infinitely in front of you, a point replicated to a line. Clearly the variation of an inner product can not be continuous here.</maths>

The upshot of the above maths bit is that the world has no easily definable sense of distance. It would be easy to create one but not one that varies nicely from point to point. Here is an example. If I were at the South edge with a ruler held flat in front of me and I were to cross the edge, I would appear at the North point, during that crossing the ruler must have crossed with me and at the moment it had just crossed must've intersected with the two adjacent rulers.

This is of course the converse of MartianIvader's last point that travelling to the actual North point is imposible because you bump into yourself. A reasonable explanation for this might be that there is a region of space around the pole and the edge which (and we might need a theoretical physicist to explain this) does not hold to laws of exclusivity. ie. that matter can co-exist in the same space of time, but slightly out of phase. Thoughts?

My explanations may be unclear, but I hope I can convey that there is a clearly definable problem with the South edge wrapping to the North point. Still this is quite technical stuff. Who'd've thought a pie shaped world could cause so many problems?

Jatopian
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Chard wrote:
Who'd've thought a pie shaped world could cause so many problems?

It's pretty obvious to those who go around overanalyzing things all the time (e.g. me).

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Actually, maybe you can't reach the North pole at all. What if the pie-shapedness of the Eights is caused by it being more and more condensed towards the North side. So it's actually rectangular (which explains how dungeons are made of *square* tiles, not trapezoids like you would expect in a pie-shaped world). A rectangle in which the space is more and more condensed towards the North side, becoming infinitely condensed at the North pole. This means that you can't reach the pole because as you come nearer you become smaller. If it is so, on the South side, the circumerence, while being circular, is actually a straight line.

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AtkinsSJ
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Woah. So as you get nearer, you get smaller, so it takes longer to travel, etc. Would you eventually disappear?

coppro
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AtkinsSJ wrote:
Woah. So as you get nearer, you get smaller, so it takes longer to travel, etc. Would you eventually disappear?

No, I'm pretty sure that's not how it works. There was a long, drawn-out discussion to this effect and that's what
Erik said. Plus, otherwise, how would fegundoes mate?

trick
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Nah. I think that, if space is logically rectangular, as you approach the North pole, everything gets larger and larger relative to space, and vice versa for the South pole. At the edge, you quickly approach infinity +/-, somewhat like tan behaves around pi/2. It's simple, really

~ Gerry

zex20913
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I think this could be an interesting thing that the hyperbolic plane could take a look at. The outstanding feature of this (aside from an infinite number of possible parallel lines) is the expansion of the plane. There is more space the further you travel from the center. It's a bit weird to describe in words, but that's a (fairly) good general idea. We're studying it in geometry (a bit), and we've found some interesting takes on it. (None of which are certain to be true, but they are interesting.)

One being, as you move along the plane, your size actually changes relative to the plane, so to appear euclidean planar. Our universe is potentially hyperbolic as well.

Anyway, how this relates to the discussion: What if The Eighth is hyperbolic, but hyperbolic that changes its radius, so as to become more rectangular, up to a radial length where the measurable difference between rectangular and The Eighth is negligible. Then, The Eighth has rectangular space, where, when you get to the south edge, wraps around to the bottom, and then you continue to go north.

This is a very unpolished idea (I just woke up), but I think it may be my view of the topology/geometry of The Eighth.

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Chard
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zex, I thought about various geometries for a while, the major problem with a hyperbolic geometry would be that there is already a map of the Eighth, which is apparently finite, so you can travel to the edge. We know you can travel to the point because the fegundos do so for their progenesis. I'm beginning to suspect that while it would be nice to encapsulate the Eighth in a nice well understood mathematical construct that it would not be so simple as we should hope, indeed the mathematics behind the physics of the Eighth's universe may be significantly more complicated than that of ours.

MartianInvader
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Don't forget Chard, that there's the sideways wrap-around. In your analogy about identifying two antipodal points of a sphere, you need to identify the sphere to itself via an action by Z/8Z (I think technical term for this is a Moore Space, if I'm remembering this right). I guess this doesn't really affect the problems with that point, though. Actually, that's a nice way to succinctly describe the topology of the Eighth (at least of a 2-d cross section): A Moore space with two points glued together. Of course, all this glueing wrecks the geometry.

EDIT - Turns out I remembered wrong about what a Moore space is. Topologically, yes, a 2d slice of the eighth is just a sphere with two points identified.

I guess you could think of the Eighth as an almost-Riemannian almost-manifold, with a problematic singularity-like point.

As for having more complicated geometry than our own space... you may be underestimating our own space. I'm not a physicist, but from what I understand of Einstein our universe has non-constant curvature, which gets warped away from zero (negatively, I think?) by objects with large mass. Maybe the north pole of the eighth is just some sort of black hole!

Okay, maybe it's time to cool it with the crazymathspeak. I'm starting to feel like I should put references at the end of my posts

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[Last edited by MartianInvader at 11-19-2006 06:26 PM]

Jatopian
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MartianInvader wrote:
I'm starting to feel like I should put references at the end of my posts

I think many of us have felt thus for a while.

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Mattcrampy
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Creating a mathematically boggling but easy-to-describe topology is certainly the easiest way to keep the canon geeks amused, I have to say.

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AlefBet
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I always thought it would be cool if the south edge of the Eighth behaved such that when you walked beyond it, you were translated 1/16th of a turn east/west and reflected (right hand becomes left hand, etc.). Then you could continue your travel home and greet your friends, giving them a reversed handshake. This eliminates the south/north line-to-point wrapping that I always thought was rather strange, without creating a special point on the southern border.

But this is Erik's baby and he has it working the way it does. Oh, well. I still wonder why the southern sea isn't constantly being sucked into the northern tip of the world. Unless, the process of being squished into a point creates a hard-to-pass barrier of some sort, in which case the wrapping behavior is rather moot. Either way, I wonder what it looks like to be next to it.

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