New Special properties

[ax0n]

Hi Klintus,

I was the perpetrator mainly responsible for the rules on Plane Descriptions (although many others on the team are also guilty of aiding ). First, I'd like to welcome you to our forums. We're always on the lookout for feedback and comments, especially those as intelligent and insightful as yours. Keep 'em coming.

The Plane Descriptions play hard and fast with any known rules of geometry, mathematics and physics, mainly to simplify and expediate the rules and maximise fun . This is especially true of 'planar borders' - the rules for which are still heavily in development (see other threads on our board). In the later versions (which are still in development) the rules make no statements about whether a plane is bounded or unbounded. This will be determined in future versions by whether or not a plane has planar borders, and their number and type.

If you don't like what you see you're more than welcome to get involved . We can us all the help we can get. I can email you the latest version, if you would like?

I mean if you redefine the word dimension to mean: an infinite plane that has no beginning and no end. Then all of a sudden simple common sense statements like "the world in which I live has 3 dimensions" become nonsensical, because the world in which I live does not have "3 infinite planes that have no beginning and no end".

Please, please don't get stuck on our terminology. The words are just there as placeholders for concepts are are, fundamentally, OOC terms used to categorise planes and have no other function beyond that.

My explanation for the misuse of these terms is that I needed to come up with a series of terms for the various sizes of planes. If you think about it, its actually very hard to come up with variant terms for 'plane'. I use 'dimension' in the science-fiction sense of the word, where it is often used to describe parallel or alternative universes. Thinking about it, we could change the term 'dimension' to 'universe'?

As for 'space', in version 1.2 of our rules, a space is redefined to be a 'solar-system' size plane, for Spelljammer style Material Planes and so forth.

the terminology the document uses instead: dimension, space, world and realm confuses the stuffing out of me. I understand what world and realm mean of course, but in that respect ,I don't understand why there needs to be special terminology for different sizes of finite planes.

The size categories are used to define various, standard plane sizes. Hypothetically, they could be used as measures of the relative power of each plane, or to determine the number of Planar Borders each plane has. I, myself, have never been quite happy with them so I'm open to suggestions.

Also the 'finite' and 'infinite', 'bound' and 'unbounded' definitions of planes are MotP stuff and are unfortunately legally unsound for us to use.

Finally, is there anything you liked about our rules for Plane Descriptions?

 

[Klintus Fang]

finite and infinite, bounded and unbounded are standard mathematical terms that you will find in the opening chapters of any topology textbook or any differential geometry textbook.

WoTC can't copyright those terms!

and the manual of the planes doesn't use the terms bounded an unbounded either, it uses a different term to describe that property.

 

[ax0n]

WoTC can't copyright those terms!

You'd be surprised what some people believe, including Ryan Dancey and his slavouring fanboy hordes on the OGF mailing lists believe is WotC copyright.

Actually, I concede that you are right on this point. Unfortunately, despite this we still have to be careful of similarities between our work on the MotP. We also believe that its important to develop something completely different for the aesthetic and fun reasons.

It also leads to another interesting theory of mine and the reason that I designed my plane rules the way I did: no reachable, and thus playable, plane can be truly said to be unbounded, otherwise it would be unreachable!

Let me explain: quite simply, if a plane is unbounded, how can anyone reach it? Of course, a plane may be physically unbounded, in which case you can't just walk onto it, but require some spell like plane shift or ethereal jaunt to reach it. But, if it requires such a spell to reach it, it must be connected in someway, either through a between (or transitive) plane, or some coexistent, bordering plane like the Ethereal Plane.

This leads to the conclusion that the bound and unbounded planar borders in MotP describe only one type of planar border, the simplest and most trivial, a physical border. What we are trying to do is capture multiple types of planar borders, from coexistent, incorporeal, to other stranger variants.

This aside, my offer still stands: if you don't like what you see then you are more than welcome to step in and help us improve things. Alternatively, you welcome to take our rules and write your own, completely different variant - its all covered by the OGL! We'd be interested to see what you come up with.

 

[Klintus Fang]

hmmm.

I'm not sure I quite understand. But let me go on a tangent and explain how I am approaching tackling my campaign's cosmology.

I start by visualizing things geometrically. My very first conclusion from this is that either

1. all planes are finite, or
2. some are finite and some are infinite, and the infinite ones must be "occupying the same space" as all the others

one must draw conclusion either 1 or 2 if one assumes that the planes all exist within a universe that consists of only 3 physical dimensions and that the measure of "distance" is the same everywhere.

but if one allows for the possibility that there are more than 3 physical dimensions the possibilities break wide open and lead to:

3. there can be any number of infinite planes and any number of finite planes. and none of these planes need necessarily be occupying the same space nor do any of them need necessarily be in contact.


As I am constructing my cosmology I am basically assuming that the number of physical dimensions I have at my disposal is unlimited (at a bare minimum I've decided I need 4, but to keep the relation between them pleasing in my mind I've decided I need at least 5, but nonetheless, I freely assume there are an infinite number of dimensions so I can safely assume that there is always room to draw a line between any two points that doesn't intersect any other plane that I've already constructed).

But the point is that as soon as you allow for the possibility that you may have more than 3 physical dimensions to work with you're possibilities become endless:

you can construct a finite unbounded 3-dimensional plane by imagining it as the surface of a 4-dimensional sphere. there is room in a 4 dimensional space for an arbitrary number of such spheres, and none of them have to intersect. I don't know how much this idea bothers other people, but if you are wondering, I assume that these 3-dimensional "surfaces" that curve in 4-space appear to be uncurved by the people who live in them. And that there is simply some "law of nature" that prevents 3-dimensional objects from leaving the confines of that 3-dimensional surface (and thus prevents them from drifting into that 4th, unseen, dimension). as another aside: I'm usually assuming that planes like the plane of shadow and the astral plane (that connect planes) are actually 4-dimensional planes that "appear" 3-dimensional.

But if one is willing to go even further, and imagine that the measure of "distance" might vary in different points, the options are even more extreme.

For example, if I allow myself to vary distance, I can easily fit a plane that extends infinitely in all directions into the tiniest thimble, if I choose the measure of distance appropriately. You mentioned that you have some mathematical training. In mathematical terms, any shape that is homeomorphic to R^3 can be visualized as containing the entirety of a plane that extends infinitely in all directions. Hence, as I construct my cosmology, I am freely saying things like: the plane of water is an infinite 3-plane (extends infinitely in all three physical directions) in which the points at infinity are tied together at a single point. Therefore, this infinite 3-plane can be visualized as the surface of a 4-dimensional ball. I can put it next to another infinite 3-plane that is also tied up into a ball and claim that these two infinite planes are disjoint, but are sitting next to each other in some tiny corner of the universe. Thus, I have two infinite planes that take up almost no space at all.


My point is that by thinking of it this way, I've got an image in my mind in which the number of possible shapes and sizes that a plane can have is infinite. and the number of possiple ways that two planes can sit in relation to one another is also infinite. and also, the number of possible ways that two planes could "border" one another is also infinite.

This is why my first look at the planar descriptions document left me thinking I probably couldn't contribute here. When I see an attempt to enumerate the possible sizes of planes or to enumerate the number of ways in which planes can border one another I become dismayed. The first thing I assumed when I began building my cosmology is that both of those things are infinite.

I'm not trying to criticize, I'm just explaining how my take on the problem differs from the approach that the people here appear to be taking. I'm still open to possibly contributing but for now, I'm probably going to sit on the sidelines and observe and maybe pipe in with comments or questions, assuming of course, that people here don't mind me doing so.

 

[ax0n]

This is why my first look at the planar descriptions document left me thinking I probably couldn't contribute here. When I see an attempt to enumerate the possible sizes of planes or to enumerate the number of ways in which planes can border one another I become dismayed. The first thing I assumed when I began building my cosmology is that both of those things are infinite.

What you have to remember is that the set of possible cosmologies and planes is infinite. But, we are dealing in rather realistic, game-realted terms with the sub-set of playable cosmologies and planes. Its still an infinite set, just a slightly smaller infinity.

That is, GMs and cosmologists want to be able to describe the relative 'sizes' of their planes. This still allows you to describe your planes in the mathematical, abstract way you have, but at the end of the day you'll want to let people into your planes to play around and explore which is where our rules come in.

A commmon misconception about our rules is that they represent an attempt to classify planes not only in game terms, but in metaphysical tersm. We leave all the metaphysical details of planes upto the cosmology designer (or cosmologist as we term them). The rules are mostly a helpful shorthand to categorise planes in a way helpful to GMs.

3. there can be any number of infinite planes and any number of finite planes. and none of these planes need necessarily be occupying the same space nor do any of them need necessarily be in contact.

This is the general assumption I've made when designing plane's, as it makes for the most magical, non-scientific cosmology. The condition that they don't need to be in contact, however, is wrong.

What I was trying to say above is that every plane needs to be in contact because if it is isn't in contact and how can it exist? If we make the assumption that a plane exists but is unreachable, with nothing connecting it, then what is between the plane's we know and this unreachable plane? This leads to the fallacious and contradictory idea that we have to consider the something that is nothing between us and the unconnected plane. Hence, by contradiction our initial assumption must be false, there can never be an unconnected plane.

 

[Klintus Fang]

"there can never be an unconnected plane"

of course there can! one may never get there, but that's another story..... are you telling me that if a tree falls in the woods, and no one is there to hear it, that it doesn't make a sound?!?




but anyway, when I said "not necessarily in contact" I did mean "with the possibility of any arbitrary amount of truly empty space between them" but I'm also assuming that there can be any number of "tunnels" (or tiny "border planes" if you like) connecting them if they aren't directly in contact.