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<blockquote data-quote="Klintus Fang" data-source="post: 157678" data-attributes="member: 3580"><p>hmmm. </p><p></p><p>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.</p><p></p><p>I start by visualizing things geometrically. My very first conclusion from this is that either </p><p></p><p>1. all planes are finite, or</p><p>2. some are finite and some are infinite, and the infinite ones must be "occupying the same space" as all the others</p><p></p><p>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. </p><p></p><p>but if one allows for the possibility that there are more than 3 physical dimensions the possibilities break wide open and lead to:</p><p></p><p>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.</p><p></p><p></p><p>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).</p><p></p><p>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:</p><p></p><p>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.</p><p></p><p>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.</p><p></p><p>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.</p><p></p><p></p><p>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. </p><p></p><p>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.</p><p></p><p>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. <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite1" alt=":)" title="Smile :)" loading="lazy" data-shortname=":)" /></p></blockquote><p></p>
[QUOTE="Klintus Fang, post: 157678, member: 3580"] 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. :) [/QUOTE]
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