Ghyll:Orthogonalities - Revision history

Jcowan: Updating per "Down There" (apparently it's real, unless Morbus is crazy)

2005-06-21T17:38:45Z

Updating per "Down There" (apparently it's real, unless Morbus is crazy)

Jcowan: /* Visualizing the Theory */ Copy editing

2005-05-31T02:55:46Z

Visualizing the Theory: Copy editing

Morbus Iff: Minor tweaks for a larger resolution.

2005-05-26T14:02:49Z

Minor tweaks for a larger resolution.

Morbus Iff: Endless tweaking, endless tweaking, part 2.

2005-05-25T22:53:23Z

Endless tweaking, endless tweaking, part 2.

Morbus Iff: Endless tweaking, endless tweaking, part 1.

2005-05-25T22:49:12Z

Endless tweaking, endless tweaking, part 1.

Jcowan: Copy editing game note

2005-05-25T16:23:43Z

Copy editing game note

Morbus Iff: Stupid ugly wrapping junk.

2005-05-25T16:21:56Z

Stupid ugly wrapping junk.

Morbus Iff: s/MAY NOT/MUST NOT/; per the RFC terminology.

2005-05-25T16:21:05Z

s/MAY NOT/MUST NOT/; per the RFC terminology.

Morbus Iff: Adding note that creating new ortho's are not allowed.

2005-05-25T16:17:59Z

Adding note that creating new ortho's are not allowed.

Jcowan: Less definite reference to gates in the PIF

2005-05-25T15:31:25Z

Less definite reference to gates in the PIF

@@ Line 1: / Line 1: @@
 <div class="oog" style="border:1px solid #ccc;float:right;margin:1em;padding:0.5em;width:335px;">As scholar and player, you '''MUST NOT''' create a new orthogonality unless existing text or phantoms already suggest its unique existence. The Encyclopedants (i.e., [[Special:Listadmins|the admins of the game]]) will decide when and how new ones spring into existence. This is a game balance issue.</div>
-[[Rancticirchiretic]] worked on the theory of '''orthogonalities''' from shortly after his investiture as president of the [[Bureau of Forgotten Knowledge|Bureau]] until well after his retirement. It is considered the greatest scientific discovery of the previous century.
+[[Rancticirchiretic]] worked on the theory of '''orthogonalities''' from shortly after his investiture as president of the [[Bureau of Forgotten Knowledge|Bureau]] until well after his retirement. It is considered the greatest scientific discovery of the past century.
-"Ghyll proper", used herein to refer to the greater area surrounding [[Folktown]], is just one of many orthogonalities that jointly make up what he termed "MetaGhyll", though common usage applies the term "Ghyll" to both the primary orthogonality, or "Ghyll proper", and the entire collection of otherwise known orthogonalities. In the first year of this Encyclopedia, we have written mostly about Ghyll proper, but the [[Xurient]] is a separate orthogonality of this "MetaGhyll". It is not entirely clear yet whether [[Down There]] is another orthogonality or simply mythical.
+"Ghyll proper", used herein to refer to the greater area surrounding [[Folktown]], is just one of many orthogonalities that jointly make up what he termed "MetaGhyll", though common usage applies the term "Ghyll" to both the primary orthogonality, or "Ghyll proper", and the entire collection of otherwise known orthogonalities. In the first year of this Encyclopedia, we mostly wrote about Ghyll proper, but the [[Xurient]] and [[Down There]] are separate orthogonalities of this "MetaGhyll".
 ==Visualizing the Theory==
 <div style="background-color:#eee;border:1px solid #ccc;margin:auto;margin-bottom:10px;padding:0.5em;width:90%;">
-The following pictures and their captions are excerpted from [[Mother_Mutton%27s_Golden_Books|Mother Mutton's Golden Book of Orthogonalities, Neither Orthogonal Nor Nervous, But Always Coloring Fun]]. These images purport to illustrate a four-dimensional concept in a three-dimensional space; as such, they are analogous approximations at best. For the sake of clearer understanding, the [[:Category:Encyclopedants|Encyclopedants]] have partaken in the coloring fun and colored each orthogonality for you. Seek out your nearest bookseller for your own coloring fun.</div>
+The following pictures and their captions are excerpted from [[Mother Mutton's Golden Books|Mother Mutton's Golden Book of Orthogonalities, Neither Orthogonal Nor Nervous, But Always Coloring Fun]]. These images purport to illustrate a four-dimensional concept in a three-dimensional space; as such, they are analogous approximations at best. For the sake of clearer understanding, the [[:Category:Encyclopedants|Encyclopedants]] have partaken in the coloring fun and colored each orthogonality for you. Seek out your nearest bookseller for your own coloring fun.</div>
-[[Rancticirchiretic]]'s theory is an application of four-dimensional geometry and, as such, impossible to visualize in three-dimensional space, nor is it easy to understand formally. What follows is an analogy that preserves the appearances of the theory rather than a strictly correct model.
+[[Rancticirchiretic]]'s theory is an application of multi-dimensional geometry (at least six, maybe more, dimensions) and, as such, impossible to visualize in three-dimensional space, nor is it easy to understand formally. What follows is an analogy that preserves the appearances of the theory rather than a strictly correct model.
 [[Image:Orthogonalities 01.png|frame|right|"The three orthogonalities in this picture, named A, C, and T, intersect at a single turning point. We'll name this directional triple A-C-T, but if you prefer the triple C-A-T, so do we! Hugs!"]]
-Let us completely ignore the third dimension and visualize the surface of Ghyll proper as a pure two-dimensional disk with its center near [[Folktown]]. Each alternative orthogonality is another disk intersecting Ghyll along some line (or possibly circle, ellipse, parabola, or hyperbola or part thereof), known as an ''intersection line''. Thus, it is not really true that the [[Xurient]] is 230 [[lele]] east of [[Egron]]; rather, the intersection line (which is marked by the Pretty Impressive Fence) is. It is believed, but not proved, that every orthogonality intersects every other orthogonality. Don't even bother trying to visualize a shape for MetaGhyll.
+Let us completely ignore the third dimension and visualize the surface of Ghyll proper as a pure two-dimensional disk with its center near [[Folktown]]. Each alternative orthogonality is another disk intersecting Ghyll along some line (or possibly circle, ellipse, parabola, or hyperbola or part thereof), known as an ''intersection line''. Thus, it is not really true that the [[Xurient]] is 230 [[lele]] east of [[Egron]]; rather, the intersection line between the Xurient and Ghyll proper (which is marked by the Pretty Impressive Fence) is. (It is believed, but not proved, that every orthogonality intersects every other orthogonality. Don't even bother trying to visualize a shape for MetaGhyll as a whole.)
-However, you cannot cross from one orthogonality to another just anywhere on an intersection line.  Rather, you must go to a ''turning point'', which is the intersection of two intersection lines.  At these points, it is possible to transition into either of ''two'' orthogonalities. There is only one turning point for each possible combination of three orthogonalities, which creates a directional triple such as "Ghyll proper-Xurient-Down There" (a hypothetical example). The probabilities of passing into either alternative orthogonality, or remaining in the one you are in, are roughly equal, so it may take several tries to cross over.  People tend to do so at a running leap so as to minimize the possibility that different body parts end up in different orthogonalities. The [[Xurient]]'s Pretty Impressive Fence has gates clearly marking safe turning points to other orthogonalities.
+You cannot cross from one orthogonality to another just anywhere on an intersection line.  Rather, you must go to a ''turning point'', which is the ''intersection'' of two intersection lines.  At these points, it is possible to transition into either of ''two'' orthogonalities. There is only one turning point for each possible combination of three orthogonalities, which creates a directional triple such as "Ghyll proper&#x2013;Xurient&#x2013;Down There" (a hypothetical example). The probabilities of passing into either alternative orthogonality, or remaining in the one you are in, are roughly equal, so it may take several tries to cross over.  People tend to do so at a running leap so as to minimize the possibility that different body parts end up in different orthogonalities. The [[Xurient]]'s Pretty Impressive Fence has gates clearly marking reasonably safe turning points to other orthogonalities.
 [[Image:Orthogonalities 02.png|frame|right|"Another example of three orthogonalities, this time G, C, and A. That's right! Here, the turning point is G-C-A! Or A-C-G! oOOh, G-A-C! Your friends told you orthogonalities were hard! You're smarter than your friends! Hold back a superior chuckle!"]]

@@ Line 15: / Line 15: @@
 Let us completely ignore the third dimension and visualize the surface of Ghyll proper as a pure two-dimensional disk with its center near [[Folktown]]. Each alternative orthogonality is another disk intersecting Ghyll along some line (or possibly circle, ellipse, parabola, or hyperbola or part thereof), known as an ''intersection line''. Thus, it is not really true that the [[Xurient]] is 230 [[lele]] east of [[Egron]]; rather, the intersection line (which is marked by the Pretty Impressive Fence) is. It is believed, but not proved, that every orthogonality intersects every other orthogonality. Don't even bother trying to visualize a shape for MetaGhyll.
-However, you cannot cross from one orthogonality to another just anywhere on an intersection line.  Rather, you must go to a ''turning point'', which is the intersection of two intersection lines.  At these points, it is possible to transition into either of ''two'' orthogonalities. There is only one turning point for each possible combination of three orthogonalities, which creates a directional triple such as "Ghyll proper-Xurient-Down There" (a hypothetical example). The probabilities of passing into either alternative orthogonality, or remaining in the one you are in, is roughly equal, so it may take several tries to cross over.  People tend to do so at a running leap so as to minimize the possibility that different body parts end up in different orthogonalities. The [[Xurient]]'s Pretty Impressive Fence has gates clearly marking safe turning points to other orthogonalities.
+However, you cannot cross from one orthogonality to another just anywhere on an intersection line.  Rather, you must go to a ''turning point'', which is the intersection of two intersection lines.  At these points, it is possible to transition into either of ''two'' orthogonalities. There is only one turning point for each possible combination of three orthogonalities, which creates a directional triple such as "Ghyll proper-Xurient-Down There" (a hypothetical example). The probabilities of passing into either alternative orthogonality, or remaining in the one you are in, are roughly equal, so it may take several tries to cross over.  People tend to do so at a running leap so as to minimize the possibility that different body parts end up in different orthogonalities. The [[Xurient]]'s Pretty Impressive Fence has gates clearly marking safe turning points to other orthogonalities.
 [[Image:Orthogonalities 02.png|frame|right|"Another example of three orthogonalities, this time G, C, and A. That's right! Here, the turning point is G-C-A! Or A-C-G! oOOh, G-A-C! Your friends told you orthogonalities were hard! You're smarter than your friends! Hold back a superior chuckle!"]]
-Turning points are rare in the central of an orthogonality, but become more common the further one goes from the center. [[Rancticirchiretic]] measured the distance between known turning points and found that they increase exponentially as one travels towards the borders - which is why, of course, exploration of these areas becomes increasingly difficult as turning off onto another orthogonality becomes ever more difficult to avoid. The outer edges of an orthogonality are very dangerous: if you cross over, there may be another turning point just a few [[inanit]]s away, or even ''inside'' your body!
+Turning points are rare in the central region of an orthogonality, but become more common the further one goes from the center. [[Rancticirchiretic]] measured the distance between known turning points and found that they increase exponentially as one travels towards the borders - which is why, of course, exploration of these areas becomes increasingly difficult as turning off onto another orthogonality becomes ever more difficult to avoid. The outer edges of an orthogonality are very dangerous: if you cross over, there may be another turning point just a few [[inanit]]s away, or even ''inside'' your body!
 There is, technically speaking, no final outer edge to any orthogonality, but there is an ''effective'' edge based on the distance from the center which is incompatible with life.  We don't know how far away from the center this is, or even if it's the same for every orthogonality.  It is believed, however, that turning points increase uniformly in every direction, which is why Ghyll proper and the other orthogonalities can be modeled as having circular surfaces.
@@ Line 27: / Line 27: @@
 Though [[Rancticirchiretic]] has been unable to explain why [[Pinky]] and [[Perky]] look exactly the same from every orthogonality, he has been able to provide the best available approximation of the number of safely transitionable orthogonalities, based on some complex mathematics involving the increase of repetition of turning points into orthogonalities as one approaches the border of Ghyll proper. In summary, he believes there to be a hundred and fifty orthogonalities though, of course, only twenty are significantly populated.
-[[Image:Orthogonalities 03.png|frame|center|"Remember how we said that intersections ''could'' be a straight line, but they might be curved as well? Here's an example of a curved intersection, where the orthogonality C intersects orthogonality G in a circular path. We'll throw a third orthogonality in, T, so that we have a valid turning point and thus, directional triple: T-C-G!"]]
+[[Image:Orthogonalities 03.png|frame|center|"Remember how we said that intersections ''could'' be a straight line, but they might be curved as well? Here's an example of a curved intersection, where the orthogonality C intersects orthogonality G in a circular path. We'll throw a third orthogonality in, T, so that we have a valid turning point and thus, directional triple: T-C-G! Orthogonality C isn't really funny-shaped like this; that's just the result of viewing a two-dimensional image of a three-dimensional model of a four-dimensional reality."]]
 [[Image:Orthogonalities 04.png|frame|center|"Our final concept! Here, we add a fourth orthogonality, A, and suddenly, we have a total of three turning points: T-G-A (or G-A-T, etc.), C-A-G (G-A-C!), and our old friend T-C-G. There's also a fourth C-A-T turning point but, due to our petty third-dimensional limitations, we can't show it. So... which colors did ''you'' choose for your orthogonality coloring fun!? Not as nervous as you once was, are ya?"]]

@@ Line 10: / Line 10: @@
 [[Rancticirchiretic]]'s theory is an application of four-dimensional geometry and, as such, impossible to visualize in three-dimensional space, nor is it easy to understand formally. What follows is an analogy that preserves the appearances of the theory rather than a strictly correct model.
 Let us completely ignore the third dimension and visualize the surface of Ghyll proper as a pure two-dimensional disk with its center near [[Folktown]]. Each alternative orthogonality is another disk intersecting Ghyll along some line (or possibly circle, ellipse, parabola, or hyperbola or part thereof), known as an ''intersection line''. Thus, it is not really true that the [[Xurient]] is 230 [[lele]] east of [[Egron]]; rather, the intersection line (which is marked by the Pretty Impressive Fence) is. It is believed, but not proved, that every orthogonality intersects every other orthogonality. Don't even bother trying to visualize a shape for MetaGhyll.
-[[Image:Orthogonalities 01.png|frame|right|"The three orthogonalities in this picture, named A, C, and T, intersect at a single turning point. We'll name this directional triple A-C-T, but if you prefer the triple C-A-T, so do we! Hugs!"]]
+However, you cannot cross from one orthogonality to another just anywhere on an intersection line.  Rather, you must go to a ''turning point'', which is the intersection of two intersection lines.  At these points, it is possible to transition into either of ''two'' orthogonalities. There is only one turning point for each possible combination of three orthogonalities, which creates a directional triple such as "Ghyll proper-Xurient-Down There" (a hypothetical example). The probabilities of passing into either alternative orthogonality, or remaining in the one you are in, is roughly equal, so it may take several tries to cross over.  People tend to do so at a running leap so as to minimize the possibility that different body parts end up in different orthogonalities. The [[Xurient]]'s Pretty Impressive Fence has gates clearly marking safe turning points to other orthogonalities.
-However, you cannot cross from one orthogonality to another just anywhere on an intersection line.  Rather, you must go to a ''turning point'', which is the intersection of two intersection lines.  At these points, it is possible to transition into either of ''two'' orthogonalities. There is only one turning point for each possible combination of three orthogonalities, which creates a directional triple such as "Ghyll proper-Xurient-Down There" (a hypothetical example). The probabilities of passing into either alternative orthogonality, or remaining in the one you are in, is roughly equal, so it may take several tries to cross over.  People tend to do so at a running leap so as to minimize the possibility that different body parts end up in different orthogonalities. The [[Xurient]]'s Pretty Impressive Fence has gates clearly marking safe turning points to other orthogonalities.
+[[Image:Orthogonalities 02.png|frame|right|"Another example of three orthogonalities, this time G, C, and A. That's right! Here, the turning point is G-C-A! Or A-C-G! oOOh, G-A-C! Your friends told you orthogonalities were hard! You're smarter than your friends! Hold back a superior chuckle!"]]
 Turning points are rare in the central of an orthogonality, but become more common the further one goes from the center. [[Rancticirchiretic]] measured the distance between known turning points and found that they increase exponentially as one travels towards the borders - which is why, of course, exploration of these areas becomes increasingly difficult as turning off onto another orthogonality becomes ever more difficult to avoid. The outer edges of an orthogonality are very dangerous: if you cross over, there may be another turning point just a few [[inanit]]s away, or even ''inside'' your body!
 There is, technically speaking, no final outer edge to any orthogonality, but there is an ''effective'' edge based on the distance from the center which is incompatible with life.  We don't know how far away from the center this is, or even if it's the same for every orthogonality.  It is believed, however, that turning points increase uniformly in every direction, which is why Ghyll proper and the other orthogonalities can be modeled as having circular surfaces.

@@ Line 7: / Line 7: @@
 ==Visualizing the Theory==
 <div style="background-color:#eee;border:1px solid #ccc;margin:auto;margin-bottom:10px;padding:0.5em;width:90%;">
-The following pictures and their captions are excerpted from [[Mother_Mutton%27s_Golden_Books|Mother Mutton's Golden Book of Orthogonalities, Neither Orthogonal Nor Nervous, But Always Coloring Fun]]. These images purport to illustrate a fourth dimensional concept in a third dimensional space; as such, they are analogous approximations at best. For the sake of clearer understanding, the [[:Category:Encyclopedants|Encyclopedants]] have partaken in the coloring fun and colored each orthogonality for you. Seek out your nearest bookseller for your own coloring fun.</div>
+The following pictures and their captions are excerpted from [[Mother_Mutton%27s_Golden_Books|Mother Mutton's Golden Book of Orthogonalities, Neither Orthogonal Nor Nervous, But Always Coloring Fun]]. These images purport to illustrate a four-dimensional concept in a three-dimensional space; as such, they are analogous approximations at best. For the sake of clearer understanding, the [[:Category:Encyclopedants|Encyclopedants]] have partaken in the coloring fun and colored each orthogonality for you. Seek out your nearest bookseller for your own coloring fun.</div>
 [[Rancticirchiretic]]'s theory is an application of four-dimensional geometry and, as such, impossible to visualize in three-dimensional space, nor is it easy to understand formally. What follows is an analogy that preserves the appearances of the theory rather than a strictly correct model.
@@ Line 28: / Line 28: @@
 [[Image:Orthogonalities 03.png|frame|center|"Remember how we said that intersections ''could'' be a straight line, but they might be curved as well? Here's an example of a curved intersection, where the orthogonality C intersects orthogonality G in a circular path. We'll throw a third orthogonality in, T, so that we have a valid turning point and thus, directional triple: T-C-G!"]]
-[[Image:Orthogonalities 04.png|frame|center|"Our final concept! Here, we add a fourth orthogonality, A, and suddenly, we have a total of three turning points: T-G-A (or G-A-T, etc.), C-A-G (G-A-C!), and our old friend T-C-G. There's also a fourth C-A-T turning point but, due to our petty third-dimensional limitations), we can't show it. So... which colors did ''you'' choose for your orthogonality coloring fun!? Not as nervous as you once was, are ya?"]]
+[[Image:Orthogonalities 04.png|frame|center|"Our final concept! Here, we add a fourth orthogonality, A, and suddenly, we have a total of three turning points: T-G-A (or G-A-T, etc.), C-A-G (G-A-C!), and our old friend T-C-G. There's also a fourth C-A-T turning point but, due to our petty third-dimensional limitations, we can't show it. So... which colors did ''you'' choose for your orthogonality coloring fun!? Not as nervous as you once was, are ya?"]]
 <br /><div align="right"><big><strong>--The Encyclopedants</strong></big></div>
 [[Category:Encyclopedants]]

@@ Line 1: / Line 1: @@
-__TOC__
+<div class="oog" style="border:1px solid #ccc;float:right;margin:1em;padding:0.5em;width:335px;">As scholar and player, you '''MUST NOT''' create a new orthogonality unless existing text or phantoms already suggest its unique existence. The Encyclopedants (i.e., [[Special:Listadmins|the admins of the game]]) will decide when and how new ones spring into existence. This is a game balance issue.</div>
 [[Rancticirchiretic]] worked on the theory of '''orthogonalities''' from shortly after his investiture as president of the [[Bureau of Forgotten Knowledge|Bureau]] until well after his retirement. It is considered the greatest scientific discovery of the previous century.
@@ Line 8: / Line 6: @@
 ==Visualizing the Theory==
 [[Rancticirchiretic]]'s theory is an application of four-dimensional geometry and, as such, impossible to visualize in three-dimensional space, nor is it easy to understand formally. What follows is an analogy that preserves the appearances of the theory rather than a strictly correct model.
 Let us completely ignore the third dimension and visualize the surface of Ghyll proper as a pure two-dimensional disk with its center near [[Folktown]]. Each alternative orthogonality is another disk intersecting Ghyll along some line (or possibly circle, ellipse, parabola, or hyperbola or part thereof), known as an ''intersection line''. Thus, it is not really true that the [[Xurient]] is 230 [[lele]] east of [[Egron]]; rather, the intersection line (which is marked by the Pretty Impressive Fence) is. It is believed, but not proved, that every orthogonality intersects every other orthogonality. Don't even bother trying to visualize a shape for MetaGhyll.
-[[Image:Orthogonalities 01.png|frame|An example of a turning point at the intersection of three orthogonalities. More examples below.]] However, you cannot cross from one orthogonality to another just anywhere on an intersection line.  Rather, you must go to a ''turning point'', which is the intersection of two intersection lines.  At these points, it is possible to transition into either of ''two'' orthogonalities. There is only one turning point for each possible combination of three orthogonalities, which creates a directional triple such as "Ghyll proper-Xurient-Down There" (a hypothetical example). The probabilities of passing into either alternative orthogonality, or remaining in the one you are in, is roughly equal, so it may take several tries to cross over.  People tend to do so at a running leap so as to minimize the possibility that different body parts end up in different orthogonalities. The [[Xurient]]'s Pretty Impressive Fence has gates clearly marking safe turning points to other orthogonalities.
+[[Image:Orthogonalities 01.png|frame|right|"The three orthogonalities in this picture, named A, C, and T, intersect at a single turning point. We'll name this directional triple A-C-T, but if you prefer the triple C-A-T, so do we! Hugs!"]]
 Turning points are rare in the central of an orthogonality, but become more common the further one goes from the center. [[Rancticirchiretic]] measured the distance between known turning points and found that they increase exponentially as one travels towards the borders - which is why, of course, exploration of these areas becomes increasingly difficult as turning off onto another orthogonality becomes ever more difficult to avoid. The outer edges of an orthogonality are very dangerous: if you cross over, there may be another turning point just a few [[inanit]]s away, or even ''inside'' your body!
 There is, technically speaking, no final outer edge to any orthogonality, but there is an ''effective'' edge based on the distance from the center which is incompatible with life.  We don't know how far away from the center this is, or even if it's the same for every orthogonality.  It is believed, however, that turning points increase uniformly in every direction, which is why Ghyll proper and the other orthogonalities can be modeled as having circular surfaces.
@@ Line 22: / Line 27: @@
 Though [[Rancticirchiretic]] has been unable to explain why [[Pinky]] and [[Perky]] look exactly the same from every orthogonality, he has been able to provide the best available approximation of the number of safely transitionable orthogonalities, based on some complex mathematics involving the increase of repetition of turning points into orthogonalities as one approaches the border of Ghyll proper. In summary, he believes there to be a hundred and fifty orthogonalities though, of course, only twenty are significantly populated.
 [[Image:Orthogonalities 03.png|frame|center|"Remember how we said that intersections ''could'' be a straight line, but they might be curved as well? Here's an example of a curved intersection, where the orthogonality C intersects orthogonality G in a circular path. We'll throw a third orthogonality in, T, so that we have a valid turning point and thus, directional triple: T-C-G!"]]
 [[Image:Orthogonalities 04.png|frame|center|"Our final concept! Here, we add a fourth orthogonality, A, and suddenly, we have a total of three turning points: T-G-A (or G-A-T, etc.), C-A-G (G-A-C!), and our old friend T-C-G. There's also a fourth C-A-T turning point but, due to our petty third-dimensional limitations), we can't show it. So... which colors did ''you'' choose for your orthogonality coloring fun!? Not as nervous as you once was, are ya?"]]

← Older revision		Revision as of 16:17, 25 May 2005
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	__TOC__		__TOC__
		+
		+	<div style="background-color:#eee;border:1px solid #ccc;float:right;margin:1em;padding:0.5em;width:375px;">'''GAME NOTE:''' As a scholar and player, you MAY NOT create new orthogonalities unless existing text or phantoms already suggest its unique existence. The Encyclopedents (i.e., [[Special:Listadmins\|the admins of the game]]) will decide when and how new orthogonalities spring into existence. This is a game balance issue.</div>

	[[Rancticirchiretic]] worked on the theory of '''orthogonalities''' from shortly after his investiture as president of the [[Bureau of Forgotten Knowledge\|Bureau]] until well after his retirement. It is considered the greatest scientific discovery of the previous century.		[[Rancticirchiretic]] worked on the theory of '''orthogonalities''' from shortly after his investiture as president of the [[Bureau of Forgotten Knowledge\|Bureau]] until well after his retirement. It is considered the greatest scientific discovery of the previous century.