Post/Author/DateTime	Post
sciborg2 06-14-07, 04:45 AM	Since the original thread was archived, I figure we can start fresh here and now. And I can't seem to find the archive of the original. :(
sciborg2 06-14-07, 01:30 PM	that was easier...than I expected: http://boards1.wizards.com/wotc_archive/index.php/t-504226
sciborg2 06-16-07, 04:06 AM	One of the things that I don't think made the archive was the idea that Math is not discovered but rather it is created. As such, though Mechanus cannot simply recreate math so that there are no irrational numbers (a beautiful set of proofs relates to this) it can send out agents to ensure that a more orderly set of mathematics is believed and thus - if we accept belief is power - *becomes* true. Imagine such an assassin of theory stalking the academic halls, conversing with old professors on their ideas and slowly shifting conjectures into theorems with just the right nudge...And before you know it, the Multiverse is suddenly more predictable.
sciborg2 06-26-07, 03:28 PM	Some problems based in the real world can only be solved by converting to the imaginary (complex) numbers and then converting back... But where are these imaginary numbers? In Mechanus? Or perhaps closer to where the vestiges are...And was Ipos then a mathematician? Maybe a member of the Guvner sect?
Mai_ariti 06-30-07, 10:12 AM	It could be argued that Math is discovered, not created as it is simply the mechanics of every thing that is seen. Therefore, it would be impossible to eliminate imaginary numbers. Inherent in your argument, however, is the assumption that imaginary numbers are something that is not deiserable. I'm not sure that this is the case. It seems to me that it is completely possibe that Mechanus needs imaginary numbers just as Math, in its current incarnation, needs them. Now, one must ask: where are imaginary numbers in math? I would appear that they are on another axis, apart from the standard the imaginary axis (where is 3 + 4i? over 3 up 4 on this axis). Is it not possible, then, that Mechanus has another axis that no one can see because they have no imaginary componant in themselves. Perhaps Mechanus is the intersection point from which another set of planes exand out on the imaginary axis and therefor it is the center of the multiverse. Logically, this would mean that at any point where math reveals an imaginary number there is an intersection between the real and imaginary planes. Thoughts? **Appologies** I dont have time to read all of the archive so it is possible that I am derailing this thread. If so, tell me to shut up I don't want to destroy what seems to be a very interesting thread.
zzo38 06-30-07, 12:40 PM	It could be argued that Math is discovered, not created as it is simply the mechanics of every thing that is seen. Therefore, it would be impossible to eliminate imaginary numbers. Inherent in your argument, however, is the assumption that imaginary numbers are something that is not deiserable. I'm not sure that this is the case. It seems to me that it is completely possibe that Mechanus needs imaginary numbers just as Math, in its current incarnation, needs them. Now, one must ask: where are imaginary numbers in math? I would appear that they are on another axis, apart from the standard the imaginary axis (where is 3 + 4i? over 3 up 4 on this axis). Is it not possible, then, that Mechanus has another axis that no one can see because they have no imaginary componant in themselves. Perhaps Mechanus is the intersection point from which another set of planes exand out on the imaginary axis and therefor it is the center of the multiverse. Logically, this would mean that at any point where math reveals an imaginary number there is an intersection between the real and imaginary planes. Thoughts? I agree with you. This is one way it could work in D&D. Mathematics cannot be changed, created, or destroyed, it just is. Of course, there are more things other than just complex numbers. Then you can learn to create spells to manipulate things mathematically in Mechanus.
Bob the Efreet 07-01-07, 04:40 AM	Is it not possible, then, that Mechanus has another axis that no one can see because they have no imaginary componant in themselves. Perhaps Mechanus is the intersection point from which another set of planes exand out on the imaginary axis and therefor it is the center of the multiverse. Logically, this would mean that at any point where math reveals an imaginary number there is an intersection between the real and imaginary planes. I think that's a very interesting idea.
Phalo 07-01-07, 09:07 AM	I have to agree all science is discovered. Example lighting rod Was developed in ancient Rome along with cement and some other rather nifty inventions. Fall of Rome happens and that technology is lost for centuries. Eventually that information is recreated through either trial and error(al la edison) or math (al la telsa). But what can't be rediscovered is music/art.
Mai_ariti 07-01-07, 11:36 AM	So here is my question: does every character, assuming my statements above are correct, have a counterpart that is on the Imaginary axis, and, if so, could that character affect the 'real' world? Also, could a person who, on Mechanus, discovers a new use of math unlock a section of Mechanus that noone knew existed?
Eye of the Beholder 07-01-07, 12:25 PM	While it's true that, in the real world, all math and science is discovered rather than invented, this is the outer planes we're talking about. The multiverse having an underlying set of rules that can be discovered/exploited is something lawful exemplars (and guvners) believe to be true. In our world we believe the same thing because the science and math we discover still works as time passes (barring refinement of the theory) and we can do cool stuff with it, like predict the weather or send people to the moon. But someone from, say, Limbo would have no reason to believe the science is valid because everything there is in flux. Sometimes the gravitational constant isn't. Sometimes circumference divided by diameter equals four. Both law and chaos, then, try to spread their ideologies to the multiverse at large. Mechanus has done an excellent job spreading belief in math, because even in the Outlands people use it for everything from architecture to siege warfare. But Limbo stops some 'discoveries' from working in predictable ways, so except for on a few variant prime worlds (where material matters more than belief) saltpetre plus charcoal plus sulfur won't make anything but a dangerous mess. Returning to the imaginaries and irrationals: I think both sides probably claim victory. Limbo thinks it's thrown a monkey wrench in the precious science of law, 'proving' that disorder and inexplicable results manifest even in lawful systems. Some from Mechanus agree, and try to discover/create a system where imaginaries and irrationals aren't necessary. Others use Mai_ariti's argument, that the imaginary/irrational elements of math aren't a weakness, but a sign that math is just that good, that it can describe and calculate even impossible situations. (And the idea of Mechanus being the intersection point of all mathematical planes plays well with Planescape's 'center of all' theme... good stuff!)
hazhar 07-01-07, 06:58 PM	While it's true that, in the real world, all math and science is discovered rather than invented I personally believe the exact opposite in regards to mathematics (not science, that is discovered), but I know that's just going to derail this thread so I won't say anymore. Just pointing out that not everyone holds that view :P
sciborg2 07-02-07, 01:49 AM	I think an argument on the subject would be of interest. And I love what y'all have done with the place.:D
Mai_ariti 07-02-07, 09:51 AM	While it's true that, in the real world, all math and science is discovered rather than invented, this is the outer planes we're talking about. The multiverse having an underlying set of rules that can be discovered/exploited is something lawful exemplars (and guvners) believe to be true. In our world we believe the same thing because the science and math we discover still works as time passes (barring refinement of the theory) and we can do cool stuff with it, like predict the weather or send people to the moon. But someone from, say, Limbo would have no reason to believe the science is valid because everything there is in flux. Sometimes the gravitational constant isn't. Sometimes circumference divided by diameter equals four. If, however, one believes in the true universal influence of math, one could argue that Limbo simply presents a different view of math than Mechanus. There are branches of math that deal with the irrational and the chaotic. Is it not possible, then, that Limbo is trying, not to destroy mathematics, but make it more complete? It is my understanding that the Outer Planes are focused mostly on the ballance of the multiverse and that should the ballance be disturbed the multiverse would be greatly changed. Since the argument is oftem made that good would be incomplete without evil, it would be logical to believe that the same is true of law and chaos. If this is true, then one must consider wheter they are opposed or if they are complimentary. While good and evil are often seen as opposed, the evil individual doesn't always want to undo all that a good person has done and the same is true in reverse. Therefore, one could assume that chaos is an integral aspect of the multiverse that cannot exist without law. Math therefore, must be able to explain 'Chaos' in some fashion. Since most people will agree that if math could explain chaos, it would not be chaos, it would be law. Perhaps then chaos is a different math then Mechanus, but still a math. The thing about Limbo, is that there is a law to it, if you are standing in fire, you will be burned, the chaos appears when the rules change. Is it not conceivable then that chaos is the math of change? Since if we assume that the statements in the previous posts are true and math is discovered, not created, it has not changed, it is all that is, was , and will be. What then of change? Change is a mathmatical concept that is not well defined. If I roll a ball across the floor and say 'predict where the ball will go,' you can use math to tell me mathmatically where the ball must go, but you may be wrong. This is the chaos aspect. Perhaps Limbo then is this other facet of math, explaining all of those things that math cannot, change in a word. Mechanus cannot cope with the change of math. A flaw? Perhaps, but then, the essence of change is chaotic. Math itself, however, is reality and must be able to explain this. Limbo is the other extreme: the math there cannot explain consistancy. When these two forms are merged, one can yield a form of math that could predict anything, if one could understand it. The problem arises in that humans require order and law. When one looks at Limbo, one cannot see the math there. In this way, perhaps the flaw is not in math, but in those interperting it. Even the Rimani, who supposidly want to keep a ballance between the extremes require order. Ballance is a lawful concept and, because of this, noone can actually link the Lawful Math of Mechanus to the Chaotic Math of Limbo. Thoughts?
Bob the Efreet 07-02-07, 02:57 PM	Change is a mathmatical concept that is not well defined. Isn't that what calculus is about? I'm pretty sure derivatives are all about rates of change. If I roll a ball across the floor and say 'predict where the ball will go,' you can use math to tell me mathematically where the ball must go, but you may be wrong. Only if the understanding of the system is incomplete. Since we're not dealing with quantum forces, if we know all the initial conditions, we can predict both the outcome and the path taken to get there.
zzo38 07-02-07, 11:59 PM	Try to use cellular automata. Some are simple (rule 0), some are structured easily (rule 90), some are chaotic and seems random (rule 30), some are complex and have localized structures movement and stuff (rule 110). It is easy to write a computer program so that you can try it yourself: f(t,s,r)=1&(r>>(4*f(t-1,s-1,r)+2*f(t-1,s,r)+f(t-1,s+1,r))) (where t=time, s=space, r=rule, >> is right shift bits, & is binary AND). And then you can learn what kinds of mathematicals are chaotic and stuff like that.
Mai_ariti 07-03-07, 12:13 PM	Isn't that what calculus is about? I'm pretty sure derivatives are all about rates of change. True, but also not the point. Derivitives will tell you how the numbers in the function are changing. Derivitives will not work if the line's equasion itself changes. I was talking about change not within an function, but of the function itself, while the function is 'running.' More of a piece-wise function than a standard function, or something with a corner or cusp on the graph, where the derivitive cannot be taken. This is the change I mean. Only if the understanding of the system is incomplete. Since we're not dealing with quantum forces, if we know all the initial conditions, we can predict both the outcome and the path taken to get there. But this is my point exactly, that our understanding of the situation is inherently flawed because we do not see all the aspects of the situation and the math requires that all the variables be defined in the equasion. I agree that if all variables were accounted for, the prediction would be correct, but my point is that they cannot be because not all of them are something that can be predicted from moment to moment. Tell me, when will you feel the next gust of wind? You cannot know. You can guess, perhaps even be right, or give a thousand possibilities that account for all possibilities and one will be correct, but you can't tell me which. This is my point.
sciborg2 07-03-07, 03:09 PM	I think Limbo's influence is worse than any quantum forces...but I may be missing the point here...
Bob the Efreet 07-03-07, 03:46 PM	But this is my point exactly, that our understanding of the situation is inherently flawed because we do not see all the aspects of the situation and the math requires that all the variables be defined in the equation. I agree that if all variables were accounted for, the prediction would be correct, but my point is that they cannot be because not all of them are something that can be predicted from moment to moment. Tell me, when will you feel the next gust of wind? You cannot know. You can guess, perhaps even be right, or give a thousand possibilities that account for all possibilities and one will be correct, but you can't tell me which. This is my point. I think the forces of Mechanus would like to think that they are capable of tracking all the variables. I'll leave it up to individual discretion as to whether or not they can actually do so ;)
Phalo 07-03-07, 11:48 PM	That whole ball thing is not really a good description. Because if you could get every detail about the environment and contributing factors you could determine where it is going to go every time. But that gets down to the minutia of particles of dust picked up on each consecutive roll. Think of the prime as a drop of water in space mechanus is the waters on forced trying to become a perfect sphere. And pandemonium is like rocks moving around with their own gravitational pulls trying to deform that sphere. You don;t really know how all the fields will react but they in and of themselves still obey some internal laws. Example in limbo there are creation stones that spew froth matter. And even the natives of that plane sladi follow their own rules. I would also say on a side note that i would think that mechanus being infinite would have a infinite set of gear islands. That being said mapping this plane would be very difficult. for several reasons. 1. no magnetic poles 2. all the gears are moving granted it is in a predictable manner , but it only takes on wrong turn.
Mai_ariti 07-04-07, 04:59 PM	I think Limbo's influence is worse than any quantum forces...but I may be missing the point here... My point was that Limbo may not be so much an opposed force as an alternate view of math. I was trying to convey, perhaps ineptly, that while Mechanus is the math we all understand, that doesn't mean that Limbo is anti-math or out to distroy it. My idea was that Limbo would fill in the gaps in the math Mechanus uses, such as derivitaves at points where graphs change the function that dertirmines them, while Mechanus does the same for Limbo. The over all implication was that Limbo and Mechanus require each other just as, some say, good would be meaningless without evil. It's a variation of the old 'what's pleasure without pain' theme. this variation is 'what if pain reflects something that pleasure cannot?' Sorry if my bizzare thoughts aren't coherent.
sciborg2 07-05-07, 01:47 AM	I think when we're going this abstract, its sometimes hard to be coherent -- But I'm reading you loud and clear now, and I like it.:D
Mai_ariti 07-08-07, 10:08 AM	That whole ball thing is not really a good description. Because if you could get every detail about the environment and contributing factors you could determine where it is going to go every time. But that gets down to the minutia of particles of dust picked up on each consecutive roll. Think of the prime as a drop of water in space mechanus is the waters on forced trying to become a perfect sphere. And pandemonium is like rocks moving around with their own gravitational pulls trying to deform that sphere. You don;t really know how all the fields will react but they in and of themselves still obey some internal laws. Example in limbo there are creation stones that spew froth matter. And even the natives of that plane sladi follow their own rules. I think this is an interesting concept. If this is true and Limbo does function according to its own 'rules' is it actually chaotic? Alternately, is Chaos just the word that is applied when the order cannot be observed? This viw would be, I think, a problem because then the planes of Mechanus and Limbo wouldn't be opposed on the basis of Law vs. Chaos, but rather Ignorence vs. Understanding. Does anyone else have a different view?
sciborg2 07-08-07, 03:21 PM	Chaos doesn't have to be the absence of all rules all the time, just the absence of any consistency in which things can be pinned down. Really, as humans we're designed to seek out patterns and to believe in the existence of patterns. True chaos frightens us, a look back at early civilization is an example of that. However, there are peoples like the Dagon who, at the highest levels of initiation, see Chaos and Order in a more positive relationship. Most people will insist that there is no Chaos if you have perfect measurement, but near as I can tell this remains in doubt. Any physicists in the crowd willing to answer to this would be much appreciated.
Yanagita Kunio 07-08-07, 03:53 PM	I think this is an interesting concept. If this is true and Limbo does function according to its own 'rules' is it actually chaotic? Alternately, is Chaos just the word that is applied when the order cannot be observed? This view would be, I think, a problem because then the planes of Mechanus and Limbo wouldn't be opposed on the basis of Law vs. Chaos, but rather Ignorence vs. Understanding. Does anyone else have a different view? I'm not really the guy who call tie it all into a tidy mathematical concept (yay wimpy social sciences), but: What makes Limbo chaotic is that the rules are subjective in a way that essentially reduces one's interaction with the environment to a kind of manifest sollipcism: the plane exists in flux until a will/mind exerts an influence on it. [Which does lead to an interesting question along the lines of the Heisenberg Uncertainty Principle--ie, does the act of observing Limbo ultimately structure it enough that the viewer cannot fully perceive Limbo in its entirity.] Limbo can be characterized as possessing qualities of both Chaos in the mythological sense--unrealized potential by way of Ovid's description of an unfashioned void*--and in the mathematical sense--which is not true "randomness" but rather a specific set of conditions within a dynamic system that produce a sensitivity to initial conditions, producing a cause-effect chain that can appear random. By the former conceptualization, Limbo is the vortex of potentiality: its undifferentiatedness can both spew forth autochthonous "creations"--often as not, randomized dross, though there seems to be an underpinned anthropic/sapient principle to all the planes--or act as the seed bed in which the drives of others can be made manifest. Via the latter, Limbo is like a giant nonlinear dynamic system, in which determinism forms around attractors if and when specific conditions are met that generate a sensitization of the total system to an initial condition for a brief time interval. In most cases the active attractors and repulsors within a deterministic arc are imperceptible both because of the size of the action (too small or big) and system condition change over time--that is, the premised result of the initial condition might be "A causes B," but in fact "A causes C" because of the action of repulsors D and E. The merger of these two conceptions occurs when the individual experiences Limbo and realizes that the plane includes a set not just of integers, but of all concepts: by being in Limbo the perceiver act as a powerful strange attractor, and the things they form from Limbo are comparable to a basin of attraction. * The actual planar description of Limbo fits a lot of the description flourishes Ovid uses for Χάος in the Metamorphoses: a bottomless gulfs in which one falls forever, and that lacks orientation. Arguably it also has the womblike quality of Hesiod's Χάος. I tend to think that Limbo would have no fixed position on the subject of math--neither for nor against--though there would be a recognition of its deterministic qualities when applied to the end of "describing" a function. I could see Chaos essentially denying the basic premise of math: there is no such thing as a perfect circle, there is no such thing as a line, thus all systemic logic emanating from this pure forms in ultimately moot. Slaadi, in a sense, might have an implicit appreciation of the idea of strange attractors...if one were to look at their random actions, whether a mere fidget or an elaborately plan, as experiments in triggering cause-and-effect--seeing what they could put into motion--then they cease to seem crazy and start to seem more...expressionistically artistic.
sciborg3 03-30-08, 03:16 PM	Anyone have details on the Pythogoras cult?
beej_silver 04-09-08, 11:34 AM	I fail to see why imaginary numbers are unlawful. I spent 3 units on Complex Analysis, and inherent in this is the Imaginaries' structurally sound form. And on one of more traditional Analysis classes, my professor showed us a method of using imaginaries to manipulate reals. (eg. 13 is not factorable, you say? Why, 13=(3+2i)(3-2i)) You'll be amazed at how structured and necessary imaginaries are. And Physics use imaginaries to describe very real phenomena (or so I've been told by my friend the physics major). Math is LAW.
sciborg3 04-09-08, 05:25 PM	I don't think anyone (I haven't gone through these posts in awhile) was suggesting imaginary eq? chaotic. As you say, the "imaginary" axis is really a mathematical idea that describes real world events. Irrationals, on the other hand I'd like to think of as chaotic though there is room for debate if not outright refutation of that. I asked one my old professors about the question of whether math is discovered or created, and he said math was created yet had an almost eerie ability to describe things in reality. I kinda think math is created - after all there are times when the math gets created first, then we find some use for it. Like all of number theory which ended up being useful for purposes of cryptography.
sciborg3 04-14-08, 06:53 PM	The Proof Web Images of giant spiders made of metres, of those logical equivalences that transcend death, are a flash harbinger's lightning across the eye of your mind. These beings, large as crystal spheres, weave a web that seems to extend itself through all the timelines of all possibilities... The Proof Web is a dream that the Guvner sect known as the Mathematicians believe in with a religious vigor. To their eyes, the Law can only encompass what can be proven mathematically. This at first seems like a weakness, for them Xaos can exist everywhere else. Yet the ideal is that the Law can find it's way through the barriers of the Multiverse, via a supposed "imaginary axis" of Mechanus. Now, it is fact that the so called Real Numbers cannot describe everything Real, and that certain solutions require transformation to the Imaginary aka Complex Number Axis to be solved. Yet does this then translate to a planar path in Mechanus leading to mysterious elsewhere's? And if this Proof Web was real, does it mean any aspect of reality that can be captured by mathematical fields of study is open to the mysterious Axioms (see original thread)? And what then of this strange field told in whispers among the sect, these professors and students fearing to leave Mechanus lest they be set upon the the assassins of Ygorl's pet Soren - Slaad Lady of Anarcy? Could they have found a gateway into the heart of Xaos via their "Chaos Theory"? If so, does this mean that Law might defeat Chaos or will Chaos seep over the threads of rationality the Mathematicians so cling to?
sciborg3 04-14-08, 08:25 PM	perhaps if the Proof Web attempts to find a plane whose size is between the size of integer -- aleph_0 ("aleph-null") -- and the size of the reals 2^{\aleph_0} -- it causes a rupture into the Far Realms?
Bootchie! 04-19-08, 06:27 PM	The sermon of Highest Prime Forteas at the Grand Gearworks, the Grandest of Mathematician Auditoriums in Mechanus: In the beginning there was the void, an endless expanse of nothingness, and there was limbo, an endless expanse of roiling chaos. This was the Zero time. From out of the void roared a voice, saying only: "I"[/B]. We call this the Primal Moment: for in that moment, the First Moment, the first Singular presence in existence came to be, and he took within one hand the Limbaic soup and in the other endless Void and forged from it all Existence. For Limbo represented rawest potential and endless malleability. And the void represented the largest possible quantity of room to work within; which is to say, all Creation. In the Primal Moment, the One and Prime stamped his imprimatur on all existence, organizing existence from meaninglessness, for from him all can be divided. And in that moment was created the impossible, that we refer to as the square root of -1, that is also called Ssendam, not properly a being, but a Limbaic curiousity that acts in such a way to undo all reality. And in that same moment was the equal and opposite reaction to Primus: the negative one, a being of entropy, who would return all to Zero, who would remove all that was singed with the singular in the Primal Moment, that is also called by some Ygorl. And so, having defined existence in the numerical, Primus withdrew to the first point of Creation to witness Existence as so ordered, and was satisfied.
sciborg3 04-22-08, 03:30 PM	great ideas bootchie, ties into some stuff I'm reading about how even the integers can be thought of as arising from set theory, with the empty set being zero and then a successor for each number x being x unioned with {x}....sadly it's a little out of my league at the moment...