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Challenging Cyclicity


Nimrodel
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Erm.. Reading all about spheres, cubes and circles in the pinned up thread, i remembered a question i encountered while preparing for my engineering exams( i m not an engineer i am a doctor. I prepared for both)

The question was what would you relate a circle with radius equalling infinity to? The options given were a cube, a sphere, a line or a point.

The answer is very simple. I'l let you people figure it out. Its a paradox.

Hmm. My question is something you will understand after you figure out the answer. You see, I would like to point that the principle of cyclicity will not hold good in case of an infinite circle. If it does, then it should hold good in case of every shape.. Because an infinite circle finally is the basic building block of every shape.. Meaning all the shapes should be cyclic. Its a complex question. You will understand it only if you manage to get an answer to the above question. If you dont, please post, i'l let you know by pm....

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[spoiler]Since it's for engineering, there's no doubt that it the question is about projective geometry and the answer is a line. Projective geometry is build upon lines that always meet (if necessary at 'infinity'), even if you would usually call them parallel. Hence the paradox.
Another way to look at it is by using the curvature ( 1/R ) which is a measure for how bent something is. An infinite radius equals zero curvature. A line is not bent and thus has zero curvature. If you check the dimensionality a line is the only option.

A line is not the building block of anything finite. An interval and a point are candidates for building blocks.[/spoiler]

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[spoiler]i would intentionally add option 5, a plane... but i'd think it's a line, as radius infinity would mean that the visible part of said circle is resembled by a straight line at any given point in space where you could technically not look at it as it's not there, but in infinity...[give me mooooore... i love such things^^]

but no matter what figure it becomes, the cyclicity doesn't seem to fail imo, as every shape whatsoever can resemble cyclicity, even the line, which meets its own end in the point 'infinity' which is the same point on both the ends of such a line, as they say...
at least they say that about parallels [lines that don't cross each other, except for in infinity]

but enough of such nice brain-teasing, and back to boring old brain-killing work with me -.-

EDIT: ouch, now it looks as if i had copied it form Kafuuka :lol: [/spoiler]

Edited by Burns
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You spoke my mind burns. So that means every shape is cyclic. Including the cube. Well.. Now then everything that did originate from the cube is cyclic.. So how does that make the shades different from us? Refering to the association of shades to cyclicity of spheres and spirals, i would say even we should be associated with spheres and spirals... Then how do you explain that the shades mirror us?

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[quote name='Fenrir Greycloth' post='35567' date='Jun 28 2009, 09:22 PM']Both of them are correct. A line is a never ending figure. On a 2d plane, it would appear to be a circle viewed from a 3d perspective.[/quote]

And if we were to put the circle on a curved plane (or whatever the English term for that is), we can make it look like a pretzel. I don't think the engineering faculty would like that answer though.

Besides the distance and angle to the 2d plane matter a lot too when talking about appearing to be.


@Esme:
Burns said every shape can resemble cyclicity. This is not the same as being cyclic.
It isn't difficult to mirror a spiral. Clockwise becomes counterclockwise or you get something in another plane. While a spiral has cyclic properties it also has properties that change under said transformations...

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Hmm, please define cyclicity for me.. I guess I am getting confused.. Because when i say cyclic, i mean the whole thing starts and ends at the same point no matter which way i go or move my pencil..

Well now for spirals.. Erm i agree when you say that spirals go clockwise and anti clockwise when you change the planes. What does that have to do with cyclicity?

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cyclicity doesn't mean that things necessarily start and end in the same point, but that a certain cyclical event (something that happens over and over again) can be seen in them, like in a circle the turning of a point around an axis, in a sphere around a point, or in a spiral around an axis while constantly adding radius
[those are the cyclical events that are easy to explain, like seasons and such, while the cyclicity of an regular object, like a tetrahedron or a cube might be harder to see, and that of a irregular object even impossible to grasp]

the next part is wildest theory-crafting, and just what jumped to my mind in a desperate attempt to forget all about state responibilty :lol:

so, yes, there could be an explanation with spirals turning the other way round for us and the shades, but it could as well be reasonable to see us as orbs, meaning that the shades couldn't find a perfect mirror to the orb without resembling us in every aspect, and therefore decided to replace the point in the middle of the orb by an axis, and in their evolution added a constant to the radius [far-fetched, but not impossible]

as for the cubes around, those might be a step in evolution which contains things, but no life, and as life got added, the whole structure got more dense and formed a sphere instead of a cube, with the extra-complexity of a soul and mind

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Hmm.. Well.. In a square, you can go around and around too.. Cyclically.. I dont want to sound obstinate or imposible. But I just cant grasp what you are trying to say.

Now for the shades and a perfect sphere, erm.. Isnt there a charecter who is a perfect sphere, i think MRD. the one who floats in the air and went to golemus, to gain knowledge, so what about him? Does that interfere with the balance?

Hmm.. And when the shades mirror us.. Erm.. They should also mirror our negative side right? That means they should be having positive sides too right? And erm.. They say that angiens are the natural enemies of shades. So if the shades mirror our negative side, would they still be natural enemies of angiens?

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the square is indeed one of the cyclical objects that meet their own ends, their algorithm is *forward-90° left-forward-90° left...* or an equilateral triangle *forward-60° right-forard-60° right...*, but also things like a stair *forward-90° up-forward-90° down-forward-90°up-forward...* have their cyclical algorithm without meeting their own end (except for in infinity, if you wish)

more complex objects have more complex algorithms, obviously, but only little objects out there can not be broken down to some simple formula explaining how they were created

MRD is a ghost, not a sphere... the traveler from the AL turned into a sphere

and hell, you would have loved to talk to Khalazdad, he had perfect explanations on how the shades work and how they mirror us...

They are not just plainly showing the opposite of what we are showing, but mixing things up a bit...
for example, they showed aggression when we showed pacifism, and got pacifists as we answered with aggression, but they were brave as Wodin was brave, even though you might think they would get cowards when facing bravery...
they are not as simple as they might look at first glance, Peace will be able to tell you excellent stories written by Khalazdad :)

PS: they are not fighting each other, as you might expect when first seeing them as dark and light, but merely coexist... both have their little corner of the realms and are not fihgting when it can be avoided, just like bears and sharks...
and they are not going to try and extinct each other, either, as they plain and simply couldn't... they would never fail to defend their own base, but would always fail to invade the other base, just like bears wouldn't kill a shark in the sea and a shark wouldn't win against a bear in the forests :angry:

Edited by Burns
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*scratches her head* hmm.. Khalazdad has been inactive from the past few days..

And liberty, erm.. Ok.. Erm.. Shades are not natural enemies of angiens.. Why?

Shades are the dark, angiens are the light.. Erm.. They antagonise each other. Arent they like.. Erm.. How do I put it? Like the day and the night. Erm.. How can light exist in dark and dark in light without trying to hide when the other dominates?

Ok.. So now.. I have another question. Tainted angien. How can light be contaminated, erm perveted by darkness? Ok.. Tainted means disgraced.. So why are they disgraced?

Edited by Esmerelda
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no? angiens balance each other :angry: there are two types of angiens if ya dont know :) i dont know to what to compare it only one thing from one other game comes to my mind but then it would be interpreted wrongly

well and angiens and shades arent from same realm :P same as sharks and bears, bears originally live in forest while sharks in ocean :P

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Let's put it simple:

Light can't exist without Dark and vice-versa. does thise mean light is the enemy of dark? NO! this means [b]balance[/b] .

If you look at the genesis of [url="http://magicduel.invisionzone.com//index.php?showtopic=4178"]Golemus[/url] and [url="http://magicduel.invisionzone.com//index.php?showtopic=4179"]Necrovion[/url] , you will realize that it is a balancing of all territory's.

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Erm.. What about loreroot?

And why did golemus create instability? It was a totally different land of its own. I mean it was unconnected to the mainland of magic duel, till the bridge was built..

Edited by Esmerelda
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