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Thread: Rogue One (Shameless Spoilers)

  1. #136
    can't be bothered Eldorian's Avatar
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    Quote Originally Posted by Joshuas Randallus View Post
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    All circles are flat. If they had anything more than two dimensions they wouldn't be circles.
    Circles are one dimensional, being parameterizable by a single variable, for example angle. I could go into detail on what "flat" might mean, but in the common sense of the word, it means something that can exist in a plane. Unless you mean a filled in circle, but that's usually more technically called a disc. Still flat, though 2d.

 

  • #137
    4e's diaglo Joshuas Randallus's Avatar
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    I was always taught that a circle was all points on a plane at a given distance (the radius) from a center point. "On a plane" = "flat".

    (Later, for me...) Oh, I see that circle can mean either the entire disc or just the boundary. Well, whatever. That's too esoteric.
    Still excited about 4th Edition!
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  • #138
    can't be bothered Eldorian's Avatar
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    Quote Originally Posted by Joshuas Randallus View Post
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    I was always taught that a circle was all points on a plane at a given distance (the radius) from a center point. "On a plane" = "flat".
    Yeah, more or less. That object is one dimensional.

  • #139
    Fascinating COMMUNITY SUPPORTER Mustrum_Ridcully's Avatar
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    Quote Originally Posted by Mistwell View Post
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    1) I don't think Vader ever sees the disk itself. The plans were beamed to the main ship, and he knows once he gets to that main ship that they're on the small ship docked with that main ship (though he doesn't know the identity of that smaller ship). He sees that smaller ship leave, so he knows the plans must be on board it, but he has no reason to think it's on a disk as opposed to in it's computer.

    2) He never saw Leia on that ship in Rogue One. Nor does he have certain identity of that ship (there is no reason for them to broadcast their identification while fleeing). Presumably it's a model with more than one of those types in the galaxy.

    So while Vader is pretty darn sure he has the right ship, and therefore Leia is a spy, it's not necessarily as blatant as that blog portrays it to be. He didn't just see HER flee with a DISK. He saw a ship that looks remarkably like hers flee in this direction with a transmission of the plans on board in some manner.

    The only good point I think he makes is:

    3) "I have traced the Rebel spies to her. Now she is my only link to find their secret base!"

    Yeah. Kinda hard to claim she is his only link. Unless the implication is that, because he's not really in charge of everything left behind on Scarif but is instead only in charge of plans-chasing, that from his inter-empire office politics perspective she's his only link barring having to go back to Tarkin empty handed concerning the base location. But yes, Rogue One does change that line. Might have been better in Rogue One to show the remaining ships either getting away or blowing up.
    One could look at it like this: He has just captured a big Rebellion battleship and whatever he found there, it wasn't the location of their secret base. From all the thousands that might be working on that ship, either no one with the knowledge survived, talked or knew the location. (And as I understand, Yavin IV is not a secret location. The secret is that the Rebels are there and not on some of the other million planets, asteroids or space stations in the galaxy.) He might have learned that only very few people in the Rebel Alliance actually know the real location of the base, and that Leia is one of them. (Which might also be why she was tasked with transporting the data, too, and is docked to that ship in the first place.)

  • #140
    Pony Up! Ovinomancer's Avatar
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    Quote Originally Posted by Eldorian View Post
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    Yeah, more or less. That object is one dimensional.
    Huh? Circles can be parameterized with angle, but you still need a distance. Otherwise all circles are the same. Even if you consider the path along a circle to be a single, looping dimension, the concept of circle requires at least 2 parameters.

    Else please describe the single dimension transform of a circle with radius 2 and a circle with radius 9.
    Quote Originally Posted by PWD View Post
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    I think ovi's right.

  • #141
    Fascinating COMMUNITY SUPPORTER Mustrum_Ridcully's Avatar
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    Quote Originally Posted by Ovinomancer View Post
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    Huh? Circles can be parameterized with angle, but you still need a distance. Otherwise all circles are the same. Even if you consider the path along a circle to be a single, looping dimension, the concept of circle requires at least 2 parameters.

    Else please describe the single dimension transform of a circle with radius 2 and a circle with radius 9.
    Well, topologically speaking, aren'T all circles, squares, rectangles, triangles and what not the same deal?

  • #142
    can't be bothered Eldorian's Avatar
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    Quote Originally Posted by Ovinomancer View Post
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    Huh? Circles can be parameterized with angle, but you still need a distance. Otherwise all circles are the same. Even if you consider the path along a circle to be a single, looping dimension, the concept of circle requires at least 2 parameters.

    Else please describe the single dimension transform of a circle with radius 2 and a circle with radius 9.
    Technically a circle needs a center, radius, and plane of orientation in 3d Euclidean space. Assuming we're talking about a 2d space, and both circles are centered at the origin, then the transformation (x,y) -> (9x/2,9y/2) transforms a circle of radius 2 into a circle of radius 9, but that has nothing to do with the dimensionality of the circle. Same transformation will take a disc of radius 2 to a disc of radius 9 as well, and the transformation is by no means unique. Being parametrized by a single quantity, for example angle, is a sufficient condition to prove an object is one dimensional. edit: Such a parametrization: c(t) = (2 cos t, 2 sin t), t between 0 and 2 pi, for your radius 2 circle.

    Quote Originally Posted by Mustrum_Ridcully View Post
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    Well, topologically speaking, aren'T all circles, squares, rectangles, triangles and what not the same deal?
    Yes. A simple closed loop.
    Last edited by Eldorian; January 4th, 2017 at 09:50 PM.

  • #143
    56% of an excuse nail bunny's Avatar
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    Ugh, temporal philistines. Do I have really have to explain what "flat" means when discussing space/time?
    "We will have so much winning if I get elected that you may get bored with winning. Believe me. - Trump

  • #144
    I can't believe it's an admin COMMUNITY SUPPORTER Bront's Avatar
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    I liked it for the most part, but:

    Vader felt off. Between how he walked, and in particular the neck line of his helm bugged me, as that wasn't how I remembered it.

    There were at least 2 spots with the Star Destroyers where I looked at them and said "That looks like a plastic model". Something about the almost entirely white ship with the only color being the engines just didn't match what I remember. It looked like an unpainted miniature they forgot to add some extra color to in post production a few times.

    The score missed John Williams. It felt like someone tried to emulate him by changing the tempo and key to his music.

    I liked how it addressed the darker side of the Rebellion though.

    It had merits, and I liked more than I disliked, but those aspects took me out of the movie a bit too often.

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    Quote Originally Posted by Eldorian View Post
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    Technically a circle needs a center, radius, and plane of orientation in 3d Euclidean space. Assuming we're talking about a 2d space, and both circles are centered at the origin, then the transformation (x,y) -> (9x/2,9y/2) transforms a circle of radius 2 into a circle of radius 9, but that has nothing to do with the dimensionality of the circle. Same transformation will take a disc of radius 2 to a disc of radius 9 as well, and the transformation is by no means unique. Being parametrized by a single quantity, for example angle, is a sufficient condition to prove an object is one dimensional. edit: Such a parametrization: c(t) = (2 cos t, 2 sin t), t between 0 and 2 pi, for your radius 2 circle.



    Yes. A simple closed loop.
    Your c(t) isn't a single parameter, though. It also has parameter r, which in that case is 2. Angle (t) and radius r are both required to define the circle.

    c(t) = r (cos t, sin t) for t between 0 and 2 pi (radians).

    Edit, shouldn't that be (r, t) not r(cos t, sin t)? The latter is the x,y transform of the circular parameters. Essentially, your c(t) above is still providing a set of x and y points, so still not one dimensional.
    Last edited by Ovinomancer; January 5th, 2017 at 01:00 AM.
    Quote Originally Posted by PWD View Post
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    I think ovi's right.

  • #146
    can't be bothered Eldorian's Avatar
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    Quote Originally Posted by Ovinomancer View Post
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    Your c(t) isn't a single parameter, though. It also has parameter r, which in that case is 2. Angle (t) and radius r are both required to define the circle.

    c(t) = r (cos t, sin t) for t between 0 and 2 pi (radians).

    Edit, shouldn't that be (r, t) not r(cos t, sin t)? The latter is the x,y transform of the circular parameters. Essentially, your c(t) above is still providing a set of x and y points, so still not one dimensional.
    I think your confusion stems from the definition of parameter, for which a circle in 2d space as 3, the two coordinates of the center and the radius, and parametrization, which is the process of finding the parametric equations for something, in this case a curve. In this case, I can find a parametric equation from a line segment to the circle on the plane, and this is sufficient proof that the circle is a one dimensional object. Look at that equation again, and see that r need not vary to pick out the points on the circle. Varying r would in fact vary the circle. I've shown that the circle of radius 2, center origin is parameterizable by a single variable: angle. It's trivial to show that all circles are also parameterizable by angle, with some slightly different equations.

    Another confusion I can clear up, you see the circle as something that exists in 2d space, and it does. It's a one dimensional object in 2d space. A sphere (the surface of a ball) is a 2 dimensional object that exists in 3d space, and you can get strange objects like a Moebius strip which is a single sided, 2 dimensional surface that can only exist in 3d space, or a Klein bottle, which is a 2 dimensional object that can only exist in 4d space. A way to think about these things if you don't like parametric equations is the thought experiment to imagine yourself walking along the object. A circle would look like a line if you're very close to it, and a sphere will look like a plane, etc.

  • #147
    self admitted prolifer kirinke's Avatar
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    How did math get into a discussion about a space fantasy opera?
    Madness does not always howl. Sometimes, it is the quiet voice at the end of the day saying, "Hey, is there room in your head for one more?"

    I is before E except after C, then it's chaos man, mass chaos! Letters coming together into words, but then you go English and they put U's in places that just shouldn't go there... AHHHHHH!!!!!!!!

    My sanity left town along time ago and didn't leave a forwarding address. It's not missed.

  • #148
    can't be bothered Eldorian's Avatar
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    Quote Originally Posted by kirinke View Post
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    How did math get into a discussion about a space fantasy opera?
    Because Rust Cohle spoke memetic nonsense.

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    Quote Originally Posted by Eldorian View Post
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    I think your confusion stems from the definition of parameter, for which a circle in 2d space as 3, the two coordinates of the center and the radius, and parametrization, which is the process of finding the parametric equations for something, in this case a curve. In this case, I can find a parametric equation from a line segment to the circle on the plane, and this is sufficient proof that the circle is a one dimensional object. Look at that equation again, and see that r need not vary to pick out the points on the circle. Varying r would in fact vary the circle. I've shown that the circle of radius 2, center origin is parameterizable by a single variable: angle. It's trivial to show that all circles are also parameterizable by angle, with some slightly different equations.

    Another confusion I can clear up, you see the circle as something that exists in 2d space, and it does. It's a one dimensional object in 2d space. A sphere (the surface of a ball) is a 2 dimensional object that exists in 3d space, and you can get strange objects like a Moebius strip which is a single sided, 2 dimensional surface that can only exist in 3d space, or a Klein bottle, which is a 2 dimensional object that can only exist in 4d space. A way to think about these things if you don't like parametric equations is the thought experiment to imagine yourself walking along the object. A circle would look like a line if you're very close to it, and a sphere will look like a plane, etc.
    You would no doubt be right, if all circles were radius 2. But they aren't. To know a point on an unknown circle you must know 2 things, so it cannot be 1 dimensional. That you can know a point on a known circle with a single parameter doesn't mean that a circle is actually one dimensional. You're just conveniently skipping over information because it's computationally easier to do so.
    Quote Originally Posted by PWD View Post
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    I think ovi's right.

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    can't be bothered Eldorian's Avatar
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    ???

    Quote Originally Posted by Ovinomancer View Post
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    You would no doubt be right, if all circles were radius 2.
    Why should a circle's radius matter? All circles are basically the same object, and they're each one dimensional.

    But they aren't. To know a point on an unknown circle you must know 2 things, so it cannot be 1 dimensional.
    What? Where did you study this shit? How about a line, then? To know a point on an unknown line you must know "2 things," so they cannot be one dimensional? Because you need a point and a direction to specify a line, just as you need a point and radius for a circle.

    That you can know a point on a known circle with a single parameter doesn't mean that a circle is actually one dimensional. You're just conveniently skipping over information because it's computationally easier to do so.
    Jesus, this is like any other conversation with you. You're either a troll or an idiot. I can create a homeomorphism from a line segment to a circle, Jesus, I thought you claimed to be an engineer. If you're not mathematically literate then you should at least know that you aren't. No wonder you dismiss global warming, if you're willing to argue with me about the dimensionality of a circle (something mathematically trivial) when wikipedia is a simple google search away, and when I've already explained my point.. Maybe if the Koch brothers told you that a circle was one dimensional, you'd believe it.

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