Rate Flesh and Stone

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Total votes: 1
Selaboc

chap with wings wrote:rules are made to be broken , logic only constrains imagination.
"Logic, my dear Zoe, merely enables one to be wrong with authority"

Sorry, couldn't resits. Any discussion of logic always brings to mind one of my favorite Doctor Who quotes :)
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toxicspurge wrote:Well, that's not exactly true. If you're at the precise center of the inside of the hollow sphere, the gravity is essentially zero. However, if you're inside the sphere but not at the center, there is gravity. The gravity force and direction would be depended upon where you are in the sphere.
No, it is true! That's the whole point of Newton's calculation -- *anywhere* inside the hollow sphere the total gravitational force due to the sphere is zero. Of course, by symmetry, at the very center the force must automatically be zero. The surprising but true fact is that the force is zero everywhere else inside the shell, too. There's mass all around you, and the forces cancel out exactly.

cheers
Vin
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LizR
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vindu wrote:
LizR wrote: You happen to be wrong about that, because the gravity of a sphere is effectively concentrated at its centre, which is why it's called the "centre of gravity" !
There's a nice calculation, originally due to Newton, which establishes that, for a hollow sphere of mass M:

(i) outside the sphere, the gravitational field is the same as the field due to a point mass M at the centre of the sphere;
(ii) inside the sphere, the gravitational field is zero.

The sudden shift between the inside and the outside has wonderful imaginative consequences. And it means that the "centre of gravity" concept is a bit odder than it might seem at first.

cheers
Vin
That's what I was trying to say. Sorry if it came across otherwise. To summarise the summary of the summary: inside a hollow sphere of uniform thickness, density etc there's no gravity, because the geometry is such that it all cancels out.

Us pedants should stick together....though I have to point out that I only mean that in a metaphorical sense :mrgreen:
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Shaving Foamasi
 
 
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Here's a question for you. If the crack in Amelia's bedroom and that in the forest on the Byzantium were supposed to be the same, how come one linked to another part of reality and the other emitted energy from the end of the Universe that could make it so you had never existed?

And what happened to the one in Churchill's bunker?
You mean you believed the Doctor would never regenerate into a woman?
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Shaving Foamasi wrote:Here's a question for you. If the crack in Amelia's bedroom and that in the forest on the Byzantium were supposed to be the same, how come one linked to another part of reality and the other emitted energy from the end of the Universe that could make it so you had never existed?

And what happened to the one in Churchill's bunker?
"I'll explain later."
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Shaving Foamasi
 
 
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LizR wrote:
Shaving Foamasi wrote:Here's a question for you. If the crack in Amelia's bedroom and that in the forest on the Byzantium were supposed to be the same, how come one linked to another part of reality and the other emitted energy from the end of the Universe that could make it so you had never existed?

And what happened to the one in Churchill's bunker?
"I'll explain later."
:D
You mean you believed the Doctor would never regenerate into a woman?
mican

Shaving Foamasi wrote:And what happened to the one in Churchill's bunker?
They took it with them when Starship UK left Earth .....
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vindu wrote:
toxicspurge wrote:Well, that's not exactly true. If you're at the precise center of the inside of the hollow sphere, the gravity is essentially zero. However, if you're inside the sphere but not at the center, there is gravity. The gravity force and direction would be depended upon where you are in the sphere.
No, it is true! That's the whole point of Newton's calculation -- *anywhere* inside the hollow sphere the total gravitational force due to the sphere is zero. Of course, by symmetry, at the very center the force must automatically be zero. The surprising but true fact is that the force is zero everywhere else inside the shell, too. There's mass all around you, and the forces cancel out exactly.

cheers
Vin
That seems counter-intuitive to me. I haven't done the math, but it seems to me that if you're anywhere other than directly in the center, since gravity is inversely proportional to the square of the distance from the mass, the force vectors couldn't cancel out.

To think of another construct, drill a whole through the center of the earth and presume the construct remains stable. If you drop a ball into the hole, it will oscillate back and forth throught the whole, eventually it will come to rest at the center because that's the only place where the forces will cancel each other out.

If you remove the mass from the inside of the solid sphere (giving you the hollow sphere), you maintain all the same symmetries, therefore the final gravity effects within the sphere should remain the same.

If we assume for a second there's no gravity anywhere within the sphere, what happens if you then add one molecule directly at the center of the sphere? Does the one molecule at the center of the sphere now induce gravity everywhere within the sphere except at the exact center?
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Newton was right, dammit! (Well, apart from the perihelion of Mercury...but that took 300 years and Einstein to sort out.)
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After the retcon of "the Angels freeze because they THINK you can see them", no 2 on my list of big gripes with this story was, not the crack in time doohickey itself, but the way it was used. I'll forgive Moffat for having it lead to a prison in the first episode and the end of the universe now, maybe these are 2 different cracks :roll: . However, there's also this memory erasing business, and that just ties the story in knots.

The best I can make of the "reset" ending is that it happened for the Doctor, Amy and River Song, because time travellers have special memories, but it didn't happen for anyone else. Hence Amy remembered her escorts after they'd disappeared into it, but the soldier who was left behind with her didn't. Logical so far, but what do the soldiers actually think they're doing there, at the end of the story? And why does River Song, apparently a seasoned time traveller herself, think she might get a pardon?

As far as I can see, her next trip to the parole board is going to go like this:

"Well, Doctor Song, we sent a task force to the wrecked starship like you said, but there was nothing there."

"But it was full of Weeping Angels! . . . . Oh. Hang on. They got erased from history, didn't they? But they were there! We saved the entire planet."

"All we know is that several men had their necks broken. Since you and your friends were the only people on the scene..."

"No, it was the Angels!"

"Well it sounds to me like you made up the whole thing in the hope you'd get a chance to give your guards the slip, and killed a few of them into the bargain."

"But..."

(As she is taken back to her cell, RS makes a mental note that next time, she musn't erase all traces of her good deeds from the space-time continuum.)

PS - of course it's possible those men didn't die after all, once the Angels were erased. Have I missed another "Everyone lives!" ? Vomiting Smiley Face
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Did anyone notice that when the Doctor leaves Amy in the forest and he has that big close-up conversation with her about trusting him that he has his jacket on?

Someone in continuity wasn't paying attention or perhaps it is a clue to something in the finale... :shock:
You mean you believed the Doctor would never regenerate into a woman?
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toxicspurge wrote: That seems counter-intuitive to me. I haven't done the math, but it seems to me that if you're anywhere other than directly in the center, since gravity is inversely proportional to the square of the distance from the mass, the force vectors couldn't cancel out.
One argument (Newton's) goes like this. Pick any point p inside the sphere. Look in some direction and contemplate a small piece of the shell. Look in the opposite direction, and contemplate the diametrically opposite piece of shell (from your vantage point). The areas of the two pieces are proportional to their squared distances from you, divided by Cos(T), where T is the angle of tilt of each piece away from your line of sight. However, by a standard theorem on circles and subtended angles, both pieces have the same angle of tilt. The area of the two pieces are therefore just proportional to their squared distances from you. So their gravitational forces cancel out. Now integrate over your whole visual field.

Another, cleaner, argument uses the divergence theorem (aka Gauss' theorem). The total gravitational flux through a closed surface is proportional to the total mass enclosed by the surface. Consider a sphere inside the shell, with the same center. By Gauss' theorem, the total gravitational flux through such a sphere is zero. By symmetry, this means that the normal-direction gravitational field is zero at every point on the sphere. Again by symmetry, this means that the gravitational field is zero.
toxicspurge wrote: To think of another construct, drill a whole through the center of the earth and presume the construct remains stable. If you drop a ball into the hole, it will oscillate back and forth throught the whole, eventually it will come to rest at the center because that's the only place where the forces will cancel each other out.
True.
toxicspurge wrote: If you remove the mass from the inside of the solid sphere (giving you the hollow sphere), you maintain all the same symmetries, therefore the final gravity effects within the sphere should remain the same.
No, that doesn't follow at all.
toxicspurge wrote: If we assume for a second there's no gravity anywhere within the sphere, what happens if you then add one molecule directly at the center of the sphere? Does the one molecule at the center of the sphere now induce gravity everywhere within the sphere except at the exact center?
That's true, but not at all paradoxical. The same thought experiment applies if you introduce a single atom into an otherwise empty Newtonian universe.

cheers
Vin
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I need to think about this for a bit, then I'll respond.
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I need to think about this for a bit, then I'll respond.
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So, who was the good man River Song killed? (My bet is that she's really Pontius Pilate...)

And what's going on here? As some people have noticed, the clock changes to the next day at mid-day rather than mid-night! Continuity error, or strange timey-wimey stuff?

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"The clock on the mantel! It is broken! It is time!"
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DaReverendMrMagister
 
 
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Shaving Foamasi wrote:Did anyone notice that when the Doctor leaves Amy in the forest and he has that big close-up conversation with her about trusting him that he has his jacket on?

Someone in continuity wasn't paying attention or perhaps it is a clue to something in the finale... :shock:

...more annoying/intriguing, is the fact that we first see him touch Amy's hands and we see his his right forearm which is totally bare (no shirt or jacket).

WTF
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toxicspurge
 
 
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LizR wrote:So, who was the good man River Song killed? (My bet is that she's really Pontius Pilate...)

And what's going on here? As some people have noticed, the clock changes to the next day at mid-day rather than mid-night! Continuity error, or strange timey-wimey stuff?

Image
Image

"The clock on the mantel! It is broken! It is time!"
The good man River killed was the Doctor. It hasn't happened in his timeline yet.
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LizR wrote:So, who was the good man River Song killed? (My bet is that she's really Pontius Pilate...)

And what's going on here? As some people have noticed, the clock changes to the next day at mid-day rather than mid-night! Continuity error, or strange timey-wimey stuff?

Image
Image

"The clock on the mantel! It is broken! It is time!"

When have you ever known a woman understand how electrical clocks are set. :lol:
My next door neighbour mixed up her KY jelly with the superglue. I asked her how she managed that but her lips are sealed.
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LizR
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Shaving Foamasi wrote:Did anyone notice that when the Doctor leaves Amy in the forest and he has that big close-up conversation with her about trusting him that he has his jacket on?

Someone in continuity wasn't paying attention or perhaps it is a clue to something in the finale... :shock:
I hope it means he travelled back in time, but my pessimistic side says continuity error.

But they did make a big point of showing the jacket swaying in the Angel's hand after he escaped, so perhaps it's all part of some complicated timey-wimey stuff...
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toxicspurge wrote:The good man River killed was the Doctor. It hasn't happened in his timeline yet.
Is that a fact, or are you guessing?
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