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Puella Magi Adfligo Systema

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Infinite computation is basically infinite energy. If we have that, we should phone QB and happily iinform him the entropy problem is solved.

DB_Explorer said:
wait ok can someone explain this in simple terms or you know, at least in terms without a background in ...whatever field of study this is covering.
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I'm not sure if this will actually be simple, but here goes.

There's a basic foundational axiom in set theory that asserts that certain sets exist without saying how to construct them. It's very useful for proving a lot of important theorems which mathematicians find intuitive.

However, when you go out of your way to apply it in the most evil way possible, you can prove the existence of some really weird sets. Like pieces of a single ball that can be reassembled into two identical balls.

The Banach-Tarski Paradox is only a paradox in name. It contains no logical contradictions, the proof is perfectly valid. But the result is physically impossible, and you can't even look at it directly because, again, it only shows the procedure is possible without showing how.

The whole thing is controversial among mathematicians to this day. I'm fairly confident trying to replicate it with Grief will fail, in any case.
 
I feel this enchantment science project practice thing might shift and change a lot. For now, I'm gonna vote for this:

[X] The Phoenixian

If we're doing enchantment, making progress towards Pocket Brina could actually be useful, as a security measure in case of Gem snatching, and could help Mami perfecting her own clones.
 
Can we do this?

Firnagzen said:
"What are your research goals?" Niko asks, dipping her chin to rest on her knees.

"De-witching, obviously," you say. "I admit, I don't know exactly how feasible it is. But it's definitely on the list, the other thing being mainly ethical substitutes for Grief Seeds."

"Some way of imbuing your Grief kinesis into a static object?" Niko mumbles. "It sounds like something you might be able to enchant."
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This seems important. And if Niko thinks we should be able to do it, we should keep trying.
 
Roomba said:
Infinite computation is basically infinite energy. If we have that, we should phone QB and happily iinform him the entropy problem is solved.
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I'll point out that, to the best of our knowledge, our grief may well have infinite energy. The actual limits of our energy supply and power-output are difficult and dangerous to test --- and formulating a safe test would be quite valuable --- but we can certainly apply oodles of force and enough light to vaporize a car without appreciably diminishing the volume of a marble.

Wirikidor said:
Can we do this?

"What are your research goals?" Niko asks, dipping her chin to rest on her knees.

"De-witching, obviously," you say. "I admit, I don't know exactly how feasible it is. But it's definitely on the list, the other thing being mainly ethical substitutes for Grief Seeds."

"Some way of imbuing your Grief kinesis into a static object?" Niko mumbles. "It sounds like something you might be able to enchant."
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This seems important. And if Niko thinks we should be able to do it, we should keep trying.
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I put that as session-two goals. :p

More seriously, I think the ability to apply our grief-kinesis to an enchantment depends a lot on exactly how it works and so I kinda want a better handle on what exactly our grief-kinesis is doing in order to provide a basis for such an enchantment.

After all, if we're taking control of our own barrier and witch-flesh that implies very different things than if we're turning grief into a solid substance. In the first case the metaphysics may require a thinking being to control it --- necessitating either an A.I. or a item to imbue others with our own power --- while the second might not and can be applied to essentially just a rock.
 
Right then. One more attempt for tonight, and then I'm probably disappearing for like 24 hours while I screech at exams. "Dimensionality/quantization of grief. True 3D fractals?", "Imbuing Grief kinesis into a static object?", and "what happens if we move a sufficiently large amount of grief outside our control radius" can all probably be folded into grief science time with Homura as our spotter in case it goes pear shaped, since we're already planning on blocking out time for that later, and it is, given, all something of a diversion from the "enchantment" part of enchantment practice time.

150 words by the count.

[x] Airi: Be mild, neutral, polite.
-[x] "Me."
-[x] Explain what's going on and where she'll be staying.
-[x] Telepathically, non-specifically: You'll keep working on what Oriko discussed.
-[x] Address her replies. Ensure she doesn't spill witchbomb.

[x] Vote in abeyance.
-[x] Ensure Oriko's okay with the 'Kures' thing.

[x] Telepathy Masami, Hiroko: re: Ono, progress finding Kuroki.

[x] Mami: Thoughts about O&K, freedom, parole.
-[x] Homura and Sayaka's security/justice concerns.
-[x] Potential solution: O&K tracking, monitoring methods? Technology? Magic?

[x] Practice session.
-[x] With Madoka and Hitomi, if they want.
--[x] Update them about alliance. We're reasonably optimistic.
-[x] Homura: Suggest protective magic development.
--[x] "Her shield might indicate an affinity for it."
-[x] Assist Sayaka with power testing
-[x] Confer with Mami on enchantment curriculum
--[x] Practice analyzing/copying enchantments?
--[x] Non-witchy clone, and components thereof, (sight, coloration, etc.)
--[x] Default: Try replicating basic elements of your power.


Edit: And that sounded a touch more snappish than I meant, sorry.
 
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Roomba said:
Infinite computation is basically infinite energy. If we have that, we should phone QB and happily iinform him the entropy problem is solved.



I'm not sure if this will actually be simple, but here goes.

There's a basic foundational axiom in set theory that asserts that certain sets exist without saying how to construct them. It's very useful for proving a lot of important theorems which mathematicians find intuitive.

However, when you go out of your way to apply it in the most evil way possible, you can prove the existence of some really weird sets. Like pieces of a single ball that can be reassembled into two identical balls.

The Banach-Tarski Paradox is only a paradox in name. It contains no logical contradictions, the proof is perfectly valid. But the result is physically impossible, and you can't even look at it directly because, again, it only shows the procedure is possible without showing how.

The whole thing is controversial among mathematicians to this day. I'm fairly confident trying to replicate it with Grief will fail, in any case.
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...Blech. Thanks for that. I've just spent an hour trying to brute-force away the need for the axiom of choice in the case of "all nonempty subsets of the real numbers". Was drafting it in a Math StackExchange question box under the title "what am I missing?"

Then I hit enough of a dead-end to realize what I was doing.

If anyone's curious, here's the piecewise choice function I had going. It's incomplete because that's where I dead-ended.

1. For a bounded interval, take the midpoint.
2. For a right-unbounded left-bounded interval, take the value that is the left bound multiplied by 2.
3. For a left-unbounded right-bounded interval, take the value that is the right bound divided by 2.
4. For the set of all real numbers, take 0.
5. For a set of reals which is not an interval but which can be defined as "the set containing (some finite set of intervals) and nothing else", apply this choice function to each contained interval, and take the least of those.
6. For a set of reals which is as the one for (5) but for an infinite set of intervals...
I'm pretty sure that if I had something for point 6, I'd have everything necessary. But that's where I got stuck not having any ideas that didn't assume the axiom of choice.
 
Wirikidor said:
Can we do this?



This seems important. And if Niko thinks we should be able to do it, we should keep trying.
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Isn't this essentially what we tried last time we tried enchantment, and instead would up turning the object as malleable to us as Grief is?


Torgamous said:
If they haven't made any progress with Kuroki, should we ask if Sayaka can copy Hiroko's power so she can do it herself?
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Uh... Hiroko's power is illusions, so is it particularly useful for finding people?
 
Why is taking apart an apple and reassebling said apple into two apples of equal volume such a big deal? Wouldn't all apples made from the original have collectively the same mass as the original did alone?

And there is also the problem of dividing infinitely because of a lower limit on the granularity of space at the planck scale. As in, even space itself isn't infinitely divisible.
 
Matou Sutegobana said:
Why is taking apart an apple and reassebling said apple into two apples of equal volume such a big deal? Wouldn't all apples made from the original have collectively the same mass as the original did alone?

And there is also the problem of dividing infinitely because of a lower limit on the granularity of space at the planck scale. As in, even space itself isn't infinitely divisible.
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The Banach-Tarski paradox doesn't correspond to any actual physical process, so asking what happens to the mass is mostly a nonsensical question.
 
Matou Sutegobana said:
Why is taking apart an apple and reassebling said apple into two apples of equal volume such a big deal? Wouldn't all apples made from the original have collectively the same mass as the original did alone?

And there is also the problem of dividing infinitely because of a lower limit on the granularity of space at the planck scale. As in, even space itself isn't infinitely divisible.
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Your two new apples have twice the surface area of your single original apple.

Despite this, you didn't create any new apple skin. You didn't stretch the original skin to be twice as big. You didn't leave half of each apple naked. You just cut the skin apart, shuffled it a bit, and reassembled it as two instances of itself. Ta da!

That's why it doesn't work with actual matter, only with math.
 
BTW, regarding the vote, should we be worried about Yuuri trying to get an ally out of Sakura out of shared dislike (putting it very mildly) for Sabrina?
 
Maths! I love maths!
Roomba said:
Banach-Tarski
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Qwertystop said:
piecewise choice function
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Matou Sutegobana said:
collectively the same mass?
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Alright ladies and gentlemen! Step up and learn about the Banach-Tarski paradox!
Let's imagine we have a ball. This is a mathematical ball, not a physical one, so it's made out of grid lines and geometry, not rubber and matter.
Our ball is made of infinitely many points. There are different kinds of infinity, and the one we have here is "uncountable". That's important because it means that while we can hope to put the points in some kind of order on a line, we can't make progress down it. I can count by finite numbers to get to 4. "1, 2, 3, 4." I can at least TRY to count towards the countable infinity of the integers. "1, 2, 3, 4..." but I'll never finish. I can even count by the rational numbers through a pretty nifty and clever diagonalization method that has me go "0, 1/1 and its negative, 1/2 and its negative, 2/1 and -, 1/3 and -, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1..." and so on. And that will make sure I don't miss any, even though I still can't ever finish because I don't have infinite time.
But against the uncountable infinite of the real numbers, I can't even get started. I mean, sure, zero is the obvious place to start. And whenever we say a number the next one should automatically be its negative, so we count both ways at once. But where do you go next? Any choice is just as wrong. If we try our clever diagonalization again, we can prove we're missing some of the points.
Uncountable doesn't mean there's so many of them that you'll never finish if you try. It means you can't try.
So, we have this ball. And it has uncountably infinite points. It has that many points in a finite volume which is what makes it different from an apple.
We're going to cut it in half. But we're not going to cut it in half like a knife through a melon. We're going to pixel blur it, grab apart the even and odd pixels, and then increase the resolution of that pixelation to infinity to get uncountably infinite pixels, to decide which ones are part of which ball.

If I take this ball:


And I divide it like that, you intuitively expect it would be half as dense, since I took every "even" point, and we expect conservation of mass.


Except that's how real apples work, not math apples. Math apples have an infinite density of points. So when we make it half as dense to cut our second ball from, the new density is still infinite. Which means nothing has changed but now we have two balls.


The step where you increase the pixel resolution to infinity to map pixels to points is the part where you need infinite computing power. If you have the axiom of choice, you assume someone's done that for you and you can just declare your sets as you wish by defining your means to pick them, even if it would take forever to do. If you try it with a real apple, you get two piles of apple-smelling ashes of equal size. Or possibly some kind of nuclear binding force reaction that blows you up for E=(apple)C^2 of damage. Which is a lot.
 
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We also need to talk to Nagisa again - let her know that we have not forgotten about her.
 
E1ChristO said:
We also need to talk to Nagisa again - let her know that we have not forgotten about her.
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Perspective issue is a serious thing in this quest xD I think its only been two or three days since the big picnic we had? For a (much?)-younger random pity-friend we met by chance (as far as her Uncle is concerned!) we might like text her about a tv show or somethin but not really worry about "maan i havent seen you in years!" you know? Or at least its a risk of seeming odd, and since she isn't contracted and not an existing friend like Hitomi I'm a bit unsure what topic would be.
 
The Narrator said:
Isn't this essentially what we tried last time we tried enchantment, and instead would up turning the object as malleable to us as Grief is?
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What I think we should make is an object that removes Grief from a Soul Gem and expels it as a grief cube.
Once we've made that, we need to copy it a bunch -- perhaps Sayaka can make us an enchantment-copying enchantment?
Combine those two magic items and we can adfligo the system pretty thoroughly.

Last time, we were just generally trying to produce an enchanted object, and we had no intent to use it for grief control:

Firnagzen said:
The scratching of her pen is a gentle accompaniment as you exhale and let the thoughts fall away from your mind. You don't want for anything, not right now. No pressing need to create anything, or even try to produce the barrier enchantment or anything, so you just feel the tingle of magic in your body. You guide it out your fingers, into the little porcelain doll held in your hand, and let it take what shape it might.

It... diffuses, for lack of a better word, thinning throughout the ceramic like a drop of ink dropped in water.

You tentatively push more magic into it, trying to see if you can saturate it without breaking it like that cup all the way back then. It seems like not forcing it works, but the magic doesn't really seem to do much other than clinging to the porcelain like a fiery cloud.

"Mm... Sabrina?" Mami asks.

"Yep?" you ask, setting the doll dow-

You don't set the doll down. It sticks to your hand, brittle ceramic suddenly mutable under your fingers. "Huh."

"Hmm?" Mami asks.

You peer down at the ceramic figure, squeezing - and it oozes between your fingers like soft clay, black dress and cheery face smearing.
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So uhm. We can suck grief out of soul gems into griefballs and feed them to Kyubes.
Grief seeds, which have been witches for a while until some magical girl kills them with magic, are filled with enough grief to make a witch from and then to cleanse a magical girl a few times. Then they get fed to Kyubes, who sucks the grief out of them too.
What happens if we attach a magical girl's soul gem to a fishing line, and drop it into Kyubey's back, and then pull it back out again?
Can't he just eat the grief and spit the gem out again?
Because if he can do that and is just turning us into witches just to be a bastard without mentioning his own ability to consume our grief and cleanse any of these girls...
Well my opinion of him will change quite a lot.

Though... I wouldn't want to test this with our gem. Geeze, human testing is annoying to do ethically.
 
Roomba said:
Infinite computation is basically infinite energy. If we have that, we should phone QB and happily iinform him the entropy problem is solved.
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The Phoenixian said:
I'll point out that, to the best of our knowledge, our grief may well have infinite energy. The actual limits of our energy supply and power-output are difficult and dangerous to test --- and formulating a safe test would be quite valuable --- but we can certainly apply oodles of force and enough light to vaporize a car without appreciably diminishing the volume of a marble.
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Huh, that might explain why Kyuubei hasn't gone actively hostile on Sabrina. He's noticed the potential here and seeing if she might be a final solution to the entropy issue.
 
rkyeun said:
So uhm. We can suck grief out of soul gems into griefballs and feed them to Kyubes.
Grief seeds, which have been witches for a while until some magical girl kills them with magic, are filled with enough grief to make a witch from and then to cleanse a magical girl a few times. Then they get fed to Kyubes, who sucks the grief out of them too.
What happens if we attach a magical girl's soul gem to a fishing line, and drop it into Kyubey's back, and then pull it back out again?
Can't he just eat the grief and spit the gem out again?
Because if he can do that and is just turning us into witches just to be a bastard without mentioning his own ability to consume our grief and cleanse any of these girls...
Well my opinion of him will change quite a lot.

Though... I wouldn't want to test this with our gem. Geeze, human testing is annoying to do ethically.
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As it was explained to me, an active Witch slowly generates her own Grief. By suffering, apparently.

So yeah, Grief Seeds? Not fuel.

Generators.
 
"Some way of imbuing your Grief kinesis into a static object?" Niko mumbles. "It sounds like something you might be able to enchant."
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... Did anyone else picture it as a model railway? Like, the tracks are enchanted and grab adjacent Grief to form into mini trains and carriages, which they send on an infinite loop around and around and around.
Maybe I need more sleep.

rkyeun said:
So uhm. We can suck grief out of soul gems into griefballs and feed them to Kyubes.
Grief seeds, which have been witches for a while until some magical girl kills them with magic, are filled with enough grief to make a witch from and then to cleanse a magical girl a few times. Then they get fed to Kyubes, who sucks the grief out of them too.
What happens if we attach a magical girl's soul gem to a fishing line, and drop it into Kyubey's back, and then pull it back out again?
Can't he just eat the grief and spit the gem out again?
Because if he can do that and is just turning us into witches just to be a bastard without mentioning his own ability to consume our grief and cleanse any of these girls...
Well my opinion of him will change quite a lot.

Though... I wouldn't want to test this with our gem. Geeze, human testing is annoying to do ethically.
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I don't think we know if Kyuubey can extract Grief non-destructively? He can accept grief balls, but that's Sabrina's magic at work to get them out. Otherwise, it might be like trying to extract egg yolk without at any point breaking the shell of the egg.

Extraction methods aside, if Grief is the intended product, turning MG's into Witches is hundreds of times more efficient than just feeding from MG's, as can be seen from relative capacities of Soul Gems and Clear Seeds - by Witching, the MG instantly produces Grief equivalent to a century or two of her own usage.
So, if the fishing line approach worked yet he isn't doing it, it's not just to be a bastard. He merely happens to be taking an extremely efficient yet very bastardy route.
 
rkyeun said:
So uhm. We can suck grief out of soul gems into griefballs and feed them to Kyubes.
Grief seeds, which have been witches for a while until some magical girl kills them with magic, are filled with enough grief to make a witch from and then to cleanse a magical girl a few times. Then they get fed to Kyubes, who sucks the grief out of them too.
What happens if we attach a magical girl's soul gem to a fishing line, and drop it into Kyubey's back, and then pull it back out again?
Can't he just eat the grief and spit the gem out again?
Because if he can do that and is just turning us into witches just to be a bastard without mentioning his own ability to consume our grief and cleanse any of these girls...
Well my opinion of him will change quite a lot.

Though... I wouldn't want to test this with our gem. Geeze, human testing is annoying to do ethically.
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Witch outs generate most of the energy KB needs. Every other source of energy generation is paltry by comparison.

Racoras said:
Perspective issue is a serious thing in this quest xD I think its only been two or three days since the big picnic we had? For a (much?)-younger random pity-friend we met by chance (as far as her Uncle is concerned!) we might like text her about a tv show or somethin but not really worry about "maan i havent seen you in years!" you know? Or at least its a risk of seeming odd, and since she isn't contracted and not an existing friend like Hitomi I'm a bit unsure what topic would be.
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But see, it makes sense. Nagisa is a little kid, and kids experience time differently than adults, since they're so young, time seems to last longer, so for Nagisa a couple of days is an eternity.

This also explains the way Sabrina experiences time, as she's just two weeks and hours old.

E1ChristO said:
We also need to talk to Nagisa again - let her know that we have not forgotten about her.
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We also need to repair Kuroki's phone with Grief so we can go through it, and we haven't contacted Hijiri again.
 
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