My understanding is that the cone in question wasn't truncated at two angles, but rather along planes roughly perpendicular to its long axis. That simplifies matters tremendously. Also, we're not going to get precise geometric descriptions, so it's kind of pointless to treat this as a hard problem. Much more practical to simplify it into something easy to solve and use that as a rough approximation that gives us an answer within a factor of two or so.

Oh, yeah, no, the problem in front of us (such as it is because wtf lol) can be simplified, but I was speaking from a general standpoint - is it actually difficult?

Whenever I complained about math as a child my dad always asked me if I knew how to find the volume of a truncated cone yet. The specifics always involved multiple angles. Keep in mind this was the days back before you could google the answer to anything.
 
Oh, yeah, no, the problem in front of us (such as it is because wtf lol) can be simplified, but I was speaking from a general standpoint - is it actually difficult?

Whenever I complained about math as a child my dad always asked me if I knew how to find the volume of a truncated cone yet. The specifics always involved multiple angles. Keep in mind this was the days back before you could google the answer to anything.
Suffice to say that it is difficult. I won't say "very difficult" because that's a moving target, but it's certainly a very grownup-level problem within the confines of classical and semi-classical geometry.
 
Does that even have a solution from pure geometry? I can't find a way to section it up that doesn't eventually require an integration, even if we assume that we're given things like the area of a particular conic section. There just don't seem to be any symmetries to exploit. If you go to calculus it's pretty easy, you can integrate circle segments upward or hyperbolas forward and backward or parabolas at the cut angle, but I'm trying to get the lower bound down below calc and not having any luck.
 
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No, the solution to that requires integral calculus, and you'd need the area of the conic section defined by slicing the cone. If you want to approximate it - well, you could stick a box or ball around it or tile it just using trig, but it's not going to be a very good approximation, and I'm willing to bet that you're not going to get any without a lot of work (i.e. more than using calculus). In terms of difficulty - that would be considered a reasonably hard four-unit (highest level) maths problem for final year high school students here in Australia. I'm unclear where this lies in regard to other educational systems.

(And no, this isn't me getting the difficulty hilariously wrong because I do maths for a living - I've actually tutored students in similar problems).

[q] Calculate the volume of the mana crystals holding Delight's prison together.
[q] Ask Delight what the volume of the mana crystals was when she was imprisoned.
[q] Assuming Delight has been imprisoned for 30 years, how fast have the ants been removing the crystallised mana from the prison?
[q] Using the same calculation, how long will it be until Delight is free, assuming no interference from others?

:p
 
[q] Calculate the volume of the mana crystals holding Delight's prison together.
[q] Ask Delight what the volume of the mana crystals was when she was imprisoned.
[q] Assuming Delight has been imprisoned for 30 years, how fast have the ants been removing the crystallised mana from the prison?
[q] Using the same calculation, how long will it be until Delight is free, assuming no interference from others?

:p


.... I'm going to need a LOT of paper and a caculator...

oh yeah and my calculus book I sold 6 years ago.
 
If you want to approximate it - well, you could stick a box or ball around it or tile it just using trig, but it's not going to be a very good approximation, and I'm willing to bet that you're not going to get any without a lot of work (i.e. more than using calculus).
I mean, if we're going to go with a brute force sampling-based approach, just sample uniform random from the unit cube, drop the sample if it's outside the cone or above the cutting plane, divide to get an estimate, and run until you have enough decimal points. Bonus: embarrassingly parallel, so you can do it on a GPU or a HPC cluster without slowdown! :V

Reminds me of my time in the research lab. It's almost like MCMC.
 
My understanding is that the cone in question wasn't truncated at two angles, but rather along planes roughly perpendicular to its long axis. That simplifies matters tremendously. Also, we're not going to get precise geometric descriptions, so it's kind of pointless to treat this as a hard problem. Much more practical to simplify it into something easy to solve and use that as a rough approximation that gives us an answer within a factor of two or so.
Which is honestly probably good enough, for our purposes. And 4000-7500 cm3​ is...what, about 4-to-7 liters? They're a bit big to haul around, but not completely infeasible.

Although, for any sort of naturally growing crystal, that's...sizable, to say the least. Especially for a solid chunk of crystal. Quartz is the only thing I can think of off the top of my head that would be even relatively commonly found at such sizes. But even with quartz, that sort of size is pretty uncommon. Maybe that indicates they can make them?

Thsn again, there could be parallels to evaporites. Those are water soluble crystals that can form massive deposits, when lots of mineral-rich water evaporates (like rock salt). Mana crystals could likely form in the same way. But, since mana can also saturate the air, you'd likely need a pretty super saturated environment to form crystals of such size.

If that's the case, these are probably pretty damn rare. That sort of environment would be a haven for monsters, and the magical 'radiation' would potentially harm any miners who worked there. And it would probably be really uncommon in-general, barring unusual circumstances.

Edit: ...That moment when you realized you just assumed based on worlds with all three types of mana (crystal, air, and water). Sh*t.
having successfully sidetracked Simon_Jester on a pedantic aside and Vebyast on a calculus problem, I am free to enact my cunning plan to seize control of the thread for once and for all
Meanwhile, I have distracted myself for about 40 minutes with geology.
 
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having successfully sidetracked Simon_Jester on a pedantic aside and Vebyast on a calculus problem, I am free to enact my cunning plan to seize control of the thread for once and for all
Fool! Getting pedantic about math problems only makes me stronger!

If you were trying to weaken me, you would have had to use baleful, forbidden forms of pedantic distractions, such as the terrible morality debate!
 
Fool! Getting pedantic about math problems only makes me stronger!

If you were trying to weaken me, you would have had to use baleful, forbidden forms of pedantic distractions, such as the terrible morality debate!
Well, Delight is CLEARLY [insert moral alignment that directly contradicts your position on the subject here].

:V
 
Could we trade Delight's freedom for knowledge, like just knowledge without erasing any of the knowledge that we currently have?
 
[Q] Engage Delight in a conversation on the mathematics needed to calculate how long the ants will take to finish.
 
I think if we want anything significant from Delight besides "get us out of here," it would be best to free her first, then ask for a reward. She has, in a very unsubtle fashion, warned us that she is likely to act like a jerkass genie if we try to barter with her and haggle to get a reward in return for her freedom.

"The very fact that you have yet to break my bonds indicates you do not properly trust me—or you have yet another gap regarding how Astrals work. Unlike many mortals, we often repay debts more generously than we would if we traded for the equivalent action. I am no exception. Meanwhile, coercion encourages us to give as little as possible.

"I invite you to review your memories of myths and stories. When an Astral was forced to agree to a deal in order to be freed, how often did they seem reluctant and only agreed to the bare minimum? Now please, compare it to the tales of those freed for no set reward. Do you remember which were better?"


Seriously, this is the equivalent of jumping up and down and waving flags and screaming "no haggling, just let me out!" It's couched in a certain amount of indirection, yes, but so is nearly everything Delight says, to the point where I strongly suggest that this is a habit of her style of speaking. It's not as though there aren't plenty of ordinary humans who routinely speak in indirect terms. It's part of being a species adapted for high social intelligence; most members of such a species will be able to parse indirection, and often view it as a form of politeness rather than an attempt to conceal the truth.

[NOTE: I am not denying that she may act like a jerkass genie if we free her first. I am affirming that she will act like a jerkass genie if we try to force concessions out of her as the price for her freedom.]
 
I think if we want anything significant from Delight besides "get us out of here," it would be best to free her first, then ask for a reward. She has, in a very unsubtle fashion, warned us that she is likely to act like a jerkass genie if we try to barter with her and haggle to get a reward in return for her freedom.

"The very fact that you have yet to break my bonds indicates you do not properly trust me—or you have yet another gap regarding how Astrals work. Unlike many mortals, we often repay debts more generously than we would if we traded for the equivalent action. I am no exception. Meanwhile, coercion encourages us to give as little as possible.

"I invite you to review your memories of myths and stories. When an Astral was forced to agree to a deal in order to be freed, how often did they seem reluctant and only agreed to the bare minimum? Now please, compare it to the tales of those freed for no set reward. Do you remember which were better?"


Seriously, this is the equivalent of jumping up and down and waving flags and screaming "no haggling, just let me out!" It's couched in a certain amount of indirection, yes, but so is nearly everything Delight says, to the point where I strongly suggest that this is a habit of her style of speaking. It's not as though there aren't plenty of ordinary humans who routinely speak in indirect terms. It's part of being a species adapted for high social intelligence; most members of such a species will be able to parse indirection, and often view it as a form of politeness rather than an attempt to conceal the truth.

[NOTE: I am not denying that she may act like a jerkass genie if we free her first. I am affirming that she will act like a jerkass genie if we try to force concessions out of her as the price for her freedom.]

Hence my idea for a course of action was to establish *why* we don't trust her, that is to say we are from a different reality and then offer to trade personal stories for personal stories to help establish common understanding and a means to gauge each sides postions in a deal.

Then we let her out if we decide that its reasonable with a basic agreement to do no harm to us and establish the system under which a larger scale deal would occur. Basically we let her out under the deal of 'No harming me and I get a chance to talk about another deal'

Or not let her out at all.
 
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Status report: My cat got a rabies booster just in case, should be fine otherwise. Meanwhile, I'm operating off a cumulative 11 hours of sleep across the past three nights.

Braiiiiiinnnnssss...



Alivaril. If they've been deliberately shaped, or obviously modified, rather than just being unshaped chunks of crystal, it should be obvious, and may tell us something about how this works.

You don't know. It doesn't look like anyone has gone out of their way to smooth their surfaces, but there don't seem to be any especially jagged protrusions. You're not sure why anyone would bother with shaping crystals; as far as you know, shape doesn't matter. Size does.

Also, does Melia know if there are different kinds of mana crystals?

She does not.

[q] Calculate the volume of the mana crystals holding Delight's prison together.
[q] Ask Delight what the volume of the mana crystals was when she was imprisoned.
[q] Assuming Delight has been imprisoned for 30 years, how fast have the ants been removing the crystallised mana from the prison?
[q] Using the same calculation, how long will it be until Delight is free, assuming no interference from others?
[q] Realize you're not sure what you're doing because your mathematical education is sorely lacking. :V
 
[X] You're not sick, by the way. That was just a side-effect of coming here and your translation spell.
[X] Ask more general questions.
-[X] What is an Astral?
-[X] Does she know a way to hug fire elementalsbecome fireproof
[X] While you are chatting, let your Elementals go poke the Mana to see what happens
-[X] See if your stone Elementals can use them as a body.
-[X] See if they can eat them
 
Seriously, this is the equivalent of jumping up and down and waving flags and screaming "no haggling, just let me out!" It's couched in a certain amount of indirection, yes, but so is nearly everything Delight says, to the point where I strongly suggest that this is a habit of her style of speaking. It's not as though there aren't plenty of ordinary humans who routinely speak in indirect terms. It's part of being a species adapted for high social intelligence; most members of such a species will be able to parse indirection, and often view it as a form of politeness rather than an attempt to conceal the truth.
I can believe that. I mean, I typically qualify my statements just so I'm not stating unfounded absolutes.
You don't know. It doesn't look like anyone has gone out of their way to smooth their surfaces, but there don't seem to be any especially jagged protrusions. You're not sure why anyone would bother with shaping crystals; as far as you know, shape doesn't matter. Size does.
Ah, but Melia also didn't know you could use mana crystals like this before she saw it. Also, thanks.

Hm. The lack of jagged protrusions could just be due to the crystalline structure. Numerous types of crystal don't typically form jagged protrusions. Erosion or degradation could perhaps be a factor, since jagged segments generally tend to be smoothed out over time by such processes. If they're formed by mana having fully saturated the environment, then they might also 'evaporate' in environments that lack mana, to keep the environment saturated.
 
[x] Right back at her.
-[x] She's right, you don't have any basis to compare her to. Fairy tales from another world are useless here. For the same reasons, you can't know whether she's the "trustworthy" type - her own words - or the type you have to be cautious with. Her story about the Priestess seemed reasonable given the circumstances, but also served to make you careful about exact details. Maybe that's terribly unfair to her, but it's the impression you got.
-[x] At the same time, based on her assumptions, you're fairly sure she doesn't have any idea what you are either. If she's looking for new experiences, it doesn't get much better than a talent that can randomly portal you into a dragon's lair, or to any number of places that no one on this world has ever seen before. At this point you're farther from home than she is. Does that sound remotely interesting to her?
[x] Explain how you're from another dimension and only in this world temporarily. Weeks at most. And no, you're not sick.
-[x] Her prison seemed like the most interesting of your last set of choices. Satisfying your curiosity is pretty much why you chose to come here.
-[x] That said, given that you have to make snap decisions on where to travel, knowledge and safety are your two biggest challenges right now.
-[x] Do you have anything to fear from freeing her?

It's just SWB's vote, not to worry. Just figured I would copy it here wholesale so that people know what the current winning vote is.

Also this discussion of crystal erosion is fascinating but also really really weird to me... Like... I know why we're talking about this? But at the same time why are we talking about this?
 
Also this discussion of crystal erosion is fascinating but also really really weird to me... Like... I know why we're talking about this? But at the same time why are we talking about this?
SWB already explained this. It's a cunning plan:
having successfully sidetracked Simon_Jester on a pedantic aside and Vebyast on a calculus problem, I am free to enact my cunning plan to seize control of the thread for once and for all


(srs: "what the hell am I doing" is always a hilarious feeling. it tickles my sense of the absurd. like the time i got a quarter of the way through the controls theory for teaching a humanoid robot to throw a grappling hook optimally.)
 
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Question: @Alivaril Are these crystals bigger than Meila's Head?
In the sense of "No matter how tempted I am with the prospect of unlimited power, I will not consume any energy field bigger than my head."?
1. I think it'd be the elementals eating* it, so their headsize is the important one.
2. Happily, the ants have shown that this energy source can be broken up, so we can consume it without violating the rule!

*Clearly the light elemental will have eaten the delicious candy crystal while we have this talk with Delight. They get the generosity. :p
 
Because, my dear Waltz, we are NERDS.
Oh, excessively so.
Yes. However, your elementals shouldn't have any problems consuming mana crystals larger than themselves.
Well. That brings up the awkward question of how we divide them up. I'm for roughly even, though maybe not including the Water Elementals, who have gotten a head-start on the whole growth thing.

On the other hand, I can see an argument for prioritizing our Light and Fire elementals, since they're the ones with the least commonly mana-charged elements. Since the Water Elementals grew so fast in mana-charged water, assumably the same is true for the Air Elementals in high-mana atomospheres, and the Earth and Stone elementals in mana-charged earth. Though maybe the Stone ones will get more of a boost from the crystals? I dunno.
 
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