Her brain indeed interpolates something!  It interpolates intermediate values between the sphere she starts with and the sphere she's getting.  Power flows out of Opalyn, and she can feel it happening but that doesn't mean she gets all the details on what's happening, any more than you know in numbers how fast your hand is moving when it moves--though it doesn't feel like throwing a stone by moving your hand, more like throwing a stone without moving your hand--

Anyways, the ball of sorcery does something that looks more than slightly unnatural--as if you threw a stone and then it didn't move quite the way Newton said it should--and ends up matching the target magic-ball's intensity pretty well.

The weave is still too far apart, though.

Seems all right! Wouldn't do to get too many things perfect on the first try! Opalyn resists the urge to tighten up the weave.

"That's good enough to charge a lightline!  And we're running out of time so I'm going to go faster from here than is actually smart because the rules say I have to, sorry."

"Next, match the frequency shift I'll produce in my falash.  I'll do it with wizardry, but don't imitate that part, do it with sorcery and will your ball to shift its frequency to match mine.  End."

"Similar to the thing where you said to say fizzbuzz fifteen times, I am not confident I can get this correct on the first try, especially if I'm limited in how I am supposed to do it! But if failure is non-catastrophic, then I am ready. Ready!"

Opalyn repeats the last word to indicate that she actually means it and saying it was not ill-considered.

"Try it anyways, this time.  Go!"

His hand, beneath its own ball of energy, makes gestures; power coalesces, flattens into a very sharp plane, seems to bounce and then sweeps upward through the sphere moving at an exactly constant velocity; dissipating as it exits the sphere fully.  In its wake, the falash nodes are all resonating twice as fast, while having ended up preserving the phase lock of the nodes; though there were brief out-of-phase moments in the wake of the power-plane's passage, and a corresponding tiny energy dissipation.

(Orphan's memories, or maybe just some innate instinct of sorcerers, make it feel like these local interactions make local sense.)

Opalyn switches off her brain as much as possible and tries to will a plane just like Fdera's to move through her sphere just like Fdera's and leak a tiny bit of energy just like Fdera's...

And she tries desperately, with partial success, not to think about how to plug the leak.

That works!

"Okay, so, I really hope you're not just messing with me, here, because you do get punished if we finish without being able to charge the lightline at all and they try to make it unpleasant rather than sexy."

"What you just did was use your sorcery to imitate wizardry.  The problem is that then your falash leaks, the same way mine did, because the phases are not all changing simultaneously.  I need you to just will the node frequencies to shift all at once.  Don't do it using a flat-plane-of-power.  Just do it."

"I'm going to double my frequencies again.  Double yours to match, using sorcery.  End."

Opalyn has no freaking clue what's sorcery and what's wizardry and what's sorcery imitating wizardry! She's just willing things left and right and definitely not doing any math and if no one will explain to her what wizardry is because they don't have time then that's on them!

"Rea-ady," she croaks with a hitch in her voice. Being set up to fail is getting to her.

"You don't sound ready.  Is it possibly the case that the things I said made no sense and you're about to do something weird?"

"Honestly I was about to just do the exact same thing again, because it did seem to work, and I have absolutely no idea what you want me to do. You keep saying to use sorcery as though I know how to do that or what that even means."

Fdera is increasingly lost at sea about the concept of somebody who knows how to differentiate a sine function and has apparently never heard of sorcery.  He doesn't know where to find a person like that, or how to deal with it if as a result they start out with an enormous tendency to think in wizard terms, and he doesn't actually, have time to figure out any of what is going on with her, and he's already stated that if she's faking she'll get punished severely and if she's not faking then saying that again will not help.

"Do not, ever, do the same thing again, if I told you that you did it wrong last time.  Stop and ask more questions."

"Everyone can do at least a little magic.  Everyone can learn to cleverly structure that magic, which is wizardry.  Some people are so powerful that their magic obeys them directly, even after it leaves their soul and body; they're called sorcerers.  Sorcerers can do things by instinct and direct command which wizards take years to learn how to do by fiddling carefully with magic.  The part where you directly command your magic after it's left you, and it still obeys you because you're just that powerful, is sorcery."

"When I change the oscillation frequency of my falash by sweeping through it with more magic that I made, I'm changing magic by influencing it with other magic, which is what wizards have to do.  When I do that, though, the frequencies don't change all at once, they change in the lower part of my sphere and then the middle part and then the upper part.  So while that's going on, some nodes are vibrating faster than others that haven't been sped up yet, and while the gradual change hasn't been completed, my falash is leaking power.  The higher the frequency, the more power it leaks.  If it doubled a few more times it'd explode during the final doubling."

"You're a sorceress, so you can just want the frequency to double, and it will double, all at once in all the nodes, without leaking anything on the next step or exploding in three steps.  You do it with your continuing command over your magic, and not by making more magic that interacts with your first magic.  You don't need to calculate how fast the plane needs to move to synchronize with the node phases as it sweeps past, you want the frequency to double and it just does.  That is something you can do because you are a sorceress and I am not."

"Do you now understand what it is that I want you to do as a sorceress and not as a wizard?"

"That really helps a lot, actually! Thank you for taking the time to explain! I have been so confused!"

"So I think you are telling me that when you demonstrate, the plane is not part of the demonstration. I could look at the sphere, and then close my eyes while the plane went through the sphere, and then look at it again, and that would actually be more informative than watching how you went about it. Is that right?"

"Don't bother thanking me, we're on a time limit.  You aren't actually using your eyes and it shouldn't make a difference if you close them.  That said, yes, you should care about the change from start to end and not how it got there."

Opalyn closes her eyes. Sure enough, there's the sphere. Huh.

"I'm going to double my sphere's intensity again.  You should be able to see the end result of double, remember double, and then will your sphere to do double all at once simultaneously.  End."

"I am still not sure I am going to nail exact doubling, but I think I will at least manage a simultaneous increase. If that's good enough, then: ready."

"Go."  He sweeps a plane through his sphere again; this time about a third of the energy leaks out during the process.

A third! Jeez Louise.

Opalyn wills the frequencies of all of the nodes in her sphere to double. She doesn't use a plane.

She wills; magic obeys.

"Great!  Remember that.  Later we're going to start with a long slow frequency that's easy for your senses to feel and duplicate, then double it exactly 32 times to reach the charging frequency for the lightline."

"Next step, hopefully easy now that you've realized you just need to will things: sending out a beam of energy like that."

He demonstrates, again with an incredibly small amount of power by Healthy-Orphan's standards:  From the palm of his hand comes a soft continuous wave of falash-nodes, spilling out of him and into outer space aimed at nothing in particular.

"Can you imitate that magic as exactly as you can, in frequency and node separation interval and propagation speed, at an intensity that isn't tiring at all?  End."

Double it 32 times? Two to the thirty-second power? That's a lot. Opalyn wonders if everyone has to charge at that frequency and what changing the frequency does to the power draw on her and the power output or if something else changes when the frequency changes such that power is not affected to quite that degree.

Like, is this the Grand Duchess lightline charging plan, and Barons only have to double eight times, or something, and it's nowhere near as effective, but at least it's still resonant? Or... what?

Opalyn starts paying attention again. Okay, beams. "Not tiring at all" is an interesting directive. This is an opportunity to leave some headroom for herself.

She attempts the beam. She is a little confused about how frequency and node separation interval and propagation speed are implied to be three independently varying quantities, but she just tries to copy exactly what he did, at a somewhat lower intensity.

She wills; magic obeys.

"Don't dispel your beam yet, as should be your default since I didn't order that.  Now..."

He creates a circle of--not falash, a lesser three-dimensional weave, like a cross-section of falash.  As the previous falash was 4-D and intersected classical space as a sphere, this one is 3-D and intersects classical space as a circle.  It leaks like crazy; he's visibly maintaining it all with his own power.

"This is me imitating a charging port.  I want you to move your beam so that it intersects this circle squarely; and then, by your will, adjust the phase so that the cross-section of your falash beam which intersects it, is exactly in phase with this fake charging port.  Divergences will be visible to you as dissonance and leakage; will the beam's phase to shift in the counter-direction of the sensed divergences causing those sensed leakages, until the leakages are gone."

"Did that make enough sense so you can try it and I can see what you tried?"