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Constants Obscura	By : AliceIW Category: Harry Potter > Het - Male/Female > Snape/Hermione Views: 1413 -:- Recommendations : 0 -:- Currently Reading : 0
Disclaimer: I do not own Harry Potter, nor any of the characters from the books or movies. I do not make any money from the writing of this story.

Chapter List
- 1-Constants Obscura
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Disclaimer: I do not own Harry Potter. There are reasons my classics education is costing me more than I'll ever make, and this is one of them. Just playing with JKR's toys.

A/N: yes, therehisthistory in this. No, it doesn't really matter. Yes, I'm making most of it up. No, knowing anything about post-Dante Florence will not affect your understanding of the story one whit. On with the mindless entertainment, then.

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It is tempting to think that there are just three special mathematical constants: pi, e, and i. In fact, there are many, each with its own definition, each originating in some natural way in its own area of mathematics, each given a special symbol and a name too.... The number now universally known as Gamma is accepted to be the most significant of the 'constants obscura'...

—Julian Havil, Gamma: Exploring EulerConsConstant

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Prologue

'It'll be fine, kitten,' her father had said soothingly. 'You'll be perfectly comfortable! Ralph does a—er, a very thorough pre- and post-surgery medication regimen.'

'I know, Dad, but really, Madam Pomfrey can take them out just like that—'

'We've already seen what Madam Pomfrey can do, thank you,' her mother had answered tartly.

'Yes, she kept me from having to go to that ridiculous school dance looking like an over-dressed rodent.'

'Drop it, missy. It's not open for discussion. Some things just oughtn't to be waved away with a magic wand.'

She, Hermione Granger, the ugly little duckling, had just had her wisdom teeth out, and though as far as she could tell looking at her reflection in the window glass she had not become a swan, she felt a certain swell of pride to know that she couldn't be called little anymore. She was finding the whole process very interesting, even now that it was done. For a start, she'd never been drunk or even tipsy before, and that Valium was something else. But more than that, this was one of the traditional coming-of-age experiences, and she had missed most of those that weren't directly connected to her physiology. She grinned as broadly as she could with a rubber prop in her mouth: she had passed the universally recognized dental mark of maturity. All she had to do now was sit her N.E.W.T.s and get laid.

'Now, then, Hermione, just one more stitch and we'll be all through,' Ralph-her-parent's-friend was prattling on behind his double-decker dentist's glasses. Hermione gurgled an acknowledgment, still beaming at the bright window of the fifth-floor London office. She wouldn't particularly care if the fellow wanted to do open heart surgery on her; the world was too lovely a place to bother getting upset about things.

But still, hadn't he better let in the owl at the window?

'Thgh gagh arwl ath'inder,' said Hermione, as the handsome eagle owl pecked impatiently at the glass.

'Oh, no, we're done now, really, just have to clip the sutures,' said Ralph-the-parents'-friend reassuringly. Which he did, and removed the rubber prop. The owl, beginning to look off-put (oh dear), pecked louder and waved the scroll on his foot officiously.

'Thanghs,' said Hermione politely. 'Buh ood you geh th'window, I tshink ih's for me.'

'You're very welcome! Now I'm just going to give you a pain prescription for your parents to fill, wait just one moment...'

Hermione blinked blearily at Ralph's back as he turned to the counter in the corner, ignoring the owl. She sighed in very mild irritation and stumbled to her feet. Fine, she'd get it.

'Whah y'goth'ere?' she asked the owl, and opened the window.

The eagle owl pelted in with a very annoyed hoot, circled the room once, and lighted on the back of the chair. He stuck out his leg for her and glared. Ralph-the-dentist spun around and dropped the remains of Hermione's wisdom teeth as he watched her untie the heavily-sealed scroll from the owl's leg and fall face-first into the dentist's chair.

Hermione righted herself and gazed at the letter she held. A great seal. Red and purple and gold. Thick official ribbon, thick official parchment. What could it be?

Dear Miss Granger,

We are pleased to inform you of your status as an adult witch effective as of 6 July, 1997, 10:53 a.m. As such, you are now eligible to take the International Standard Apparition Examination and are no longer subject to the Decree for the Restriction of Underage Magic. Please find enclosed fair notice of your legal rights and responsibilities and details of your use of a Time-Turner in the 1994-1995 academic year. Happy birthday.

Yours Sincerely,

Mathilda Crabbage

Ministry of Magic

Department of Civil Records

The owl looked at Ralph and her wisdom teeth most coldly, gave a single hoot of disdain, and turned its back on them and launched itself out the window. Hermione gave a drooly grin and waved to his tail feathers from the dentist's chair.

This was the best birthday ever.

* * * *

Whump.

Hermione groaned and opened her eyes. Two great yellow ones stared unperturbedly back from a squashed orange face.

'Go away, Crookshanks,' she croaked, then moaned again as pain and the taste of blood flooded her mouth. The oversized ginger cat blinked, then wandedowndown from her chest to sit on her knees. Hermione shut her eyes and mentally searched through her fuzzy head. She felt dreadful now; what in the name of Merlin's hemorroids had she been so happy about earlier?

Just as she was drifting away from the pain in her mouth and into semi-consciousness, there was a soft knock on her bedroom door. 'You awake, kitten?'

Daddy yes and could you please do something about it?

'I'm up,' she mumbled, spitting out gauze.

John Granger pushed open the door. He was a tall, lanky man with a bulge in the middle, neat wire-rim glasses and thinning gingery hair. In tan trousers and a grey jumper, he looked, as he always did, utterly canny and comfortingly Muggle. He held up a glass of water and an orange bottle in one hand and gave her one of his gentle smiles.

'Got the prescription finally; took a bit longer than it would have... er, otherwise,' he said as he stepped into the room; when he left the medication on her night table and turned to her she could see that his smile, usually small but sure and warm, was rather strained. Then she remembered: Dentist's. Window. Owl. Time-Turner. Parents. Time-Turner.

Oh, no.

Her father drew up her desk chair and perched there, turning over the book that he'd carried in his other hand. He cleahis his throat. 'I, uh, brought you something else, too. I got you this so you'd have something to keep yourself occupied with, but, uh, I suppose I'll have to give it to you as a birthday present.' He looked up at her, all trace of his smile now gone.

'Dat'st's—I'm very sorry about Ralph, really I had no idea I'd get that owl there—'

'Did you know when you'd be getting it?' he cut in quietly. Hermione studied the quilt on her lap and didn't answer. She heard him sigh. 'Were you ever planning on telling us about this?'

'Yes! Well—I mean, I wasn't exactly supposed to talk about the Time-Turner at all, but I would have told you, only it's awfully hard to explain, isn't it? And I didn't realize they'd count it towards my age, I—' She stopped at her father's look, and knew she'd better try for a more coherent explanation than that. 'Professor McGonagall arranged for me to have it my third year, when I took all those classes, and I couldn't even tell Harry and Ron I had it. It's a time-travel device; it let me do hours over again so I could take conflicting classes. That's all.' All but three hours.

Her father rested the book on his knee and looked across at her. 'Hermione, your mother's out in the kitchen and she's—well, you know how your mother is.' Hermione winced; she did indeed know how her mother was. 'I got her to let me talk to you first, but I'm going to have to go out there and give her the explanation she deserves. So I'm only going to ask you once: have you been keeping anything else from us?'

There it was, the question she'd managed to avoid for five years. John and Alice Granger didn't read the Daily Prophet, and their daughter had maintained harmony by simply not telling them about the sort of things she, Harry and Ron really got up to. She wasn't stupid, anymore than Dean Thomas was, and, as she told herself, she wasn't actually being dishonest, either. But now her father, sun and moon and one-man science fair, was asking her point-blank what she'd kept from him. She simply couldn't lie.

'No, Dad,' she lied, 'it was just—well, I knew you and Mum'd never go in for the Time-Turner, but I wanted to take all the classes so much, and really I learned my lesson anyway; that year was horrible.'

He gave her a relieved smile. 'Oh, thank goodness. For a minute there I thought I was about to hear five years' accumulated horror stories.' Hermione smiled very weakly. 'Well,' he said, holding out the book to her, 'I found this for you at that used bookshop you like so much. It's more than high time you read a little of it, and somehow I suspect that you'll like it.'

Hermione took the book: it was heavier than it looked, suggesting thin pages and small type. She turned to the spine, where a coat of arms and a neat '11' were stamped in gold on blue cloth, and on black above them, in lieu of a title, 'Euclid - Archimedes - Apollonius of Perga - Nicomachus'.

'Wow!' she whispered excitedly, the pain in her mouth forgotten.

Her father smiled the indulgent smile that he always reserved just for her, when he was showing her something special. 'There's a lot of particular books I've been collecting for you over the years. I thought I might have a rather fine set for you by the time you're ready for university, but this seemed like a good time to give you that one early.' He frowwithwith mock severity. 'There isn't any proper maths at that school of yours, and I refuse to see my daughter turn out without a decent background in logic.'

'Oh, Daddy!' Hermione threw one arm about his neck in a fierce hug. 'It's beautiful! And I bet once I've read it I can do so much more in Arithmancy!'

He laughed. 'You're strangling me, kitten.' He ruffled her hair (which really made no difference anyway) and handed her the water. 'That should keep you occupied for a while. But I'll tell you what, if you finish with that one, come back and we'll see what els can can get you started on.' He smiled at her fondly. 'There's a whole world out there, even without magic.'

* * * *

Hermione paced her bedroom furiously, demolishing a nail and and wishing for the library at Hogwarts, or Flourish and Blotts, or something.

Of course, it wouldn't have done her a bit of good to be in Diagon Alley right now; the clock on her bookcase read half-past two in the morning. That dream again...

They weren't nightmares, precisely, only... strange. Terribly strange.

There's a whole world out there, even without magic.

Yes, well, there might have been, but it certainly wasn't the same as the world with magic.

She turned on her heel furiously to make another sharp lap across her room, past caring if her footsteps were audible in her parents' room. She couldn't care; she was on fire, her very brain was on fire, and there was nothing she could find to put the fire out.

She loved logic—she'd always loved logicnd snd she'd always loved magic... even before she knew it was real, the idea had had a secret pull on her. She'd never understood it, and had certainly never owned up to something that she'd never understood—what would her classmates say? She was the little science brat, after all; how could you be a science brat and think about things like magic? And now that was precisely her problem: how could she? How could she be cool, and rational, and know for herself that the rectangle contained by rational straight lines commensurable in square only is irrational, and at the same time confront... magic?

And this was what she'd pushed away all summer. She'd read, and read, and learned dozens charms and spells she was free to, learned to cook and knit cables and even to Apparate, and she knew right now at two forty-seven a.m. that it had all been above all to stay too busy to have to think about this biggest of all the questions in her . . Pushing away a question was something she never did, but she'd done it this time... because she had to. She'd shrunk from its size, weight, and what she knew it would do to her when she was finally caught up in it.

How could the world be at once intelligible and magical?

Was there—could there be a rational account of magic? How, how, how could there not?

And what was she going to do if there wasn't?

She bit down on the raw quick of her finger so hard she made an audible cry of pain, then groaned and slumped into her desk chair. She hung her head in her hands and watched her view of her desk planner blur as her eyes filled with tears. This was killing her.

Ironically, it was one of her 'keep busy' summer projects that had got her into this mess of not being able to ignore the problem anymore. Apparition: she had her license now, and it was magic executed without a wand. This interesting fact—not much dwelt on by those who already knew how to Apparate, and so news to her—she had catalogued in her brain with the brilliant pink label given to information which was interesting for reasons she couldn't quite put her finger on. Unfortunately, the reasons had hit her only minutes after she had cleared the last practical skills test (starting in the Department of Magical Transportation and Spontaneous Manifestation and landing within twelve feet of a given mailbox in Perthshire): Apparition wasn't the only magic done without a wand. It couldn't be; if it were, her parents would never have been vexed by the mysterious happenings that had followed in her wake long before she got her Hogwarts letter, and Harry couldn't have blown up his aunt.

On the one hand, this was thrilling—if she had done wandless magic once, why should there be any barrier to her doing it again?—and she was dying to get back to the Hogwarts library to see if the phenomenon had been documented, or if there were any how-to's. On the other, it destroyed the theory to which, in the back of her mind, she'd been hanging desperately: that the wand was not fundamentally different from a gun, or a torch, or any other tool. That the work of magic was somehow up to the wand: a physical object she could hold, look at, take apart if she wanted.

Unfortunately, the theory was patently untenable, and she ought to have always known it. There was no getting around the fact that she lived in a world where the will itself lifted up feathers and defied gravity.

How?

The physics book that her father had given over to her with something like alarm at the pace at which she was reading said that objects could not behave that way—for that matter, even the science textbooks she had always been reading before Hogwarts said that much. But she was a witch, and she knew perfectly well that they could. And the law of non-contradiction told her that the world could not be both.

¬(p & ¬p). Not p and not-p. Not p and not-p, damnit.

She slammed her open palm against the innocent desk planner with a smack that made Crookshanks jump with a yowl. She needed to work through this, she needed to work through it right now. If only Harry or Ron were here...

She snorted to herself. If Harry or Ron were here, the only difference would be that she wouldn't look like she was talking to herself. Harry and Ron were wonderful, the best friends she'd ever had, and she loved them both dearly, but there were areas where they simply didn't align, and this was sure to be one of them. She simply didn't understand what went through their hearts when they talked for hours about Quidditch, aney wey would never understand what was going through hers with this. Their eyes would be glazed in about forty seconds flat. She bit her lip, hard. She was going to explode. She was sure of it. Five, four, three, two, one...

Something scratched at the window and she jumped.

She threw up the window, expecting either Hedwig or Pig, and so was surprised when instead a large tawny owl hopped in and extended his foot politely. She didn't reize ize the owl, but as she seized the letter and scanned it, she did recognize the seal. Viktor. She blinked rapidly, unable to believe that the perfect answer had literally just flown in through her window.

'Are you in a hurry?' she asked the owl almost desperately. The owl blinked warily, as though waiting for a clarification. 'Any hurry at all? Can you wait... can you wait about four hours?'

For answer the owl alighted further in the room, by the water tray she kept for Hedwig's visits, and stuffed his head under his wing without further comment. Hermione sank back into her desk chair in profound gratitude, and, without even opening the letter, grabbed handfuls of parchment and began scribbling as fast as she could.

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Constants Obscura