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something very strange is going on here
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There is, appropriately, a dream. It is not a particularly interesting dream, but even uninteresting dreams are good places to learn about what is not. It goes like this:

She is alone in a dead place. She is comfortable, there, because dead things do not lie and dead places less still. She is still and she is playing mindless in the sand. Then: there is a sound, and she is no longer alone, because the sound has taken residence in the dead place with her. She greets the sound (but secretly she begrudges it greeting, because sounds are not dead, and so she is no longer safe). She hopes quietly (because sounds have excellent hearing, and she does not wish to offend) that it will leave her, but although she shares its company for as long as she can bear, it does not.

She sets toward the source of the sound. She worries that she may be drawn out of her dead place, but quickly she finds that this worry is unfounded; presently she finds a thing alone in the sand, singing. She wakes up.

This is the oddity: Jane recognizes the thing in the sand -- now, to her slowly-waking mind, the person. She doesn't think that's ever happened to her before. They're in one of the classes she TAs, she thinks? Some undergraduate kid. Maybe they came in for office hours, or something, and she forgot about it. A strange thing to dream about, in any case; she wonders how her mind fixated on this person (what was their name, anyway?) in the absence of any particular emotional attachment -- and why don't people show up, anyway, while emotionally-valent objects do? And why -- (here she forgets about the particular event that launched the chain of enquiry)

 

She doesn't think of it again until later. She's tutoring for an intro chem class, trying to explain orbitals to someone who really should've learnt this in high-school, when she spots a face that is slightly more familiar than it should be.

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The name on the registration is Tomomi Nakano. The name her few friends call her is Ink, for some reason known only to college students.

She'll wait outside the door, quiet (she's always quiet; Jane would be forgiven for not recalling what her voice sounds like, since it's unclear if she's ever talked) until Jane's done with the other student.

She comes in, then, and says, slowly, voice barely audible as she stares at her feet, "I. Need help. With the - a thing."

It's definitely the same voice as that incomprehensible song from Jane's dream. The same face.

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How odd. Perhaps she's more forgetful than she thought; she can't remember having ever heard this girl before, but clearly some part of her subconscious picked up on it as important.

"Sure, come in. What thing can I help you with?" She tries to smile reassuringly, but she's never been good at that.

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"Uh. This."

'This' is a paper with neat handwriting, and carefully succinct questions about redox reactions. Quite a lot of questions. Not all of them on things the class will actually cover, though there's definitely some class material in there. She saw the term 'species' in chemistry, was confused about it, she seems to have trouble remembering which reaction's reduction and why it's reduction, she's mostly got combustion down but disproportionate reactions: weird, she's kind of figured out how to balance simple redox reactions but not how to scale that to complex ones, the entire Nernst equation...

(She also has a question at the bottom if there's more resources elsewhere, explaining that the professor keeps skipping around in the book and it's hard to tell what'll be on tests, and the professor really talks too fast for her to take notes.)

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Ah, wonderful, lots of things to explain! Nice. Hopefully she won't have to explain things twice, because that takes a lot of the fun out of it.

She skims the list, trying to give brief clarifications on things that seem to be common threads -- "Ah, see, when we say "species" in chem we're talking about some substance which is homogeneous in this property we're interested in, it's not really anything to do with animal species -- redox terminology is kind of confusing -- have you done any electronics stuff? It's like how people called current the movement of positive charge; we called the loss of negative charge "oxidization" because oxygen takes electrons and it was the first thing studied -- "reduction" is then the gain of negative charge, which is a little unfortunate --"

She'll happily ramble for quite a while unless she's interrupted.

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Tomomi needs her to repeat herself a lot, and once she relaxes a little gets out a tablet with pictures she can tap to string generated bits of sentence together (which seems to go faster than her trying to do this verbally) as she hums under her breath.

(The song's familiar).

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Jane will repeat things with minimal visible irritation -- this is, after all, her job.

When she recognizes the humming, she startles and stops mid-sentence. That is -- extremely odd.

"Hey, uh, do you happen to know where you heard that song?"

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She startles a bit at the question. "A. Friend?"

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Well. Mystery: frustratingly unsolved, but interrogating the random semi-verbal undergrad doesn't seem likely to help, so.

"Uh, alright. Sorry for interrupting. Where were we -- ah, see, this really makes more sense if you derive it from its parts, instead of just learning the most complex version of the equation, if we look at the ratio of the probabilities of an electron going in one direction or the other..."

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She nods, flips through her notes -

One page, barely visible as she goes past it, is a drawing of a familiar vista. The one the girl would've been overlooking in Jane's odd dream.

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Well. Isn't that interesting-slash-baffling. There is a known algorithm for resolving this kind of confusion, and that is: withhold judgement, acquire evidence, perform judgement. Interrogating the random semi-verbal undergrad suddenly seems much more likely to help.

"-- Okay, you know what, actually, I'll make you a deal. I'll tell you what I know about -- standard potentials, or whatever -- if you tell me what you know about strange dreams in deserts. That sound fair?"

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That is not the face of someone confused about what Jane's talking about. That is the face of someone who's been caught in a lie, mostly familiar from students accused of cheating.

"Uh," is her eloquent answer. "Dreams. Aren't. Real?"

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Jane relaxes fractionally -- it is infinitely more comforting to catch someone being bad at lying than observe someone always seeming to tell the truth. And now, at least, she knows someone who thinks they know what's going on. Probably -- some kind of psychological trick to make people more likely to dream about a particular thing or person? And then she would be a test, of course, some random person unlikely to notice -- (and here she catches herself violating the "withhold judgement" step)

The curious thing is -- why say that? Why not "I don't know anything about that"? Why does this student -- apparently -- think that dreams are real, such that she jumps to deny their reality when questioned?

"... Alright, sure. Unrelated to whether dreams are real or not, would you mind showing me that picture you flipped past? The desert one? And explaining to me how you came to draw it?" She tries very hard to avoid bouncing her leg, because it would completely ruin her persona as some suave professional Adult who definitely-knows-everything-already-and-just-wants-you-to-admit-it. (She doesn't completely succeed.)

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She bites her lip, then flips back to the drawing, takes it out of her binder, and passes it forward. "Imagined it."

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"Thank you."

Yep, that sure is a dream-desert. She leans forward and rests her chin in her hands.

"Alright, here's the thing. I had a dream last night about you. I cannot think of any reason that that would happen, and certainly no reason that the dream-you and the you which I am sitting in front of would have the same musical repertoire. I'm getting the impression that you can think of a reason. Especially since this picture appears to be the setting of that dream.

"I would appreciate it if you would tell me what you know. If someone would punish you for telling me, as I suspect, it may not be in your best interest to tell me in a way that can be easily traced back to you, because I am very poor at keeping secrets. If you can, and if it would be safer, I would ask that you point me at leads such that I can independently find out what this is all about.

"Is this acceptable?"

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She hesitates, then nods, slowly, and taps a picture on her tablet that makes it say, "I need a moment to put my thoughts together" in its usual bland voice.

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Her reply is a few scribbles on a piece of paper - 

813/.52

1985

306-407

cats

And a rough sketch, of what appears to be a ship on a stormy sea, before mountainous islands:

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Oooo, exciting. A puzzle. Are those operators, or symbols? -- is fifteen-hundred-something also a date, one-hundred-and-one probably isn't -- is there some correspondence between boats and cats that she's missing -- is the dash a range? perhaps more likely if they're dates --

"... Ah, uhm. Thank you. And this is all you can tell me? And isn't calculated to be appealing to me specifically? And actually leads somewhere true?"

She probably shouldn't have arranged things this way, because now she's going to have to give an uninteresting lesson with a rather intense distraction. That was a bad idea.

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A lot of slow typing, and:

"It leads somewhere. The first step is some pieces of truth. I don't know somewhere public with more pieces."

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"Right, okay."

And with no obvious way to get more information without threatening the undergrad -- (so irritating to stop digging! but necessary, if she needs to ask more questions later --)

"Uh, I suppose I did say that I would finish helping you with your classwork. Anything else you need me to explain?"

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She's very relieved as she returns to her list of questions.

She's a quick study, at least, once she has someone one-on-one to help.

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Oh, good. She can teach quickly, then.

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She generates a few questions past what she initially was confused about - she really does seem intensely interested in the subject - and leaves kind of awkwardly when she's done.

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Bye, dream-person. And, after confirming that nobody's waiting outside just now--

She feels kind of silly, because she spends ten minutes looking at number correspondences before she just googles them and finds that "813.52" is just part of a book's library call number. American fiction, 1900-1944; presumably "1985" is an edition, the hundreds are page numbers, "cats" is a keyword, and the boat is -- a symbol for something in the book? A symbol for the book itself?

In any case, after she spends another couple of scheduled hours tutoring, she heads to the university library for probably the first time in her life. And sends a quick mental apology to scihub for her infidelity.

How many books are there under 813.52?

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If she looks online, it's hard to search books by Dewey Decimal category, but: thousands, even just those accessible through the library (digitally or hard copy). On the shelves: there's a section for American fiction, which takes up three shelves in this particular library. American fiction, 1900-1944, is a lot smaller, and a solid portion is highly recognizable classics: Great Gatsby, a lot of Steinbeck, the Jungle, the Little House on the Prairie books, Ayn Rand, Gone With the Wind, Lovecraft, Ernest Hemingway, Earth Abides, Tarzan, Hardy Boys...

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