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"You start to see the pattern, hear the rhythm of the world."
  • title-quote

Said by Dumbledore later in this chapter.


primes
  • link

https://en.wikipedia.org/wiki/Prime_number

(Note in particular that every number has a unique prime factorization.)


P=NP
  • link

https://en.wikipedia.org/wiki/P_versus_NP_problem


There couldn't possibly be anything he could master on the first try
which would baffle Hermione, and if there was and it turned out to be
broomstick riding instead of anything intellectual, Harry would just
die.
  • original

This is, in fact, the case in the original series.


"GREGORY GOYLE!" screamed Harry. "I challenge you to a contest for
possession of Neville's Remembrall!"
  • original

The Remembrall was stolen in a similar way in the original series, but with a very different execution. The modified version is meant to show how Harry solves his problems with cunning and words instead of force.


The Remembrall was glowing bright red in his hand, blazing like a
miniature sun that cast shadows on the ground in broad daylight.
  • spoiler

Harry has forgotten an entire life as Voldemort. See the page on his mysterious dark side.


Harry blinked. "But then I'd have lost -"
  • foreshadowing
  • spoiler

Harry has a mental blindspot with regard to plans that require him to lose. Professor Quirrell is going to try to remedy this shortly (19/how to lose). This is related to his intent to kill seen in Chapter 16 (TODO: link), and Harry is finally noticing it is a problem.


I am fated to sit in the Headmaster's office and hear some hilarious
tale about Professor Quirrell in which you and you alone play a
starring role
  • original
  • foreshadowing

"What do I get if I can make it happen on the last day of the school
year?"
  • foreshadowing
  • spoiler

Harry comes very close to this, although it's not clear how "last day" is defined.


a bracelet bearing a lenticular crystal that sparkled with a thousand
colors
  • reference
  • link

Probably a Lens from the Lensman series (https://en.wikipedia.org/wiki/Lensman_series).


a wooden cup filled with what looked like blood
  • reference
  • link

Possibly the Holy Grail, filled with the blood of Christ. Might also be a reference to the Holy Grail from Fate/Stay Night, although that hole grail isn't wooden. (https://en.wikipedia.org/wiki/Holy_Grail)


a statue of a falcon encrusted in black enamel.
  • reference
  • link

Possibly the Maltese Falcon (https://en.wikipedia.org/wiki/The_Maltese_Falcon_(novel)).


one of the three Deathly Hallows and reputed to hide the wearer from
the gaze of Death himself.
  • foreshadowing
  • spoiler

The true meaning of this is that the cloak allows you to hide from dementors.


For a moment Dumbledore's face grew wistful...
  • original
  • spoiler

When he was younger, Dumbledore tried to find and unite the Deathly Hallows, so it is tough for him to let one go.


And so I cannot help but wonder if by some strange chance you have
found not just an invisibility cloak, but the Cloak of Invisibility
  • spoiler

Note that the cloak was left by Dumbledore, just like in the original, probably as part of his prophecy-threading project (79/"Albus," Minerva said, surprised at how steady her own voice was, "did you leave those notes under Mr. Potter's pillow?"). That's the real way he knows Harry has it, not the story-logic he gives as part of his plan to pretend to be insane.


I will only ask that you think twice and ponder three times again, the
next time someone tells you to distrust me.
  • spoiler

Since Dumbledore is the one who left him the cloak, it's likely that he added the note specifically so that he could have this moment where Harry's doubts proved unfounded.


Dumbledore got himself under control again with a visible effort. "Ah,
Harry, one symptom of the disease called wisdom is that you begin
laughing at things that no one else thinks is funny, because when
you're wise, Harry, you start getting the jokes!" The old wizard wiped
tears away from his eyes. "Ah, me. Ah, me. Oft evil will shall evil
mar indeed, in very deed."
  • spoiler

Dumbledore knows the truth about Harry's mysterious dark side, or at least mostly understands it. The joke he's getting is that Tom Riddle's own cold, calculating intelligence is now being turned toward redeeming Draco Malfoy.


I selected him for redemption specifically because he's the heir to
House Malfoy and if you had to pick one person to redeem, it would
obviously be him."
  • original

This is a reference to the original series, in which Draco is the secondary antagonist (behind Voldemort). Over the course of the series, he struggles with his beliefs and upbringing before finally deserting the Death Eaters prior to the final battle.


Speaking of which, Harry, I have a certain something to give you,
something which belonged to your father.  Speaking of which, Harry, I
have a certain something to give you, something which belonged to your
father.
  • original

In the original series, this was the Cloak of Invisibility, but now Harry already has the cloak.


Dumbledore nodded. "But just because I can't think of a reason doesn't
mean there is no reason."
  • spoiler
  • foreshadowing

It's likely Dumbledore is telling Harry to carry the rock around as part of his prophecy-threading project. Harry later uses the rock to kill the troll that killed Hermione. (89/The troll's head blew off its spine as the rock expanded back into its old form)


"I'm feeling thirsty," Harry said, "and that is not at all a good
sign."
  • callback

This is the comed-tea warning Harry that something which would make him choke is about to happen.


Less like an ordinary young hero and more like a young mysterious
ancient wizard.
  • foreshadowing
  • spoiler

At the end of the series, Harry becomes Hermione's mysterious wizard, and Hermione is made out to be the real hero.


potion of eagle's splendour
  • reference

A D&D potion which increases charisma.


Scrawled in the margin was a handwritten annotation saying, I wonder
what would happen if you used Thestral blood here instead of
blueberries? and immediately beneath was a reply in different
handwriting, You'd get sick for weeks and maybe die.
  • spoiler

Dumbledore was writing instructions on how to turn the potion of eagle's splendor into a potion which makes someone permanently more beatiful, as part of his prophecy-threading project. Lily gave the improved potion to Petunia (1/I drank this potion and I was sick for weeks), which led to her marrying Michael Verres instead of Vernon Dursley, which is why Harry is so well-educated.


let's call them sneezes
  • speculation

I've always assumed these were orgasms, based on the principle that any obscure reference about which you have no other information except that it's being withheld from children is probably sexual in nature.


And this one with the golden wibblers is my own invention and Minerva
is never, ever going to figure out what it's doing.
  • foreshadowing

This is mentioned one more time after Dumbledore dies and Minerva takes over as Headmistress. The exact use is never revealed. This also foreshadows that Minerva will become Headmistress.

(119/Minerva's hand passed over one of those objects, the one with golden wibblers, her eyes closing briefly.)


Harry came over, rather puzzled. "This is Fawkes?"

"Fawkes is a phoenix," said Dumbledore. "Very rare, very powerful
magical creatures."
  • spoiler

Dumbledore doesn't actually answer the question - this is in fact a chicken.


Dumbledore's hand dipped into a pocket, and then the same hand sifted
through the ashes and turned up a small yellowish egg.
  • subtle

Dumbledore fished the egg out of his pocket like an incompetent stage magician, probably to make Harry think he's insane.


Dumbledore leaned forward, gazing at him intently.
  • subtle
  • spoiler
  • speculation

It's possible Dumbledore is using legilimency here to check his story. (He asked what they do so that those thoughts would be on the surface of Harry's mind and he wouldn't have to go deeper.)


"Of course," Harry said. "It wasn't reasonable of me to expect the
door to open before I put the quest items in my inventory."
  • reference

In many video games, scenes are written in such a way that players cannot put themselves in a position where it is impossible to win. The implication is that if Harry were to leave without the rock (a quest item), the rest of the story would be unbeatable.


I wanted to tell you as early as possible, in case something happens
to one of us later, that I am truly, truly sorry. For everything that
has already happened, and everything that will.
  • foreshadowing

Dumbledore is later locked outside of time.


"I understand," said Dumbledore. "One last thing then, Harry. You are
not to attempt the forbidden door on the third-floor corridor. There's
no possible way you could get through all the traps, and I wouldn't
want to hear that you'd been hurt trying. Why, I doubt that you could
so much as open the first door, since it's locked and you don't know
the spell Alohomora -"
  • original
  • spoiler

A jab at the original series, where the super-secure chamber holding the Philosopher's stone is secured in such a way that first-year students can enter. In HPMOR, it's a clever trap for Voldemort which the Headmaster pretends is a fake set of traps designed as on obstacle course for Gryffindors trying to get to the "forbidden" thing at the end.