Hermione Granger and Newcomb's Paradox

post by lsusr · 2020-12-14T05:27:11.667Z · LW · GW · 18 comments

Contents

  Money
  Bits
None
18 comments

Omega hovered before Hermione Granger. Between them rested two boxes labelled "A" and "B".

"Do the boxes have any special powers beyond modifying my Muggle bank balance?" Hermione asked.

"No," Omega said.

"Where do you get the money?" she asked.

"What do you mean?" Omega said with mock incomprehension.

"Fiat currency is a zero-sum agreement between human beings. It is not a physical thing. You cannot conjure one half of a mathematical equation out of nothingness. For you to have a million dollars, a human must have given it to you," Hermione said.

Omega opened an orifice. Its tentacle withdrew an infinite deck of transparent envelopes. Its claw extracted an infinite deck of opaque envelopes. The top envelope of each stack was labelled "#1".

"If you open the transparent envelope then one pound will be deducted from your Muggle bank account and the opaque envelope will have contained nothing. If you never open the transparent envelope then the opaque envelope will have always contained a debt of one pound. You can ensure the opaque envelope contains a debt of one pound by burning the transparent envelope. Do you choose these envelopes over either box?" asked Omega.

"You already know my answer," Hermione said.

"I derive pleasure from you saying it anyway," said Omega, "As do you."

"I choose the envelopes," Hermione said.

"Granted," Omega flew away.

"Wait!" Hermione shouted to the stars, "What did my Box B contain?"

Money

Hermione opened transparent envelope #1. It contained a note stating that "one pound has been deducted from your bank account." Then she opened opaque envelope #1 which contained nothing.

Hermione opened opaque envelope #2. It contained a note stating "one pound has been deducted from your bank account". She burned transparent envelope #2 without opening it.

Hermione flipped a coin eight times. She got THTTHTTH. She opened transparent envelopes #3,5,6,8,9. £5 pounds were deducted from her Muggle account. She opened opaque envelopes #4,7,10. £3 pounds were deducted from her Muggle account. Hermione opened the empty opaque envelopes #3,5,6,8,9. Hermione burned transparent envelopes #4,7,10.

Hermione flooed to Gringotts the next morning where she confirmed the transactions with her account manager Chauna. Together they identified the highest-vega security that could be traded on time-horizons of one hour. Hermione gave opaque envelopes #11-#20 to Chauna and instructed Chauna to open one envelope every hour on the hour. If the envelope contained a note declaring a debt of £1 then Chauna was to buy a fresh demi-wisp skin and then sell it after an hour. It the envelope contained no note then Chauna was to do nothing. At the end of the day, Chauna was to owl Hermione a list of which trades would have earned money that day.

Hermione returned to Hogwarts. At the end of the day, she received her owl. Hermione burned the envelopes corresponding to hourly increases in the price of fresh demi-wisp skins and opened the rest. She and Chauna had netted 79 galleons, 16 sickles and 17 knuts.

Bits

Hermione ordered the construction of a transparent robot to open or burn transparent envelopes. From another contractor, she ordered an opaque robot to quickly log whether opaque envelopes contained a note. The transparent robot sent binary bits back in time. The opaque robot received them.

Hermione paid Chauna to enchant the transparent robot to receive irreversible commands from an enchanted galleon. Then Hermione instructed Chauna to hide the transparent robot somewhere Hermione could never find it. Hermione stored the opaque robot in her own Gringotts vault.

Hermione used her invention to send individual binary bits back in time further than six hours at the price of £1 per bit.

18 comments

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comment by Measure · 2020-12-14T23:03:49.266Z · LW(p) · GW(p)

What would have happened if she had opened transparent envelope #2 instead of burning it after having already discovered that opaque envelope #2 was not empty?

Replies from: lsusr, tetraspace-grouping, ADifferentAnonymous, larry-qiu
comment by lsusr · 2020-12-15T07:25:19.807Z · LW(p) · GW(p)

Only William Newcomb knows the answer.

comment by Tetraspace Grouping (tetraspace-grouping) · 2020-12-15T17:53:24.217Z · LW(p) · GW(p)

Just before she is able to open the envelope, a freak magical-electrical accident sends a shower of sparks down, setting it alight. Or some other thing necessiated by Time to ensure that the loop is consistent. Similar kinds of problems to what would happen if Harry was more committed to not copying "DO NOT MESS WITH TIME".

comment by ADifferentAnonymous · 2020-12-15T17:24:49.480Z · LW(p) · GW(p)

The answer looks something like "if she had been planning to do that, the opaque envelope would have been empty".

Replies from: Measure
comment by Measure · 2020-12-15T18:24:54.682Z · LW(p) · GW(p)

Specifically, what if she had also been planning to do the opposite if it had been empty?

Replies from: ADifferentAnonymous
comment by ADifferentAnonymous · 2020-12-15T21:17:28.156Z · LW(p) · GW(p)

Had she been the sort to do that, Omega wouldn't have made her the offer in the first place.

Replies from: Measure
comment by Measure · 2020-12-15T21:42:25.728Z · LW(p) · GW(p)

This must be why Omega never visits me.

comment by Larry Qiu (larry-qiu) · 2020-12-16T05:10:05.438Z · LW(p) · GW(p)

Her grandfather kills her before she can kill him.

comment by Flaglandbase · 2020-12-15T22:51:55.613Z · LW(p) · GW(p)

"If you never open the transparent envelope then the opaque envelope will have always contained a debt of one pound" .

A debt from who to whom?

Replies from: lsusr
comment by lsusr · 2020-12-15T23:28:18.798Z · LW(p) · GW(p)

From Hermione to Omega.

comment by Measure · 2020-12-14T23:07:00.624Z · LW(p) · GW(p)

Who/what is "Chains"?

Replies from: Pongo
comment by Pongo · 2020-12-14T23:52:01.822Z · LW(p) · GW(p)

90% autocorrect of "Chauna"

Replies from: lsusr
comment by lsusr · 2020-12-15T03:05:17.719Z · LW(p) · GW(p)

Yes. Fixed.

comment by D0TheMath · 2020-12-14T14:24:00.658Z · LW(p) · GW(p)

Typo:

If you open the transparent envelope then one pound will be deducted from you your Muggle bank account and the opaque envelope will have contained nothing. If you never open the transparent

Replies from: lsusr, MondSemmel
comment by lsusr · 2020-12-14T18:42:52.876Z · LW(p) · GW(p)

Fixed. Thanks.

comment by MondSemmel · 2020-12-15T00:27:31.282Z · LW(p) · GW(p)

More typos:

  • "No," Omega says. -> said
  • which contain nothing -> contained
  • Hermione gave opaque envelopes #11-#20 to Chains -> Chauna?
Replies from: lsusr
comment by lsusr · 2020-12-15T03:04:59.003Z · LW(p) · GW(p)

Fixed. Thanks.

comment by Pongo · 2020-12-14T07:26:31.979Z · LW(p) · GW(p)

Should I be reading all the openings of transparent envelopes as actual openings, or are they sometimes looking at the sealed envelope and seeing what it contains (the burnings incline me towards the second interpretation, but I'm not sure)?

EDIT: Oh, I think I understand better now