Newcomb's Paradox: Angels as Super Intelligent Predictors

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Royal
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Newcomb's Paradox: Angels as Super Intelligent Predictors

Post by Royal » Thu Mar 01, 2012 7:59 am

Before you are two closed Arks, or boxes, labeled "Ark 1" and "Ark 2". An angel explains that Ark 1 contains a golden goblet worth $1,000. Ark 2 contains either a spider worth absolutely nothing or the Mona Lisa painting worth millions of dollars.


You are given two choices:
1. Take what is in both arks, or
2. Take only what is in Ark 2.


The angel says "We have made a prediction about what you will decide. We are almost certainly correct. When we expect you to choose both arks, we put only a worthless spider in Ark 2. When we expect you to take only Ark 2, we have placed the Mona Lisa inside of it. Ark 1 contains $1,000, no matter what we think you will do."


At first, you think you should select only Ark 2. The angels are excellent predictors, and therefore you will get the Mona Lisa. If you take both Arks, the angel will very likely have anticipated your choice and have put a spider in Ark 2. You will only get the $1,000 cup and a spider.


And now the angel confuses you. "Forty days ago, we made a prediction about which you would choose. We already have either put the Mona Lisa or the Spider in Ark 2, and we're not going to tell you."

Now you think you should take both Arks and get everything possible. It seems foolish for you to select only Ark 2, because if you do so, you can't get more than the Mona Lisa. Why give up the $1,000?


This is the essence of Newcomb's Paradox, formulated in 1960 by physicist William A. Newcomb. The puzzle was further elucidated by philosopher Robert Nozick in 1969. Experts still tear their hair out over this dilemma and disagree as to your best strategy.

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Royal
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Re: Newcomb's Paradox: Angels as Super Intelligent Predictor

Post by Royal » Tue Mar 06, 2012 11:58 pm

Sooo...


Ark 1 or Ark 2?

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Pigeon
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Re: Newcomb's Paradox: Angels as Super Intelligent Predictor

Post by Pigeon » Wed Mar 07, 2012 1:45 am

A bit like the Monty Hall problem

The Monty Hall problem is a probability puzzle loosely based on the American television game show Let's Make a Deal and named after the show's original host, Monty Hall. The problem, also called the Monty Hall paradox, is a veridical paradox because the result appears odd but is demonstrably true. The Monty Hall problem, in its usual interpretation, is mathematically equivalent to the earlier Three Prisoners problem, and both bear some similarity to the much older Bertrand's box paradox.

The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. (Selvin 1975a) (Selvin 1975b) A well-known statement of the problem was published in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 (vos Savant 1990):

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Vos Savant's response was that the contestant should always switch to the other door. If the car is initially equally likely to be behind each door, a player who picks Door 1 and doesn't switch has a 1 in 3 chance of winning the car while a player who picks Door 1 and does switch has a 2 in 3 chance. The host has removed an incorrect option from the unchosen doors, so contestants who switch double their chances of winning the car.

Many readers refused to believe that switching is beneficial. After the Monty Hall problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine claiming that vos Savant was wrong. (Tierney 1991) Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy.


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Royal
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Re: Newcomb's Paradox: Angels as Super Intelligent Predictor

Post by Royal » Wed Mar 07, 2012 4:37 am

The light's close in on Pigeon and the camera makes a closeup as 8.5 Million families are at the edge of their seat watching from home: "Which door is he going to pick!" After Pigeon's long stare, the announcer asks again "So which door is it going to be?".

The camera turns back to pigeon. He stops and looks up to the light beating down on him, he escapes the pressure of the audience by pondering the lamps above him, making him sweat. He turns to the camera instinctively with a blank stare on his face, and says the following:

"Humans of the world, I have a message...". It takes 1 minute for him to finish his speech before he returns the situation at hand to pick door two.

The audience is flabbergasted and a sense of mystery fills the airspace. Producers and opportunists seek him as he will have enough book deals and movie royalties to fill a garage with sport cars. ;)

It came to him, during that moment against the light, that the game wasn't going to be him versus boxes, but him versus an entire world. But to do this, he would fight himself- His pride, his selfish nature, his arrogance, his bias, his past, his expectations, and his model of reality.

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Pigeon
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Re: Newcomb's Paradox: Angels as Super Intelligent Predictor

Post by Pigeon » Wed Mar 07, 2012 1:31 pm

"I had hoped to trade them sports cars in on a tractor. Everyone out here knows that you're lucky to get a #3 wash tub and 2 bags of corn for a goat. Curse that darn Wikipedia internet contraption."

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Pana
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Re: Newcomb's Paradox: Angels as Super Intelligent Predictor

Post by Pana » Sat Mar 17, 2012 2:20 am

Wouldn't you take both because it's the only way you can be sure of actually receiving something? It's the only thing you have control over - you don't have control over the decision that was made forty days previous.
“Integrity has no need of rules.”

-Albert Camus

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Pigeon
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Re: Newcomb's Paradox: Angels as Super Intelligent Predictor

Post by Pigeon » Tue Apr 22, 2014 4:55 am

Pana wrote:you don't have control over the decision that was made forty days previous.
Or did you?

The more you know of the past, the more you know of the future.

I think the second law of thermodynamics is some how in here.

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Pigeon
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Re: Newcomb's Paradox: Angels as Super Intelligent Predictor

Post by Pigeon » Tue Apr 22, 2014 4:58 am

You can test out Monty Hall here

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