You know how people who get trapped on desert islands throw messages in bottles out to sea… THEY’RE LITTERING! For shame…
Actually I think I want to do that. Not get stranded on a desert island (why are they always “desert” islands anyway? Aren’t there other types of islands people get stranded on?) I want to write a message/letter in a bottle and fling it as far as I can into the ocean and just let the Hand of God deliver it to whatever recipient. Maybe a cute tiki girl in Hawaii… maybe a little boy in Panama who dreams of being a rockstar so he jams on his mother’s pots and pans… maybe a penguin? It’d be cool to have some random penpal that fate just decided to dump into my lap.
My roommate drove over a small divider while driving on the freeway and dented his wheel so he had to switch it out for a spare. He’s currently deciding if he wants to save money and buy one mismatched wheel or just buy a set of 4. I proposed a compromise, that he buys a set of two and puts them both on the same side of his car so no one can tell.
The solution to exposing Newcomb’s paradox as fallacy is to view the potential monetary gains against the probability of the beings prediction being correct. For a given probability P the best choice is the one that gives the greatest return.
Return = P(Correct) + (1-P)(Wrong)
Lets assume a probability of 1 (ie. the being has a 100% chance of predicting correctly).
Return from taking B:
1(1,000,000) + 0(0) = 1,000,000
Return from taking both A and B:
1(1,000) + 0(1,001,000) = 1,000
As can be seen, if the being has a 100% chance of predicting correctly then the rewards of taking box B are much more favourable than taking both box A and box B. You may notice that this outcome is equivalent to Argument 2 above. Now let’s assume a probability of 0.5 (the being has a 50% chance of predicting correctly).
Return from B:
0.5(1,000,000) + 0(0) = 500,000
Return from A and B:
0.5(1,000) + 0.5(1,001,000) = 501,000
With a probability of 0.5 the rewards of taking both box A and box B are slightly greater than taking only box B. This means that if the being only has a 50% chance of correctly predicting your choice then you should take both box A and Box B. Now let’s assume a probability of 0 (The being has no chance of predicting correctly).
Return from taking B:
0 + 1(0) = 0
Return from taking both A and B:
0 + 1(1,001,000) = 1,001,000
This time the rewards of taking both box A and box B are far greater than taking only box B.
You may have noticed that the two formulas Return = P(1,000,000) + (1-P)(0) and Return = P(1,000) + (1-P)(1,001,000) are in fact straight lines and can be graphed as such:
The two lines intersect when P is at a value of 0.5005. That is to say that if the being has a greater probability than 0.5005 of being correct then you should take box B. If the probability of the being being correct is less than 0.5005 then you should take both box A and box B.
The paradox should now be exposed to you as a fallacy. If it is not, let me state more clearly why. Argument 1 relies on an implicit assumption that there are equal chances* whereas Argument 2 asserts that there is every chance that the being will correctly predict your choice.
At the end of the day you could say the being is either going to predict correctly or not, ascribe a probability of 0.5 and take both box A and box B. But if the being had previously made 1000 correct predictions then surely this line of action would be 1000 times more foolish than the other? If you say no then I guess you’d give yourself a 50/50 chance of beating Garry Kasparov at chess?
A couple entries ago, I presented a simple thought experiment and received some replies asking what the correct was.
The answer is… there is no answer. Or rather… there are two conflicting answers both with convincing arguments.
The being either has or has not put the money in box B. If the being has put the money in B then taking B results in $1,000,000 whereas taking A and B results in $1,001,000. If the being has not put the money in B then taking B results in $0 whereas taking A and B results in $1000. In both cases the best option is to take both A and B and therefore you should take both A and B.
—————————- Money in B Money not in B
Take Box B———— $1,000,000 $0
Take Box A and B— $1,001,000 $1,000
The being has been correct in all his previous predictions and is therefore likely to predict correctly again. If the being predicts correctly then taking A and B results in $1000 whereas taking only B results in $1,000,000. Therefore you should take B.
Not the peace of a cease-fire,
not even the vision of the wolf and the lamb,
as in the heart when the excitement is over
and you can talk only about a great weariness.
I know that I know how to kill,
that makes me an adult.
And my son plays with a toy gun that knows
how to open and close its eyes and say Mama.
without the big noise of beating swords into ploughshares,
without words, without
the thud of the heavy rubber stamp: let it be
light, floating, like lazy white foam.
A little rest for the wounds -
who speaks of healing?
(And the howl of the orphans is passed from one generation
to the next, as in a relay race:
the baton never falls.)
Let it come
suddenly, because the field
must have it: wildpeace.
You are presented with two boxes, labeled A and B. You are permitted to take the contents of both boxes, or just of box B. Box A contains $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor (an entity somehow exceptionally skilled at predicting people’s actions) makes a prediction as to whether you will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000.
By the time the game begins, and you are called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, you are aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor’s prediction, and knowledge of the Predictor’s infallibility. The only information withheld from you is what prediction the Predictor made, and thus what the contents of box B are.
If he predicted you will take only B, then by taking A&B you will win $1,001,000 rather than $1,000,000 by only taking B. But if he predicted you will take A&B then by taking only B you end up with $0 rather than $1,000 by taking A&B.
“…Like Eli I’m from New Orleans I’m a giant in this b*tch
move the G and add an S and put the I before the N
and put the A in front of that and that is what I am to the end
That’s a Saint muthaf*cka simplify it for them
where your funeral comes with a 2nd line at the end yeah…”—lil wayne - demolition 1 freestyle