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Subject: Help understanding the Ambiguous Results example. rss

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Enon Sci
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Example embedded below.

The bit that confuses me, and is holding the introduction of this to my group is the reasoning behind the eliminations concluded in the text.

I get that the sign was correctly intuited, but the color is unknown. Since the game has only three possible colors, and we know it wasn't green, the ambiguous red/blue even makes sense. What I don't get is why the text appears to be treating it as if we *did* create both a red and blue potion? Isn't it possible that I could have created a red + potion, but the blue could be negative?

We know the frog is Red+ due to the previous experiment with mushrooms, and I can even understand why the X's are there for fern, but only if I assume this ambiguous test is telling me anything about Blue. But is it? The outcome could have been read, so why do I assume it was telling me anything definitely about blue?

 
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David Goldfarb
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The combinations eliminated are the ones where both red and blue are negative. Since you made a red or blue positive (though you don't know which) then the combinations with both negative are impossible.
 
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Jeff Carter
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The only ones they are eliminating are the ones where both blue and red are negative, since we now know that at least one of them is positive.

Edit: ninja'ed
 
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Enon Sci
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David Goldfarb wrote:
The combinations eliminated are the ones where both red and blue are negative. Since you made a red or blue positive (though you don't know which) then the combinations with both negative are impossible.


But this is only true if the game is saying that red and blue are definitely positive. Is this what I should be assuming?

The way I see it, I have a positive, and reason leads to to conclude it is either red or blue, but *only* because I know it wasn't green. So what is allowing me to make the leap to assuming blue wasn't negative?

 
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David Goldfarb
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Nothing. Blue could be negative, and there are two combinations that haven't been ruled out in which it is.

ETA: you have noticed that we have a previous result in which toad + mushroom is red positive, right? That's why all the red negatives have been x'd from toad. Fern still has two possibilities where red is negative.
 
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Jeff Carter
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Anarchosyn wrote:
So what is allowing me to make the leap to assuming blue wasn't negative?

You DON'T make that leap. What you rule out is that IF red is negative, then blue can't be negative also.
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Robert Stewart
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Anarchosyn wrote:
But this is only true if the game is saying that red and blue are definitely positive. Is this what I should be assuming?

The way I see it, I have a positive, and reason leads to to conclude it is either red or blue, but *only* because I know it wasn't green. So what is allowing me to make the leap to assuming blue wasn't negative?


The logical content of the ambiguous token is: "{Red is positive} OR {Blue is positive}". There are 6 alchemicals with Red+ or Blue+ or both, and 2 alchemicals with both Red- and Blue-. It's those two where both are negative which have been eliminated for Fern.

In other words, you have "R+ OR B+", which is equivalent to "NOT (R- AND B-)", so you can eliminate the alchemicals with Red- and Blue-.

If you want, you could also convince yourself by finding all pairs of alchemicals that make either R+ or B+ potions and seeing which alchemicals are involved sometimes, and which never are.
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