@Tacoタコス no, but it's generally easier to understand and process logically if you state it that way
@Tacoタコス this could also be inverted as "The inverse of "you look terrible today" is false", which makes things very difficult
also, it may not even force an inversion
inversion is just a possibility, brain explosion is a certainty
This was my logic: flippedOdd XOR c = F XOR c = c flippedOdd XOR ~c = T XOR ~c = ~(~c) = c ~flippedOdd XOR c = F XOR c = c ~flippedOdd XOR ~c = T XOR ~c = ~(~c) = c ~(flippedOdd XOR c) = ~(T XOR c) = ~(~(c)) = c ~(flippedOdd XOR ~c) = ~(F XOR ~c) = ~(~c) = c ~(~flippedOdd XOR c) = ~(T XOR c) = ~(~(c)) = c ~(~flippedOdd XOR ~c) = ~(F XOR ~c) = ~(~c) = c
but then I realized that c can be substituted for ~c silently
thus screwing up the whole logic
if you had a way of signalling that inversion occurred, it would work
Which may as well be exclaiming "Gobstoppers!" or something
x.x
in which case you could make a social convention that all lies are followed by a commonly acknowledged signal (e.g., create a new word used only for signalling truthfulness/lies)
Let's have a safe which unlocks by rotating a disc clockwise and counter-clockwise. The disc has numbers from 1 to 100. Three
different two digit numbers are required to open the safe. The following sequence contains the
combination.
120008558588588585855180024424442422400066888668.
What is the u...
You can probably prove that since c can be substituted by ~c at any time, it is indistinguishable what is the truth. Therefore, the only way to handle it is post-processing. That is, limit each compliment to a single statement, and handle its truthiness by commenting after it's been said.
Commenting must then be not a statement (i.e., impossible to negate) and socially acknowledged to be an inversion indicator.
"You can probably prove that since c can be substituted by ~c at any time, it is indistinguishable what is the truth. " - this is going to be because the negation of c is not uniformly "It is not the case that c". Instead, it could be a negation of words inside c that negate the meaning.
Then the listener doesn't even know whether a negation took place, or not (you would still know, since you know your intent)
So I could say "You look awful today. It does not look like you got ran over by a truck. Gobstopper!"
and it should be relatively clear what the meaning is
similarly:
"You look awful today. Gobstopper! It does not look like you got ran over by a truck."
would be clear
obviously you'd have to invent a word or carefully choose something not used as a sentinel
otherwise "I don't want to eat. Gobstopper" could be misinterpreted
as not wanting to eat gobstoppers
I think it's relatively straightforward to come up with the post-processing scheme. The difficult part is showing that the valid types of negation substitution make determining the truth indistinguishable
uh, I'll be heading to university. back in 30 mins
@oAlt i've met a few! they're no longer active on Puzzling, but i met up with both Sp3000 and ffao at the MIT Mystery Hunt
@Avi Are you intending for the answer to your question to be the trick we talked about yesterday? If so, that doesn't work, because the compliment-receiver can't read minds, and so they can't tell whether the statement was inverted
@Deusovi No - I was going for a variation on the XOR trick
however, I realized that the inability to determine inversion makes it impossible to effectively determine the truthiness of a statement
therefore, it must be explicitly specified in a post-processing step including the presence of a sentinel word/words
So a correct answer would (a) show that you can't make a single statement f(p) = p, because f(~p) = ~p is indistinguishable, and (b) bring up the sentinel trick
but the sentinel trick only works with some sort of prior communication protocol, and if you have that you can do anything you want (e.g. set up two uninvertible values, and communicate with binary)
I think simply saying "Sike!" would be relatively clear (i.e., sike is not invertible, and it's an existing way to imply "what I just said is not true")
I'm not sure what you mean there. It seems to me that any reasonable inversion process would make any statement, including things not stated directly, into its opposite: "sike" would become "I meant exactly what I just said".
But it seems very hard to properly define that sort of process. I'm not sure it's even doable.
Again: this requires that the inversion process necessarily doesn't invert things according to their actual meaning, but what their meaning would "normally" be
if you say "potato" to indicate "my statement was not inverted", then "potato" in this context means "my statement was not inverted"
that's one way that the inversion process could work - if you don't want it to work that way, you would have to define exactly how the process parses natural language and understands its meaning
so if I specify that "The inversion process doesn't necessarily invert words according to their actual meaning, but what their meaning would normally be." then the question would be much clearer?
The inversion process doesn't necessarily invert words according to their actual meaning, but what their meaning would be in the same sentence, in a world without inversions.
The inversion process doesn't necessarily invert statements according to their actual meaning, but what their meaning would be in the same sentence, in a world without inversions.
Sure, that deals with both of them in this particular case. But some sentences can't be directly inverted like that - "sike" is an example. So your inverter has to be able to reword things, and therefore it has to "understand" the meaning of the sentence.
Take another example: "What do you think about that performer?"
"He's good!" --- vs --- "He's good..."
The latter has an implicit "...but I didn't like him", or something to that effect. It's a negative comment. If you just said "he's not good", that wouldn't invert the meaning.
Does the inverter then understand exactly what the person speaking is trying to imply? What if the listener would not have caught that implication that the inverter makes explicit?
You can keep patching cases, but weirder and weirder ones will pop up. That's the point I've been trying to make - there's no way to capture the meaning of sentences precisely.
The inversion process doesn't necessarily invert statements according to their actual meaning, but what their meaning would be in the same sentence, in a world without inversions. The inverter is magically able to capture implications and invert statements in a way that listeners will glean the exact same negative information as they would have positive information from the un-altered statement.
because at any point you could be arbitrarily silenced or say something that you didn't mean to
so then, there has to be a specific imperfection in the inverter
which then leads to the puzzle's solution
The inversion process doesn't necessarily invert statements according to their actual meaning, but what their meaning would be in the same sentence, in a world without inversions. Nuances such as sarcasm and hesitation may be lost in inversion, but we assume that straightforward compliments will not include nuance lost in inversion.
"What did you think about that performer?" "Ehh......."
The problem is the same as the problem all the other times: it is fundamentally not possible to determine the meaning of a sentence from the sequence of words chosen.
The same sentence in the same context can mean different things to different people. ("You know that old rich guy who got sick recently? I went and took care of him." can mean something very different to the person who doesn't realize that the others talking are mafiosos.)
The problem is the same as the problem all the other times: it is fundamentally not possible to determine the meaning of a sentence from the sequence of words chosen.
