68 replies to this topic

[phaze]

P.S.

In no-one's solution do we ever learn if Ja=Yes or if Da =Yes

This is not possible given that we are only given one question to each God (three questions in total) possible replies are

Da Da Da
Da Da Ya
Da Ya Da
Da Ya Ya
Ya Da Da
Ya Da Ya
Ya Ya Da
Ya Ya Ya

8 possible state in order establish the position of the Gods and what Da and Ya mean we need 12 States

Da T R L
Ya T R L
Da T L R
Ya T L R
Da R T L
Ya R T L
Da R L T
Ya R L T
Da L T R
Ya L T R
Da L R T
Ya L R T

So we can only know either the position of the Gods or what they mean when they say Da or Ya but not both
#$@$@! I was hoping in changing the topic

[Yoruichi-san]

Lol...why? The puzzle is solved, the state of existence is not ;P.

(If you want something to do you could always try your hand at the latest Chromatic Witch segment, links on my 'About Me' page )

[mmiguel]

Ah...I think I see now. You're one of the many people who fear uncertainty (the general concept, not the scientific principle). You believe in determinism because you want to, even though none of it, not even the one-to-one and onto nature of cause and effect, can be proven.

(The below is not directed at you, you are personally much more articulate than this, but general arguments with determinists who fear uncertainty and are not so articulate go like this)

"There is an exact one-to-one correlated cause for everything." "Okay, what about spontaneous photonic emission. Why does a particular event happen at that exact time and produce a photon of that exact trajectory?" "Because of reasons we cannot understand yet." "Why does there have to be a reason?" "Because everything has an exact one-to-one correlated cause."

*Sigh*

Personally, I like a little adventure, a little not-knowing what's to come. What it amounts to in the end, I suppose, is a matter of personality and belief system. *shrugs*

Not really, it's more like I feel that there is insufficient evidence to make a confident conclusion one way or the other. I know people say things like, "well it was published in a respected magazine, and all the leading scientists believe it", but I prefer to evaluate how logical something is for myself before blindly believing what someone else says. In most cases, I find articles published in respected magazines very logical, and find that they make sense. If something doesn't make sense to me, I don't necessarily assume it's because it's wrong, and I usually try to dig a little deeper, or simply just reserve judgment. I have not found anything to convince me that randomness exists, mostly just restatements that the popular position is X, without much reasoning. Either that or insufficient reasoning that is cleverly worded to make it seem it accounts for every possible case, when it is in fact limited to certain cases.

Given that there is insufficient evidence, I can really just choose which one seems to be more in line what my other observations about the world. If I turn out to be wrong, then oh well.
Everything else I've observed so far, is readily explained by the philosophy which I've chosen, as far as I can judge. And every time someone says: hey! - this thing isn't explained, I feel that I can come up with a way of showing that what they are pointing out is in fact consistent with my belief.
By believing the opposite side, you are doing the same thing, you just have the benefit of having the more popular belief.

I think we've beat this topic to death.

Edited by mmiguel, 22 September 2012 - 04:46 AM.

[mmiguel]

This is not possible given that we are only given one question to each God (three questions in total) possible replies are

Da Da Da
Da Da Ya
Da Ya Da
Da Ya Ya
Ya Da Da
Ya Da Ya
Ya Ya Da
Ya Ya Ya

8 possible state in order establish the position of the Gods and what Da and Ya mean we need 12 States

Da T R L
Ya T R L
Da T L R
Ya T L R
Da R T L
Ya R T L
Da R L T
Ya R L T
Da L T R
Ya L T R
Da L R T
Ya L R T

So we can only know either the position of the Gods or what they mean when they say Da or Ya but not both
#$@$@! I was hoping in changing the topic

Yeah that makes sense... nice observation!

[Yoruichi-san]

Lol...you're the one who keeps beating it with massive posts bringing up new points .

Speaking of blindly following...that's exactly what determinism is. We are taught as a kid that cause and effect operate one way, and we blindly accept. There is no, and has never been, any evidence that causation is necessarily one-to-one and onto. In fact, in experimental results, there is always a degree of error, which people try to explain with various things, but could this error not be caused by the inherent randomness of the universe? Phenomena such as Brownian motion and spontaneous photonic emission also pose questions that determinism cannot answer other than to use the circular argument that there has to be an underlying cause we don't understand yet because everything has a cause.

In the end whether you want to believe in determinism is a choice, one that you make based on your personality and beliefs. Many good people (including Einstein) choose to subscribe to it, but to think that "it sucks" not to be able to prove causation bespeaks an underlying fear of uncertainty, which is a very human trait. Everyone likes to be in control.

[mmiguel]

Lol...you're the one who keeps beating it with massive posts bringing up new points .

Speaking of blindly following...that's exactly what determinism is. We are taught as a kid that cause and effect operate one way, and we blindly accept. There is no, and has never been, any evidence that causation is necessarily one-to-one and onto. In fact, in experimental results, there is always a degree of error, which people try to explain with various things, but could this error not be caused by the inherent randomness of the universe? Phenomena such as Brownian motion and spontaneous photonic emission also pose questions that determinism cannot answer other than to use the circular argument that there has to be an underlying cause we don't understand yet because everything has a cause.

In the end whether you want to believe in determinism is a choice, one that you make based on your personality and beliefs. Many good people (including Einstein) choose to subscribe to it, but to think that "it sucks" not to be able to prove causation bespeaks an underlying fear of uncertainty, which is a very human trait. Everyone likes to be in control.

Ok no more beating then. No evidence for determinisim because errors always can be explained by randomness - agree, but on flip side, all errors can also be explained by complexity (and/or trying to evaluate something that is not well-defined).

I wasn't saying it sucks that I couldn't prove I was right --- I was saying it sucks that we can't come up with a better answer other than, "we can pick whichever one we like better".

[Yoruichi-san]

Alright, I'll let the horse rest since you will, but just in case anyone else is actually reading this and is curious (or if you're curious), it's worthwhile to take a look into the evolutionary and neuroscience perspectives of why humans develop/use the concept of cause and effect .

[joef1000]

Spoiler for Official Answer

http://philosophy.hk...gic/hardest.php
http://en.wikipedia....gic_Puzzle_Ever

The solution I read constructs an answer using the if-and-only-if (iff) construct.

The Truth Table for this, if treated as a boolean operator is:
T iff T = T
T iff F = F
F iff T = F
F iff F = T

A iff B is essentially equivalent to the statement:
the truth of A is equal to the truth of B.

Yoruichi's construction has a similar function to this, although it may not be obvious.

I spent some time thinking about this and came up with what I think is a neat way of looking at iff (sometimes called XNOR).

First some properties:
A iff B iff A = B
A iff T = A
A iff F = not A
where T=True, F=False

It is possible to model the True and False gods using iff.
Suppose the question asked is X.

Here is the programming behind them, given inputs D and L where
D = (Da means Yes)
L = (I am the lying god)

Z = D iff (not L) iff X
If Z is true, answer Da otherwise answer Ja


The neat thing about this is that you can use the fact that if you include a statement an even number of times in a sequence of iff's it is effectively removed
i.e. the property that A iff B iff A = B

If X is the statement for which you are asking the truth of, let X itself have the form:
X = D iff (not L) iff Y
where Y is some other question

Substituting this into the programming for the True/False gods:

Z = D iff (not L) iff X = D iff (not L) iff D iff (not L) iff Y
If Z is true, answer Da otherwise answer Ja

becomes equivalent to:
Z = Y
If Y is true, answer Da, otherwise answer Ja

This is all independent of whether Da=Yes or Ja=Yes (i.e. we don't need to know if D is true in order to get rid of D from this algorithm).

Using X = D iff (not L) iff Y, you can derive a truthful answer to any question (Y) that you want regardless of whether you are talking to True or False and regardless of what Da/Ja means.

This is where you use Hint Puzzle 1, to ensure at question 2 you are talking to someone who is not Random.
You can use question 2 to figure out if you are talking to Truth or False:
X = D iff (2+2=4)
Since 2+2=4 is clearly true, the algorithm becomes:

Z = D iff (not L) iff D iff T = not L
If (not L) is true, answer Da otherwise answer Ja

For the last question, figure out who is Random (basically step 2 from Yoruichi's solution).


Anyway, I thought that the analysis above was pretty neat, and actually provides lots of tools for constructing questions to decipher answers from beings obeying logical algorithms.

Congrats for solving the purported hardest logical puzzle (as claimed by someone anyhow).


P.S.

In no-one's solution do we ever learn if Ja=Yes or if Da =Yes

How would you word a question in the form D iif ¬L iif Y? Can you give me an example of a question in that form?

[mmiguel]

How would you word a question in the form D iif ¬L iif Y? Can you give me an example of a question in that form?

Y = any true/false statement you want e.g. the sky is blue, e.g. I am taller than four inches, e.g. next lotto numbers are X, ...etc etc

Way 1:
Does Da mean yes if and only if you are the True god if and only if the statement Y is true?

Since the three gods know what iff means, they will have no trouble understanding what you are asking.

For those less comfortable with iff, we can restate as follows.

Way 2:
Let C = A iff B
A and B are statements (meaning either of them can be true or false).
C is also a statement (can be true or false).
C states that the truth of A is equivalent to the truth of B.
C states that either:
1. A and B are both True
or
2. A and B are both False

If A and B are both True, or A and B are both False, then C is True.
If one of them is True, and the other False, then C is False.

Now to understand that original expression: D iff ¬L iff Y

Use the associative property of iff: ((D iif ¬L) iif Y)
i.e.
Let Q = D iif ¬L
Evaluate Q first, then evaluate Q iff Y

Since iff is associative, we could have combined (¬L iff Y) first then evaluated the result against D iff .... and we would get the same answer.

Using the truth equivalence concept, the statement in English can be written as:
Is the truth of the statement ( the truth of the statement (Da means yes) is equivalent the truth of the statement (you are Truth) )
equivalent to the truth of the statement Y?

Suppose Y is true. If the God were truthful and Da meant yes, then the God would reply Da.
If the God is not truthful, and Da means yes, then the god still answers Da thanks to the (you are Truth) part of the question.
This is because the god attempts to lie (i.e. flips from Da to Ja), and the (you are Truth) part flips his answer around once again (from Ja back to Da).
If Da actually means no, then the god still answers Da thanks to the (Da means yes) part of the question. The God would attempt to answer Ja, but the (Da means yes) part flips it back to Da.

If Da means no and the god is a liar, then it will still answer Da, following same reasoning as above.
Thus regardless of what Da/Ja means, and regardless of whether the god is Truthful or lying, the question always equates the Truth of Y to Da and if Y is false, to Ja.

Edited by mmiguel, 02 October 2012 - 06:35 AM.