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Three Gods

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First of all, don't assume I'm talking about general relativity. What I refer to, especially in terms of the influence of relativistic speeds, is special relativity, which has been tied with quantum mechanics (by Dirac), and it is that model that gives the best results and is generally accepted. Einstein himself was a proponent of quantum, he accepted the uncertainty principle and that it resulted in implications of indeterminacy, but he thought the theory was incomplete, and somewhere in completing it he would find something that would allow for determinacy. He never did.

Second, sure there are some extreme cases in which things like "position" or "speed" do not seem to apply, but for the waveforms of real objects, whether it be an electron or a wave on the beach, these things do apply, or "fit". Also, I used position/speed pair since that's the most famous one, and easiest to see why it implies physical uncertainty, but the other pair, energy/time, which does make sense for the waves in question. The mathematical conclusions of Heisenberg hold for all waveforms, even if they are not physically meaningful for extreme, non-physical cases.

Agree that physics is incomplete, and an unifying theory is needed. However, the wave-particle duality is not "peacemaking", or trying to explain results after the fact, but an essential and key concept in QM. Many of the theories (which resulted in such excellent experimental results) were derived specifically based on this duality.

Yes, there are other theories, i.e string theory, and maybe one of them is the correct one. But the thing is, none of the theories I know of overturn quantum's validity on what it is applied to or the uncertainty principle. If we think about it, Newtonian physics were 'good' for centuries, until they discovered microscopic particles and realized the models they had failed on that scale. Quantum and relativity don't overturn the validity of Newtonian physics on macroscopic phenomena, but incorporates a new 'layer', so to speak, one which explains the new phenomena while preserving Newton's equations for macroscopic objects at non-relativistic speeds (since the equations reduce to Newtonian equations on that scale). Of course, I can't be certain :P, but I would hazard to guess that any new theory would similarly reduce to the quantum model in the observed cases.

There are plenty of experiments that prove that particles do exist, albeit they are not necessarily exactly what we think they are at the moment. They might be strings or some other thing we can't envision *shrugs*. Our understanding of microscopic phenomena is constantly changing, but very rarely is what is known overturned, but instead, it is refined. Whatever the truth is, quantum physicists aren't going to be like "OMG we were completely wrong", but instead, like..."aha, that explains it! And that reduces to our model in these cases..."

On determinism, a quote from Heisenberg:In the sharp formulation of the law of causality-- "if we know the present exactly, we can calculate the future"-it is not the conclusion that is wrong but the premise.

--Heisenberg, in uncertainty principle paper, 1927

The key thing about the uncertainty principle is that it is NOT a limitation of technological ability or anything like that, but a fundamental rule of existence, like "matter can be neither created nor destroyed, only changes forms". Sure you can conjecture all you want about "well, if matter could be created or destroyed, then..." and it would be interesting, but the conclusions cannot be applied to the world we live in, since the premise is untrue.

Saying "if we could know the position and velocity (or energy and time) of all particles/waves..." is basically something like a paradox, since you can't know both. And I seem to recall someone saying paradoxes aren't useful...;P

On randomness: where does the reverse causality end? If we trace the causality back to the big bang, then what? Okay, so if the big bang send particles/waves out with certain velocities and energies and you would say that caused everything else, but what caused them to have those exact parameters? (And please don't say God XP)

I think everything you said above is reasonable, and you aren't really attacking the points I made which I find important.

The last paragraph... when does causality end is a very good point.

To me it's pretty much the same as asking: why does the universe exist?

What caused the universe to exist?

Maybe that was the one thing without a cause... although that would be pretty weird....

Maybe we are wrong about the big bang - maybe it wasn't the beginning, maybe the universe has circularly expanded and compressed back to a singularity and big-banged ad-infinitum in the past and will continue to do so in the future.

I have no answer for this, and I'm pretty sure no one else does either.

I'm pretty sure I will end before the universe does.... so by the time this ever happens, I suppose it won't matter to me haha.

No scientific theory I know explains why the big bang happened..... so I don't feel that bad for not being able to answer the question :).

That was a fun conversation, although the three gods might be irritated with us for dropping them out of the spotlight.

Have a good night.

Edited by mmiguel
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Um...I was attacking your points...but in a way that was mainly building my case, since my goal is usually to elucidate what is scientifically right, not to show others are wrong...summarizing my points:

1) Your point about my point about relativity was incorrect as you were citing a different form of relativity than I was, general relativity has to do with the bending of space time and stuff (and honestly, I'm not that familiar with it), whereas special relativity has to do with the effects/implications of moving at relativistic speeds, which was what I was referring to, and is tied in nicely with quantum physics to achieve the best empirical results.

2) Heisenberg's principle does fit the examples you claimed it did not fit, if you use the energy/time form. The mathematical principle can be (and is) interpreted as either you cannot know either the position/momentum OR the energy/time of a particle/wave.

3) Regardless of what new theory is ultimately correct, it probably will not refute/disprove the uncertainty principle since the vast majority of the time new theories 'refine' the results of existing theories for situations that the old theories are not good for and reduce to the existing model/equation for things that already the older theories already are good describers of.

4) The argument "If we had all the information, we could predict everything that happens, hence the world is deterministic" is wrong because the premise is wrong.

Thanks for admitting my arguments are reasonable ;).

I don't think it's weird that the big bang did not have a cause. It would make sense for it to be the random event that precipitated the universe being the way it is.

I enjoyed it too...a good debate with an intelligent, articulate person is always fun :D.

Edited by Yoruichi-san
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Um...I was attacking your points...but in a way that was mainly building my case, since my goal is usually to elucidate what is scientifically right, not to show others are wrong...summarizing my points:

1) Your point about my point about relativity was incorrect as you were citing a different form of relativity than I was, general relativity has to do with the bending of space time and stuff (and honestly, I'm not that familiar with it), whereas special relativity has to do with the effects/implications of moving at relativistic speeds, which was what I was referring to, and is tied in nicely with quantum physics to achieve the best empirical results.

2) Heisenberg's principle does fit the examples you claimed it did not fit, if you use the energy/time form. The mathematical principle can be (and is) interpreted as either you cannot know either the position/momentum OR the energy/time of a particle/wave.

3) Regardless of what new theory is ultimately correct, it probably will not refute/disprove the uncertainty principle since the vast majority of the time new theories 'refine' the results of existing theories for situations that the old theories are not good for and reduce to the existing model/equation for things that already the older theories already are good describers of.

4) The argument "If we had all the information, we could predict everything that happens, hence the world is deterministic" is wrong because the premise is wrong.

Thanks for admitting my arguments are reasonable ;).

I enjoyed it too...a good debate with an intelligent, articulate person is always fun :D.

Not the points which are important to me.

(1) - I don't really care about getting into relativity after this. You were the first one to mention it, and I never said anything prior to this which is at odds with relativity (nor quantum mechanics for that matter, if you consider the theoretical model to be separate from the interpretation). This point is not one I care about.

(2) - I know it does - I said it does in all of my posts about that. What I said didn't fit was the concept of position in certain cases, and the concept of velocity in other cases. If everything around us is accurately depicted by a bunch of imaginary waves super-imposing, like QM assumes, then it's no surprise that some cases at some points in time resemble the extreme cases I mentioned such that position and momentum are not entirely well-defined. Despite your best efforts, you asserted the same thing I did.

(3) - I don't think anything can refute the uncertainty principle, it's something inherent when trying to interpret a wave with non-wave properties (although the non-wave properties may seem to be present in certain waveforms - when appropriate). About the refining stuff... you can't assume that the current theory will never be replaced by something else. The old theory was that the world was flat... that was tossed, not refined.... although if you think about it, it's kind of still around as an approximation.... it's practical to assume flatness when the curvature of the earth just doesn't really matter for your problem. Same with Newtonian physics... it's good enough when you don't really care about quantum/relativistic effects. Maybe one day, the same will be said of quantum mechanics. There is no real argument you can make against that. Well, I suppose you could, but I can't imagine that it would be a good one, and I probably wouldn't be convinced.

(4) I feel like my other answers have already covered this on each specific front we have talked about. Since you bring up the topic of information, let me mention something else I find interesting and have thought about before ----> is there anything more fundamental to existence than information? Information is essentially the potential for difference to exist. Think of a bit, a bit is the most basic unit of information. If the universe had one bit of information in it, it would have two possible states, and it would exist. If you remove that bit, and think about what could remain... the only conclusion is nothing. Difference is what allows for existence, and information is a measure of how many possible ways things can be different. This ties into our discussion in the following way. In determinism, the amount of information in the universe is constant with time, since future states are implied by past states, and vice-versa. In non-determinism, the amount of information in the universe increases with time and with every (truly) unpredictable event. Don't use the 2nd law of thermodynamics as an argument here to say that the information in the universe must be increasing, reasoning about entropy always increasing, and entropy being a measure of the possible microstates of a system --- there is a difference in the information I am talking about and the evolution of statistical-mechanical microstates, since the 2nd law refers to "usable information" or "usable energy" as opposed to the total information capacity of a system. Unusable energy is like heat, as opposed to voltage. Unusable information is like white noise, as opposed to a transmitted signal. Unusable stuff tends to have more micro-states than usable stuff, just like a room can be messy in more ways than it can be clean. The information I'm talking about lies beyond what is usable vs. not usable, but what is possible.

Anyway, I think that is the crux of the determinism vs. non-determinism. It is consistent with your non-determinist view. You say knowing all the information at one point in time will not allow prediction of the future, because by the time the future gets here, new information that did not previously exist has been added at random into the universe.

I say, no, the universe isn't randomly adding information as time goes forward, and that anything that appears to be random is actually just complexity in disguise.

Both of these perspectives are not inconsistent with Heisenberg's uncertainty principle which is a statement about the application of one set of concepts (position,momentum,energy,...etc), to another (waves). It is not inconsistent with with either of our views because it has nothing to do with the information of the universe increasing. It only has to do with trying to discern the meaning of position, momentum and energy out of a wave. The only reason it comes up in debates like these, is because someone (not Heisenberg I'm guessing) chose to use the word uncertainty to describe Heisenberg's observation, and uncertainty can be interpreted as something being fundamentally unknowable, and unknowability is a central dividing point behind the determinist argument. This is really the only connection <---> re-use of a word. Heisenberg's observation about the nature of waves, and applying the concepts of position, momentum, and energy to these waves, has no real direct connection to our main dividing point.

Your statement:

'The argument "If we had all the information, we could predict everything that happens, hence the world is deterministic" is wrong because the premise is wrong.'

is essentially just an assertion that the non-determinist principle is true.

My statement:

"If we had all the information, we could predict everything that happens, hence the world is deterministic"

is the opposite assertion.

Neither of us have any proof, nor can we attain it.

What's the point of "winning" an argument if there is no real evidence to support either side?

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1) I don't care about relativity either, other than clarifying why my argument relating relativity (special relativity) and quantum are sound. Like I said, it's not about you, it's about scientific rightness :P.

2) I'm not sure what your argument is then. You basically admitted your own arguments support quantum physic's viewpoint...I'm fine with that ;P My point was that even if the concept of velocity or position doesn't apply to certain cases, but Heisenberg's principle still does in its other interpretation.

3) I put 'refine' in parenthesis for a reason. Yes, a new theory will likely replace quantum, perhaps string theory, and by 'refine', I don't mean it will further prove quantum, but, as I've said many times, but the point is that it is not likely to drastically change our current effective view of things we have comfortable results in, like quantum didn't change our effective views about billard balls and collisions on a macroscopic scale for example. Why would I argue against it? I've been arguing for it since it supports my general argument that the uncertainty principle and its implications about indeterminacy are here to stay, regardless of what new theory comes along.

4) Information is constantly changing, due to probabilistic causation. The uncertainty principle not only implies that we can't predict the future, but it also implies we can't fully explain the past. At no point can there be concrete information. We can't conclude A causes B that causes C, because we cannot know for certain that B was caused by A, B might have been caused by Z. Every layer of probability gives us more possibilities, more information to consider.

No my statement was an effort to encourage a different view point and open-mindedness. I.e. if someone was arguing "the world is flat, therefore...", I would argue that the world is not flat and encourage them to try to re-evaluate their beliefs with this new information.

As I've stated, I'm not trying to "win the argument", I'm fighting for scientific rightness ;P.

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mmiguel's uncertainty principle:

There is a fundamental uncertainty in evaluating a characteristic for an object for which that characteristic is not well defined.

Evaluate the characteristic: "mood" for each of the following life forms:

[person, cat, insect, tree]

Is the inability to evaluate the mood of a tree an argument for the existence of randomness?

Now replace mood with "position",

and replace the list of lifeforms with increasingly non-localized waveforms.

...

and replace mmiguel with heisenberg....

Edit: just typed this due to thinking thoughts... didn't see you had responded above.

Edited by mmiguel
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1) I don't care about relativity either, other than clarifying why my argument relating relativity (special relativity) and quantum are sound. Like I said, it's not about you, it's about scientific rightness :P.

2) I'm not sure what your argument is then. You basically admitted your own arguments support quantum physic's viewpoint...I'm fine with that ;P My point was that even if the concept of velocity or position doesn't apply to certain cases, but Heisenberg's principle still does in its other interpretation.

3) I put 'refine' in parenthesis for a reason. Yes, a new theory will likely replace quantum, perhaps string theory, and by 'refine', I don't mean it will further prove quantum, but, as I've said many times, but the point is that it is not likely to drastically change our current effective view of things we have comfortable results in, like quantum didn't change our effective views about billard balls and collisions on a macroscopic scale for example. Why would I argue against it? I've been arguing for it since it supports my general argument that the uncertainty principle and its implications about indeterminacy are here to stay, regardless of what new theory comes along.

4) Information is constantly changing, due to probabilistic causation. The uncertainty principle not only implies that we can't predict the future, but it also implies we can't fully explain the past. At no point can there be concrete information. We can't conclude A causes B that causes C, because we cannot know for certain that B was caused by A, B might have been caused by Z. Every layer of probability gives us more possibilities, more information to consider.

No my statement was an effort to encourage a different view point and open-mindedness. I.e. if someone was arguing "the world is flat, therefore...", I would argue that the world is not flat and encourage them to try to re-evaluate their beliefs with this new information.

As I've stated, I'm not trying to "win the argument", I'm fighting for scientific rightness ;P.

I admitted from the beginning that I find the theory agreeable... I just separated theory from the interpretation... and said that i don't like the most popular interpretation

(3) - looks like we got nothing to disagree about here

(4) - information within a subjective perspective can change, that is certain... that is why i like the bayesian interpretation of probability (another contentious debate). but if we attempt to step outside of subjectivity, and ask about what is really out there, real information in the fabric of existence, and not just the little bits and pieces that we have been able to process in our brains,... then whether or not such information is increasing when taking into consideration the entire universe as a system is not so certain.

I suggest a truce, parting with mutual respect :)

Edited by mmiguel
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What is really out there? What information is in the fabric of existence? If you can't know for certain causes and effects, how can you be certain causation is one-to-one and onto?

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What is really out there? What information is in the fabric of existence? If you can't know for certain causes and effects, how can you be certain causation is one-to-one and onto?

We cannot be certain.... that's what sucks so much.

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What is really out there?

Kittens. Lots and lots of furry kittens.

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We cannot be certain.... that's what sucks so much.

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*

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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

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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 ;))

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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
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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!

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

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.

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

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".

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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 ;).

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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?

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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
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