Three Gods

[mmiguel]

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

[mmiguel]

What happens when you ask the truth teller or the liar a question they can't answer?

Since that is a topic of interest for many posters, I guess I need to make something up here.

If you ask any god a non-well-formed question which cannot be evaluated as either true or false in the eyes of omniscience...

then there is no rule that you may rely on regarding how they will answer. It's up to them.

Example:

Is the sentence "this sentence is a lie" a true statement?

The gods may answer however they choose in that case (they all act like random).

The OP still applies for well-formed yes-no questions.

[mmiguel]

I would ask, "Is the card to the right/left an ace?" If yes pick that one if no pick the other one. Still trying to apply that to the OP though.

Correct-a-mundo.

Point at a card, and ask if some other card is an Ace.

Say you are pointing at A, and you ask about B (C is the remaining card).

If A = Ace and B = Ace, then he will say Yes ---> Choose B

If A = Ace and B = Jack, then he will say No ---> Choose C

If A = Jack and B = Ace, then he will say ? ---> Doesn't matter which of B or C you choose, you will get an Ace since A is the Jack, so can still follow same rule above.

Here is Hint Puzzle 2:

Suppose that somehow, you have learned that you are speaking not to Random but to True or False -- you don't know which -- and that whichever god you're talking to has condescended to answer you in English. For some reason, you need to know whether Dushanbe is in Kirghizia or not. What one yes-no question can you ask the god from the answer to which you can determine whether or not Dushanbe is in Kirghizia?

Edited September 19, 2012 by mmiguel

[mmiguel]

They know his pattern, but since I specify it is random at which point in the pattern I'd ask the question, they cannot know which his answer will be.

How will you choose such a random number?

Will you roll some dice?

What if they know how the dice will happen to land when you decide to roll them?

What if you decide to throw away the first roll and roll a second time --- what if they know how the dice will land at the second time?

What if for each of your possible choices, they know how every coin flip, dice roll, wheel spin, etc will turn out based on having tons of information, the laws of physics, and assuming we live in a world of causes and effects.

Your number can only be 0, 1 or 2 though, since you get 3 questions, and you need to save one question to ask about the sky.

I think trying to find questions that cannot be answered is not that helpful to finding the logical solution to the overall puzzle - but you are doing a good job thinking of possible paths of thought.

Edited September 19, 2012 by mmiguel

[phaze]

What would the other God who is not the random answerer say if I asked him if Dushanbe is in Kirghizia? Take the opposite answer

[Rob_Gandy]

Correct-a-mundo.

Point at a card, and ask if some other card is an Ace.

Say you are pointing at A, and you ask about B (C is the remaining card).

If A = Ace and B = Ace, then he will say Yes ---> Choose B

If A = Ace and B = Jack, then he will say No ---> Choose C

If A = Jack and B = Ace, then he will say ? ---> Doesn't matter which of B or C you choose, you will get an Ace since A is the Jack, so can still follow same rule above.

Here is Hint Puzzle 2:

Suppose that somehow, you have learned that you are speaking not to Random but to True or False -- you don't know which -- and that whichever god you're talking to has condescended to answer you in English. For some reason, you need to know whether Dushanbe is in Kirghizia or not. What one yes-no question can you ask the god from the answer to which you can determine whether or not Dushanbe is in Kirghizia?

It would be the standard, "If is asked you yesterday how would you respond?"

[mmiguel]

Right, but I'm adding an extra hypothetical random, i.e., one that is not on the sheet of paper, that is hypothetically at some point which is randomly determined (and independent of the random god's 'random') if I ask that question what will he say. I.e. if I randomly pick a point on that paper...

And I don't care how omniscient these gods supposedly are...there are some things that are just unknowable...or do I need herr Heisenberg to let loose the hounds? ;P

However, if you want to specify that questions are could be unanswerable are disallowed, fine...

Ask A, "If I ask you if B is the random god, would you say ja?" If he says ja, then either A or B is the random god. If he says da, either A or C.

Ask the one you know is not the random god, "If I ask you if A is the random god, would you say ja?", if he says ja A is the random god, if da, the other one.

Finally ask one of the non-random gods: "Does ja mean yes?" If ja, he's the truth teller, if da he's the liar.

correct.. pretty much.

i think you may have switched around the conclusion for Q1.

I'll just put the 3rd Hint puzzle here just because

You are now quite definitely talking to True, but he refuses to answer you in English and will only say "da" or "ja". What one yes-no question can you ask True to determine whether or not Dushanbe is in Kirghizia?

Edited September 19, 2012 by mmiguel

[phaze]

Would you say "da" if I asked you if Dushanbe is in Kirghizia

"Da" now confirms if it is the case

[mmiguel]

correct.. pretty much.

i think you may have switched around the conclusion for Q1.

I'll just put the 3rd Hint puzzle here just because

You are now quite definitely talking to True, but he refuses to answer you in English and will only say "da" or "ja". What one yes-no question can you ask True to determine whether or not Dushanbe is in Kirghizia?

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

Edited September 19, 2012 by mmiguel

[Yoruichi-san]

How will you choose such a random number?

Will you roll some dice?

What if they know how the dice will happen to land when you decide to roll them?

What if you decide to throw away the first roll and roll a second time --- what if they know how the dice will land at the second time?

What if for each of your possible choices, they know how every coin flip, dice roll, wheel spin, etc will turn out based on having tons of information, the laws of physics, and assuming we live in a world of causes and effects.

Your number can only be 0, 1 or 2 though, since you get 3 questions, and you need to save one question to ask about the sky.

I think trying to find questions that cannot be answered is not that helpful to finding the logical solution to the overall puzzle - but you are doing a good job thinking of possible paths of thought.

It's exactly due to my familiarity with the laws of physics, especially quantum physics, that I assert, as Heisenberg would, that there are things that are unknowable. The future is probabilistic, not deterministic. No matter how omniscient these gods are, they can not know based on the laws of physics and the universe we live in.

The question is not asking about something that will actually happen, it's something that hypothetically could happen. So even if we grant the existence of Maxwell's demon and break the uncertainty rule and allow them to predict the future of any random physical event, the event is not something that actually will occur, it's rather a family of events that could occur, and it is not specified which member will actually be the one in question. It is not a paradox because it not self-contradictory, but rather is not truly answerable in a way that is certain to be either true or false.

And no, I didn't switch around the conclusions.

Edited September 19, 2012 by Yoruichi-san

[mmiguel]

It's exactly due to my familiarity with the laws of physics, especially quantum physics, that I assert, as Heisenberg would, that there are things that are unknowable. The future is probabilistic, not deterministic. No matter how omniscient these gods are, they can not know based on the laws of physics and the universe we live in.

The question is not asking about something that will actually happen, it's something that hypothetically could happen. So even if we grant the existence of Maxwell's demon and break the uncertainty rule and allow them to predict the future of any random physical event, the event is not something that actually will occur, it's rather a family of events that could occur, and it is not specified which member will actually be the one in question. It is not a paradox because it not self-contradictory, but rather is not truly answerable in a way that is certain to be either true or false.

And no, I didn't switch around the conclusions.

Paragraph 1

Hmmm...

I've never been totally convinced that quantum mechanics is a proof for the existence of true randomness.... I'm a determinist.

I think that pretty much everything we call random, is really just complexity/lack of knowledge in disguise.

I think the question is philosophical, and not really provable by physics.

The fact that QM predictions are consistent with experiment means that those phenomena are well modeled by a probabilistic model, and all would agree that such a model is useful and definitely a good thing.

Consistency with experiment does not imply to me that reality itself is random.

Is it possible for anyone to say with certainty that there is no possible way that QM could be replaced by a deterministic theory that takes into account some further layer of complexity or requires measurements beyond what we are currently capable of performing?

I think science in general has ignored that as being in the realm of philosophy (why) instead of the characterization of nature (how).

Anyways - if randomness doesn't exist, and we do live a deterministic universe, and everything that appears random to us can be explained by our lack of knowledge, -If that were true- then the gods can predict what Random will do at any given point in time.

This may come down to a difference in belief in something which is not as of yet provable, so I may respectfully agree to disagree.

Paragraph 2

Agree, so this is a question which is not answerable due to ambiguity. I still consider this a not well-formed question.

If I ask you, what is the color of the animal's fur? - you can't answer because you don't know what animal I'm talking about.

I suppose something with omniscience could in that case figure out what you were talking about.

But that's not really the end of the conundrum - because you could deliberately ask a question about no specific object, but rather an abstract object.

What is the weight of a father?

Either way - it is not a well-formed yes-no question.

To not let you get away with answering the riddle too easily - I made up the rule that if you ask a non-well formed question, any god may essentially answer randomly i.e. you won't get anything useful out of them.

(Lol - this is not inconsistent with me not believing in true randomness... Here, I colloquially use the word random to mean that you can not know for sure how they will behave, and you never will be able to unless you are omniscient).

Paragraph/Line 3:

Yeah you're right. It's been a long day.

Edited September 19, 2012 by mmiguel

[Yoruichi-san]

Yes, it's been a loooonnnngggg day for me too (and oh look it's 2:30 and I have to work tomorrow , so I'm not going to get into an argument about quantum physics. But if you say things can't be truly random, that is a paradox, since then how can the god's answers be truly random?

And my question is a perfectly well-formed yes-no question, just not one that can be answered.either always truly or falsely.

I have no qualms with clarifications/additions...it's usually better to make sure the question is clear before dropping hints.

[mmiguel]

Yes, it's been a loooonnnngggg day for me too (and oh look it's 2:30 and I have to work tomorrow , so I'm not going to get into an argument about quantum physics. But if you say things can't be truly random, that is a paradox, since then how can the god's answers be truly random?

And my question is a perfectly well-formed yes-no question, just not one that can be answered.either always truly or falsely.

I have no qualms with clarifications/additions...it's usually better to make sure the question is clear before dropping hints.

Stubborness is unhealthy for both of us.

Here is how I am not contradicting myself:

Random, as I used it, is a single word that represents two concepts, that in order for successful communication in a conversation where we are splitting hairs, we should distinguish.

True Randomness = What I don't think exists - an effect without a cause completely determining it

Apparent Randomness = What we as humans superstitiously attribute to things that we cannot make sense of due to lack of information and understanding about it.

In the puzzle, every time I mentioned Randomness, I basically meant apparent randomness. This is consistent with the other Gods being able to predict what Random is doing. Apparent randomness arises from lack of information (which is not a problem for the omniscient --- I won't argue here about whether or not omniscience is feasible, since that would start getting religious). Anyway, let's assume you are not omniscient. If that is the case, I can tell you that a coin flip is random (which of course, we should all interpret as apparent randomness), and this is not inconsistent with the non-existence of true randomness.

We are ignorant to the complete list of all the factors that could cause a coin to land one way or another. In our ignorance, we give up trying to characterize and predict it's behavior, and we say ...."it's just random".

In our debate, I sometimes switched to talking about true randomness. It may have been confusing then, but hopefully we have now cleared up any ambiguity.

Anyway, the bottom line is that what I said does not contradict itself, I just used bad communication practice by using the same word for two different things without qualifying.

Well-formed yes-no question - Is there an official definition for that? I assumed there wasn't (it was free for me to claim) and claimed that phrase as meaning basically, a question that can be evaluated as true or false. Maybe I didn't clearly express that.

You have a different idea about what that phrase means....

In the end it doesn't matter - what I was trying to say is that stuff like that ain't allowed.

I copied the original question from George Boolos - blame him for the ambiguity

haha

Edited September 19, 2012 by mmiguel

[superprismatic]

There is a logical solution.

Yep. I didn't think things through enough.

[Yoruichi-san]

Speaking of defining things differently...what you call "stubbornness" I call "strong will", which has been very healthy for me since it's what drives me to work out and push myself (and run a marathon ;P).

I see. Thanks for the clarification. But I have to point out that what (emphasis added):

Apparent Randomness = What we as humans superstitiously attribute to things that we cannot make sense of due to lack of information and understanding about it.

Sure there is plenty of info we do not have, but my point is, and has always been, that there are pieces of information we cannot have, such as is stated in Heisenberg's Uncertainty Principle. Hence the future is unpredictable with certainty, and the more complex an event is, the more uncertainty there is.

Secondly, I was basing "not a well-formed yes-no question" on your example, which was "what is the weight of a feather", which is obviously not a yes-no question. My question was definitely a yes-no question, just not one that can be answered with certainty.

Hey, don't worry about it, I'm not trying to complain about the question, I actually like it , and found trying to resolve the problem with new parameters fun , so thanks for that.

[phaze]

@Y-san so what happens when the truly omniscient God attempts to predict the truly random number?

[Yoruichi-san]

@Phaze: he's smited by the the mighty Heisenberg leading an army of zombie (cuz they're neither alive nor dead) cats.

[Aside] Wow CG has gotten really good...just watched Resident Evil Damnation...[/aside]

[mmiguel]

Speaking of defining things differently...what you call "stubbornness" I call "strong will", which has been very healthy for me since it's what drives me to work out and push myself (and run a marathon ;P).

I see. Thanks for the clarification. But I have to point out that what (emphasis added):

Sure there is plenty of info we do not have, but my point is, and has always been, that there are pieces of information we cannot have, such as is stated in Heisenberg's Uncertainty Principle. Hence the future is unpredictable with certainty, and the more complex an event is, the more uncertainty there is.

Secondly, I was basing "not a well-formed yes-no question" on your example, which was "what is the weight of a feather", which is obviously not a yes-no question. My question was definitely a yes-no question, just not one that can be answered with certainty.

Hey, don't worry about it, I'm not trying to complain about the question, I actually like it , and found trying to resolve the problem with new parameters fun , so thanks for that.

I was talking about when it leads to loss of sleep.

Heisenberg:

There exists info we cannot have <---> equivalent to saying omniscience cannot exist, and no predictions are certain;

Completely agree, and all I was saying earlier that I believe that lack of information is the source of all things that we label as being random.

I don't have any issues with Heisenberg or any results of QM verified by experiment. It's more of the interpretations that some apply to it.

I don't think any of the actual scientific results contradict my philosophy, but some (not all) interpretations of QM do. I suppose in the end, it is a choice.

I wasn't trying to point out those questions weren't yes-no questions, but rather that they are unanswerable since they are asking about concrete properties of abstract objects that don't actually exist (and do not include specifications for those properties within their definitions - there is no weight requirement for being a Father for example).

Questions like that don't really make sense, and that is exactly why they are unanswerable. There are a myriad of questions you could ask that don't make sense (and are unanswerable), but they aren't useful to the point of the puzzle, which was to flex your logic muscles.

[Yoruichi-san]

Hmm..hmm...if by "the interpretations some apply to it" you mean the existence of non-deterministic processes that are widely accepted by renowned physicists (including Richard Feyman)...

Out of curiosity, what do you make of Brownian motion?

And the question does make sense; everyone one who read it knows clearly what it means, and it's clearly a yes-no question, unlike ("what is the weight of a feather")...the beauty of it is in those things and IMO flexing creativity muscles is just as valuable as flexing logical ones.

Yes, yes, losing sleep is bad...so you should be warned now...in a battle of wills, I always win ;P.

[mmiguel]

Hmm..hmm...if by "the interpretations some apply to it" you mean the existence of non-deterministic processes that are widely accepted by renowned physicists (including Richard Feyman)...

Out of curiosity, what do you make of Brownian motion?

And the question does make sense; everyone one who read it knows clearly what it means, and it's clearly a yes-no question, unlike ("what is the weight of a feather")...the beauty of it is in those things and IMO flexing creativity muscles is just as valuable as flexing logical ones.

Yes, yes, losing sleep is bad...so you should be warned now...in a battle of wills, I always win ;P.

Yes, many accept that interpretation, but not all, Einstein and Bohr has some famous debates about this. I do not disrespect any who believe that, I just don't believe it.

I have read Feynman's QED, and I think it is a wonderful theory, and useful. But use of the theory to model the world does not require an interpretation that non-determinism is a fundamental reality.

Brownian motion is a perfect example of complexity being mistaken for true randomness.

A billiards player may predict the path of a ball that he hits with another ball that he hits with a stick.

Now add billions of balls, make them not constrained to two dimensions, and take away any other simplifying assumptions that a college or highschool physics problem might allow a student to assume in modeling such a scenario, and now no one can predict anything, because there is too much information to practically process.

We can give up on trying to predict the micro-scale evolution of the state of such a system and instead focus on aggregate properties: e.g. averages, frequencies, etc.... We characterize such systems based on how it is practical and convenient (and feasible) for us to do. If knowledge were not an issue, processing were not an issue (including time to process), and you were given an isolated system (assume so for now), and a set of micro-scale characteristics that each component of such a system has always been observed to obey, i.e. you are given all of the information of a current state of a system plus how these characteristics behave with time ----- what is to stop such a prediction from being possible? Heisenberg?

Heisenberg didn't remove information -> he just noted some difficulties in apply classical ideas such as position and momentum to things that are modeled as waves.

A plane wave may have a well defined velocity, but has amplitude in an infinite plane throughout all of space.

A localized wave packet in space-time on the other hand may have a well defined position, but if you look at its Fourier transform, it has amplitude components across all wavelength and frequencies (making it meaningless to interpret the velocity of such a thing) - this is hard to visualize for those not familiar with it, but something like a dirac delta impulse can be treated as an infinitesimally scaled sum of an infinite number of cosines, with different relative amplitudes, at all real frequencies that may exist. It just so happens that if you were to add all those things together, they would destructively interfere everywhere except for one point, at which they all constructively interfere into something with "infinite-looking" amplitude, but finite energy. This is of course not possible, and all real impulses and bursts are things that are simply closer to this ideal, than the opposite (which is a cosine).

Anyway - the inability to apply these particle characteristics to different extremes of waves is true for all waves. If you go to the beach and watch the waves, and ask about the position and velocity of each ripple, and we find that it is hard to apply such concepts to something which doesn't really fit. It may fit for some waves, but it won't for extreme cases. Does that mean that there is something crazy, random, and non-deterministic about the wave? Even identifying something as an object (which can obviously be done for particles) may not make sense for some waves. If two ripples collide and super-impose, are they considered one object in that moment? Who is to even judge what is an object or what isn't? I might point at a still pond and say look at that awesome wave packet with zero amplitude, or look at those two waves which are identical in all ways except they have reverse amplitudes, or I might say there are no wave objects moving through the pond at all.

This is all red-herring about whether or not nature itself is causal and deterministic.

Other times, I see people using chaos theory as a proof for randomness, and I never really understood what was so special about the big conclusion behind it. This ties into your Brownian motion question. Chaos theory books say: a butterly's wing flapping could cause a hurricane somewhere else in the world.

I see this and say.... well yeah... it could... since nothing explicitly forbids this in the universe (that we know of haha).... what's the big deal? I must be missing the point. Anyway, I agree that this is true. The ultimate conclusion that I draw about this topic, is that you cannot fully predict the future state of a system by considering only isolated parts of it, you need to know all the information in the system in order to predict with certainty. You may make the greatest weather prediction device ever, but did you account for all those flapping butterfly wings? What about things bigger than butterfly's like jumbo jets? What about the gravity of nearby planets? What about the gravity of the Andromeda galaxy? No weather person is likely to worry much about these things, and that is reasonable, since it is more practical, given their incomplete knowledge of the universe, to pursue other, more obvious factors might affect the weather. Chaos theory seems to be the gotcha saying, well... don't forget that you don't really know everything that could possibly affect the weather. Why this isn't obvious to everyone in the world confuses me.

Anyway, given the amount of information that exists in the universe, and the amount of information our little tiny minds (in comparison) can process, it's no surprise that apparent randomness exists.

Here is a challenge: Find something that implies the existence of true randomness, that cannot be explained as a consequence of apparent randomness due to the complexity of the universe and lack of knowledge.

You keep saying feather instead of father, which seems less abstract to me, and in my mind loses the point of what I was trying to say in the example in the first place. I suppose it isn't really less abstract though, I mean if I step into a more objective perspective... so it's a moot point.

Question making sense ---- to me that meant a meaningful answer can be inferred ---- to you that meant that it can be successfully parsed such that what is wanted by the asker is understood. It's so easy to miscommunicate.

Edited September 20, 2012 by mmiguel

[Yoruichi-san]

Einstein's attempts to come up with alternative explanations that would reconcile quantum with determinism were refuted (such as 'local realism').

And no, it's not the limit of our minds or our ability to process the information, it's the limit of the information itself. I.e. if you can't know where the particle is and how fast it is going at the same time, you cannot predict where it will go.

I'm not sure about chaos theory and whatnot, but the things I think your analysis is missing: the failure of classical mechanics at relativistic speeds and the wave-particle duality of matter.

The wave nature of things on the order of particles is exactly why you can't look at them as billard balls. You can model macroscopic things in terms of classical mechanics, on the scale of which the effects of the wave nature are negligible. But it is exactly due to the fact that those models fail at the microscopic level and relativistic speeds that quantum physics was discovered/theorized in the first place. Similarly, the waves of the ocean do not travel at relativistic speeds ;P.

I.e. the things you say "do not fit" do fit, but their effect is so small on the macroscopic scale that they are negligible, as their effects on phenomena are proportional to ((speed of wave)/(speed of light))^2 (in most cases), so for waves on a beach (presumably moving at far sub-relativistic speeds), it has pretty much no observable effect.

Heisenberg's principle says the uncertainty is >(planck's constant)*(frequency). Planck's constant is very small (O~10^-34 in joules), so unless the frequency is very high, the uncertainty is very small. For things of non-relativistic speeds, frequency is very small, so that the uncertainty is negligible, particularly to the ability of human observation (i.e. watching a wave on a beach).

Take for example the billard balls, the rules you think govern them, based on classical mechanics, are not 100% accurate, but are accurate to like 99.99999999999% on that scale (okay, that's just a guess, not an actual calculation ), and hence sufficient for any purposes any person would ever need them for, but if you change the billard balls into particles moving at speeds for which ((speed of wave)/(speed of light))^2 is no longer negligible, then they no longer can be sufficiently characterized by those rules.

Yes, it is difficult to visualize, especially the wave-particle duality, but that is essential in understanding uncertainty and indeterminacy. Sure, if you know how much force, friction, mass, etc of a billard ball you can predict its motion, and if you know the forces on a wave you can predict its motion, but can you visualize a billard ball that is a wave or a wave that is a billard ball (note: NOT a billard ball moving in a wave-like motion, that is not what the wave-particle duality is about)?

You are right about Heisenberg's principle being derived based on the nature of waves, and it applies to real things, not just our understanding of them, because it is fundamental to the nature of waves, and particles are waves.

Sorry about 'father', 'feather', but my point was that the question "What is the weight of a father/feather" is still not a yes/no question .

How much wood could a wood chuck chuck if a wood chuck could chuck wood?

What is the meaning of life?

Where will I be in 20 years?

Is the cat alive or dead?

All questions for which a meaningful answer cannot be inferred, but I still would say they make sense. *shrugs*

Edited September 20, 2012 by Yoruichi-san

[Yoruichi-san]

Err...correction, please ignore the frequency stuff on Heisenberg...(wow I am getting really tired if I'm mixing the energy equation with the uncertainty principle ) ...I mean Heisenberg's principle is that uncertainty says that (uncertainty in speed)*(uncertainty in position) > (planck's constant)/2, which is on the order of 10^-34 in joules so unless you care about and/or can observe the speed and/or position of wave on the beach to the accuracy of 10^-34 then you won't notice its effects. (Or you could use any of the other forms...momentum, energy, etc.)

Edited September 20, 2012 by Yoruichi-san

[phaze]

I would classify the uncertainty principle as being something that is not knowable by physics (or empirical evidence)

and the question if a truly random number or a truly omniscient God also out of the realm of what is knowable but into the realm of what is believed

[mmiguel]

Einstein's attempts to come up with alternative explanations that would reconcile quantum with determinism were refuted (such as 'local realism').

And no, it's not the limit of our minds or our ability to process the information, it's the limit of the information itself. I.e. if you can't know where the particle is and how fast it is going at the same time, you cannot predict where it will go.

I'm not sure about chaos theory and whatnot, but the things I think your analysis is missing: the failure of classical mechanics at relativistic speeds and the wave-particle duality of matter.

The wave nature of things on the order of particles is exactly why you can't look at them as billard balls. You can model macroscopic things in terms of classical mechanics, on the scale of which the effects of the wave nature are negligible. But it is exactly due to the fact that those models fail at the microscopic level and relativistic speeds that quantum physics was discovered/theorized in the first place. Similarly, the waves of the ocean do not travel at relativistic speeds ;P.

I.e. the things you say "do not fit" do fit, but their effect is so small on the macroscopic scale that they are negligible, as their effects on phenomena are proportional to ((speed of wave)/(speed of light))^2 (in most cases), so for waves on a beach (presumably moving at far sub-relativistic speeds), it has pretty much no observable effect.

Heisenberg's principle says the uncertainty is >(planck's constant)*(frequency). Planck's constant is very small (O~10^-34 in joules), so unless the frequency is very high, the uncertainty is very small. For things of non-relativistic speeds, frequency is very small, so that the uncertainty is negligible, particularly to the ability of human observation (i.e. watching a wave on a beach).

Take for example the billard balls, the rules you think govern them, based on classical mechanics, are not 100% accurate, but are accurate to like 99.99999999999% on that scale (okay, that's just a guess, not an actual calculation ), and hence sufficient for any purposes any person would ever need them for, but if you change the billard balls into particles moving at speeds for which ((speed of wave)/(speed of light))^2 is no longer negligible, then they no longer can be sufficiently characterized by those rules.

Yes, it is difficult to visualize, especially the wave-particle duality, but that is essential in understanding uncertainty and indeterminacy. Sure, if you know how much force, friction, mass, etc of a billard ball you can predict its motion, and if you know the forces on a wave you can predict its motion, but can you visualize a billard ball that is a wave or a wave that is a billard ball (note: NOT a billard ball moving in a wave-like motion, that is not what the wave-particle duality is about)?

You are right about Heisenberg's principle being derived based on the nature of waves, and it applies to real things, not just our understanding of them, because it is fundamental to the nature of waves, and particles are waves.

Sorry about 'father', 'feather', but my point was that the question "What is the weight of a father/feather" is still not a yes/no question .

How much wood could a wood chuck chuck if a wood chuck could chuck wood?

What is the meaning of life?

Where will I be in 20 years?

Is the cat alive or dead?

All questions for which a meaningful answer cannot be inferred, but I still would say they make sense. *shrugs*

Don't have too much time to continue this chit chat tonight.

Hidden variable interpretations are only disproven for local effects, not non-local.

Now that you bring up relativity ---> QM itself is inconsistent with general relativity, but you make them sound like they come hand in hand and imply one another.

I know that particles can't be modeled as billiard balls at the micro-scale, I was just trying to use a simpler-than-real-life example of billiard balls to show that complexity on it's own can induce apparent randomness such as Brownian motion - even without the complexity of QM/Relativity adding to the mix.

I say position and momentum as characteristics "do not fit" for every waveform and you say they do.

Let's look at a simple case: one spatial dimension (X-axis), one time dimension (Y-axis), and one wave amplitude dimension (Z-axis).

Let's say the waveform we are interested has amplitude z= f(x,y).

Let's consider the frequency-localized case:

z = f(x,y) = cos(k*x-w*t) for some constants k, and w.

This is a traveling wave which exists over all of space and time.

Tell me, what is the position of this wave in space-time? I'm looking for a single x and y value that you can say is the "position" of the wave.

I think you will find it hard to answer this since position here is not well-defined.

What is the velocity of this wave in space-time? That one's easy: it's w/k

Let's consider the spatio-temporal localized case:

z = f(x,y) = DiracDelta(x-a)*DiracDelta(y-b)

(In case you are not familiar - I will not assume - http://en.wikipedia.org/wiki/Dirac_delta)

This is essentially something that is zero-in amplitude at all points in space-time except for one. It "pops" into existence at one point in space at one point in time and then is never heard of again.

Tell me, what is the velocity of such a wave?

The position is easy! The position is (x=a,y=b).

All other waveforms are mixtures of combinations of aspects of these extreme cases. Some waveforms are closer to the (position making sense, velocity not making sense) case, and some waveforms are closer to the (velocity making sense, position not making sense) case.

What Heisenberg says, is that no matter where you are in this spectrum, one thing is clear - uncertainty in position and velocity (or momentum) follows some rule.

This is expected, since position and velocity are not really natural properties of waveforms in general, they are merely properties that may make sense for some waveforms, but not all. As position starts to make less, sense, velocity starts to make more sense or vice-versa. When position makes no sense at all, it's because the concept doesn't even apply to the waveform e.g. cosine case above.

I understand wave-particle duality, what I'm saying is that "position" and "momentum" come from the concept of a particle, and they are not suitable for every waveform. If waves are more real than particles then we shouldn't even care about the particle concepts.... The reaction I expect from saying this is that.... well you can't get rid of the particle aspect... they call it a wave-particle duality for a reason. That reason is that certain interactions between seemingly different wave objects seem to only occur in discrete "packets"... eg. energy transfer and stuff like that.

The wave particle duality seems to be a peace-making of unlike concepts.... perhaps this is and indication that the theory is incomplete. I would expect that all theories are incomplete to some extent, so it's no jab at QM to say such a thing.

Do we really need particles to exist in order to explain discrete energy transfer? Could there be another mechanism? Perhaps we should redefine our view of the concept of a particle to exactly describe these discrete phenomena we are seeing, and no more and no less. This means removing all of the traditional concepts associated with particles from our minds except for those associated with this discrete phenomena. Would position and velocity fall into that category?

Perhaps we just need to let science do it's thing for a little while longer, but until then, what you believe about things like determinism come down to a choice.

Edited September 21, 2012 by mmiguel

[Yoruichi-san]

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 , 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)

Edited September 21, 2012 by Yoruichi-san

[mmiguel]

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 , 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 September 21, 2012 by mmiguel