Jump to content
BrainDen.com - Brain Teasers

mmiguel

Members
  • Posts

    142
  • Joined

  • Last visited

  • Days Won

    1

Posts posted by mmiguel

  1. 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.

  2. A captain hires a crew for his ship, "The Flying Scotsman" and sets out to sail for a voyage to last many years across the seven seas.

    As the years pass, The Flying Scotsman succumbs to wear and tear:

    In the Atlantic ocean, the ship's mast is blown away by a storm, and it is replaced in the Caribbean.

    In the Pacific ocean, the ship runs aground and the hull is severely damaged. Fortunately, they are able to hire natives to aid in the repairs.

    ...etc

    After 8 long years, the captain looks at his beloved "Scotsman", and thinks fondly of how it has served him, he has a realization: over the course of this grand adventure, every piece of The Flying Scotsman has been replaced due to wear and tear.

    The captain begins to feel uncomfortable.... if I'm standing on different wood.... aren't I standing on a different ship?

    Question:

    Is it the same ship?

    So what (materials/subcomponents) things are made of doesn't matter when considering identity?

    Would this even apply if we were talking about you and not a ship?

    What if you stepped into a teleporter that disassembled all of your atoms, transmitted the information through space to a habitable facility on Mars and re-assembled you using atoms from Mars ?

    Would that still be you?

    What if the teleporter malfunctioned, and after you were disassembled, both devices on Earth and on Mars re-assembled you so that there are two copies of you.

    Which one is the real you? Do they have separate identities or are they same?

    What properties of these perfect clones could you use to distinguish their identities?

    Could such properties be used to distinguish every possible pair of arbitrary things that anyone might claim to be identical?

    What about applying those properties to distinguish yourself now to one moment ago?

    If everything can be distinguished, does true sameness exist?

    If every possible thing is different, should we really be so attached to our common ideas of objects?

    If you have a cup on a table, where does the cup end and the table begin? Would it be wrong to consider them both as part of a single object, let's call it a cup-table. Is the concept of a cup-table more or less in tune with reality (outside of our own subjective perspectives) than that of a cup by itself, or a table by itself?

    If we can call anything we want an object, is there any fundamental meaning to the concept of objects outside of a subjective perspective?

    Stepping outside of human subjective perspectives (pretend that we can), is there any objective basis for defining anything around us as objects outside of our own subjective perspectives .... is that object I'm looking at a cup on my table, or is it a cup-table, or a cup-table-atmosphere-house-earth-space-universe?

    In essence, do objects (e.g. cup, horse, car), as we know them, actually exist outside of our minds?

    When did it stop being the same ship? Was it when the mast blew over?

    What if the wood is constantly interacting with the air and water around it, such that sometimes, wood particles fly off of the ship, and air/water particles get stuck in the wood. This is all completely undetectable to unaided senses. Suppose this started happening from the moment the ship was exposed to the elements forward.

    Is it a different ship whenever such a particle transfer occurs?

    What about you?

    Are you a different person in each moment as you age?

    Can two objects ever truly be the same?

    If not, does this mean sameness does not exist?

    Is it an arbitrary judgment to even define things as objects? Where does the ship end and the water begin?

    What if you thought that the Ship+Water was actually a single object, let's call it ship-water. This object includes all the atoms of both the ship and water together. Is it justifiable to call this an object?

    Stepping outside of human subjective perspectives (pretend that we can), is there any objective basis for defining anything around us as objects outside of our own subjective perspectives .... is that object I'm looking at a cup on my table, or is it a cup-table, or a cup-table-atmosphere-house-earth-space-universe?

    In essence, do objects (e.g. cup, horse, car), as we know them, actually exist outside of our minds?

    The captain fainted from philosophical exhaustion.

  3. 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 :P.

    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.

  4. 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.

  5. If a mod is reading this, it should probably be moved to the Games section.

    Granted, but it turns out that the universe is completely deterministic and nothing is decided by luck.

    I wish for all the dirty dishes piling up in my sink to be cleaned, undamaged, not poisoned, not on fire or at any reasonable risk of combustion, and sitting in their proper places in my cabinets. ("Sitting" implies that they are at rest and not traveling at near-light speed about to bore a hole through the walls.)

    Well... it's almost like each response is a new riddle.

    :)

  6. I did gain something...information (about how genies grant wishes) :P.

    "Any situation"? Okay, you are in control of what you type next on your computer. Done.

    I wish I to be able to shape-shift into any and all things, at any and all times I want, for whatever length of time I choose.

    (C'mon, I can't be the only one who wants superpowers? ;P)

    haha

  7. My answer would depend on a clarification of the OP. But I think I should put the clarification questions in a spoiler because I feel like understanding what clarification questions need to be asked is really the heart of the riddle.

    When you open the problem by saying that this happens in the real world, meaning that no magic, wizardry or other funny business exists, do you mean to imply that we must also account for the possibility that the astrological prediction of Ethos may be wrong despite the fact that he's never been wrong before? Also, when it says that the king makes decisions based only on logic and not using his gut, and that he knows nothing of the stars, does that imply that neither he nor any of his advisers would consider the possibility that Ethos is wrong? If he can consider the possibility that Ethos is wrong, is there any extra data available that he could use to estimate Bayesian probabilities of Ethos really being an infallible astrologer based on the information that the king has at his disposal (like the number of predictions he's made correctly before, the probability that those predictions would be correct based purely on chance, whether or not Ethos was selected from a pool of potential advisers by having the potential advisers all make predictions on events and then weeding out adviser candidates who made a wrong prediction until just Ethos was left?) And would the king would be willing to make a baseline estimate of the probability that astrology is true in the absence of any of the data mentioned above?

    As for the video, curr3nt and Rob_Gandy already made the main points about not accounting for non-extreme cases, and not accounting for the possibility that interventions will fail. I would also add the need to account for the possibility that environmental destruction through pollution and whatnot might not be the factor that ultimately determines when humanity devolves into a mess of savages barely able to survive. World War III, comet collisions, and alien invasions might all happen first. In fact, excessive pollution might be just the thing that kills off a mutating multidrug-resistant bacteria before it fully evolves and spreads to cause a plague that makes the Black Death look like a case of the sniffles.

    yeah that is pretty much the heart of what i concluded from thinking about this ---> there is another probability that should always be considered whenever anything is heard --- what is the probability that everything that i am hearing is correct?

    this may seem obvious to always assess this probability, but i felt that the video maker was able to skillfully disarm the viewer into forgetting this fundamental suspicion.

    if something is completely outrageous - like a bunny suit stopping a plague, then it might not even be worth considering as a possibility. if you do consider it as a possibility, they could lie about the numbers in such a way that it makes it seem like you should do whatever they suggest. you would only be safe if you make your own judgment about the probability of them telling the truth to offset the effect on the expected value from whatever numbers they throw at you. what if you don't go low enough?

    how do we determine this probability when we make conclusions about things?

    is it a judgment call?

    does it come from the gut?

    maybe the king is too scared to make that leap.

    this probability is certainly subjective, and changes from case to case;

    stuff to think about, if anyone is still reading :)

  8. The advisor said the probability was 15%.

    i know i know.... it doesn't matter what the phony says... the real probability is whether or not he is right.

    the 15% is just there to distract people - so that they think they are considering probability, but in actuality they are not considering the right one.

    probably not something that people on this site would fall for, but i posted this not really to challenge you fine folks, but to think about things.

    i feel like the video used a lot of distraction, and disarms the viewer into thinking that no matter what numbers they put in, the videomaker will be right.

    people who enjoy logic puzzles are not likely to be fooled by distractive techniques though

  9. Wow, so the big conspiracy is that this guy just changed the headers on Pascal's wager.

    If scientists listen to him then all scientists should believe in God and be religious.

    Awesome! I was looking for an example of this in religion, but couldn't find it -- didn't know the right search term.

  10. What's the probability of the plague happening? It seems like an easy enough value analysis...

    Expected value of preventative measures = Cost of preventative measures - (Probability plague happens)(cost of plague)

    E=100,000-10,000,000p

    Hence if p<0.01 (1 percent), then then no point of taking action.

    Also, is it certain that the preventative measures will prevent the plague? If not, then modify:

    Expected value of preventative measures = Cost of preventative measures - (Probability plague happens)(cost of plague)(probability preventative measures will succeed)

    The advisor said the probability was 15%.

  11. 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.

  12. -Assume this takes place in the real world, no magic, wizardry or other funny business exists-

    King Rashunal rules over the kingdom of Logicia with a level head.

    He is well known for using logic and data for making important decisions, and never makes a decision with his gut.

    One day, the king's most trusted advisor, Ethos, who has never been wrong before in consultation to the king approaches the king.

    "I have come bearing a most ominous warning!" exclaims Ethos.

    "It has been revealed to me, by discerning the relative positions of the celestial bodies, that a plague, a million-fold worse than the great plague of 100 years ago may fall upon this city if immediate preventative action is not taken."

    "The precision of my instruments indicate that if no action is taken, disaster will occur with probability 15%."

    Knowing nothing of the stars, and remembering the many difficult decisions that Ethos has guided him through before, listens patiently.

    Ethos continues: "The alignment of Jupiter and Saturn tell me that the only way to prevent this tragedy is for the King to encircle the entire capital city 5 times, hopping on one foot, in a bunny costume, while the townsfolk pelt him with fruits..... and also 20,000 pieces of silver are given to me, ... and a statue should be erected with a great plaque that says Ethos,... the savior of Logicia.".

    King Rashunal then speaks: "We are a people of analysis! We will consider all options and make the most reasonable decision! Court historians, scribes, calculators, economists, men and women of learning, provide to me an estimate of the costs the kingdom shall incur if the great plague were to resurface if and we do nothing, and also the costs of implementing this preventative action".

    For two days, the men and women of learning in the court make estimates of costs incurred due to loss of life and cattle from the plague, costs incurred due morale and threats of enemy invasion to the weak image of the kingdom from the shamed King in his bunny suit, .... and many other such costs.

    In the end, the King is presented with the following information:

    If the great plague resurfaces at a million-fold, then the costs to the kingdom would be -10,000,000 pieces of silver.

    If Ethos' preventative plan is implemented, then the costs to the kingdom due to the plan will be -100,000 pieces of silver.

    If the preventative plan is implemented, we expect there to be no plague.

    The King then draws a 2x2 box with columns corresponding to whether the plan is taken or not, and rows corresponding to whether the disaster will occur or not. He populates each cell with the corresponding cost.

    Realizing he cannot control which row the kingdom might end up in, Rashunal focuses on the columns, and calculates the expected value of cost across each column.

    By his reasoning,if taking preventative action, the kingdom can expect to lose 100,000 pieces of silver with certainty.

    With no action, the expected value is a loss of 1,500,000 pieces of silver (considering both whether the plague does or does not occur).

    The king knows what he must do...

    Question: What went wrong here, and how can one defend in general from this type of problem if it were more subtle (yeah the bunny suit is overkill).

    Now, what do you think about this - is this the same breed of argument, or do you think the problem is not of logical nature?

    Before anyone sends any angry posts - I'm only interested in the logical validity of the argument in the video, not trying to debate the underlying topic. I'm not asserting that anything in the video is as ridiculous as Ethos' proposal.

  13. 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

  14. In the words of Adrian Monk: "You'll thank me later" ;P

    I wish you would grant this wish.

    Zap* Done.

    Nothing happens and you regret that you didn't gain anything from your wish.

    I wish to always be in control of any situation (any situation external to my own thought process - since genie can't control my mind).

  15. 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. :P

    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.

  16. I'd say 'Can you find all the roots?,' but I know this will get solved. ^_^

    This problem was posted a few years ago in the math department of the college I attended. I got a math club t-shirt and a certificate for getting the correct answer.

    Find all the roots of the following equation without the use of technology.:

    x6sin(x)+240-14x5sin(x)-308x+69x4sin(x)+22x2-126x3sin(x)+126x3-22x2sin(x)-69x4+308xsin(x)+14x5-240sin(x)-x6=0

    There are four consecutive integer roots.

    put all the non-sin(x) terms on other side of equation to get

    sin(x)*(x^6-14x^5+69x^4-126x^3-22x^2+308x-240) = (x^6-14x^5+69x^4-126x^3-22x^2+308x-240)

    Let y = (x^6-14x^5+69x^4-126x^3-22x^2+308x-240)

    sin(x)*y = y

    If y != 0, then we have sin(x) = 1, which is true for x = pi/2 + 2*pi*k for any integer k.

    if y == 0, then we need to find the roots of the polynomial

    y = (x^6-14x^5+69x^4-126x^3-22x^2+308x-240)

    Looking at the prime decomposition of 240,

    we get 240 = 2^4*3*5

    This makes it seem likely that (x-5), (x-3), and (x-2) are factors.

    Polynomial long division to get

    y/((x-5)*(x-3)*(x-2)) = x^3-4x^2-2x+8

    Prime decomp of 8 is 2^3,

    (x-2) doesn't work, try (x-4) [which agrees with hint]:

    success:

    y/((x-5)*(x-4)*(x-3)*(x-2)) = x^2-2

    x^2-2 = 0 if x = plus/minus sqrt 2

    Therefore......

    roots are:

    2,3,4,5, +sqrt(2), -sqrt(2), [pi/2 + 2*pi*k for any integer k]

  17. 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

    :(

  18. 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?

  19. 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.

  20. 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?

  21. 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.

  22. Okay, let me get this straight. We're assuming:

    1) Random means the god will randomly answer YES or NO regardless of the question, not will randomly answer truthfully or not.

    2) The gods all know what random's YES/NO pattern will be.

    Ask two of them: "If I ask the random god a random number of questions, then ask him 'Is the sky blue', will he answer the ja/da equivalent of YES?

    This will tell you who the random god is since only the random god will be able to answer. Ask the one (or one of them if both couldn't answer): "Does da mean YES?" If he answers da, it's the truthteller, if he answers ja, he's the liar.

    This is not a paradox, it is a strategy that utilizes the fact that random is random ;).

    Could we really distinguish between someone whose policy is to randomly select yes or no to each yes-no question against someone whose policy is to randomly select to be truthful or false, and then correspondingly select yes or no to each yes-no question?

    I don't really see how the other two gods would be unable to answer.

    The only possibilities that I can think of where they might not be able to answer is if the question is bad -> if the question doesn't make sense, if it has no answer, if it has multiple different answers depending on some ambiguous context, or if it is a paradox.

    The solution I have in mind does not require asking questions that any god may not be able to answer.

  23. If I happen to point to the jack, then your response will convey no information to me since that response depends only on a process (the random yes-no generator) which is completely hidden from me. This is, therefore, a case where I could not learn anything about where an ace may be. I conclude, then, that any answer to this puzzle must depend on trick wording or some such chicanery.

    There is a logical solution.

×
×
  • Create New...