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  1. #51

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    Yes, it's a semantic trick which doesn't depend on probability. At least, it looks that way since probability isn't applicable.

    Paul can say it's a logic puzzle and the clue's in post #1, that's fair enough. But he also said that jameslovestal's answer in #9 was a clue. That dealt with percentage estimation so, if the answer is merely semantic, that's not true either.

    So the question is: is this only a semantic puzzle or not? If Paul is being straight with us then no. If he isn't then it's nonsense.

    I think I'll stick to jazz theory. On the other hand, maybe I won't :-)

    I need something better to do!

  2.  

    The Jazz Guitar Chord Dictionary
     
  3. #52

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    Should really write xor instead of or haha

  4. #53

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    haha would be sensible

  5. #54
    Yes, Cosmic is uncannily sharp, but his reading of the poor description is not the intended solution. Nothing tricky about the marbles; "identical in all respects other than color" is indeed a sloppy way to summarize "identical in all respects other than color for which the pair may be BB, BW, or WW".

  6. #55

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    I see you've not answered my points. Upthread you said the answer involved probability.

    Quote Originally Posted by pauln
    It uses probability calculations.
    It can't, there's not enough data. Two marbles from a pool of two colours means either BB, WW, or BW. That's inevitability, not probability.

    Your 'clues' deal with scenarios that contain a third element to which probability can be applied. Therefore they're irrelevant.

    Time to give it up, Paul. Let's see your answer.

  7. #56

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    Not that it matters, you won't have one :-)

  8. #57

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    Did you know the harmonic series is a naturally occurring phenomenon, a property of nature and vibration itself? It is what our tuning system is derived from and what our ear/brain are built to perceive.

    It is not a product of our instruments, rather we are a product of it.

  9. #58
    OK, I will provide the method and answer this afternoon.

    In an earlier post, I described the answer as surprising and impossible. It is surprising because it is in the form of a specific configuration of BB, BW, or WW rather than a probability. It is impossible because it is exclusive, yet we know the other possibilities occur.

    It might have been wiser to present this business as a paradox rather than as a puzzle, since the heart of the thing is what looks like perfectly good logic leading to a perfectly wrong answer, where the focus should really be finding the flaw. I'll be as clear as possible in the logical steps but I myself have not found a flaw yet (I just know there must be one).

  10. #59

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    Quote Originally Posted by ragman1
    Did you know the harmonic series is a naturally occurring phenomenon, a property of nature and vibration itself? It is what our tuning system is derived from and what our ear/brain are built to perceive.

    It is not a product of our instruments, rather we are a product of it.
    Not really. Maybe a small bit, but not really

  11. #60

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    Quote Originally Posted by pauln
    OK, I will provide the method and answer this afternoon.

    In an earlier post, I described the answer as surprising and impossible. It is surprising because it is in the form of a specific configuration of BB, BW, or WW rather than a probability. It is impossible because it is exclusive, yet we know the other possibilities occur.

    It might have been wiser to present this business as a paradox rather than as a puzzle, since the heart of the thing is what looks like perfectly good logic leading to a perfectly wrong answer, where the focus should really be finding the flaw. I'll be as clear as possible in the logical steps but I myself have not found a flaw yet (I just know there must be one).
    Where I am it is the afternoon :-)

    Well, I suppose we can have some fun with it...

  12. #61

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    Quote Originally Posted by christianm77
    Not really. Maybe a small bit, but not really
    It's a quote. I don't know if it's true or not. In fact, it's worse than that, I don't even understand the harmonic series :-)

    'A harmonic series is the sequence of sounds - pure tones, represented by sinusoidal waves in which the frequency of each sound is an integer multiple of the fundamental, the lowest frequency.'


    You wot?

  13. #62

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    While you’re waiting, you can amuse yourself by reading this one, which sounds a bit similar:

    Two envelopes problem - Wikipedia

  14. #63

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    I am NOT waiting!

    You want an honest answer? I couldn't care less so I'd just take the first one. If I won, okay. If I lost, too bad. No, really.

    (Not very sporting, I know, but all that stuff is way beyond my pay grade )

  15. #64

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    Quote Originally Posted by ragman1
    It's a quote. I don't know if it's true or not. In fact, it's worse than that, I don't even understand the harmonic series :-)

    'A harmonic series is the sequence of sounds - pure tones, represented by sinusoidal waves in which the frequency of each sound is an integer multiple of the fundamental, the lowest frequency.'


    You wot?
    well that makes complete sense to me but I have a degree in that shit.

    it’s stuff you’d probably have a practical interest if you got into analogue synths for instance, about how you can break down sounds as combinations of simpler sounds...

    When it comes to the laws of harmony it’s a lot more complicated, basically. The debate has been raging for ages. Hindemith and those that were opposed to atonality in music were keen to demonstrate a link between the laws of physics and tonality.

    that is tempting, but problematic. There are aspects of music that have to do with this stuff but:

    - research has shown that a preference for Western tonality is culturally determined. Becoming less Western centric in our understanding of music has really made this tonality/physics thing much less arguable
    - just intonated intervals aren’t necessarily the ones in the harmonic series either - there’s a number of ways to derive a major third for instance
    - some intervals in use in music are nowhere found in the overtone series like the perfect fourth and minor third (that’s where all the negative harmony bullshit comes in btw)
    - this all ties up with that Aesthetics thing, which is the idea that you can prove beauty. It’s an ultimately dumb idea, as we are perhaps in a better situation to say at this time (though Kant called it), but that doesn’t stop clever people from the ancient Greeks on for falling for it.

    anyway, it’s complicated.

  16. #65

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    I can't do that but I can do this:

    'A harmonic series is the sequence of sounds'

    That should either be 'The harmonic series is the sequence of sounds' or 'A harmonic series is a sequence of sounds'. It can't be both and make sense.

  17. #66

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    There are some things you can say; such as intervals that are more or less mathematically complex sound more or less complex to the ear, which in our culture sounds more or less dissonant, but how this is expressed in music varies throughout the world.

    furthermore the fact that we are willing to hear equal tempered thirds as thirds when they are really rather out of tune, shows the extent to which culture governs these things.

  18. #67

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    And

    the idea that you can prove beauty. It’s an ultimately dumb idea
    Absolutely.

  19. #68

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    Quote Originally Posted by ragman1
    I can't do that but I can do this:

    'A harmonic series is the sequence of sounds'

    That should either be 'The harmonic series is the sequence of sounds' or 'A harmonic series is a sequence of sounds'. It can't be both and make sense.
    sounds are waves. Sine waves are the simplest type of sound. They are so called because the are generated by a mathematical function called ‘sine’. The closest thing to this sound on the guitar is the sound of the harmonics on a string.

    A rich musical sound such as a note on a guitar or piano is not itself a sequence but a combination of these sounds related by frequency. the frequency relationship between these notes is the sequence bit, not the sounds.

    Musicians call frequency relationships ‘intervals.’ We call frequencies ‘pitches’; A B C etc.

    so in musical terms a note ‘E’ on a guitar might be mostly E, a bit A, a touch of flattish G# and so on.

    Or, root, octave, compound perfect fifth, compound major third etc

    You find these notes on the harmonics of the E string. These notes are given by mathematical ratios given by the maths above.

    1, 2, 3, 4, 5 .... or in one octave

    unison - 1
    octave - 2
    perfect fifth - 3:2
    octave again - 2:2
    major third - 5:4
    and so on


    So this type of thing is not limited to music, hence the use of mathematical language.

    in maths, there are many areas where you want to break down complex repeating patterns (waveforms) into combinations of sine waves. You would do this in seeking to understand the electromagnetic spectrum of a star for instance, or the acoustic spectrum of a piano note.

    We call this a Fourier transform.

  20. #69

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    That wasn't the point. It's bad English. Might be a typo, of course.

  21. #70

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    A harmonic series is the sequence of sounds for any given note

    the harmonic series of D is different to C?

    But it has the same ratios/intervals so
    irs arguable either way. The harmonic sequence is always the same in ratio terms, but the frequencies change.

  22. #71

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    Ah, got it, thanks.

    Well, I must be conditioned by Western culture because I prefer that sound to, say, Indian music. They see in it something that eludes me. I can listen but not for long.

    Perhaps if I lived there a long time I'd absorb it and begin to understand it. But that's tenuous too.

  23. #72

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    Quote Originally Posted by ragman1
    Ah, got it.

    Well, I must be conditioned by Western culture because I prefer that sound to, say, Indian music. They see in it something that eludes me. I can listen but not for long.

    Perhaps if I lived there a long time I'd absorb it and begin to understand it. But that's tenuous too.
    Indeed. Indian music is better intonated too, so it definitely holds.

    but you get acclimatised. I actually heard middle Eastern quarter tones properly for the first time last year. Before then they’d always sounded like out of tune notes to me.

  24. #73

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    I don't hear them as out of tune. In fact, I don't think they are. But my brain objects to a long exposure. It's possibly a lack of ongoing resolution.

    Go to 9.35.


  25. #74

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    Another way to think of the harmonic spectrum in intuitive terms.

    Pick near the bridge and you’ll have more overtones in the sound - more
    upper frequency info than if you pick over the soundhole. Same goes for pickups - neck pickup has less overtones than the bridge, and so on.

    So an oboe has more overtones than a flute... the ear also has an amazing ability to reconstruct the lower harmonic spectrum from the upper bits. This is why we can still hear bass when playing music on small speakers even though the speaker might not reproduce the sound that we can feel like a woofers in a high end sound system. (and why bass players using in ears monitors might choose to use a buttkicker.)

    overtones he often hear as ‘cut’ in the mix... In classical singing ‘blade’ is where you produce a very bright, overtone rich sound that carries over an orchestra. On guitar think Django, or a country telecaster.

    That might help with why jazz guitar can sound small or disappear in the mix...

    pop producers are really hip to this. They’ll eq stuff specifically with this in mind

    Probably shit you know already but I’m bored...

  26. #75

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    Well, I might just be a proll, or whatever they call it. It's whether I like it or not.

    You'd think that I'd spend time listening to sweet folk music sounds, especially on acoustic guitar, but I find the 'wrong notes' in jazz intriguing too. That's why I enjoy playing them so much.

  27. #76

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    Quote Originally Posted by ragman1
    Well, I might just be a proll, or whatever they call it. It's whether I like it or not.

    You'd think that I'd spend time listening to sweet folk music sounds, especially on acoustic guitar, but I find the 'wrong notes' in jazz intriguing too. That's why I enjoy playing them so much.
    Sure. To be honest the way I most enjoy feeling when I respond to music these days is - ‘I don’t know if I quite like or understand this’ which usually means I become obsessed with it far more than something I’ve decided about.

    Not something totally out of my area, where I just wouldn’t really enjoy it, just something pushing it out a bit. (That said I’ve heard a lot of stuff now... but real avant- garde sound oriented music usually leaves me cold.)

    Things I don’t like are normally things that I recognise. Things that I like right away are often things I recognise too, you know I’m going to hear a Sonny Stitt or Dexter solo right away... or most jazz tbh.... but things I don’t quite get... that’s kind of fascinating to me. It’s an interesting sensation...

  28. #77

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    Agreed, the extreme avant-garde stuff isn't really music, in my opinion. I just see it as musical noise.

    As we're on it, I can't take too much classical music either, it sends me to sleep.

    Probably I prefer lyrics. A good song lasts 3 to 5 minutes and, if the words have depth and meaning, I'm a pretty happy bunny

  29. #78

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    I think what I think of as avant garde might be different to you. To me anything played on instruments is basically mainstream haha

  30. #79

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    Quote Originally Posted by ragman1
    I don't hear them as out of tune. In fact, I don't think they are. But my brain objects to a long exposure. It's possibly a lack of ongoing resolution.

    Go to 9.35.

    i don’t know much about Indian music really... was talking about Maqams.



    its taken me a while to hear Rast as something other than an out of tune major scale.

  31. #80

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    I have a bottle containing 100 200mg Ibuprofen tablets. If I swallow 3 of them what is the probability that the headache I have after reading this thread will go away within a half hour?

  32. #81

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    D quarter-flat. Right... :-)

    You probably need to know this stuff for the Hot Club band. It's all Kit whassisname's fault.

  33. #82

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    Quote Originally Posted by Jack E Blue
    I have a bottle containing 100 200mg Ibuprofen tablets. If I swallow 3 of them what is the probability that the headache I have after reading this thread will go away within a half hour?
    Little. Besides, he hasn't even started with his proof yet.

    But if you swallow 3 bottles that should do it

  34. #83
    Here it is. I have stripped it down to clearest straight path without trying to talk of mapping or symmetry.
    Ask if something is not clear.

    Probabilities of the two marble bag:
    BB 1/4
    BW 1/2
    WW 1/4


    Three marbles and the probability of selecting a black:
    BBB 1
    BBW 2/3
    BWW 1/3


    A - Three marbles, two black and one white, must mean 2/3 probability of selecting a black.
    B - Three marbles with 2/3 probability of selecting black must mean two black and one white.



    Noticing that the three marble sets can be produced by adding a black marble to the two marble bag:


    B BB
    B BW
    B WW


    We know two marble probabilities of random selection
    We know three marble probabilities of selecting a black


    What is the probability of selecting a black marble if we add a black marble to the two marble bag?


    (1 x 1/4) + (2/3 x 1/2) + (1/3 x 1/4) = 2/3


    By B above, with three marbles and 2/3 probability of selecting a black marble, of the three possibilities created by adding a black to the two marble bag, those marbles must be BBW two black and one white. Since we added a black marble we may now remove it.
    BBW - B = BW one black and one white were originally in the bag.

  35. #84

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    That’s nonsense. It is on the same level as proving you have 11 fingers by counting backwards on one hand—-10, 9, 8, 7, 6—and adding 5 on the other, 6+5=11. Gotcha! (not)

  36. #85
    Quote Originally Posted by pcjazz
    That’s nonsense. It is on the same level as proving you have 11 fingers by counting backwards on one hand—-10, 9, 8, 7, 6—and adding 5 on the other, 6+5=11. Gotcha! (not)
    It would help me if you could point to the nonsense part.

  37. #86

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    Paul -

    one black and one white were originally in the bag.
    Your answer is BW.

    But it could also be BB or WW. If two random balls are selected from a pool of two colours all three possibilities are possible, not just one.

    Your answer implies that it will always be BW, which evidently isn't so.

  38. #87

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    Quote Originally Posted by pauln
    It would help me if you could point to the nonsense part.
    This is not about the likelihood of selecting a black marble. It is about the specious certainty of the BW mix. There are lots of perfectly logical marble selection puzzles but this is not one of them. In this case (viewed from the selection perspective) the first marble tells you nothing about the second. There is a 50% chance that the first marble is B. Whether the first is B or W there is a 50% chance that the second marble is B. Given your initial premise there is no logical path to determining with certainty the bag’s contents, except opening the bag and looking at the marbles.

  39. #88

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    Quote Originally Posted by pcjazz
    there is no logical path to determining with certainty the bag’s contents, except opening the bag and looking at the marbles.
    Or popping in another black one, doing the hokey-cokey, and getting the wrong answer anyway

    Sorry, Paul :-)

  40. #89
    Quote Originally Posted by ragman1
    Paul -

    You're falsely introducing a third element where none existed before. I can't see any justification for that.
    The three-marble possibilities already exist, along with the four-marble and five trillion-marble possibilities, I'm just noticing that the three-marble probabilities include a subset of the two-marble probabilities.

    Notice that although the two-marble bag was created by random selection, the three-marble set used to find the two statements "A" and "B" were randomly selected - they were given, for "A" by indicating the quantity and the color, for "B" by indicating the quantity and the probability of an operation. Whether BBW arises from random selection or whimsical declaration, the relations regarding BBW in the statements hold universally true.
    That justifies the application of statement "B" to the probabilities in the compound question.

  41. #90
    Quote Originally Posted by pcjazz
    This is not about the likelihood of selecting a black marble. It is about the specious certainty of the BW mix. There are lots of perfectly logical marble selection puzzles but this is not one of them. In this case (viewed from the selection perspective) the first marble tells you nothing about the second. There is a 50% chance that the first marble is B. Whether the first is B or W there is a 50% chance that the second marble is B. Given your initial premise there is no logical path to determining with certainty the bag’s contents, except opening the bag and looking at the marbles.
    I know all that, I've mentioned that the solution is surprising and impossible.
    That suggests there is a flaw in the method. Do you see a flaw?

  42. #91
    Quote Originally Posted by ragman1
    Paul -



    Your answer is BW.

    But it could also be BB or WW. If two random balls are selected from a pool of two colours all three possibilities are possible, not just one.

    Your answer implies that it will always be BW, which evidently isn't so.
    I know, that is the surprise (that the answer is not a probability but in the form WB specifying one black and one white) and impossibility (because we know there are other possibilities, not just the single one).
    Yet, I am not finding a flaw in the logic of the method that gives the surprising and impossible answer.

  43. #92

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    Quote Originally Posted by pauln
    I know all that, I've mentioned that the solution is surprising and impossible.
    That suggests there is a flaw in the method. Do you see a flaw?
    well, the obvious flaw is that the purported “solution” is impossible. I’m out of here ...

  44. #93

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    I am pretty useless at probabilities, but is there possibly a flaw as follows:

    The overall probability after adding a 3rd black marble is 2/3. But this relates to the combined probability across 3 possible scenarios, i.e.
    BBB
    BBW
    BWW

    But when you work back from your end result of 2/3, you have assumed it only relates to the 2/3 result which attached to one of those 3 scenarios, i.e. BBW, from there you can get to the BW answer.

    But it would seem the overall 2/3 result includes the BBB and BWW scenarios as well?

  45. #94

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    By B above, with three marbles and 2/3 probability of selecting a black marble, of the three possibilities created by adding a black to the two marble bag, those marbles must be BBW two black and one white. Since we added a black marble we may now remove it.
    BBW - B = BW one black and one white were originally in the bag.
    This makes no sense, there is no logical argument here. The odds of selecting a black marble from the three is 2/3, but the MUST part is BS, BWW and BBB remain possibilities. Adding a third black marble provides no information about the composition of the first two. Dont know if this is trying to rework the very real Monte Haul paradox, but that is a very different scenario


  46. #95
    Quote Originally Posted by BWV
    This makes no sense, there is no logical argument here. The odds of selecting a black marble from the three is 2/3, but the MUST part is BS, BWW and BBB remain possibilities. Adding a third black marble provides no information about the composition of the first two. Dont know if this is trying to rework the very real Monte Haul paradox, but that is a very different scenario

    Nothing to do with Monty Hall.

    I make a series of logical arguments, but I'm looking for the flaw. I can't tell what parts you may be denying true...
    Please read Clue #1. The MUST comes from the three marbles in each scenario being given, declared, not randomly selected.
    Do you deny that if I look at and place three marbles in a bag and tell you the probability of selecting a black one is 2/3, then there are two black and one white marble?
    Do you deny that after adding the third marble, three marbles exit in the bag with some definite color combination.?
    Do you deny that my compound calculation of 2/3 is correct?

  47. #96

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    It would have been better if you just posed the challenge as finding the flaw in the argument. It may take some head scratching but obviously there is a refutation.

    It was misleading to pose it as a puzzle implying that there is a valid solution to be found.

  48. #97

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    Quote Originally Posted by pauln
    Do you deny that if I look at and place three marbles in a bag and tell you the probability of selecting a black one is 2/3, then there are two black and one white marble?


    yes, this is the flaw. The odds are 2/3rds because
    (1 x 1/4) + (2/3 x 1/2) + (1/3 x 1/4) = 2/3

    the odds that the bag is BBW is 1/2 - not the same. This never changes. You cannot make the jump that because the odds are also 2/3rds of selecting a black from BBW therefore that must be the composition of the bag

  49. #98

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    The flaw in solution is... To "unknown", first you add, then subtract from, one same element. The result must be the very same "unknown" you started with.

    Also what Grahambop pointed. out. You calculate 2/3 as total probability of 3 scenarios, then take it as if it was of only one of those 3.

    It is not even interesting.

    Sent from My Blog Page

  50. #99
    Quote Originally Posted by Tal_175
    It would have been better if you just posed the challenge as finding the flaw in the argument. It may take some head scratching but obviously there is a refutation.

    It was misleading to pose it as a puzzle implying that there is a valid solution to be found.
    I described it as surprising and impossible, but yes.

  51. #100
    Quote Originally Posted by BWV
    yes, this is the flaw. The odds are 2/3rds because
    (1 x 1/4) + (2/3 x 1/2) + (1/3 x 1/4) = 2/3

    the odds that the bag is BBW is 1/2 - not the same. This never changes. You cannot make the jump that because the odds are also 2/3rds of selecting a black from BBW therefore that must be the composition of the bag
    The odds that the bag is BBW is 1/2 based only on the BW segment.
    The odds of selecting a black marble from a BBW is 2/3

    I think you are right. The word "must" in statement "B" of Clue#1 makes "BBW" too exclusive an answer.