Golden ratio in guitar solos?

_{Denyse O'Leary

December 2, 2014

Intelligent Design, Mathematics, News}

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Golden rectangle/Ahrecht (Original), Pbroks13, Joo

Further to Does the golden ratio, 1.618, unify science?

A reader kindly writes to say that his high school guitar teacher told him that one can find the golden ratio in guitar solos that sneak into songs:

Golden section and golden rectangles, the harmonic series and the model of its ideal behavior simplified, equal temperament and just intonation and a description of the beat frequency conflict produced by the deviations between simultaneous sounding of harmonic partials and prime frequencies and how it affects the tone and timbre of the guitar. Read to the end for some cool videos demonstrating the properties detailed here.

Design? Chance? Chance only if there are a zillion universes that don’t have anything like this. So the evidence for their existence is… ? Uh, right.

Chances are, today’s art establishment won’t take the golden ratio seriously unless it helps chimps fling poop at each other. That’s art too, didn’t you know? Well, it will be if some project gets funded.

See also: The multiverse: Where everything turns out to be true, except philosophy and religion

and

Human origins: The war of trivial explanations

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Comments

zac says, Then there are no circles. I say, If you are a materialist then there are no circles. It must be a sad life peacefifthmonarchyman_{December 7, 2014
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You say. Sure you can, as long as there is feedback to closeness to the platonic form. I say, Yeah as Ive repeatedly said, If you know the form in advance an Algorithm can easily approximate it. You say, Evolution doesn’t work with platonic forms, I say, Therefore it can't approximate them. That is the point. You say, You don’t really think “mouse” is a platonic form? I say, Actually I very much do. I believe that species exist in reality outside the cave or in the mind of God if you like independent of anything in the physical world. That sort of thinking goes back to the very first chapter of Genesis peacefifthmonarchyman_{December 7, 2014
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fifthmonarchyman: Give a person any physical shape and enough time and resources and he will show you exactly where it deviates from the Ideal circle Then there are no circles.Zachriel_{December 7, 2014
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fifthmonarchyman: A string is either the Fibonacci Sequence or it is not there is no varying degrees of sequencehood. Sure, but an algorithm can recognize the Fibonacci sequence. Furthermore, if you provide a finite sequence, there are other patterns that fit it just as well. fifthmonarchyman: An organism is either a T-Rex or it is not there is no varying degrees of T-Rexhood. Not a T. Rex http://i.telegraph.co.uk/multimedia/archive/02725/lythronax_2725924b.jpg Species have fuzzy edges. A hybrid between a lion and a tiger is not a lion and not not a lion.Zachriel_{December 7, 2014
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Zac says Yet people will point to near circles and say they are circles. I say, Give a person any physical shape and enough time and resources and he will show you exactly where it deviates from the Ideal circle peacefifthmonarchyman_{December 7, 2014
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A couple more examples A string is either the Fibonacci Sequence or it is not there is no varying degrees of sequencehood. A structure is either a bacterial flagellum or it is not there is no varying degrees of flagellumhood. An organism is either a T-Rex or it is not there is no varying degrees of T-Rexhood. The only way to deny any of this is to deny the reality of the forms. I can't see how you would ever prove such a claim to anyone who does not assume materialism from the outset peacefifthmonarchyman_{December 7, 2014
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fifthmonarchyman: Before in the other thread I said you can fool all of the people some of the time and some of the people all of the time but my game assumes you can’t fool most of the people all of the time You said "infallibly" ten times before "can't fool", then eight times afterwards, even after we suggested you meant a statistically significant result. fifthmonarchyman: An algorithm can’t converge if we are talking about platonic forms. Sure you can, as long as there is feedback to closeness to the platonic form. Evolution doesn't work with platonic forms, in any case. You don't really think "mouse" is a platonic form? fifthmonarchyman: A shape is either a circle or it is not there are no varying degrees of circlehood Yet people will point to near circles and say they are circles. Those silly humans!Zachriel_{December 7, 2014
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Zac says The feedback is only yes/no, but for the algorithm to converge, there has to be a population that can be sorted through with varying degrees of fitness. I say, exactly!!!!! An algorithm can't converge if we are talking about platonic forms. A shape is either a circle or it is not there are no varying degrees of circlehood A string is either a Shakespearean Sonnet or it is not there are no varying degrees of Sonnethood peacefifthmonarchyman_{December 7, 2014
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Zac said. Before the test required infallibility, so that’s changed. I say, I am tired of having to repeat myself endlessly with you Before in the other thread I said you can fool all of the people some of the time and some of the people all of the time but my game assumes you can't fool most of the people all of the time I again feel the frustration level rising. We have went over each of these points before. Now for some reason you want to pretend that none of that happened. I can't for the life of me understand why you would do that unless it is that you think you will be able to find a loophole the second time around. perhaps you are hoping that a new lurker will think you are making objections that I can't answer. regardless I don't have the time or the patience for a Groundhog day experience if you have any questions I have not already answered feel free to ask them peacefifthmonarchyman_{December 7, 2014
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fifthmonarchyman: There are lots of ways I can tell it was an algorithm. You haven't provided a non-algorithmic way to determine the nth digit of pi. fifthmonarchyman: 2) Convert one or more of them to numbers by a secret key. Has to be at least two, one a control for comparison. fifthmonarchyman: 6) If a majority of observers object send it back. Before the test required infallibility, so that's changed. 6) The feedback is only yes/no, but for the algorithm to converge, there has to be a population that can be sorted through with varying degrees of fitness.Zachriel_{December 7, 2014
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You say, You just indicated you can only tell it was an algorithm by using an algorithm to compare it to. I say, Don't ever recall saying "only". There are lots of ways I can tell it was an algorithm. My game is one of them You say, If you mean a decimal expansion is always an approximation, that doesn’t require an algorithm, but can be shown by deduction. I say, I so much agree but deduction does not seem to be a strong suite among critics here. If it was no one would claim that evolution could approximate the forms sufficiently enough to fool an observer peacefifthmonarchyman_{December 7, 2014
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Zac my game can be described like this 1) Take the set of Shakespearean sonnets. 2) Convert one or more of them to numbers by a secret key. 3) Have an algorithm determine whatever patterns it detects in the coded strings. 4) Have the algorithm generate a new sequence based on the detected pattern. 5) Have observers compare this generated pattern to the original set (with feedback) to see if they can tell the genuine article from the algorithmically generated sequence. 6) If a majority of observers object send it back.fifthmonarchyman_{December 7, 2014
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fifthmonarchyman: not if it does not know what digit I want. No, it doesn't read your mind, but if you ask for the nth digit, it provides the nth digit. Of course, an expansion would do the same.Zachriel_{December 7, 2014
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fifthmonarchyman: It means the observer will always be able to tell the difference between what an algorithm produces and the form/spesfication “Pi” You just indicated you can only tell it was an algorithm by using an algorithm to compare it to. If you mean a decimal expansion is always an approximation, that doesn't require an algorithm, but can be shown by deduction.Zachriel_{December 7, 2014
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Zac says, it’s possible to calculate the nth digit of pi in certain bases without calculating all the preceding digits, so the algorithm can return your answer directly for whatever digit you want. I say, not if it does not know what digit I want. That is after all the point Peacefifthmonarchyman_{December 7, 2014
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1) Take two sonnets. 2) Convert them to numbers by a secret key, the experimental and the control. 3) From the first sonnet, have an algorithm determine whatever patterns it detect. 4) Have the algorithm generate a new sequence based on the detected pattern. 5) Have observers compare this generated pattern to the control sequence to see if they can tell the genuine article from the algorithmically generated sequence. 6) If even a single observer objects, send it back.
Is that correct? If so, there's a lot of problems with your game.Zachriel_{December 7, 2014
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zac says And this means what exactly? I say It means the observer will always be able to tell the difference between what an algorithm produces and the form/specification "Pi" peacefifthmonarchyman_{December 7, 2014
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By the way, it's possible to calculate the nth digit of pi in certain bases without calculating all the preceding digits, so the algorithm can return your answer directly for whatever digit you want.Zachriel_{December 7, 2014
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Zac says, Right. 4) Have the algorithm generate a NEW sequence based on the detected pattern. I say, yes but not 5) Have observers compare this generated pattern to the control sequence to see if they can tell the difference. The observers are not looking to see if the new sequence matches the control sequence they are looking to see if the new sequence matches the specification that the control sequence approximates. peacefifthmonarchyman_{December 7, 2014
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fifthmonarchyman: NO but I can calculate the thousandth digit once I know the specification/form. What is the difference between the model and the "actual process"? fifthmonarchyman: The model can’t know at which point I will look so it can’t (ever)know at what point to halt. And this means what exactly?Zachriel_{December 7, 2014
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Zac says, How did you determine whether the digits looked right or not? You mean you can intuit the thousandth digit of pi? I say, NO but I can calculate the thousandth digit once I know the specification/form. The model can't know at which point I will look so it can't (ever)know at what point to halt. peacefifthmonarchyman_{December 7, 2014
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fifthmonarchyman: We are not trying to duplicate any string exactly we are trying to approximate a form/specification. Why can't you provide a clear step-by-step specification for your game? fifthmonarchyman: We are not trying to duplicate any string exactly we are trying to approximate a form/specification. Right. 4) Have the algorithm generate a NEW sequence based on the detected pattern.Zachriel_{December 7, 2014
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zac says Is this the process? If so, there’s lots of problems. I say. No it's not the process at all. We are not trying to duplicate any string exactly we are trying to approximate a form/specification. I can (and have) compared 2 real "sonnets" against a model and the observer can still pick out the fake peacefifthmonarchyman_{December 7, 2014
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fifthmonarchyman: Suppose I’m modeling a process that calculates the ratio of a circle’s circumference to its diameter. Even if my model is an algorithm for computing Pi. An observer will be able to tell the difference between the actual process and the model. Huh? What is the difference between the model and the "actual process" * ? fifthmonarchyman: He will do this by simply looking a digit or two past where the model halted. How did you determine whether the digits looked right or not? You mean you can intuit the thousandth digit of pi? Did we describe your game correctly (#183)? -- * ETAZachriel_{December 7, 2014
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Let me take this a step further here is a very simple example Suppose I'm modeling a process that calculates the ratio of a circle's circumference to its diameter. Even if my model is an algorithm for computing Pi. An observer will be able to tell the difference between the actual process and the model. He will do this by simply looking a digit or two past where the model halted. There is no way around it algorithmic process like evolution can not approximate a “form” closely enough to fool an observer. I really hope that helps peacefifthmonarchyman_{December 7, 2014
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fifthmonarchyman: I run a model for a given process and compare the extrapolation produced by the model against actual results. Still have no idea what you mean. We know how to follow a step-by-step process, so not sure why we are having troubles communicating.
1) Take two sonnets. 2) Convert them to numbers by a secret key, the experimental and the control. 3) From the first sonnet, have an algorithm determine whatever patterns it detect. 4) Have the algorithm generate a new sequence based on the detected pattern. 5) Have observers compare this generated pattern to the control sequence to see if they can tell the difference. 6) If even a single observer objects, send it back.
Is this the process? If so, there's lots of problems. Zachriel: You provide instances, a blackbox determines a pattern, then, if requested, provides new instances from the class of patterns. So, do you concede that algorithms can detect patterns, such such as ellipses and the Fibonacci series as you gave above?Zachriel_{December 7, 2014
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Zac, let me try and go at this another way. Right now I use my "game" mainly to evaluate the strength of various forecasting models. I run a model for a given process and compare the extrapolation produced by the model against actual results. The strength of a particular model corresponds to how well it reproduces the actual data. What I discovered was that no matter how good the model is an observer (with no knowledge of the process) can always tell the difference between the real data and the model, given feed back of course. If you ask the observer how he can tell the difference between the two strings he will describe for you a part of the specification/form of the real process. I can then tweak the algorithmic model with this information and rerun the test. At that point the observer will notice another detail of the form and the process can be repeated. The point is the model never gets to the point that the observer can not distinguish it from the real process. This is because the model is only extrapolating from information I have given it and not intuiting the form/specification. I hope that helps you to understand what I'm trying to say. peacefifthmonarchyman_{December 7, 2014
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fifthmonarchyman: NO what I mean is the algorithm is given a string and asked to intuit the form it approximates. The same. You provide instances, a blackbox determines a pattern, then, if requested, provides new instances from the class of patterns. Keep in mind, though, that there is generally some ambiguity involved. For any finite string, there are an infinite number of patterns that includes the finite string. If shown a circle, is the circle a special case of ellipses, or ellipses a special case of oval, or ovals a special case of closed curves, or closed curves a special case of closed shapes, or closed shapes a special case of shapes? fifthmonarchyman: again my game does not ask you to extrapolate the exact string. Sorry, we just don't think you can write sonnets of the quality and character of Shakespeare, even having Shakespeare as a model. We could be wrong, but even then, it's not much of a test, as most humans would fail. Are you still considering extrapolating a sonnet from a short sequence of numbers? Humans can't do it from numbers, so not sure whether an algorithm could do it would be relevant.Zachriel_{December 7, 2014
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Zac said, So, what you really meant was that the algorithm is given a specification, either an example of a class or part of a longer sequence, then asked to extrapolate. I say, NO what I mean is the algorithm is given a string and asked to intuit the form it approximates. Extrapolation is bottom up intuition is top down. you say, if we give you the first line of a Shakespearean sonnet, one of which you have no knowledge, you can provide the rest of the sonnet? That’s seems rather doubtful. I say, again my game does not ask you to extrapolate the exact string. I'm not sure how many ways I can express this. It asks you to intuit the form and approximate it in your own string sufficiently well enough to fool an observer you say, Algorithms are excellent at extrapolating strings I say, yes and if I was asking for extrapolation that fact might be relevant peacefifthmonarchyman_{December 7, 2014
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Zac said It’s not scientific, but mathematical. I say, OK if all you mean by your claim is "there are an infinite number of algorithms for each and every finite string." Then I have never disagreed. This is true but entirely irrelevant to the point I'm making. I pointed this out to KeithS in about the 50th post of that mammoth thread. peacefifthmonarchyman_{December 7, 2014
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