When you go looking for them, signs of subtle imperfection are all
around. For this, I am very grateful.
I wouldn't recommend this search for people under the delusion of permanence, the idea that with enough effort and luck it would be possible (at least for a short time) to get everything just right, and then (and only then) to be able to be happy and relaxed. Such people are going to get frustrated and discouraged when they keep bumping up against imperfection. But people who are a little more aware of the Dharma understand that the imperfection is already perfect. The flaw lies not with the "imperfect" situation, but lies in our relationship to it - how we feel about it. To repeat myself: the imperfection is already perfect.
That's not meant to be some trite pop culture "Zen paradox". It's a simple observation of how things are when one has a more encompassing understanding of perfection. We are given a great practice opportunity to hold in awareness our desire and expectation of "perfection", and our inability to see the perfection that the world offers up every moment. Don't waste this! Everything is teaching, all the time.
This recognition and appreciation of imperfection runs counter to Western aesthetic ideals informed by ancient Greeks like Pythagoras, and can feel defeatist when you are strongly attached to "perfection". But it is well-represented in other aesthetic traditions, such as Japanese wabi sabi.
Wabi. The beauty of thusness. The lone simplicity and quietude of the remote natural world. Freshness and understatement. The maker's mark. Imperfection of design and construction. The quirky input of path dependence. The uniqueness of the thing in itself. Suchness.
Sabi. The beauty of age and experience. Serenity in the face of wear and tear. Imperfection of usage and reliability. Growth and decline in the fullness of life. The quirky outcome of paths chosen. Wisdom embodied through practice.
For those who see what I'm pointing at, actively searching out "imperfection" can actually be a satisfying source of beauty and delight. And, since there's so much of it in the world, it becomes a rich and reliable source of happiness. Let me share an example from the world of music, which I find delightful. Maybe you will too.
Pythagoras was one of the first to take clear notice of the relationship between geometry and musical harmony. He was a great believer in the perfection of the world and in the ability to see this perfection by representing the world in geometric simplicity. The simplest example of geometry and music is the octave. If you stretch a string (always of a particular thickness, and at a particular tension) over a particular length and then pluck it, it will vibrate and produce a single note. If you then do the same but over a length exactly half of what you did before, the string will now produce a note exactly one octave higher. The simple ratio of 1:2 produces notes an octave apart. If you divide the string at different lengths (instead of the midpoint) you produce other different notes. If the ratios of lengths are carefully chosen to be ratios of small numbers, the notes produced will be in other pleasant musical intervals. For example, the ratio of 2:3 produces notes that are a perfect fifth apart (think of the opening notes of Twinkle, Twinkle Little Star). The ratio of 3:4 produces an interval of a perfect fourth (the opening notes of Amazing Grace). And so on in beautifully consonant and harmonious intervals. So far, so good. Simple geometric ratios, pleasant sonorous harmonies. Close to perfection, yeah?
If you can produce a perfect fifth, you can then apply the same 2:3 trick to the new note to produce a third note that is a perfect fifth above that. For example, starting with C, 2:3 produces G. Then applying 2:3 to that G produces D. Continuing on like this eventually produces all 12 notes of the Western scale: C, G, D, A, E, B, F#, C#, G# (aka Ab), D# (aka Eb), Bb, F, C. The C that you finally reach will of course be seven octaves higher than the original C you started with. But it will be a C nonetheless (a piano keyboard is just long enough to try this yourself). You could alternatively take the original C and keep halving its length until you get up to the same octave. The two C notes should match, right?
Wrong. The C that you get by the cycle of fifths (repeating the 2:3 ratio twelve times) is a slightly higher note than the C you get by octaves (dividing the string in half seven times). The beautiful and mathematically elegant note produced by the Pythagorean method of perfect fifths is ever so slightly sharp and out of tune. Actually, it's not so "slightly". It's about a quarter of a semitone too high. Easily heard as dissonant even by non-musicians.
I suspect this difference (now called the "Pythagorean comma") drove poor Pythagoras a bit crazy. How could a perfectly just and beautiful universe behave so perversely? It's a grotesque discovery to anyone who is attached to the idea of perfection. It's as if we found out the moon does not go around the earth in a perfect circle (Narrator: It doesn't. It's not even a perfect ellipse). Argh.
And so we're forced to face this reality, to deal with things as they actually are, without attachment to ideals of what we think they should be like. Old school piano tuners (who work by ear, without an electronic tuner app on their iPhones), have therefore learned to deliberately mistune the fifths on a piano, making them all slightly flat so that if you go around the full circle of fifths you end up at a note that is in tune with where you started. How much deliberate flat mistuning do they introduce? A quarter of semitone by the twelth root of two (how's that for an ugly bit of math?) - which means they first tune each fifth (say C to G) perfectly, and then flatten the upper note until it creates a beat frequency of about one beat per second (see my earlier post "Sound is Weird" if you want to read about other weird beat-frequency stuff). The resulting tuned piano plays all intervals slightly flat and out of tune. But the out-of-tuneness is spread equally across all twelve notes of the scale (including the black keys). This "equal temperament" it sounds equally imperfect no matter what notes you play, and in whatever key.
(Aside for fellow guitarists out there: this is why tuning your guitar by matching harmonics on adjacent strings at fifth and seventh frets does not work. You're trying to tune perfect fourths with no beat frequency, which creates the Pythagorean comma problem. The farther you play from the middle of the neck, the more out of tune it will be.)
What you seek you already have (grasshopper). The damned guitar is never going to be in tune. So shut up and play it!
I wouldn't recommend this search for people under the delusion of permanence, the idea that with enough effort and luck it would be possible (at least for a short time) to get everything just right, and then (and only then) to be able to be happy and relaxed. Such people are going to get frustrated and discouraged when they keep bumping up against imperfection. But people who are a little more aware of the Dharma understand that the imperfection is already perfect. The flaw lies not with the "imperfect" situation, but lies in our relationship to it - how we feel about it. To repeat myself: the imperfection is already perfect.
That's not meant to be some trite pop culture "Zen paradox". It's a simple observation of how things are when one has a more encompassing understanding of perfection. We are given a great practice opportunity to hold in awareness our desire and expectation of "perfection", and our inability to see the perfection that the world offers up every moment. Don't waste this! Everything is teaching, all the time.
 |
| Without any help from us, every snowflake falls in exactly the right place. |
Wabi. The beauty of thusness. The lone simplicity and quietude of the remote natural world. Freshness and understatement. The maker's mark. Imperfection of design and construction. The quirky input of path dependence. The uniqueness of the thing in itself. Suchness.
Sabi. The beauty of age and experience. Serenity in the face of wear and tear. Imperfection of usage and reliability. Growth and decline in the fullness of life. The quirky outcome of paths chosen. Wisdom embodied through practice.
 |
| Well-crafted and enjoyed by many, wood returns whence it came. |
Musical Commas
For those who see what I'm pointing at, actively searching out "imperfection" can actually be a satisfying source of beauty and delight. And, since there's so much of it in the world, it becomes a rich and reliable source of happiness. Let me share an example from the world of music, which I find delightful. Maybe you will too.
Pythagoras was one of the first to take clear notice of the relationship between geometry and musical harmony. He was a great believer in the perfection of the world and in the ability to see this perfection by representing the world in geometric simplicity. The simplest example of geometry and music is the octave. If you stretch a string (always of a particular thickness, and at a particular tension) over a particular length and then pluck it, it will vibrate and produce a single note. If you then do the same but over a length exactly half of what you did before, the string will now produce a note exactly one octave higher. The simple ratio of 1:2 produces notes an octave apart. If you divide the string at different lengths (instead of the midpoint) you produce other different notes. If the ratios of lengths are carefully chosen to be ratios of small numbers, the notes produced will be in other pleasant musical intervals. For example, the ratio of 2:3 produces notes that are a perfect fifth apart (think of the opening notes of Twinkle, Twinkle Little Star). The ratio of 3:4 produces an interval of a perfect fourth (the opening notes of Amazing Grace). And so on in beautifully consonant and harmonious intervals. So far, so good. Simple geometric ratios, pleasant sonorous harmonies. Close to perfection, yeah?
If you can produce a perfect fifth, you can then apply the same 2:3 trick to the new note to produce a third note that is a perfect fifth above that. For example, starting with C, 2:3 produces G. Then applying 2:3 to that G produces D. Continuing on like this eventually produces all 12 notes of the Western scale: C, G, D, A, E, B, F#, C#, G# (aka Ab), D# (aka Eb), Bb, F, C. The C that you finally reach will of course be seven octaves higher than the original C you started with. But it will be a C nonetheless (a piano keyboard is just long enough to try this yourself). You could alternatively take the original C and keep halving its length until you get up to the same octave. The two C notes should match, right?
Wrong. The C that you get by the cycle of fifths (repeating the 2:3 ratio twelve times) is a slightly higher note than the C you get by octaves (dividing the string in half seven times). The beautiful and mathematically elegant note produced by the Pythagorean method of perfect fifths is ever so slightly sharp and out of tune. Actually, it's not so "slightly". It's about a quarter of a semitone too high. Easily heard as dissonant even by non-musicians.
I suspect this difference (now called the "Pythagorean comma") drove poor Pythagoras a bit crazy. How could a perfectly just and beautiful universe behave so perversely? It's a grotesque discovery to anyone who is attached to the idea of perfection. It's as if we found out the moon does not go around the earth in a perfect circle (Narrator: It doesn't. It's not even a perfect ellipse). Argh.
And so we're forced to face this reality, to deal with things as they actually are, without attachment to ideals of what we think they should be like. Old school piano tuners (who work by ear, without an electronic tuner app on their iPhones), have therefore learned to deliberately mistune the fifths on a piano, making them all slightly flat so that if you go around the full circle of fifths you end up at a note that is in tune with where you started. How much deliberate flat mistuning do they introduce? A quarter of semitone by the twelth root of two (how's that for an ugly bit of math?) - which means they first tune each fifth (say C to G) perfectly, and then flatten the upper note until it creates a beat frequency of about one beat per second (see my earlier post "Sound is Weird" if you want to read about other weird beat-frequency stuff). The resulting tuned piano plays all intervals slightly flat and out of tune. But the out-of-tuneness is spread equally across all twelve notes of the scale (including the black keys). This "equal temperament" it sounds equally imperfect no matter what notes you play, and in whatever key.
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| You can perfectly tuna fish |
(Aside for fellow guitarists out there: this is why tuning your guitar by matching harmonics on adjacent strings at fifth and seventh frets does not work. You're trying to tune perfect fourths with no beat frequency, which creates the Pythagorean comma problem. The farther you play from the middle of the neck, the more out of tune it will be.)
If you'd like to take a deeper dive on this stuff, look into the syntonic comma as well. It's the difference you get in a major third (e.g., C to E) by going around the cycle of fifths four times (C-G-D-A-E) versus going straight to it via a nice Pythagorean ratio of 4:5. Imperfection in art runs very deep.Interesting tidbits, maybe. But the more important thing to hold in awareness is: how do you relate to this state of affairs? Is it the deep aesthetic problem that Pythagoras saw? Is it just a neutral and pragmatic issue to be deal with when tuning musical instruments? Or is it maybe actually a positive thing? Things are they way they are, and who are we to decide that's not exactly as they should be? All things are perfect in their imperfections. It's not the case that "perfection" is unobtainable or fleeting. But rather, it's that perfection is already present.
What you seek you already have (grasshopper). The damned guitar is never going to be in tune. So shut up and play it!
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| Do cracks and variations in colour add or subtract beauty? |
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