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Beautiful Ideas.
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Do you find the natural world beautiful?
Does this world embody beautiful ideas?
Does this world embody beautiful ideas?
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i have seen inversion at sea. Sometimes you can see things that are still invisible because of the curvature of the earth so you see huge ships or islands floating upside down on the horizon. Sometimes you can see what is being reflected so you see the ghost ship or island floating over the real one. It can be a bit scary, the image is so real.
O.G.//It can not embody ideas as that would imply creation by an intelligence that had ideas.//
Consider, for example, the work of Pythagoras on the relationship between sound and mathematics, observing the length of a vibrating string and our perception of its tone. He discovered that two identical strings
(say, 2 guitars today) at similar tension make tones that sound 'good' together, exactly when the lengths of the strings are in ratios of small or whole numbers.
So. for example, when the ratio of lengths is 1:2, the tones form an octave. When the ratio is 2:3 we hear the dominant fifth; when the ratio is 3:4, the major fourth. In musical notation (in the key of C) these correspond to playing two Cs, one above the other, together a C-G or C-F, respectively.
These tones which sound good together we say are in 'harmony' and are the basic building blocks of classical music and of most folk, pop and rock. Why should we find these tone combinations, with their undoubted reliance on mathematics and the world of numbers, so appealing?
Consider, for example, the work of Pythagoras on the relationship between sound and mathematics, observing the length of a vibrating string and our perception of its tone. He discovered that two identical strings
(say, 2 guitars today) at similar tension make tones that sound 'good' together, exactly when the lengths of the strings are in ratios of small or whole numbers.
So. for example, when the ratio of lengths is 1:2, the tones form an octave. When the ratio is 2:3 we hear the dominant fifth; when the ratio is 3:4, the major fourth. In musical notation (in the key of C) these correspond to playing two Cs, one above the other, together a C-G or C-F, respectively.
These tones which sound good together we say are in 'harmony' and are the basic building blocks of classical music and of most folk, pop and rock. Why should we find these tone combinations, with their undoubted reliance on mathematics and the world of numbers, so appealing?
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PiedPiper,//most sounds are harmonious// I don't think so, our response to most sounds is subjective; you probably don't like the cuckoo because you frown on its domestic habits, and I don't think the victims of recent floods found the sound of the river flowing through their houses "like a symphony".
Most sounds are definitely not harmonious; dogs barking, babies crying, etc.
but that has nothing to do with the harmony based on mathematics, as revealed by Pythagoras.
Most sounds are definitely not harmonious; dogs barking, babies crying, etc.
but that has nothing to do with the harmony based on mathematics, as revealed by Pythagoras.