“I’m sorry, but I just don’t see any practical use for Riemann’s mapping theorem. I know you’ll say something about homeomorphism and about a coffee cup’s just being another form of a donut, but, come on, really? How many of us ever turn our coffee cup into a torus or our sugared torus into a ceramic drinking mug? Haven’t you noticed the effect of coffee on a dipped donut? I guess I’d have to say that although a donut can hold some coffee, any donut that morphs into a mug will fail to hold an amount of coffee similar to what a mug of equivalent mass holds. It will drip, dripping is not what someone wants in a mug. Anyway, I don’t see much use for his mapping theorem, but, then, I’m not a mathematician or topologist, so, those in-the-know might be inclined to dismiss me with ‘Ignorance is bliss.’
“But my inability to find practicality in the theorem is just one drop in the mug of mind. There’s much in our intellectual world that never seems to play out in everyday life of practicality. Not that everyday life is the ultimate ground for judgment and not that utilitarianism is the ultimate philosophy. Certainly, however, we see value in whatever we deem useful. That is probably why we differ so much on the value and quality of the Arts: Music, literature, painting and sculpture.
“So, I thought upon sitting to write this that I should go to YouTube to put 'Music for Brain Power: Mozart Effect' on as background. Makes sense, doesn’t it. If I play the music and somehow acquire greater brain power, then at least Mozart’s music demonstrates the practicality of one of the Arts. But maybe my approach is all wrong. The usefulness of music might lie in uselessness. Isn’t that the nature of ‘elevator music’? Surely, the music casinos and stores play is specifically designed to entice me to spend; that’s practical, at least it is for them.
“But that simply shows that impracticality can coincide with practicality when it comes to the Arts. Like to read mysteries? What about romances? Both? Neither, in favor of westerns? Allegorical tales? Can’t agree with a friend or professor on what makes a good book good? Disagree like me when my wife argues that The Scarlet Letter is a great book? (Can’t keep thinking of the torturous time I spent as a teenage boy doing an assignment on Hawthorne)
“Is there any way to reach an agreement on what makes a work worth the listening, reading, or viewing? (For adults, not teenage boys)
“Take aesthetics. We can argue incessantly about them. We can philosophize about art—or the Arts. Let’s think of an example. We could adopt the Indian principle Vakyam rasatmakam kavyam (‘Art is expression informed by ideal reality’)?* That puts us inside some mug of Platonic meaning. Does that Indian principle help us value paintings like those of Matisse that seem to be dominated by color on nonrepresentational shapes—or at least on barely identifiable shapes? Matisse said, ‘The use of expressive colors is felt to be one of the basic elements of the modern mentality, an historical necessity, beyond choice’? And he also said, ‘The chief function of color should be to serve expression.’ Does the Indian principle help us understand nonrepresentational art? If Matisse were alive, I would ask him what he means by ‘is felt.’ Why didn’t he write the idea in the active voice? He’s the one who painted nonrepresentational colored images--to some, seemingly impractical and nonsensical, brightly colored images. Why didn’t he just say, ‘I like to express my feelings in colors’? Wouldn’t that be an honest statement? Or, ‘I think I express ideal reality through colors.’
“Yeah, sure, Henri. Your ‘ideal reality,’ not mine. If it were ‘ideal,’ wouldn’t we all hold it as such?
“Even if we can never imagine an ‘ideal form,’ we can imagine what we believe are its manifestations in specific forms. Is it the same for some ‘ideal’ color? How would we know what the ‘ideal reality’ is in color? An ideal form, such as Tree, is unimaginable. Oaks are imaginable. We picture the specific and not the ideal. Go ahead; try as hard as you can to picture Tree without picturing a specific genus or species identifiable by a characteristic shape. Now, identify the ‘ideal color.’ Is it white, the combination of all frequencies of visible light? Then I guess Kazimir Malevich’s famous White on White would be, in Matisse’s view, the greatest painting ever (even though there are three different ‘whites’ on the canvas).
“Isn’t nonrepresentational art a supposed ‘representation’ or expression of feelings or of randomness? Where’s the ideal? Is it chaos? Disorder? Entropy? I’ll start with an assumption: All art is an expression of some kind. It cannot be guaranteed to convey the artist’s personal sense or knowledge of ‘ideal reality.’ There isn't any guarantee that any art is a manifestation of an ideal reality since any ‘ideal’ in the Platonic sense can’t be imagined (Can’t think of ‘Tree’ without thinking specific tree or combination of specific trees).
“Plato aside, I can’t see how any ‘ideal’ form can be mutually understood except in the most general sense. Abstract art, which some claim to be ‘concrete,’ is colors and shapes, sometimes laid in repetitive patterns, sometimes not. If repetitive, then call it fractal art. But even fractal art can’t reveal some ideal that exists in the mind of the artist. And certainly, all of us might have some problem with Martin Heidegger’s view that a great artwork brings out the ‘true nature’ of whatever is portrayed. Who’s to say what ‘true nature’ means beyond the viewer’s inferences? We can’t even agree on the ‘true nature’ of human beings. Goodness! Think portrait art, for example. Think George Washington. Napoleon. Bust of Caesar. Maybe the sculpture gives us an idea of the ideal, but it doesn’t reveal what we might understand if we knew him personally, and even then we might not come close to knowing him ‘truly’.
“Let me give you an example that might bring the idea of the ideal home. You pose for a picture. You ask the picture-taker to see the result. You say, ‘I don’t like that one; take another.’ And that might be what you say for several pictures. Then, you acquiesce, and say, ‘All right, we’ll go with that one.’ Yet, the picture-taker might disagree on which one ‘captures’ you.”
“So,” you ask, finally getting a chance to interject, “you’re saying that there’s no such thing as an ideal on which we can agree because there is no ultimately useful mechanism for deciding on its nature short of personal preference and perspective?”
“Yes. Does that bug you?”
Now involved in the discussion, you offer, “If what you are saying is true, then we’re destined never to get along perfectly because we’ll always find some nuance to the ideal that we individually see—if seeing is what we do with ideals. How can we agree on the value of anything except in a common culture? Gold, for example, is rare, shiny, and doesn’t rust. Its ductile and malleable. It can be alloyed for strength. Isn’t it a practical basis or ideal of wealth? Doesn’t it make good art?”
“But in a pre-European North American culture that used mollusk shells for money, what good was gold? And didn’t some of the medieval Central American cultures use labor as a form of payment even though they were rich in gold?”
“Hold on. You began this by referring to Riemann’s mapping theorem, and now you’re talking about wampum and labor as elements in trade and about art as a manifestation of an ‘ideal.’ Talk about a mapping problem: You’re all over the map,” you complain. “I don’t think listening to Mozart while you write has done anything to improve your brain power.”
“Yep. And that’s because we’re all over the map with regard to intellectual constructs, art appreciation, and value. With regard to the constructs, we can describe mathematically a world for which we have no use or a world that we cannot even picture, such as a ten-dimensional multiverse or spacetime, or a wave that is simultaneously a particle. I have to give credit to Riemann, however, as one of the founders of modern math, specifically geometry, and physics. Without him there might not have been ‘an Einstein.’ I just think that his mapping theorem points to what we have become intellectually: People in search of Plato’s ideals who express ideals with no practical use in daily life; people who stand in front of nonrepresentational art and comment to a dolt like me, ‘Oh! Look how he uses texture (or color, or stroke, or distorted shape) to capture the ideal’ to which I respond, ‘I’m sorry; I’m just not seeing it,’ as I stand there dipping my glazed torus in my cup of coffee.”
*Coomaraswamy, Ananda K. “The Theory of Art in Asia,” quoted in Philipson, Morris, Ed. Aestehtics Today, Cleveland, The World Publish Company, a Meridian Book, 1961, p. 57 and reprinted from The Transformation of Nature in Art, Cambridge, Mass. Harvard University Press, 1934.
“But my inability to find practicality in the theorem is just one drop in the mug of mind. There’s much in our intellectual world that never seems to play out in everyday life of practicality. Not that everyday life is the ultimate ground for judgment and not that utilitarianism is the ultimate philosophy. Certainly, however, we see value in whatever we deem useful. That is probably why we differ so much on the value and quality of the Arts: Music, literature, painting and sculpture.
“So, I thought upon sitting to write this that I should go to YouTube to put 'Music for Brain Power: Mozart Effect' on as background. Makes sense, doesn’t it. If I play the music and somehow acquire greater brain power, then at least Mozart’s music demonstrates the practicality of one of the Arts. But maybe my approach is all wrong. The usefulness of music might lie in uselessness. Isn’t that the nature of ‘elevator music’? Surely, the music casinos and stores play is specifically designed to entice me to spend; that’s practical, at least it is for them.
“But that simply shows that impracticality can coincide with practicality when it comes to the Arts. Like to read mysteries? What about romances? Both? Neither, in favor of westerns? Allegorical tales? Can’t agree with a friend or professor on what makes a good book good? Disagree like me when my wife argues that The Scarlet Letter is a great book? (Can’t keep thinking of the torturous time I spent as a teenage boy doing an assignment on Hawthorne)
“Is there any way to reach an agreement on what makes a work worth the listening, reading, or viewing? (For adults, not teenage boys)
“Take aesthetics. We can argue incessantly about them. We can philosophize about art—or the Arts. Let’s think of an example. We could adopt the Indian principle Vakyam rasatmakam kavyam (‘Art is expression informed by ideal reality’)?* That puts us inside some mug of Platonic meaning. Does that Indian principle help us value paintings like those of Matisse that seem to be dominated by color on nonrepresentational shapes—or at least on barely identifiable shapes? Matisse said, ‘The use of expressive colors is felt to be one of the basic elements of the modern mentality, an historical necessity, beyond choice’? And he also said, ‘The chief function of color should be to serve expression.’ Does the Indian principle help us understand nonrepresentational art? If Matisse were alive, I would ask him what he means by ‘is felt.’ Why didn’t he write the idea in the active voice? He’s the one who painted nonrepresentational colored images--to some, seemingly impractical and nonsensical, brightly colored images. Why didn’t he just say, ‘I like to express my feelings in colors’? Wouldn’t that be an honest statement? Or, ‘I think I express ideal reality through colors.’
“Yeah, sure, Henri. Your ‘ideal reality,’ not mine. If it were ‘ideal,’ wouldn’t we all hold it as such?
“Even if we can never imagine an ‘ideal form,’ we can imagine what we believe are its manifestations in specific forms. Is it the same for some ‘ideal’ color? How would we know what the ‘ideal reality’ is in color? An ideal form, such as Tree, is unimaginable. Oaks are imaginable. We picture the specific and not the ideal. Go ahead; try as hard as you can to picture Tree without picturing a specific genus or species identifiable by a characteristic shape. Now, identify the ‘ideal color.’ Is it white, the combination of all frequencies of visible light? Then I guess Kazimir Malevich’s famous White on White would be, in Matisse’s view, the greatest painting ever (even though there are three different ‘whites’ on the canvas).
“Isn’t nonrepresentational art a supposed ‘representation’ or expression of feelings or of randomness? Where’s the ideal? Is it chaos? Disorder? Entropy? I’ll start with an assumption: All art is an expression of some kind. It cannot be guaranteed to convey the artist’s personal sense or knowledge of ‘ideal reality.’ There isn't any guarantee that any art is a manifestation of an ideal reality since any ‘ideal’ in the Platonic sense can’t be imagined (Can’t think of ‘Tree’ without thinking specific tree or combination of specific trees).
“Plato aside, I can’t see how any ‘ideal’ form can be mutually understood except in the most general sense. Abstract art, which some claim to be ‘concrete,’ is colors and shapes, sometimes laid in repetitive patterns, sometimes not. If repetitive, then call it fractal art. But even fractal art can’t reveal some ideal that exists in the mind of the artist. And certainly, all of us might have some problem with Martin Heidegger’s view that a great artwork brings out the ‘true nature’ of whatever is portrayed. Who’s to say what ‘true nature’ means beyond the viewer’s inferences? We can’t even agree on the ‘true nature’ of human beings. Goodness! Think portrait art, for example. Think George Washington. Napoleon. Bust of Caesar. Maybe the sculpture gives us an idea of the ideal, but it doesn’t reveal what we might understand if we knew him personally, and even then we might not come close to knowing him ‘truly’.
“Let me give you an example that might bring the idea of the ideal home. You pose for a picture. You ask the picture-taker to see the result. You say, ‘I don’t like that one; take another.’ And that might be what you say for several pictures. Then, you acquiesce, and say, ‘All right, we’ll go with that one.’ Yet, the picture-taker might disagree on which one ‘captures’ you.”
“So,” you ask, finally getting a chance to interject, “you’re saying that there’s no such thing as an ideal on which we can agree because there is no ultimately useful mechanism for deciding on its nature short of personal preference and perspective?”
“Yes. Does that bug you?”
Now involved in the discussion, you offer, “If what you are saying is true, then we’re destined never to get along perfectly because we’ll always find some nuance to the ideal that we individually see—if seeing is what we do with ideals. How can we agree on the value of anything except in a common culture? Gold, for example, is rare, shiny, and doesn’t rust. Its ductile and malleable. It can be alloyed for strength. Isn’t it a practical basis or ideal of wealth? Doesn’t it make good art?”
“But in a pre-European North American culture that used mollusk shells for money, what good was gold? And didn’t some of the medieval Central American cultures use labor as a form of payment even though they were rich in gold?”
“Hold on. You began this by referring to Riemann’s mapping theorem, and now you’re talking about wampum and labor as elements in trade and about art as a manifestation of an ‘ideal.’ Talk about a mapping problem: You’re all over the map,” you complain. “I don’t think listening to Mozart while you write has done anything to improve your brain power.”
“Yep. And that’s because we’re all over the map with regard to intellectual constructs, art appreciation, and value. With regard to the constructs, we can describe mathematically a world for which we have no use or a world that we cannot even picture, such as a ten-dimensional multiverse or spacetime, or a wave that is simultaneously a particle. I have to give credit to Riemann, however, as one of the founders of modern math, specifically geometry, and physics. Without him there might not have been ‘an Einstein.’ I just think that his mapping theorem points to what we have become intellectually: People in search of Plato’s ideals who express ideals with no practical use in daily life; people who stand in front of nonrepresentational art and comment to a dolt like me, ‘Oh! Look how he uses texture (or color, or stroke, or distorted shape) to capture the ideal’ to which I respond, ‘I’m sorry; I’m just not seeing it,’ as I stand there dipping my glazed torus in my cup of coffee.”
*Coomaraswamy, Ananda K. “The Theory of Art in Asia,” quoted in Philipson, Morris, Ed. Aestehtics Today, Cleveland, The World Publish Company, a Meridian Book, 1961, p. 57 and reprinted from The Transformation of Nature in Art, Cambridge, Mass. Harvard University Press, 1934.
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