Robert Lawlor: 'Sacred Geometry.'
'All our sense organs function in response to the geometrical or proportional - not quantitative - differences inherent in the stimuli they receive. For example, when we smell a rose we are not responding to the chemical substances of its perfume, but instead the geometry of their molecular construction. That is to say, any chemical substance that is bonded together in the same geometry as that of the rose will smell as sweet. Similarly, we do not hear simple quantitative differences in sound wave frequencies, but rather the logorithmic, proportional differences in sound wave frequencies, logarithmic expansion being the basis of the geometry of spirals.'
'The early Greeks were uncertain as to whether 2 was a number at all, observing that it has, as it were, a beginning and an end but no middle. More mathematically, they pointed out that 2 + 2 = 2 x 2, or indeed that any number multiplied by 2 is equal to the same number added to itself. Since they expected multiplication to do more than mere addition, they considered 2 an exceptional case. Whether 2 qualified as a proper number or not, it was considered to be female, as were all even numbers, in contrast to odd numbers, which were male.
Division into 2 parts. dichotomy, is more significant psychologically and more frequent in practice than any other classification. The commonest symmetry is bilateral, 2 sided about a single axis, and is of order 2. Our bodies are bilaterally symmetrical, and we naturally distinguish right from left, up from down, in front from behind. Night is separated from day, there are 2 sexes, the seasons are expressed in pairs of pairs, summer and winter separated by spring and autumn, and comparisons are most commonly dichotomous, such as stronger or weaker than, better or worse than, youth versus age and so on'.
'In a way, art is a theory about the way the world looks to human beings. It`s abundantly obvious that one doesn`t know the world around us in detail. What artists have accomplished is realizing that there`s only a small amount of stuff that`s important, and then seeing what it was. So they can do some of my research for me.Mitchell Feigenbaum, quoted in 'Chaos' by James Gleick.
When you look at early stuff of Van Gogh there are zillions of details that are put into it, there`s always an immense amount of information in his paintings. It obviously occurred to him, what is the irreducible amount of this stuff that you have to put in. Or you can study the horizons in in Dutch ink drawings from around 1600, with tiny trees and cows that look very real. If you look closely, the trees have sort of leafy boundaries, but it doesn`t work if that`s all it is - there are also, sticking in it, little pieces of twiglike stuff. There`s a definite interplay between the softer textures and things with more definite lines. Somehow the combination gives the correct perception.
With Ruysdael and Turner, if you look at the way they construct complicated water, it is clearly done in an iterative way. There`s some level of stuff, and then stuff painted on top of that, and then corrections to that. Turbulent fluids for those painters is always something with a scale idea in it'
'I`ve always respected the science in the music, though I haven`t respected some of the related value systems: for instance, the concept of notation - I don`t think notation is the problem, it`s the concepts that surround notation. Bach, Beethoven, Mozart, all of the master Europeans who solidified Western art music were instrumentalists and improvisers as well as composers. Notation wasn`t used then as a choking device to stop the blood, the dynamic, of the culture; it was later, when the technocrats made the process more important than the results, that we got the so-called crisis of Western art music, which is still with us. In fact, we can see the same mind-set entering the bebop continuum: now they`re making bebop so "correct", it will be bopbe or something - it won`t be the same music that Charlie Parker and John Coltrane played'.
'You were asking about the rules. There`s a parable of Kafka`s about a man living in a country where he doesn`t know the rules. Nobody will tell him what they are. He knows neither right nor wrong, but he notes that the rulers do not share his anxiety. From this he deduces that the rules are for those who rule. What they do is the rule. That`s why all my knowledge doesn`t make me understand what Mozart did that I should also do in order to reach a state of artistic grace'
'It is sad to have to admit that most men consider it their human right to dispute, even to overpower the human rights of their fellows. Even sadder is the aspect of the world today, which offers no hope of improvement in the foreseeable future.
But this should not stifle our longing for a state of affairs in which the sanctity of each man`s human rights is intangibly self-evident. Humanity has benefited by all such blessings only because an ever-increasing number of people have yearned passionately for redemption until it was granted. All progess in social thinking and feeling which eliminated friction in community life has come about only through the force of such longing. We must never give up our longing.'
'Where in life we do everything we can to avoid anxiety, in art we must persue it. This is difficult. Everything in our life and culture , regardless of our background, is dragging us away. Still, there is this sense of something imminent. And what is imminent, we find, is neither the past nor the future, but simply - the next ten minutes'.
By now, we should be able to tentatively formulate the fundamental Feldman paradox: Each and every element of Feldman`s music is quite definite, whereas the constitution of fixed significations through the establishment of relationships among those elements is being indefinitely deferred ('differ`ed').
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