Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean."
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A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
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The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics. And here I must deal with a misconception which is still widespread (though probably much less so now than it was twenty years ago), what Whitehead has called the `literary superstition' that love of and aesthetic appreciation of mathematics is `a monomania confined to a few eccentrics in each generation'.
It would be difficult now to find an educated man quite insensitive to the aesthetic appeal of mathematics. It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind - we may not know quite what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it. Even Professor Hogben, who is out to minimize at all costs the importance of the aesthetic element in mathematics, does not venture to deny its reality. `There are, to be sure, individuals for whom mathematics exercises a coldly impersonal attraction... The aesthetic appeal of mathematics maybe very real for a chosen few.' But they are `few', he suggests, and they feel `coldly' (and are really rather ridiculous people, who live in silly little university towns sheltered from the fresh breezes of the wide open spaces). In this he is merely echoing Whitehead's `literary superstition'.
The fact is that there are few more `popular' subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.
A very little reflection is enough to expose the absurdity of the `literary superstition'. There are masses of chess-players in every civilized country - in Russia, almost the whole educated population; and every chess-player can recognize and appreciate a `beautiful' game or problem. Yet a chess problem is simply an exercise in pure mathematics (a game note entirely, since psychology also plays a part), and everyone who calls a problem `beautiful' is applauding mathematical beauty, even if it is beauty of a comparatively lowly kind. Chess problems are the hymn-tunes of mathematics.
We may learn the same lesson, at a lower level but for a wider publicm from bridge, or descending further, from the puzzle columns of the popular newspapers. Nearly all their immense popularity is a tribute to the drawing power of rudimentary mathematics, and the better makers of puzzles, such as `Dudeney' or `Caliban', use very little else. They know their business; what the public wants is a little intellectual `kick', and nothing else has quite the kick of mathematics.
We may soon discover that all babies are bom geniuses and only become degeniused by the erosive effects of unthinkingly maintained false assumptions of the grown-ups, with their conventional ways of "bringing up" and educating" their young. We now know that schools are the least favorable environment for leaming. The home TV is far more effective, but we are al¬ lowing the big money-making advertisers to poison the information children assimilate in their four to five hours a day of spontaneous tuming-on, looking at and hstening to the TV.
It is possible to identify some of the known faculties that we generally assumed to be coordinate in those whom society does concede to be adult geniuses. The publicly accredited characteristics of genius consist, for instance, of an actively self-attended intuition. The intuition, in tum, opens the conceptual and perceptual doors. With those doors self-opened, the in¬ nate faculties frequently combine and employ the individual's scientific, artistic, philosophical, and idealistic imaginings in producing physically talented, logical, far-sighted, and practical articulations. Leonardo da Vinci, who fortunately weathered the genius-eroding susceptibilities of childhood, manifested and coordinatingly employed all and more of such conceptual faculties and articulative capabilities.
In the graphically recorded history of the last eight millennia, as well as in the dim twilight of pre-Indo-Chinese, Mesopotamian, Egyptian, and South and Central American graphic documentations of history, there have appeared, from time to time, individuals who grew to maturity without los¬ ing the full inventory of their innate, intuitive, and spontaneously coordinate faculties. These unscathed individuals inaugurated whole new eras of physical environmental transformation so important as, in due course, to af¬ feet the lives of all ensuing humanity. We shall hereafter identify such un¬ scathed, comprehensively effective, and largely unidentified individual articulators as the artist-scientists of history.
Since the dawn of the most meagerly revealed human history there have been a number of importantly distinct periods of historical transformation of both the physical and cosmological environments of society. Each of these eras has been opened by the artist-scientist. The invisible power structures behind-the-visible-king first patronize and help to develop the artistscientists' advanced-environment breakthroughs, but always go on, ever more selfishly, to overexploit the breakthroughs.
The environment—everything that is "not me"—is subdivisible into two parts, physical and metaphysical. The metaphysical environment consists of human thoughts, generalized principles and customs. The artist-scientist types seem to have avoided attempting to reform the metaphysical environ¬ ment. They are documented only by their employment of the cosmic laws— generalized principles—to reorganize the physical constituents of the livingry and the scenery. The artist-scientists apparently assumed intuitively that a more man-favoring rearrangement of the environment would be con¬ ducive to humanity's spontaneous self-realization of its higher potentials. Human travelers coming to a river and finding a bridge across it sponta¬ neously use the bridge instead of hazarding themselves in the torrents.
Scientist-artists originally conceived and designed the bridges. The powerstructure-behind-the-king, seeing great exploitability of the bridge for their own advantaging, accredited the workers and materials to build the bridges.
Physiology and biology make it clear that at the outset of graphically re¬ corded history a universally illiterate—^but probably not unintelligent—hu¬ manity was endowed with innate and spontaneously self-regenerative drives of hunger, thirst, and species regeneration. The a priori chemical, electromagnetic, atomistic, genetic, and synergetic designing of these innate drives apparently was instituted by a wisdom—a formulative capability inherent in Universe—higher than that possessed by any known living humans. These drives probably were designed into humans to ensure that human life and the human mind—long unacknowledged as humanity's highest faculty—ultimately would discover its own significance and would become established and most importantly operative not only aboard planet Earth, but also in respect to vast, locally evidenced aspects of Universe. As such, mind may come not only to demonstrate supremacy over humanity's physical muscle but also to render forevermore utterly innocuous and impotent the muscle-augmented weapons and the latter's ballistic hitting powers. Mind possibly may serve as the essential, anti-entropic (syntropic) function for etemally conserving the omni-interaccommodative, nonsimultaneous, and only partially overlapping, omni-intertransforming, self-regenerating scenario— which we speak of as "Universe."
Music Theory. You will forgive me for turning, as I always do in moments of intellectual want, to my Webster's Collegiate Dictionary, which defines the word "theory" as, and we quote, "The analysis of a set of facts in their relation to one another." My friends, few words offer as much rational solace as does the word "theory." Examining the plausibility of a theory demands that we analyze facts, reason logically, think objectively, and examine comprehensively. Having done so, we will assumably arrive at a conclusion that is the end product of a process of scientific method, which is itself defined as, "Principle and procedures for the systematic pursuit of knowledge involving the recognition and formulation of a problem, the collection of data through observation and experiment, and the formulation and testing of hypotheses." Ergo, if something is a theory, it is knowable. It's something we can study. It's something we can learn. It's something that is explicable. It's something that is rational. The theory of relativity. The theory of evolution. Game theory. Complex, yes, but concepts that can be understood, compartmentalized, absorbed, and digested.
Music Theory, implied in that compact and oh so innocent-sounding phrase is the idea that there is a knowable, graspable, all-encompassing set of truisms that, once understood, compartmentalized, absorbed, and digested, the very essence of music will stand revealed, it's various elements and expressive content united int oa singularity the whole greater than the sum of its parts.
Wrong. Speaking for myself, I dislike the phrase "Music Theory" almost as much as I dislike the phrase "Music Appreciation." What we call "theory," what we call "Music Theory" is in reality a huge and varied syntax, a syntax that deals with the various ways sounds can be arrayed across time to create a musical experience. We don't grasp musical syntax the way we grasp facts and the analysis of the facts. Rather we first learn to distinguish different sonic and temporal phenomenon. Then we come to understand how those phenomenon are interrelated; after which, we can begin to understand how and why we perceive structural integrity and expressive meaning in a given section of music.
Learning musical syntax is very much like learning a language. We start with the rudiments and every so slowly accumulate understanding and insight as we comprehend that language in evermore sophisticated ways. The phrase "Music Theory" implied that there is a science of music, a set of rules and regulations of absolute rights and wrongs that govern what composers can and cannot do as they create a piece of music. Wrong again.
In reality, Music Theory, like music itself, is an art and not a science. Something much more akin to language, with all its idiosyncrasies, quirks, eccentricities, and inexplicable idioms than it is a "body of knowledge covering general truths or the operation of general laws especially as obtained and tested through scientific method," which is how my web.col defines "science."
I repeat Sturgeon’s Revelation, which was wrung out of me after twenty years of wearying defense of science fiction against attacks of people who used the worst examples of the field for ammunition, and whose conclusion was that ninety percent of SF is crud. Using the same standards that categorize 90% of science fiction as trash, crud, or crap, it can be argued that 90% of film, literature, consumer goods, etc. are crap. In other words, the claim (or fact) that 90% of science fiction is crap is ultimately uninformative, because science fiction conforms to the same trends of quality as all other artforms.
[L]et us not overlook the further great fact, that not only does science underlie sculpture, painting, music, poetry, but that science is itself poetic. The current opinion that science and poetry are opposed is a delusion. ... On the contrary science opens up realms of poetry where to the unscientific all is a blank. Those engaged in scientific researches constantly show us that they realize not less vividly, but more vividly, than others, the poetry of their subjects. Whoever will dip into Hugh Miller's works on geology, or read Mr. Lewes's “Seaside Studies,” will perceive that science excites poetry rather than extinguishes it. And whoever will contemplate the life of Goethe will see that the poet and the man of science can co-exist in equal activity. Is it not, indeed, an absurd and almost a sacrilegious belief that the more a man studies Nature the less he reveres it? Think you that a drop of water, which to the vulgar eye is but a drop of water, loses anything in the eye of the physicist who knows that its elements are held together by a force which, if suddenly liberated, would produce a flash of lightning? Think you that what is carelessly looked upon by the uninitiated as a mere snow-flake, does not suggest higher associations to one who has seen through a microscope the wondrously varied and elegant forms of snow-crystals? Think you that the rounded rock marked with parallel scratches calls up as much poetry in an ignorant mind as in the mind of a geologist, who knows that over this rock a glacier slid a million years ago? The truth is, that those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded. Whoever has not in youth collected plants and insects, knows not half the halo of interest which lanes and hedge-rows can assume. Whoever has not sought for fossils, has little idea of the poetical associations that surround the places where imbedded treasures were found. Whoever at the seaside has not had a microscope and aquarium, has yet to learn what the highest pleasures of the seaside are. Sad, indeed, is it to see how men occupy themselves with trivialities, and are indifferent to the grandest phenomena—care not to understand the architecture of the Heavens, but are deeply interested in some contemptible controversy about the intrigues of Mary Queen of Scots!—are learnedly critical over a Greek ode, and pass by without a glance that grand epic written by the finger of God upon the strata of the Earth!
As for what I have done as a poet, I take no pride in whatever. Excellent poets have lived at the same time with me, poets more excellent lived before me, and others will come after me. But that in my country I am the only person who knows the truth in the difficult science of colors-of that, I say, I am not a little proud, and here have a consciousness of superiority to many.
Just now nuclear physicists are writing a great deal about hypothetical particles called neutrinos supposed to account for certain peculiar facts observed in ß-ray disintegration. We can perhaps best describe the neutrinos as little bits of spin-energy that have got detached. I am not much impressed by the neutrino theory. In an ordinary way I might say that I do not believe in neutrinos... But I have to reflect that a physicist may be an artist, and you never know where you are with artists. My old-fashioned kind of disbelief in neutrinos is scarcely enough. Dare I say that experimental physicists will not have sufficient ingenuity to make neutrinos? Whatever I may think, I am not going to be lured into a wager against the skill of experimenters under the impression that it is a wager against the truth of a theory. If they succeed in making neutrinos, perhaps even in developing industrial applications of them, I suppose I shall have to believe—though I may feel that they have not been playing quite fair.
The function of Art is to imitate Nature in her manner of operation. Our understanding of "her manner of operation" changes according to advances in the sciences.
The cuttlefish is mostly soft-bodied; the crab is all armor. As the cuttlefish approaches, the medieval-looking crab snaps into a macho posture, waving its sharp claws at its foe’s vulnerable body.
The cuttlefish responds with a bizarre and ingenious psychedelic performance. Weird images, luxuriant colors, and successive waves of what look like undulating lightning bolts and filigree swim across its skin. The sight is so unbelievable that even the crab seems disoriented; its menacing gesture is replaced for an instant by another that seems to say, “Huh?” In that moment the cuttlefish strikes between cracks in the armor. It uses art to hunt!
At the time that the web was born, in the early 1990s, a popular trope was that a new generation of teenagers, reared in the conservative Reagan years, had turned out exceptionally bland. The members of “Generation X” were characterized as blank and inert. The anthropologist Steve Barnett compared them to pattern exhaustion, a phenomena in which a culture runs out of variations of traditional designs in their pottery and becomes less creative.
Here is a claim I wish I weren’t making, and that I would prefer to be wrong about: popular music created in the industrialized world in the decade from the late 1990s to the late 2000s doesn’t have a distinct style—that is, one that would provide an identity for the young people who grew up with it. The process of the reinvention of life through music appears to have stopped.