'Well, then, supposing there were other suns in the universe.' He broke off a little bashfully. 'I mean suns that are so far away that they're too dim to see. It sounds as if I've been reading some of that fantastic fiction, I suppose.'
'Not necessarily. Still, isn't that possibility eliminated by the fact that, according to the Law of Gravitation, they would make themselves evident by their attractive forces?'
'Not if they were far enough off,' rejoined Beenay, 'really far off -- maybe as much as four light years, or even more. We'd never be able to detect perturbations then, because they'd be too small. Say that there were a lot of suns that far off; a dozen or two, maybe.'
Theremon whistled melodiously. 'What an idea for a good Sunday supplement article. Two dozen suns in a universe eight light years across. Wow! That would shrink our world into insignificance. The readers would eat it up.'
'Only an idea,' said Beenay with a grin, 'but you see the point. During an eclipse, these dozen suns would become visible because there'd be no real sunlight to drown them out. Since they're so far off, they'd appear small, like so many little marbles. Of course the Cultists talk of millions of Stars, but that's probably exaggeration. There just isn't any place in the universe you could put a million suns -- unless they touch one another.'
Sheerin had listened with gradually increasing interest. 'You've hit something there, Beenay. And exaggeration is just exactly what would happen. Our minds, as you probably know, can't grasp directly any number higher than five; above that there is only the concept of "many". A dozen would become a million just like that. A damn good idea!'
'And I've got another cute little notion,' Beenay said. 'Have you ever thought what a simple problem gravitation would be if only you had a sufficiently simple system? Supposing you had a universe in which there was a planet with only one sun. The planet would travel in a perfect ellipse and the exact nature of the gravitational force would be so evident it could be accepted as an axiom. Astronomers on such a world would start off with gravity probably before they even invented the telescope. Naked-eye observation would be enough.'
'But would such a system be dynamically stable?' questioned Sheerin doubtfully.
'Sure! They call it the "one-and-one" case. It's been worked out mathematically, but it's the philosophical implications that interest me.'
'It's nice to think about,' admitted Sheerin, 'as a pretty abstraction -- like a perfect gas, or absolute zero.'
'Of course,' continued Beenay, 'there's the catch that life would be impossible on such a planet. It wouldn't get enough heat and light, and if it rotated there would be total Darkness half of each day. You couldn't expect life -- which is fundamentally dependent upon light -- to develop under those conditions. Besides -- '
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."
Have you ever met anyone with an encyclopedic knowledge of obscure rock bands? I knew a group of people in Los Angeles who spent their time browsing the used bins at record shops back in the days when music was recorded on vinyl (which is making a comeback these days, even though most kids have never heard anything other than compressed 128-kilobite-per-second digital recordings). Some of these people were so obsessed with obscure bands that they deserved the moniker "vinyl vermin." They collected lists of band names and knew all the rarest albums available. There could be an obscure garage band from England that rest of us would ever have heard of the band, but the vinyl vermin could tell you more about it than you ever wanted to know.
The problem with most vinyl vermin, I've found, is that they let their knowledge of trivia overwhelm their judgment. Despite their encyclopedic learning, I can't recall having a single discussion with them about whether any of the bands were actually any good. Maybe a band that released just five hundred copies of an album was an undiscovered gem, or maybe the music was so bad that no other record company would hire it to make another album. I never knew what most of the vinyl vermin thought about the qualities of musical groups or genres, because they never talked about anything other than trivial facts and statistics.
The lesson I learned from the vinyl vermin was that the most important thing about gathering information is what you do with it. The "secret language" of taxonomy might have made me feel special, but words applied to fossil species (or obscure records) didn't satisfy me. Taxonomy is a beautiful art. But without theory behind it, taxonomy amounts to words on a museum label. Even today, new species are being discovered and described at a remarkable rate, and each newly discovered species receives a unique official name. But what does the naming and ordering of species say about their relationship to other species and to us? I wanted wisdom, not just knowledge.
THOSE who have treated of natural pilosophy, may be nearly reduced to three classes. Of these some have been attributed to the several species of things, specific and occult qualities; on which, in a manner unknown, they make the operations of the several bodies to depend. The sum of the doctrine of the Schools derived from Aristotle and the Peripatetics is herein contained. They affirm that the several effects of the bodies arise from the particular natures of those bodies ariſe from the particular natures of thoſe bodies. But whence it is that bodies derive thoſe natures they don't tell us; and therefore they tell us no thing. And being entirely employed in giving names to things, and not in ſearching into things themſelves, we may lay that they have invented a philoſophical way of ſpeaking, but not that they have made known to us true philoſophy.
Others therefore by laying aſide that uſeleſs heap of words. thought to employ their pains to better purpoſe. Theſe ſuppoſed all matter homogeneous, and that the variety of forms which is ſeen in bodies arifes from ſome very plain and ſimple affections of the component particles. And by going on from ſimple things to thoſe which are more compounded they certainly proceed right; if they attribute no other properties to thoſe primary affections of the particles than Nature has done. But when they take a liberty of imagining at pleaſure unknown figures and magnitudes, and uncertain ſituations and motion of the parts; and moreover of ſuppoſing occult, freely pervading the pores of bodies, endued with an all-performing fubtilty, and agitated, with occult motions; they now run out into dreams and chimera's, and neglect the true conſtitution of things; which certainly is not to be expected from fallacious conjectures, when we can ſcarce reach it by the moſt certain obſervations. Thoſe who fetch from by hypotheſes the foundation on which they build their ſpeculations, may form indeed an ingenious romance, but a romance it will ſtill be.
There is left then the third claſs, which proſeſs experimental philoſophy. Theſe indeed derive the cauſes of all things from the moſt ſimple principles possible; but then they assume nothing as a principle, that is not proved by phenomena. They frame no hypotheses, nor receive them into philosophy otherwise than as queftions whose truth may be disputed. They proceed therefore in a two-fold method, fynthetical and analytical. From some select phænomena they deduce by analysis the forces of nature, and the more simple laws of forces; and from thence by fynthelis shew the constitution of the rest. This is that incomparably best way of philosophizing, which our renowned author most justly embraced before the rest; and thought alone worthy to be cultivated and adorned by his excellent labours. Of this he has given us a most illustrious example. by the explication of the System of the World, most happily deduced from the Theory of Gravity. That the virtue of gravity was found in all bodies, others suspected, or imagined before him; but he was the only and the first philosopher that could demonstrate it from appearances, and make it a solid foundation to the most noble speculations.
There is one great difficulty with a good hypothesis. When it is completed and rounded, the corners smooth and the content cohesive and coherent, it is likely to become a thing in itself, a work of art. It is then like a finished sonnet or a painting completed. One hates to disturb it. Even if subsequent information should shoot a hole in it, one hates to tear it down because it once was beautiful and whole. One of our leading scientists, having reasoned a reef in the Pacific, was unable for a long time to reconcile the lack of a reef, indicated by soundings, with the reef his mind told him was there.
Why Become Extinct? Authors with varying competence have suggested that dinosaurs disappeared because the climate deteriorated (became suddenly or slowly too hot or cold or dry or wet), or that the diet did (with too much food or not enough of such substances as fern oil; from poisons in water or plants or ingested minerals; by bankruptcy of calcium or other necessary elements). Other writers have put the blame on disease, parasites, wars, anatomical or metabolic disorders (slipped vertebral discs, malfunction or imbalance of hormone and endocrine systems, dwindling brain and consequent stupidity, heat sterilization, effects of being warm-blooded in the Mesozoic world), racial old age, evolutionary drift into senescent overspecialization, changes in the pressure or composition of the atmosphere, poison gases, volcanic dust, excessive oxygen from plants, meteorites, comets, gene pool drainage by little mammalian egg-eaters, overkill capacity by predators, fluctuation of gravitational constants, development of psychotic suicidal factors, entropy, cosmic radiation, shift of Earth's rotational poles, floods, continental drift, extraction of the moon from the Pacific Basin, draining of swamp and lake environments, sunspots, God's will, mountain building, raids by little green hunters in flying saucers, lack of standing room in Noah's Ark, and palaeoweltschmerz.
It is often held that scientific hypotheses are constructed, and are to be constructed, only after a detailed weighing of all possible evidence bearing on the matter, and that then and only then may one consider, and still only tentatively, any hypotheses. This traditional view however, is largely incorrect, for not only is it absurdly impossible of application, but it is contradicted by the history of the development of any scientific theory. What happens in practice is that by intuitive insight, or other inexplicable inspiration, the theorist decides that certain features seem to him more important than others and capable of explanation by certain hypotheses. Then basing his study on these hypotheses the attempt is made to deduce their consequences. The successful pioneer of theoretical science is he whose intuitions yield hypotheses on which satisfactory theories can be built, and conversely for the unsuccessful (as judged from a purely scientific standpoint).
Even more difficult to explain, than the breaking-up of a single mass into fragments, and the drifting apart of these blocks to form the foundations of the present-day continents, is the explanation of the original production of the single mass, or PANGAEA, by the concentration of the former holosphere of granitic sial into a hemisphere of compressed and crushed gneisses and schists. Creep and the effects of compression, due to shrinking or other causes, have been appealed to but this is hardly a satisfactory explanation. The earth could no more shrug itself out of its outer rock-shell unaided, than an animal could shrug itself out of its hide, or a man wriggle out of his skin, or even out of his closely buttoned coat, without assistance either of his own hands or those of others.
It surely can be no offence to state, that the progress of science has led to new views, and that the consequences that can be deduced from the knowledge of a hundred facts may be very different from those deducible from five. It is also possible that the facts first known may be the exceptions to a rule and not the rule itself, and generalisations from these first-known facts, though useful at the time, may be highly mischievous, and impede the progress of the science if retained when it has made some advance.
After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formally used, if some assumptions (which are called axioms) were granted me. They follow in this order.
There is no one center of all the celestial circles or spheres.
The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere. All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe. The ratio of the earth's distance from the sun to the height of the firmament is so much smaller than the ratio of the earth's radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.
Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth's motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.
What appears to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion. The apparent retrograde and direct motion of the planets arises not from their motion but from the earth's. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.