The precise relationship between art and science has been a mystery as long as both have been around, and it's one that no doubt will endure as long as either, along with the standard answer: Who knows? This essay, too, will close with a shrug. Yet at the end of a century that began with the first true revolutions in art and science in hundreds of years -- and the end of a millennium that witnessed the birth of powerful and enduring new models for both -- perhaps the time has finally come to ask not what their relationship is, but whether there is one.

Once, there was. In embryonic form, the disciplines we now recognize as art and science were virtually indistinguishable. To the eye of a beholder in the streets of 15th-century Florence, it would have been difficult to look at a perspective painting and tell the difference between the geometry and the draftsmanship if only because there was none. In the elimination of the two-dimensional plane and the revelation of the world that waited beyond, stretching away to a vanishing point, Renaissance man had arrived at a potent illustration of the rewards of looking harder: seeing farther.

It was a lesson that would serve artists and scientists well for several centuries. Through a new language, the evidence of the senses, they pursued a common goal, the revelation of nature, even as their individual responsibilities diverged. To the scientist fell the purely objective, the masses and motions that led to universal laws; to the artist, the purely subjective, the individual responses that spoke to universal truths. But together they set in motion the Enlightenment and its clockwork Newtonian cosmos, as well as what such a universe would suggest: the perfection of nature, the perfectibility of man's understanding of it.

By the 19th century, however, revolution was nearing its deterministic conclusion. Artists were narrowing their focus to the single irreducible element: Flaubert's mot juste, Seurat's point of paint. Scientists were confronting the universe in microscopic and macroscopic detail previously unimaginable and reporting back to us what The Times of London in 1870 called ''the certainty of these invisible operations.'' As the physicist Albert Michelson, who helped determine the modern value for the speed of light, said in 1894, ''Our future discoveries must be looked for in the sixth place of decimals.''

Something had to give. Either knowledge of the natural world was finite and the search was almost over, or some new understanding, a new way to look at the world, perhaps every bit as radical as the introduction of single-point perspective 400 years earlier, would have to break through. For scientists and artists alike, the time had come to take leave of their senses.

Mathematicians had already done so, in the mid-1800's, with their study of non-Euclidian geometry. Now physicists followed their example, and what they encountered was a highly abstract, thoroughly hypothetical realm that might or might not correspond to the natural world they previously had quantified -- a realm where a wave could be a particle, mass was energy and space was time. Artists, too, rejected materialistic certainty. Music lost its melody, literature its linearity, painting -- once again providing the most revealing illustration -- its perspective.

Critics have long noted the similarity between Cubism and relativity. Picasso and Einstein disavowed the superficial resemblance between the fractured perspectives of the one and the four-dimensionality of the other, yet this parallel development remains so striking that to this day it symbolizes what turned out to be a new way of seeing the world: one that abandoned the common language of old, the evidence of the senses, and in many cases even the common goal, the revelation of nature.

For hundreds of years, scientists had been investigating the natural world and artists interpreting those results on a human scale. But now, science was going where art could not follow, or at least where art had never ventured -- into the nonsensical, intellectual realm of theory. A rupture was inevitable. In 1949, in the foreword to the book ''Art and Scientific Thought,'' one British critic assessed the situation and mourned, ''Nowadays between Science and this poetic experience there is danger of a definite divorce. An increasing cleavage between them is rapidly becoming an abyss.''

When scientists abandoned sense evidence for the pure ether of theory, they left the rest of us behind -- laymen, artists, even one another. ''The nonmathematician,'' Einstein wrote, ''is seized by a mysterious shuddering when he hears of 'four-dimensional' things.'' Einstein was wrong: Mathematicians shuddered, too. ''I pray to God,'' wrote the home secretary of the National Academy of Sciences in 1920, ''that the progress of science will send relativity to some region of space beyond the fourth dimension, from whence it may never return to plague us.''

Some artists distanced themselves from the issue altogether. Picasso declared, ''Art has always been art and not nature.'' He was speaking of Cubism, but Picasso could have also been anticipating the guiding principle for the abstract, conceptual or post-modern movements of the 20th century: a relationship between art and art, or art and ''art,'' or art and the idea of art.

Others fled to the opposite extreme, throwing their lot in with science wholly. Piet Mondrian argued that the artist's purpose was to discover the same laws as the scientist, and he attempted to develop a painting style that would reverse art's traditional contribution to the division of labor with science: ''much less subjective, much more objective.''

The scientific approach to art probably reached its apotheosis in a controversial, deliberately provocative 1958 essay by Milton Babbitt, ''Who Cares If You Listen?'' Both a musician and mathematician by training, Mr. Babbitt traced his artistic lineage explicitly to ''the mid-19th-century revolution in mathematics and the 20th-century revolution in theoretical physics.'' He acknowledged that the product was music ''for, of, and by specialists,'' and as a result, in the most infamous passage, he warmly endorsed a ''total, resolute, and voluntary withdrawal from this public world to one of private performance and electronic media, with its very real possibility of complete elimination of the public and social aspects of musical composition.''

From the layman's point of view, the 20th-century artist and scientist have disappeared up an ivory tower or down a black hole, there to spin in-jokes, formulae and secret handshakes forever. For scientists, this departure is often necessary; to uncover the secrets of the universe they have to go where they're hiding. But what's an artist to do -- at least one with any hope of actually reaching an audience?

The problem for the artist isn't that we can't embrace counterintuitive principles. In fact, we do just that all the time. We know that the Earth goes around the Sun, not vice versa. We have absorbed this revolution in physics and adjusted our thinking, our philosophy, our civilizations accordingly. But at the end of the day, the sun still ''goes down,'' and if you tell most people that the concept of gravity is a useful fiction for describing the geometry of space-time, as Einstein held, or that it's a mysterious force that acts across a distance, as Newton wrote, it still won't hold as much weight as the factually incorrect yet emotionally resonant, ''What goes up must come down.''

WE'RE the prisoners of our senses. Physicists long ago reconciled themselves to the fundamental paradox of their profession, that they had spent hundreds of years compiling sense evidence that ultimately proved the unreliability of sense evidence. But for the rest of us, a counterintuitive principle remains counterintuitive until we see (touch, taste, hear, smell) the evidence for ourselves.

That's the impasse facing 20th-century artists: the absence of sense evidence to make the emerging universe of 20th-century physics comprehensible. It's not that an artist who tries to capture the essence of that universe can never succeed; its just that at this time a successful attempt to do so can't help but frustrate the narrative yearnings of an audience still living in a Newtonian universe, at the very latest. What's it about? we simple cause-and-effect cosmos dwellers will want to know. It's about ''4' 33'','' the composer will reply.

Still, is there no way for an artist today to meet nature on an emotional level, through the visceral impact of the evidence of the senses? One recent attempt, the opera ''Chaos,'' which played at the Kitchen in Chelsea last fall, illustrated the pitfalls and possibilities.

As an opera, it offered the practitioners of several artistic disciplines the chance to comment on science, and none of them could because none of them had a vocabulary for it. The lighting and set design flashed with formulas, the music whirled and raged with apparent intellectual tumult, the libretto articulated clearly the central principle of chaos theory, again and again: ''The movement of a butterfly's wing in Beijing can magnify till it sets a Kansas cyclone spinning.'' In the end, though, it was still a show about two young scientists who triumph over evil through the redemptive power of love -- that is, a melodrama at heart.

And with good reason. As the opera's composer Michael Gordon cheerfully admits, ''The science in our opera was totally bogus.'' He says he often reads newspaper articles and popular books about the latest advances in science, but, he adds: ''I don't know anything about what this stuff really means. I read it to get just the most basic information. The moment it starts to get technical, it's way beyond me.''

What drew him and his collaborator, the librettist Matthew Maguire, to the subject of chaos theory wasn't science but the idea of science -- not the investigation of nature but the nature of investigation. ''If you don't know anything about science,'' Mr. Gordon says, ''you might think it's this very cut-and-dried thing.'' But he wanted to capture the ''very human, very raw way'' scientists work. ''The scientific process is as human as the artistic process,'' he says. ''It's an emotionally driven, passionately driven endeavor.'' (Like the philistine art critic, they may not know much about science, but they know what they like.)

Artists today have at their disposal the instruments of science -- composers, for instance, use synthesizers, computers, samplers. And artists can appropriate the subjects of science for their metaphorical purposes while blithely ignoring their content, creating in the case of ''Chaos'' a highbrow brand of sci-fi that Mr. Gordon himself likens to ''Star Trek.'' But can they still somehow reflect the influence of that content? Rather than approaching science from the outside in, can artists ever again see it from the inside out? Can they render science not objectively, but subjectively?

There was, in fact, a moment in ''Chaos'' that hinted at this possibility. Throughout the show, Marie and Pierre Curie made occasional appearances, hovering above the action, commenting on the science taking place below, and at one point one Curie said to the other, ''They live in such a dark time.'' More than all the lever-pulling, atom-handling action, or the chaos-theory-discussing libretto, or the sampled and synthesized music put together, that single throwaway line reflected the (unconscious) influence of 20th-century science on the opera's creators: a perspective in time.

The signal achievement in the transition from a two-dimensional to a three-dimensional world view was the Copernican revolution. The heliocentric theory had been around for thousands of years, and even Copernicus's monumental mathematical hypothesizing of it in 1543 remained of only academic interest. Then Galileo, nearly 70 years later, used a new invention, the telescope, to produce tangible evidence to support it: lunar mountains, moons of Jupiter, phases of Venus. Only then did the arts respond, because only then did they have something to respond to -- and indeed the response was immediate, perhaps most famously in John Donne's sorrowful declaration, only a year after Galileo published his preliminary findings, ''The Sun is lost, and th' earth, and no man's wit/Can well direct him where to looke for it.''

The change in the 20th-century world view has gone the Copernican revolution one dimension better, from three to four. But it, too, remained of mostly academic interest -- at least until this decade, when the first tangible evidence supporting it became widely available, thanks to computer technology and other breakthroughs in telescopic instrumentation. It's one thing to say we live in a space-time continuum that places the universe in a relativistic perspective that's as much temporal as it is spatial; it's quite another to confront the implications of that perspective in four colors on the front page of the newspaper, or on the evening news, or over the Internet: the exploding suns, black hole detections, galaxy collisions, microwave snapshots of remnant energy from the Big Bang, computer projections 100 trillion years into the future, and all the other depictions of a universe alive in time and very much a work in progress.

If this comparison holds, then what we've been living through isn't the end that many scientists over the last 100 years imagined it to be, but a means, a transition: a centurylong segue to get us from one understanding of the universe to the next. Einstein is our Copernicus, and the data of the last decade our Galileo; now we await a Newton to provide the spectacular synthesis of theory and observation. Whether this will happen (physicists are working on it, indeed in Mr. Gordon's ''passionately driven'' way); how many dimensions such a synthesis might require (the safe money these days is on 11); how profoundly such a synthesis would affect our thinking, our philosophy, our civilizations -- all these questions are impossible to answer. At this point it's safe to say only that some kind of new scientific order is arising, and that artists will figure out a way to respond, or they won't.

This conclusion, of course, can't remotely satisfy our Newtonian yearning for closure. But in a universe that, as science tells us, is nothing if not uncertain, it's something.