I am thus very relieved that Everdell (pace reviews quoted on the back cover of the paperback) has no interest in modernity (beyond wondering if it means "anything at all beyond a change in the pace of change": p. 9), and concerns himself with Modernism. Matters are a bit better there, if only because we're mostly agreed on what counts as its prototypical products: paintings by Picasso and Klee, scores by Schoenberg, buildings by Mies van der Rohe, poems by Apollinaire and Eliot, things like that. We descend into the murk again when we ask what, besides usage, unites these things as Modernist, and why Modernism should have come to all these arts at the same time. Everdell thinks he knows how to answer the first question, about what makes something Modernist, though he has little to say about the second. (We'll get back to that.) It's a surprising answer, rather original, and applied with a respectable, indeed on this topic unheard-of, degree of logical rigor. Let's start with his criterion.
Essentially, he says, Modernism is about points, dots, jumps, mosaics, dissonance and sharp cuts, as opposed to smears, smooth flows, gradual change, unity, blending; "statistics, multiple perspective, subjectivity, and self-reference," all of which, Everdell assures us, "can be shown to have devolved from the collapse of ontological continuity" (p. 11). "Ontology" is another one of those words which makes me reach for my eraser, but it seems here to be used with some actual content. In the nineteenth century, says Everdell, people thought of the world as basically continuous, with categories and kinds smoothly shading off into one another, even, dare one say it, evolving into one another. Unanalyzed continuity, in some systems of metaphysics, became a fundamental postulate; hence Hegel's contempt for, even disbelief in, separate, isolated facts, "like so many pistol-shots."
The first field in which continua were broken up, Everdell says, was pure math, particularly analysis, which is what calculus becomes when it grows up. Continuity for functions was reduced to limits, and limits to purely arithmetical statements about sequences of real numbers. (This got rid of infinitessimals, which had haunted analysis since the days of Newton and Leibnitz, and cleared up obscurities in the notion of the derivative of a function which have perplexed generations of calculus students, and been taken as profound discoveries by Hegel, Marx and Deleuze.) The real numbers themselves, and so continua formed from them, were analyzed into collections of discrete, rational numbers by Richard Dedekind in 1872. Rational numbers in turn became collections of natural numbers, and the natural numbers themselves, at the hands of Frege, collections of distinct entities. Essential to all this effort, which was to eventually reformulate and refound the whole of mathematics, was the set theory developed by Cantor, a theory about classes of separate, so to speak pistol-shot, elements. Not even the infinite escaped discretization; Cantor revealed an infinite hierarchy of set-theoretic infinities, and in so doing tossed out the axiom that a whole is necessarily greater than any of its parts. (We've looked at this line of thought in the form of one of its terminal products, Quine's Mathematical Logic.)
Having begun the story of the embrace of discontinuity in math, Everdell traces it through Boltzmann's statistical mechanics, Seurat, free verse, the neuron doctrine of Ramón y Cajal, concentration camps, psychoanalysis, mutations, quantum mechanics, Russell's mathematical logic, Husserl's phenomenology, movies and relativity, before finally coming to Picasso, Strindberg, Schoenberg, Joyce and Kandinsky. These topical-biographical chapters are intercut with ones that look at specific cities, in specific years, where Modernism incubated: "The Century Ends in Vienna"; "The Century Begins in Paris"; "Meet Me in Saint Louis". (Some staples of discussions of Modernism, like Art Nouveau and Gaudi's buildings, are firmly excluded as not really meeting his criterion, but this happens in passing.) Each of these is a well-written, well-informed, sympathetic and intelligent portrait of its subject, accurate (except for nits), lively and interesting.
I'm less taken with the argument Everdell is advancing: I have reservations about some of his cases, and a scruple about method.
I don't quarrel with most of his examples. They may not be on a level with the mathematicians taking a microtome to infinity, but it's easy to see ontological discontinuity in Boltzmann's atomism, in the quantum theory, in Seurat's paintings, in the neuron doctrine, in Picasso's multiple simultaneous views. Even Russell's penchant for eliminating inferred entities in favor of logical constructions is of a piece with the rest of these.
Other choices are less happy; let me complain about physics in particular. Special relativity is about continuous transformations between reference frames, and using these to do physics without having to worry about which reference frame we're in: neutralizing Everdell's multiple perspectives at the same time as recognizing them. General relativity is as much a classical field theory as Maxwell's equations. Even quantum mechanics matches the end-of-continuity story imperfectly. In the first place, only bound particles have discrete spectra of states, have distinct energy levels; free particles have continuous spectra. Even when the pure states are separate, particles can be in a superposition of those states, and those superpositions are continuous, smooth linear blends of states. (Picking out pure states is a bit like picking out cardinal directions for navigation.) The theory as a whole can be seen as either statements about transitions between distinct states at distinct times (the Heisenberg picture) or about the undulations of continuous fields (the Schrödinger picture); the two pictures are just as old and completely equivalent. (Quantum field theory, which combines special relativity and quantum mechanics, is naturally weirder than either, but no more discontinuous, as we've discussed.)
I also want to pick on Freud. Everdell never does say why psychoanalysis is any more fragmentation-prone than the preceding fifty years or more of belief in the unconscious, or than phrenology, or associationism, or even than the Aristotelian psychology of virtues, vices, habits and desires. I'd go further and say that any psychology which aspires to adequacy has got to take the mind to pieces, and that one of the many problems with psychoanalysis is that it is far too timid in doing so.
Now let's talk about method. Even deducting the borderline-or-worse cases I've just mentioned, there's no question that there were a lot of people who, about the turn of the century, embraced discontinuity. Everdell is claiming more than that, is saying that people then were more likely --- in fact, much, much more likely --- to do so than were their predecessors. But it's easy to dig up other bits-and-pieces notions from earlier in the nineteenth century, and to his credit Everdell mentions many of them: associationism, Dalton's atomism, the cell doctrine in biology, political economy, even Mendel (who was ignored, but more because he published in an utterly obscure journal than because he was too advanced for anyone to twig). Contrarily, lots of people in Everdell's period were very into continuity, and some of those, like Bergson, even had a lot of influence over the various avant gardes; the cliche about the social science of the period (represented by men like Emile Durkheim and Bronislaw Malinowski) is that it emphasized collectives and integration, not the isolated individuals of classical liberal social thought. What I want, in other words, is a test of Everdell's thesis against the null hypothesis that Modernists were no more apt to disintegrate things than were comparable people in the nineteenth century.
It would be a hard test to design properly, but I suspect it could actually be done, and Everdell's thesis is interesting enough that it would be worth trying. Assuming he's right about what Modernism is, we could begin to ask why it happened when it did, and why it happened in all these different fields at once, questions about which Everdell is, at least in this book, happily agnostic. (One doubts that Picasso read much in analysis, let alone set theory.) If I may speculate wildly: the period where Everdell sees the origins of discretization, collage, mosaics, etc., is also the one where economic and technological historians see the birth of the information society. The age of the punch-card was when handling discrete little chunks of information first became a part of life for a significant part of the population of the industrial world, a fact of daily life. Everdell senses something of this in his chapter on the invention of concentration camps, but that is the only point in which his intellectual history connects to the histories of administration, organization and data.
If nothing else, the book is a fabulous tour through almost the whole of the European house of intellect between about 1880 and 1913. I suspect it's rather more, that Everdell has hit upon a good characterization of a rather important mutation in the history of recent thought, but it's hard to say, and not necessary to decide in order to enjoy the book and profit from it.