Paying homage seems so reasonable, so modest, such an honorable thing to do. But like the long-winded toast that becomes an aria to me, me, me, or the oversized introduction that leaves the reader with little appetite to read the book itself, the homage can be perilously self-reflexive and solipsistic.

Perhaps that’s why artists today choose more neutral, spongy terms to describe how their work relates to famous precedents, terms like “inspired by” or “in response to.” Allan deSouza’s photographic essay, “The World Series,” is presented by the Phillips Collection with the generic and not very revealing latter term, as “in response to” Jacob Lawrence’s “The Great Migration.”

The two sets of images — Lawrence’s classic work of African American modernism and deSouza’s series of 30 color photographs — both treat issues of travel and displacement. But in deSouza’s well-made and often ironic collection of images there’s clearly no homage, no modest submission to Lawrence’s earlier work, begun in 1940 when the Harlem-based artist was still in his early 20s.

Indeed, as so often with “in response to” projects, the differences seem more salient than the similarities. Lawrence’s set of 60 paintings (30 of which are on permanent display at the Phillips, the other 30 at New York’s Museum of Modern Art) deals with a specific historical drama, the mass movement of African Americans from the agricultural South to the industrial North, which began around 1910 and continued until the rusting out of American factories set in around 1970.

Lawrence told his story with boldly colored but flatly rendered panels, responding to modernist trends but focusing with anachronistic intensity on the story itself. He accompanied his panels with captions that are simple and expository but also strangely reminiscent of the voice of God narration in documentaries from the 1930s and ’40s.

Allan deSouza, ‘Crossing’ from ‘The World Series, 2010–11. (Courtesy of Allan deSouza and Talwar Gallery, New York/New Delhi)

DeSouza’s photographs tell no single story and hang together not by a narrative thread, but by webs of visual association. In his first image, a sign reads, enigmatically: “If you know what you’re looking for the backward glance can be a glimpse into the future.” Next to it, an image of men standing together shows one figure pointing, perhaps backward. Visual associations (between birds and airplanes, between the word “Indian” and Mahatma Gandhi, between icons of welcome and exclusion) give the cycle moment-by-moment, frame-by-frame coherence. But not an overall sense of message, beyond a compelling feeling of dislocation and disorientation, rather like the feeling of “if it’s Tuesday it must be Abu Dhabi.”

The differences between de­Souza’s series and the work it is “in response to” set up an unfortunate series of contrasts: Between deSouza’s cleverness and Lawrence’s depth of feeling, between a string of one-liners and an organized narrative, between the polished surface of the photograph and the often clumsy organization of Lawrence’s intentionally primitive imagery. Even the titles of the two works emphasize a gulf between irony and sincerity. “The World Series” is an obvious play on games, while “The Great Migration” is almost painfully serious in its reference to a historical event that Lawrence eagerly sought to publicize.

The juxtaposition of the two shows leaves one feeling uncertain about the ultimate worth of either. The fundamental annoyance of deSouza’s work is its (perhaps unconscious) appeal to the class of people who travel, who are rich and privileged enough to enjoy the sweet dislocation of life in multiple time zones. It’s work tailor-made for a hallway in the World Bank. He has tried to embed more serious social meaning — references to immigration and ethnic tension — but ultimately his visual games are too frothy, too ironic to have real depth. Instead, they reward the world traveler with small, inside jokes. DeSouza’s camera gravitates to visual serendipity, the funny weird things one begins to see when traveling. The “World Series” is really only a few steps removed from a tumblr Web site devoted to Ching­lish.

And if a fresh look at Lawrence’s “Great Migration” makes you wonder what all the fuss is about, well, don’t feel too bad. Generations of scholarship have been devoted to putting Lawrence’s early paintings in a context that obscures their most salient feature: crude execution. He has been called a visual “griot,” an artist heroically appropriating the visual license yet resisting the smooth execution of modernist style, a pioneer looking for forms that were uniquely African American without being drenched in nostalgia or reflexively referential. But the polish of deSouza’s work only underscores the roughness and flaws in Lawrence’s work.

And both series seem to fail some fundamental tests of the image series as a unique and holistic work of art. Few of Lawrence’s images speak with the narrative clarity of the roughly contemporaneous (and putatively less “artistic”) novels in woodcuts by Lynd Ward. Or the exactly contemporaneous work of Walker Evans. Many of deSouza’s images could be replaced or removed without fundamentally altering the impact of the whole.

“In response to” is Art Speak, generally standing for a relationship no one wants to own or clarify. Just what is deSouza’s work “in response to”? And why does Lawrence’s work need a response? Perhaps all it needs is reevaluation.

The World Series

by Allan deSouza is on view at the Phillips Collection until Sept. 17. For more information visit www.phillipscollection.