Instead of the usual discussion of Seurat's fascination with optics, with the theories of Chevreul and Ogden Rood about simultaneous contrast of colors, I'd like to say a word about Seurat's approach to his subject.
This is a very unusual subject for an Impressionist painter. There are plenty of paintings by Monet and Renoir of people taking a dip in the river, most famously at the resort spot of La Grenouilliere in the Paris suburbs. But, all the people in those paintings are very middle class at a middle class resort unsullied by factories and only occasionally by a railroad. They are all people on holiday for the weekend or an August break.
Seurat's men and boys are either on lunch break, or off for the day from the factories that employ them in the background. Some of them are wearing summer holiday clothes, white with straw hats and bowlers (the bowler hat is the clue to the class of these bathers; respectable bourgeois men did not wear bowlers in those days). There is a clear contrast between the world of toil in the background and the leisure in the foreground.
Unlike the work of Monet, Renoir, and other Impressionist painters, there is a stillness and distance about Seurat's bathers. Seurat admired the freshness and topicality of Impressionist painting. He admired its ideas about our field of vision composed of nuances of color relationships. He criticized the ephemeral quality of so much Impressionist work, and sought to bring into Impressionism something of the monumentality of the grand French tradition of public classicism. The Impressionist brushstroke is tamed into a regular unit (soon to become the famous color dots in Seurat's later work). There is a splendid architecture of verticals and horizontals with repeating and rhyming motifs throughout. The horizon line extends from the eye level of the seated young man on the left in the straw hat. The curve of the back of the reclining man in the foreground finds its answer in the diagonal of the shoreline. The repeated curves of the men's backs find an opposite rhyme in the curves of the sails on the river. As in a great painting by Poussin or Piero della Francesca, these young men are completely integrated into the satisfying architecture of the painting.
I can't imagine anything more unheroic looking than the central young man in Seurat's painting. That hunched over slouching pose is definitely not that of an ancient Greek warrior athlete or of an action movie hero. It is the pose of a tired young shlub with a bad over-bite and bad hair off from his job trying to cool off at the water's edge. Seurat is not out to glorify him or make fun of him. But, the young man does share in the grandeur of the rest of the picture.
Seurat took the unusually conservative step of making numerous studies for this picture, trying to create a complete structure out of what began as a random glance along the river bank. Monet and other Impressionists almost never worked from studies. They thought of each picture as a spur of the moment record of some passing effect.
By contrast, Seurat's painting has a the calm finality of the Parthenon.
The following century would produce stacks of paintings of heroic workers in the classical mode. But Seurat's workers are not being heroic at all. They are simply being themselves on a day off. Seurat gives these wage earners dignity rather than heroics.
Seurat's political beliefs remain unknown. He died at the age of 31 after a career of less than 10 years. He left behind only 10 major paintings and a tiny body of written material. However, he was close friends with the unusually leftwing Impressionist painter Pissarro (most Impressionists were fairly conservative), and the anarchist journalist Felix Feneon. Critics beginning with JK Huysmans insisted on seeing social satire in the robotic bourgeoisie of the famous La Grande Jatte.