NEW YORK - You enter “Nueva York (1613-1945)” feeling fairly sure of your geographic bearings, but after viewing an unusual accumulation of artifacts , you leave less certain, curious, challenged.

Instead of seeing the city and its past along an East-West axis and its conflicts and culture through interactions with Europeanborn colonizers and immigrants, we have our attention rotated 90 degrees by the exhibition at El Museo del Barrio in Manhattan. We look along the North-South axis, toward Latin America.

That is also the axis along which immigration and cultural influence accumulated in recent decades, leading to a growing Hispanic presence in the city and in American life .

The Dutch, we learn, were interested in New Amsterdam not only because of furs, pelts and lumber: they also were countering their enemies the Spanish, whose empire in the Western Hemisphere was vast . We even see examples of the Spanish treasure that inspired such rivalry. Silver mines in present-day Bolivia produced ingots like one on display here. By the mid-1500s, the Spanish had even cornered the market in Mexican cochineal insects, which were ground into paints and dyes, creating the sumptuous scarlets and reds of Renaissance Europe.

The British also had rivalries in mind when they transformed New Amsterdam into New York: Spanish power was the defining nemesis, even in the way the British shared the Dutch distaste for Spanish Roman Catholic culture. A group of Jews from Brazil was reluctantly permitted to settle in New Amsterdam , but Catholic churches were barred.

The American Revolution marked a turning point. In opposition to Britain, the colonies attracted Spanish support; in return, Spain was rehabilitated. In 1786 New York’s first Catholic church ? St. Peter’s on Barclay Street in Lower Manhattan - was built.

But revolutionary ideals also inspired challenges to Spanish power. In 1784 the Venezuelan Francisco de Miranda arrived to seek assistance “for the liberty and independence of the entire Spanish-American Continent.” His enterprise faltered, leaving it to others, like the Argentine Jose de San Martin and the Venezuelan Simon Bolivar, to lead wars of independence.

We learn of one New York celebration of South American independence at the City Hotel on March 23, 1825.

But commerce must have been a large factor in such support. Brooklyn became the world’s center for the refining of South American sugar cane.

In 19th century New York, new immigrant communities formed. They were small - in the early 1860s, about 1,300 Spaniards and Latin Americans lived in New York - but they grew. Intellectuals and politicians joined the merchants.

The 19th century’s Latin American revolutions even seemed to begin in New York, with many people fleeing oppression in Cuba and Puerto Rico. A red, white and blue flag hung here is a reproduction of the one raised by The Sun newspaper in 1850 : it was destined to become the flag of an independent Cuba, though it was meant as a call for its conquest.

New York became a locus for Cuban debates for half a century. Jose Marti, a supporter of Cuban independence, came in 1880 and worked as a journalist, while establishing New York’s Spanish-American Literary Society and writing poetry.

The exhibition cites a number of such cultural encounters while also showing their converse: the paintings of Frederic Edwin Church (like “Cayambe,” shown here) led to a local fascination with the South American landscape .

By the time we reach the show’s end, we see that even if there hadn’t been a demographic transformation, there is no way to understand the history of the city or the history of South America without the North-South axis. What is left unclear is just how that axis changed in the latter part of the 20th century under the pressures of immigration.

Although the exhibition technically ends in 1945, a film made for the show by Ric Burns is meant to fill the gap, and overturns the usual immigrant narrative, blaming today’s influx of immigrants on what American policies have done to their native countries.

The film is being shown inside an art installation called “From Here to There,” created by Antonio Martorell: a mock airplane resembling those that ferried Puerto Ricans to New York in the 1940s and ‘50s. The film’s assertions are particularly jarring because of what we have already learned. There is no claim made in this exhibition that the history of the North-South axis was untroubled or that anybody was unilaterally benevolent, but it is still a history of political inspiration, mercantile energy and cultural interaction.