In certain shots, the IDS appears like a blue monolith from the future; there should be lots of monkeys, perhaps in parkas, hooting and grunting at it, waving ice-scrapers. When it topped off in 1972, it made the Foshay — once Minneapolis’ tallest tower — look puny, a mere pencil-point. When the sun set, the IDS caught fire; when the stars came out, the IDS stacked rows of lights up into the sky in competition. Any big glass building could do that, but the IDS was different: It wasn’t a box.

American corporate headquarters had been stuffed into boxes since modernism kicked classicism out of style and stripped off the scrolls, columns, gargoyles and all the rest of the frothy ornamentation. At first they were stark and clean, buildings fit for IBM mainframes whirring in cool rooms, Selectrics clacking away in sleek office suites. One or two could give a city new life.

(Our version was the First National Bank, now Canadian Pacific Plaza, which still makes you think of the United Nations building wearing Cary Grant’s gray suit from “North by Northwest.”)

Then we got bored with yesterday’s future. Architects got lazy; boxes got big and blunt. Architects began to coat all the boxes with reflective glass, so downtowns were filled with dull towers that reflected all the other dull towers.

The IDS could have been one of those; 1968, the year it was begun, wasn’t a high point for refined details. But the decision to make the building thin, with tapered sides — a sword’s edge from one angle, a sword’s blade from another — gave it grace, as well as a huge number of higher-value corner offices. The box was dead, and in its place rose a new cool-blue form that seemed like a piece of sky shaped into something solid. Architects Philip Johnson and John Burgee would design other great towers; this is the one their work always would be measured against.

Which brings us to the original box, the stone file drawer known as the Soo Line/First National Bank Building in Minneapolis. It’s as different from the IDS as the Institute of Arts is different from the Walker, but its style influenced architecture in a peculiar way: People passed laws to kill it, and that led to buildings like the IDS.

Back up a bit. Recently rehabbed for housing, the 1914 building is one of those immovable objects that impresses without inspiring. It doesn’t soar; it sits. It could be the headquarters for the American Rectangle Institute. The stone details make you think the architect got his design back from his boss with the notation “add some Roman stuff.” For its era, it’s utterly ordinary.

And we’d be much poorer if it hadn’t been built. For one thing, the interior public spaces, now lost, were incredible. A bit chilly, perhaps, but all that marble felt like a fort around your deposits.

The 16-story building itself was rather modern — and that leads us to learning why it looks the way it looks. Tall buildings in the Twin Cities followed patterns set in New York and Chicago — architects piled one floor on top of the other, slathered the front with a riot of decorations and tried to compensate for the earthbound design with a spindly tower.

The first true skyscraper in Minneapolis, the 1887 Bank of Minneapolis — now the site of Xcel’s urban-renewal dullard — learned from the skyscrapers of Chicago, with broad expanses of glass and minimal ornamentation. For a while it seemed as if a new style, uniquely American, uniquely suited to this new type of building, would dominate skylines.

Well, no. In the early years of the second decade of the 20th century, they went big, broad and classical. It was safe, and it made money. So you got the Soo Line/First National Bank: two boxes side by side, narrow enough so everyone on the floor got light and circulating air, connected on one end, dripping with Roman flourishes to sanctify the temples of American commerce.

A version of this building was built in New York City at the same time — the gargantuan Equitable Building. Thirty-eight stories. No one had built anything that big. Determined to avoid a future of hulking leviathans that blotted out the sun, New York passed zoning laws requiring structures to taper as they rose.

New York laws spurred a redefinition of the tall building. That’s why the Rand Tower tapers as it rises — it’s an artistic interpretation of the setback, even though no such law here demanded it. That’s why the great grave bulk of the First National Bank in St. Paul steps back, making it look like an enormous throne waiting for a long-gone god.

In Minneapolis, First National Bank moved from its 1915 structure in 1960, building an ultramodern building that followed the accepted template for postwar skyscrapers: a base of three or four stories filling the entire block, a sheer tower above. Again, look to New York: The modernists got around the zoning requirements by setting the tower back from the sidewalk in a plaza. The style spread, and the thin tall box rising from a low platform became the default style of the modern corporate skyscraper.

The tower-on-the-base style reached its peak in the IDS — all the power of a stand-alone tower with none of the glum black glass and steel. Instead of an empty plaza outside with a rusty clump of modern art, we were blessed with the Crystal Court — a soaring urban oasis fed by four busy skyways that mingled shoppers and workers in a broad bright space. The Crystal Court gave downtown Minneapolis its first, and best, public square.

It looks unique, but the style didn’t come out of nowhere.

If they’d never made buildings like the Soo Line/First National Bank, they wouldn’t have passed laws requiring buildings to step back as they rose; if architects hadn’t come up with a way to junk the classic American skyscraper style and build sheer glass towers, the IDS might have been just another Empire State Building pretender, pee-wee league.

All buildings reflect their era, but only a few transcend it, and seem timeless. The Empire State. The Chrysler. The IDS. It’s one thing to consider why the IDS looks that way, but there’s another question that still mystifies.

Why didn’t anything else?