The skyscraper index, long discussed but never formally introduced, is one of the great irreverent economic indicators. The idea is that there is a correlation between the periods in which the tallest skyscrapers are built and the imminence of financial crisis.

Think of the Empire State Building opening into the Wall Street crash of 1929, the Twin Towers being completed as New York City was flirting with bankruptcy or the Petronas Towers in Kuala Lumpur taking the mantle of the world’s tallest building and presaging the Asian financial crisis. Most recently the construction of the Burj Khalifa, the world’s tallest structure, foreshadowed the collapse in the Dubai property market.

The index is not entirely surprising: super-tall buildings are almost inevitably conceived in a boom and take long enough to build that a bust cannot be far round the corner.

There is also, however, another correlation: that between corporations commissioning gargantuan headquarters and a peak beyond which there is only decline. Is the news that the world’s technology giants – including Apple, Google and Facebook – are planning ambitious buildings something we ought to be nervous about?

A number of high-profile historical examples might make us pause. Think of AOL Time Warner’s sparkling glass HQ on New York’s Columbus Circle. The company’s shares nosedived during construction; Jeff Bewkes, after becoming Time Warner chief executive, called the merger between AOL and his company “the biggest mistake in corporate history”. In midtown Manhattan, The New York Times Building designed by Renzo Piano, architect of London’s Shard, was intended as a symbol of confidence and civic pride. Within a couple of years of completion the newspaper was forced to sell its stake and lease back its own building as print advertising revenues fell.

Then there is the curious case of Gazprom’s sparkling proposed tower in St Petersburg. This “icon” proved a reversal of the usual rules. Designed by Scottish-based architects RMJM (once famed for their modernist public buildings), the project preceded severe financial strains for the firm. Unesco, meanwhile, warned that the construction of what would be Europe’s tallest building would threaten the city’s World Heritage status.

The new wave of proposed mega HQ’s for the biggest technology companies might, then, give some grounds for sweaty palms. The point at which a corporation feels it needs to be immortalised in an architectural symbol should be the point at which questions are asked about priorities.

Most striking of all is Apple, a company whose success is predicated on its penchant for design. It was co-founder Steve Jobs who commissioned Lord Foster to design the company’s HQ at Cupertino, California, a glass doughnut that evokes the space station in 2001: A Space Odyssey.

The self-consciously slick futurism of Lord Foster’s design may chime with Apple’s seamless products but, in the midst of the furore of the Edward Snowden revelations, it equally invokes the insular architecture of defence and security, the Pentagon and Britain’s GCHQ. There is something almost sinister in how self-contained it is, suggesting that this is a company that does not need to integrate with its surroundings but just sits in glorious isolation. Spiralling construction costs – in part because of the stringent requirements laid down by Jobs – have seen an increase from an initial $3bn to a new estimate of nearly $5bn.

Just across the bay, Facebook has commissioned Frank Gehry to design its vast Menlo Park campus. Designed to work like a city within a building (as well as being perhaps the largest open-plan office in the world), the client, to its credit, asked Mr Gehry to tone the design down. Facebook was keen to make the design as unobtrusive as possible – and Mr Gehry has responded by wrapping the landscape around it.

Google, too, has been making a splash with the commissioning of a huge HQ in its Bay Area home and another in London’s King’s Cross. The California building, a complex layering of boomerang forms, has been designed by NBBJ while the London canal-side development by AHMM is more sober and urbane but estimated to cost an astonishing £650m.

NBBJ is also responsible for Amazon’s proposed behemoth, a three-city-block development in Seattle’s downtown Denny Triangle, comprising three 38-storey towers, a couple of mid-rise buildings and a conference facility. The blocks are bland but the eye-catching centrepiece is a cluster of sci-fi biodomes, sitting like soap bubbles in a landscaped plaza and creating covered green space for the colder weather.

In London, Amazon will move into a new building designed by architects KPF. Following the furore over the amount of tax the company pays in the UK, however, it appears hesitant to call it an HQ.

Finally Bloomberg, like Apple, asked Lord Foster to design its new London HQ, a big building in the City on the site of a Roman Temple of Mithras. Based on a Zoroastrian cult, the Mithraeans, with their underground temples and secret handshakes, sound like a kind of early Masonic movement, an intriguing parallel for the world of finance and its mysterious trading algorithms.

If skyscrapers can tell us something about the temperature of an overheating economy, what do these groundscraping new HQs say?

Is it just that the tech companies are cash-rich and eager to shift from the virtual world to make a mark in the physical world? Is it that they have finally supplanted finance as the masters of the universe? Or is it that their hubris is beginning to show?

The writer is the FT’s architecture critic

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Letter in response to this article:

Let’s put corporate HQs in perspective / From Mr Mike Fitzgerald