Designs for a very familiar-looking building were doing the rounds at the turn of the 20th century. The so-called Beacon of Progress in Chicago was a proposal for a 1500-foot stone tower — by far the highest at the time — with a profile very similar to London's Shard. And, like our own skyscraper, the Beacon plans contained several viewing decks and a crown designed to glow at night.
The tower designs, finalised by Frenchman Constant-Désiré Despradelle in 1900, would have been erected on the site of the World's Fair (where the Museum of Science and Industry stands in Jackson Park today) as a monument to the nation. Iconography within its structure would commemorate the 13 original colonies of the US. Such symbolism is mirrored in America's tallest building today, 1 World Trade Center, whose height of 1,776 feet equates with the year of independence.
Alas, the scheme was never even started. But the plans were influential, and remained exciting in 1908, when they were displayed at the Franco-British exhibition in London. One source says the drawings "...seemed to weave a spell of fascination which the greatest of painters of our time failed to achieve".
It is debatable if the same can be said of London's tallest building. Yet of all the structures in the world, the Shard perhaps most closely resembles Despradelle's tower in shape if not purpose.
More information and images can be found on the MIT website.