They knew
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Relevant XKCD : https://xkcd.com/842/
Disappointed that it doesn't have a pink marble facade, with two spherical entry ways, and some nicely trimmed bushes around the base.

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Shout out to the PEN15 tv show, https://www.imdb.com/title/tt8324422/.
The graphic artist certainly knew, check out this infographic of how the tower will be erected:

Look at that giant... Wang! (Rest of the gag I no longer remember)
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