Blogger ate most of my last post (possibly my error, not Blogger's), so an updated reconstruction of the point is due.
In fact my original post was a bit unfair to the illustration, as I learned while writing it. In 1899, when that image was presumably drawn, the skyscraper era was only just beginning. The Eiffel Tower had demonstrated that much taller structures could be built, and the Otis elevator ('lift' to some of you) made such structures practical for mundane uses, but no office building in 1899 had yet overtopped the Great Pyramid, something that several medieval church spires had achieved, albeit by narrow margins.
So the artist was not really so much projecting a contemporary trend as imagining a yet-unrealized trend. And - given that the scale of the image is rather loose and impressionistic - they did a pretty good job of capturing the general sense of the 20th century NYC skyline, even though the tallest twin buildings are, apparently, some 5 km high.
Whether or not it really illustrates my intended point, the image is of interest for its own sake, notably the dirigibles and the kilometer-long ship in the East River.
But the intended point, the Linear Fallacy, is the tendency of predictions to project the Latest Trend into the future, whatever that trend may happen to be. In 1968, Kubrick and Clarke projected the decade just past into the future, and so that had a major interplanetary infrastructure already taking form by 2001.
This blog may also be guilty of the Linear Fallacy, operating in the other direction - presuming that the incremental progress of the last 40 years is the norm.
In fact, tech progress overall seems to be a combination of the two, with accelerando phases interspersed with (generally much longer) eras of incremental progress and gradual refinement. A good historical example is European sailing ships, which underwent an accelerando in the 15th century - the emergence of the full rigged ship - followed by 350 years of refinement until the Industrial Revolution swept the whole tech into the dustbin of quaintness.
If our path in the next 200-300 or so years does lie in the direction of extensive human space travel, it will likely as not take the form of two or three dramatic accelerando leaps separated by longer periods of incremental progress.
The image for today's post, from Astronomy Picture of the Day (h/t Tammy), has nothing whatsoever to do with the subject, but is offered for your viewing satisfaction out of sheer badass coolness. It shows a Delta IV Heavy, capable of sending 9.3 tons onto an Earth escape orbit. Click to appreciate in larger format.
Our current launch technology doesn't do all that we wish it did, but it is certainly AWESOME.