Christina then calculates that the population density of Trantor was 533 people per square mile. By way of contrast, here are the population densities of some modern American cities:
- New York City - 27,016.3
- San Francisco - 17,246.4
- Boston -13,321.0
- Chicago - 11,868.0
- Philadelphia - 11,233.6
He could not see the ground. It was lost in the ever increasing complexities of man-made structures. He could see no horizon other than that of metal against sky, stretching out to almost uniform grayness, and he knew it was so over all the land-surface of the planet.As Christina points out, if Trantor had a population density like that of, say, Tokyo proper, with 38,312 people per square mile, you would get a planetary population of 2.9 trillion people.
What we have here, then, as Christina says, is a massive failure of scale on Asimov's part. We can even pinpoint where and when it took place. The first mention of Trantor's population to appear in print was in "Dead Hand" in the April 1945 issue of Astounding Science-Fiction. Asimov wrote the story in an apartment house in Philadelphia in the summer of 1944. And he had to write in his spare time, since he had a full-time 53-hour-per-week job at the Philadelphia Navy Yard. In the story, Lathan Devers, a trader from the Foundation, is traveling to Trantor. Here is Asimov's description:
The entire world was one fuctional distortion. There was no living object on its surface but man, his pets, and his parasites. No blade of grass or fragment of uncovered soil could be found outside the hundred square miles of the Imperial Palace. No fresh water outside the Palace grounds existed but in the vast underground cisterns that held the water supply of a world.
The lustrous, indestructible, incorruptible metal that was the unbroken surface of the planet was the foundation of the huge, metal structures that mazed the planet. They were structures connected by causeways; laced by corridors; cubbyholed by offices; basemented by the huge retail centers that covered square miles; penthoused by the glittering amusement world that sparkled into life each night.
One could walk around the world of Trantor and never leave that one conglomerate building, nor see the city.
A fleet of ships greater in number than all the war fleets the Empire had ever supported landed their cargoes on Trantor each day to feed the forty billions of humans who gave nothing in exchange but the fulfillment of the necessity of untangling the myriads of threads that spiraled into the central administration of the most complex government Humanity had ever known.
Twenty agricultural worlds were the granary of Trantor. A universe was its servant --
So, Asimov most likely plucked the figure of forty billion out of his head while writing these paragraphs without ever trying to work out just how many people would actually be living on a world covered by a single vast city. And once the forty billion figure was set down in print, he kept repeating it in later stories (except, as noted above, when he got it wrong in the last story of the trilogy, "--And Now You Don't").