How we cite our quotes: (Story title.paragraph)
Quote #1
All that had been done in the mid-twentieth century on "calculating machines" had been upset by Robertson and his positronic brain-paths. The miles of relays and photocells had given way to the spongy globe of plantinumiridium about the size of a human brain. (Introduction.6)
Asimov is writing this in the mid-twentieth century when "calculating machines" were like this. So he's got to come up with a science fictional variety of technology, which is the positronic brain—and we have to accept that as our premise if we want to see where these stories lead. Also, "platinumiridium" might sound weird, but it's just two regular elements: platinum and iridium.
Quote #2
In high good-humor the family took a taxi-gyro to the airport (Weston would have preferred using his own private 'gyro, but it was only a two-seater with no room for baggage) and entered the waiting liner. (Robbie.144)
Yes, robots are the most interesting technology in these stories, but we shouldn't forget that a lot of other things have changed in Asimov's future. And here's one: people aren't traveling by car or train, but by gyro, which probably means a sort of helicopter. Also, we have to admit, when Asimov says "liner," we're not sure what to think, but we do picture something like this.
Quote #3
Even ten years, technologically speaking, meant so much. Compare Speedy with the type of robot they must have had back in 2005. But then, advances in robotics these days were tremendous. (Runaround.11)
This may be the central story of this whole book: robot technology advances from non-speaking Robbie to world-controlling Machines. This is a pretty good reminder that technology has a tendency to move forward—even though sometimes we might be fearful about what new technology will bring.