Not only is Jimmy Carr's statement inherently wrong, but the whole discussion is an example of (probably unintentional) historical revisionism, missing out on a fascinating stage in the development of computing technology.
|My dad's circular slide rule|
The analogue revolution that Carr and Bellos ignored is the slide rule, making fast complex calculations easy. We tend to look down on analogue solutions because they are approximate - though they can be made as accurate as you like - but all we're really saying there is that they're natural. Digital may be the reality at the quantum level, but the world we experience (including many aspects of the way our brains work) is analogue.
I used to have a beautiful circular slide rule that was my father's. The advantage of the circular version is that in a compact device, less than 10 centimetres across, you had the equivalent of a straight slide rule much too long to use. And it was lovely to twiddle and do those calculations. I confess I sold it, because I'm not much of a collector, and it is certainly obsolete, but it doesn't stop it being a wonderful device.
I'm all in favour of using humorous programmes to get across science and history - but do make sure you get your facts right, guys.