The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

It is a remarkable fact that, in that sense (that is to say, ignoring issues of speed, memory capacity and input–output devices), the human ‘computers’ of old, the steam-powered Analytical Engine with its literal bells and whistles, the room-sized vacuum-tube computers of the Second World War, and present-day supercomputers all have an identical repertoire of computations. Another thing that they have in common is that they are all digital: they operate on information in the form of discrete values of physical variables, such as electronic switches being on or off, or cogs being at one of ten positions. The alternative, ‘analogue’, computers, such as slide rules, which represent information as continuous physical variables, were once ubiquitous but are hardly ever used today. That is because a modern digital computer can be programmed to imitate any of them, and to outperform them in almost any application. The jump to universality in digital computers has left analogue computation behind. That was inevitable, because there is no such thing as a universal analogue computer. That is because of the need for error correction: during lengthy computations, the accumulation of errors due to things like imperfectly constructed components, thermal fluctuations, and random outside influences makes analogue computers wander off the intended computational path. This may sound like a minor or parochial consideration. But it is quite the opposite. Without error-correction all informati...