As a keen observer of nature, Leonardo da Vinci was more comfortable with geometry than with arithmetic. Shapes, being continuous quantities, were easier to fit, and disappear into, the observable world than discrete, discontinuous, numbers. For centuries since Leonardo, physics has shared his preference for analog thinking, building on calculus to describe macroscopic phenomena. The analog paradigm was upended at the beginning of the last century, when the quantum revolution revealed that the microscopic world behaves digitally, with observable quantities taking only discrete values. Quantum physics is, however, at heart a hybrid analog-digital theory, as it requires the presence of analog hidden variables to model the digital observations.
Computing technology appears to be following a similar path. The state-of-the-art computer that Claude Shannon found in Vannevar Bush‘s lab at MIT in the thirties was analog: turning its wheels would set the parameters of a differential equation to be solved by the computer via integration. Shannon’s thesis and the invention of the transistor ushered in the era of digital computing and the information age, relegating analog computing to little more than a historical curiosity.
But analog computing retains important advantages over digital machines. Analog computers can be faster in carrying our specialized tasks. As an example, deep neural networks, which have led to the well-publicized breakthroughs in pattern recognition, reinforcement learning, and data generation tasks, are inherently analog (although they are currently mostly implemented on digital platforms). Furthermore, while the reliance of digital computing on either-or choices can provide a higher accuracy, it can also also yield catastrophic failures. In contrast, the lower accuracy of analog systems is accompanied by a gradual performance loss in case of errors. Finally, analog computers can leverage time, not just as a neutral substrate for computation as in digital machines, but as an additional information-carrying dimension. The resulting space-time computing has the potential to reduce the energetic and spatial footprint of information processing.
The outlined complementarity of analog and digital computing has led experts to predict that hybrid digital-analog computers will be the way of the future. Even in the eighties, Terrence J. Sejnowski is reported to have said: ”I suspect the computers used in the future will be hybrid designs, incorporating analog and digital.” This conjecture is supported by our current understanding of the operation of biological neurons, which communicate using the digital language of spikes, but maintain internal analog states in the form of membrane potentials.
With the emergence of academic and commercial neuromorphic processors, the rise of hybrid digital-analog computing may just be around the corner. As it is often the case, the trend has been anticipated by fiction. In Autonomous, robots have a digital main logic unit with a human brain as a coprocessor to interpret people’s reactions and emotions. Analog elements can support common sense and humanity, in contrast to digital AI that “can make a perfect chess move while the room is on fire.” For instance, in H(a)ppy and Gnomon, analog is an element of disruption and reason in an ideally ordered and purified world under constant digital surveillance.
(Update: Here is a recent relevant article.)