From Analog to Digital Computing: Is Homo sapiens’ Brain on Its Way to Become a Turing Machine?

Abstract

The abstract basis of modern computation is the formal description of a finite state machine, the Universal Turing Machine, based on manipulation of integers and logic symbols. In this contribution to the discourse on the computer-brain analogy, we discuss the extent to which analog computing, as performed by the mammalian brain, is like and unlike the digital computing of Universal Turing Machines. We begin with ordinary reality being a permanent dialog between continuous and discontinuous worlds. So it is with computing, which can be analog or digital, and is often mixed. The theory behind computers is essentially digital, but efficient simulations of phenomena can be performed by analog devices; indeed, any physical calculation requires implementation in the physical world and is therefore analog to some extent, despite being based on abstract logic and arithmetic. The mammalian brain, comprised of neuronal networks, functions as an analog device and has given rise to artificial neural networks that are implemented as digital algorithms but function as analog models would. Analog constructs compute with the implementation of a variety of feedback and feedforward loops. In contrast, digital algorithms allow the implementation of recursive processes that enable them to generate unparalleled emergent properties. We briefly illustrate how the cortical organization of neurons can integrate signals and make predictions analogically. While we conclude that brains are not digital computers, we speculate on the recent implementation of human writing in the brain as a possible digital path that slowly evolves the brain into a genuine (slow) Turing machine.

The brain-computer analogy—“A special issue”

“…First and foremost, is the definition of "computer" (Brette, 2022*;Richards and Lillicrap, 2022*). And the list continues with "computing" and "recursion" (Danchin and Fenton, 2022*), "algorithm" (Brette, 2022*;Richards and Lillicrap, 2022*;Roli et al, 2022*), "computable function" (Richards and Lillicrap, 2022*), "robot, " "program, " and "software" (Bongard and Levin, 2021*), "information" (Cobb, 2021*;Gershenson, 2021*;Danchin and Fenton, 2022*), "Artificial Intelligence" (Roli et al, 2022*), "intelligence" (Gershenson, 2021*), "cognition" (Fraser et al, 2021*).…”

Computation for cognitive science: Analog versus digital

“…However, cognitive scientists and neuroscientists deploy the notion of neural computation. Neural computation—also called neural coding—is sometimes considered digital, and sometimes analog (Clark & Häusser, 2006; Danchin & Fenton, 2022; Mochizuki & Shinomoto, 2014). 1 The distinction between analog and digital in these discussions follows the general understanding that “analog” is synonymous with “continuous,” and “digital” is synonymous with “discrete.” This is unfortunate, because this leads to a rather impoverished view of analog computation.…”