The intertwined histories of computer science and the brain

Doing the rounds a while was an article posted on Aeon about how the brain is not a computer (here). How there is a fundamental difference between computers and brains in their structure, function and purpose. While it may be true that the brain does not function in the same way the laptop in front of me functions – processing bits of information in a predominantly serial fashion, with separated memory and processing components – this does not mean that the brain is not a computer in a more general sense. Though not directed explicitly at the article in question, this post will describe computation in this more general sense, and present a perspective on the brain/computer connection that makes the relation seem not so surprising.

To understand in what way the brain is a computer it’s of course instructive to first ask what makes anything a computer? Alan Turing may have provided a formal framework for digital computation in the 1930s but what we would call computers (albeit primitive) were envisioned long before then. The immediate examples that spring to mind are of course the difference and analytical engines of Charles Baggage, and the ‘programmable’ looms developed by Jacquard. These were devices that could be instructed to perform some task or calculation automatically. These machines off-load from ourselves the execution of a routine, generally but not necessarily sequential, set of tasks, and also may perform calculations for us. Critically, interpretting the machine’s behaviour in terms of elements within a set of tasks, or components of a calculation, requires that we ascribe to the machine a correspondance between its physical state and components of the task or calculation being performed. The abacus only counts if we correspond left and right beads with counted and uncounted units.

Thus representation is a core component of what makes something a computer. Indeed, a definition (though debated, as with any philosophical topic) of a computer is a physical system whose states can be put in to a reasonable correspondence with variables which perform a calculation of interest. Notice that such a definition allows for computation to be either analog or digital – a sundial acts as a simple computer. Computers today (as in laptops, PCs, mobile phones, etc), are such exceptionally powerful devices in terms of the breadth and speed with which they may perform myriad calculations of interest to us that it can seem hard to imagine how any other machine could reasonably be called a computer also. But the essential property that makes even the most powerful of servers a computer is exactly the same as the property that makes a sundial a computer – its capacity to represent and manipulate quantities of interest.

Given this general definition of computation, it may at least seem less surprising that the brain is an organ capable of computation. But we’re not done with our argument yet, we just have argued against the notion that computers need to be digital, serial, and run on electricity.

An often offered explanation for the relation between brains and computers is that our understanding of brains is often compared to the popular technology of the day. Thus in the 1600s mechanical analogies were used to understand the body’s function – Descartes envisioned pulleys and gears determining our behavior. Following the dynamical revolution of Newton (and Leibniz), cognition was viewed as a dynamical process: in terms of forces pushing and pulling our ego in conflicting direction. Finally, the digital computer last century has spurred the most recent set of comparisons. However, I would like to argue that, by looking at the history of computation, there is a more fundamental relation between computers and cognition then merely a metaphor in terms of ‘the technology of the day’. Unlike mechanical or dynamical analogies previously, the history of computation itself reveals itself as a kind of abstracted form of reasoning. If this is the case, then almost by definition, cognition must have a computational component, and brains, equally, must be implementations of computers, when suitably generally defined.

Thus the relation between brains, minds and computers dates back at least to the 30s and 40s of last century, but also in a sense much earlier. Starting with Frege, Boole, and even Leibniz, philosophers have sought after formal systems capable of expressing thought and formal rules of reasoning. Frege’s formal system presented in his Begriffsschrift and Leibniz’s notion of a ‘calculus ratiocinator’, for instance. We can look at quotes from Hobbes and Leibniz:

“By reasoning, I understand computation. And to compute is to collect the sum of many things added together at the same time, or to know the remainder when one thing has been taken from another.” — Hobbes 1655

and

“The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate, without further ado, to see who is right.” — Leibniz 1685

as evidence this view that computation is viewed as a type of mechanical reasoning.

The desire to make mathematical reasoning a purely algorithmic, or formal, process lead ultimately to Hilbert’s formalist program, and to Turing’s formulation of an ideal, mechanical, rule-following computer. Though ultimately Turing’s universal machines were physically realized as actual computing devices, originally they were devised purely as theoretical tools, models of mechanical reasoning to be used in proofs of statements in metamathematics. It is helpful to note that in the 1930s a computer referred to a person performing calculations, and that Turing’s original paper described a machine having a finite number of ‘states of mind’ – finite due to our own limited mental capacities. Starting with McCulloch and Pitts, Turing machines were envisioned as a kind of model of the mind. Indeed, his eponymous machines provided the basis for early functionalist philosophies of mind, and they still provide the basis for contemporary theories in cognitive science – the dominant view being that cognition is a type of computation. Turing maintained a strong interest in the relation between computers and the mind throughout his life.

Conversely, the other key figure in the founding of computer science, John von Neumann, also held a deep interest in the brain. In the 1940s, as part of Weiner’s cybernetics school, von Neumann engaged in much discussion about the relation between humans and machines, which lead to the brain being used very loosely as a model for the computers he was involved in designing. Von Neumann’s ‘First Draft of a Report on the EDVAC’, still the template for most computers in use today, makes reference to ‘organs’ of the computer, and discusses similarities and differences between the logical units of transistors and neurons. Later von Neumann, realizing the immense structural and functional complexity of the brain, moved away from thinking of modeling the brain so literally with a computer, and instead advocated using computers to numerically simulate some elements of the brain’s function. Though a gross charicature of their views, Turing and von Neumann serve to neatly represent the two elements of the brain-computer relation that computational neuroscience explores today – computers as models for cognitive processes and computers as tools to simulate the brain.

Given both the modern and early founders of computer science were so interested in reasoning and the brain, it is no surprise that we now find computers and brains intimately related – computation being a used as a model of a sort of formal reasoning. If mental states are computational states then they must have a physical substrate in the brain somewhere – thus brain states must also act as computational states. The connection is almost baked into the definitions.