Peter J. Gebicke-Haerter published a great review article with this title. I selected some snippets and the key conclusion:
At the end of the 20th century, analog systems in computer science have been widely replaced by digital systems due to their higher computing power.
Nevertheless, the question keeps being intriguing until now: is the brain analog or digital?
Initially, the latter has been favored, considering it as a Turing machine that works like a digital computer. However, more recently, digital and analog processes have been combined to implant human behavior in robots, endowing them with artificial intelligence (AI). Therefore, we think it is timely to compare mathematical models with the biology of computation in the brain.
In conclusion, it has to be acknowledged that the brain entails many more computing options than any supercomputer. It has been programmed by nature and not by human beings. It is hard to imagine that a man-made computer program will be able to perform complex, abstract tasks like anticipation, intuition, or express social behaviors as basic requirements to live within human populations. All of those need adquisition, reinforcement and long-term consolidation. And, last not least, unlike in electronic devices, there is no option to “erase a folder” or to reset the whole system to a certain, previous condition.

At some unknown point of origin (arrow ori) in one’s life there is a first decision-making between yes or no (0 vs. 1) followed by innumerable more bifurcations. This happens in each cell of the organism, but in human beings appears to be particularly interesting in the Central Nervous system. Obviously, those are events digital in nature, which raises the question of whether or no information processing and storage is comparable to computer devices
(A). The bifurcations exemplarily shown in the figure and their development over time display dynamic events reminiscent of the mathematical model of bifurcations, the Feigenbaum diagram
(B). It is constructed according to the differential equation in the inset. The diagram clearly shows, that after the second round of bifurcations the systems turns into a chaotic process with sporadic additional bifurcations embedded (where the Lyapunov exponent runs back to zero within the red line), but on the whole into a non-linear system almost completely devoid of digital events. In the brain, learning processes and memories stored in so-called “engrams” are founded on higher order information processing, storage and recall. Many of the bifurcations may have only little effects, but others may have strong impact during the whole life (a, arrow). There are several theories as to how the brain handles the wealth of information entering from the external world, either focusing on communication within neuronal networks and their oscillations, or putting more weight on the contribution of glial cells, on astrocytes in particular, and their information processing largely relying on analog events. Also, recently, engram cells have been identified in the hippocampus. But there is a high likelihood, that engrams are dispersed all over the brain, and to maintain the whole system, a higher order technology of hybrid computation is required. In contrast to computer technologies, however, the construction of the “hard disk” of memory engrams is time-dependent and irreversible. Nothing can be erased or reset to a previous time point to start again.
There is still a lot to learn and to understand about the computational power in our brain assembled and combined during tens of thousands of years by Nature.
It is a big challenge but fascinating.
