Chapter 1: Mind Atoms

The neuron is a cell, minimal significant portion of the nervous system, with considerable interest by itself and, even more, when complemented with equipment around. Santiago Ramón y Cajal revealed its existence more than a century ago, and soon attracted so much the curiosity of researchers that, even being only part, has given its name to the study of the whole, as today we often talk of neuro-science. We first follow here that interest, and can anticipate that the secrets of the brain in relation to its unique power and its amazing versatility and adaptability should not be sought in this basic cell, as perhaps it has been done in the past, but in the new worlds that emerge because of its relations with many others. Today it becomes obvious just by asking ourselves why a larva of the vinegar fly has ten thousand neurons, and humans multiply this number by millions. Let us go through it.

The material object, the thing we want to understand, in addition to contain neurons, may be seen as made up of many parts or “systems” that are differentiable from each other and possess appropriate structures. The whole is the nervous system that forms an intricate network extending throughout the animal. Its central part includes the brain or encephalon (etymologically, “inside the head”) and the spinal cord that, in humans, descends from behind. The former receives and sends signals through the latter, which channels them by way of nerve filaments until they reach organs, muscles, and any other part of the body.

The encephalon is particularly important in humans and other vertebrates. It is usually referred to as the brain in these cases, a term that, although used generically and sometimes inaccurately, is supposed to designate the anterior part of the encephalon. This is a relatively large mass that controls the nervous system and centralizes the processing of almost all of the information with which we operate. It is usual to highlight in it the cerebral cortex, which contains the highest density of neurons and, as shown in Fig. 1.1, has folds, which are numerous and extraordinarily irregular in the case of humans and dolphins.

An outstanding fact concerning these folds is that evolution has induced, to a greater degree the more developed the brain is, that surface to be a fractal (Marro, 2014), namely, a mathematical form that in usual, say, Euclidean terms is intermediate between surface and volume. This reflects the strategy that nature has followed to fit a thick blanket of a few thousand square centimeters of surface into a reasonable volume.¹

In a traditional classification, one discusses white matter and grey matter. The brain is characterized by concentrating (mainly in its cortex) the grey matter, composed of somas or neuronal bodies, while the white matter is predominantly made up of long nerve fibers covered with myelin. These fibers extend from the soma as axons that interconnect neurons with each other and with cells of other types. Communication occurs through dynamic discontinuities referred to as synapses—a term that here (as is usual) will be used to casually designate the whole filament. In general, synapses are not passive but, as we shall see, implement mechanisms for both transmission and signal modulation and, through these actions, determine the net result of cooperation between cells and groups of them. Neurons are, through these filaments, related to each other, even over long distances, mainly by means of signals or action potentials that, in the form of electrical impulses moving quickly (at 120 m/s in cases), have a temporary structure that carries information. These impulses thus rapidly influence other neurons as well as muscles or glands at any distance, which involves intermediate chemical processes. Specifically, neurotransmitters that act as chemical messengers are produced and transported, as we will illustrate later. Their role is similar to that of pheromones acting as messengers in more visible contexts.

The “neuron doctrine” comes to say that the thing is a structural and functional product of the neuron. Interpreted literally, with no crossing effects, it is a too simple outcome of Cajal's view, as it disregards potential effects of cooperation that he imagined. The fact is that the brain literature has tenaciously stuck to the strictest version of this, focusing on the neuron's structure, on how it reacts to stimuli, and on the electrochemical processes involved, with no attention to global consequences. Such an image, common in texts at any level, is also reflected in Nobel committees only recognizing efforts to understand these aspects of neurons.² It is essential to walk along other paths, especially those involving the cooperation among neurons, that for a long time have not been given appropriate consideration.

A general alert, which happens to be importantly related to this lack of attention, is that in the 1970s by Philip W. Anderson, who was awarded the Nobel Prize after discovering a singular contrast between order and disorder in matter. Following a trail specified a century before by Ludwig Boltzmann (who recognized the discontinuity of the microscopic world and thus initiated statistical physics), Anderson reminded us that nature permits well-defined levels of description—e.g., those termed microscopic, mesoscopic, and macroscopic—and how, in spite of their hierarchical relation, the knowledge provided by any one of them is not enough in science. Even having a perfect image of, for example, the basic level (the neurons, in the case at hand), nature (the mind, in this case) would remain mysterious if we did not progress to the superior levels, where new phenomena emerge that require new theories. He insisted that large aggregates cannot be understood just in terms of the properties of their elements. Since Boltzmann,³ we know that scientific insight needs to establish links between levels of description, so it is likely that the amazing diversity of processes that groups of neurons exhibit result from cooperation between their constituents. Recent efforts have shown that these processes indeed follow on from collaboration between neurons and the form of these relationships, including the structure of the mesh describing the links and some unceasing changes that occur in these. The ability of an isolated neuron to compute and process is like that of each of the atoms or molecules that form any portion of matter. However, through cooperation, atoms and molecules are capable of exhibiting emergent phenomena—from solidification and ferromagnetism to superconductivity and superfluidity—that are much more extraordinary than anticipated from the relatively simple properties of the constituent particles. This is the clue if we want to decipher the mysteries of the mind. Unraveling it, we shall discover scientifically appealing circumstances after careful analyses, either following others or based on our own work, throughout this essay.

One of these circumstances is universality (Chapter 2), which stubbornly manifests itself as an attractive property of nature with very important consequences. Apart from suggesting that brain dynamics is not as unique or special as we might think and that the strong personality of the neuron is minimized concerning some emergent properties of the mind, this favors the use of analogies. Universality makes most useful (often even rigorous) the current studies based on, say, mathematical metaphors—that is, models that, being super-simplified versions of reality, are faithful to the relevant facets. These metaphors will play a fundamental role in this book. This approach is not new in science. The stomach has been described as a chemical reactor and the heart as a pump that through contractions and expansions regulates our blood circulation. These are simple analogies ennobled by Leonardo da Vinci who, driven by his vision of the human body as a “miniature of the world,” already interpreted the flow of blood through the heart in light of his studies on flows, currents, and rivers. And based on such qualitative comparisons, science has developed quantitative similarities that support contrasts with experimental data. These studies rely on algorithmic descriptions of processes and systems that, taken to a computer, achieve remarkable success as faithful “cartoons” of reality. In this context, the brain metaphor is no longer a computer as before. Specific parts and functions of the brain today have their own metaphors susceptible to useful simulations. This book, a corollary of all this, explains by simple mathematical metaphors the complexity that interests us.

The nervous system contains glial cells, often starry in mammals, which serve to provide nutrients and isolate the neurons. The latter (Fig. 1.2) are specialized cells with a variety of shapes, having a soma harboring genetic material, which receives information through the dendrites that are also active in the computational process. The neurons emit signals through the axons that, coated with myelin as an insulator, can extend for meters. Both dendrites and axons are formed from the same type of structure, the neurite, which springs from the soma and grows guided by a bud that responds to the stimuli of proteins in the environment. Each neuron, characterized by excitable non-linear behavior in the presence of continuous fluctuations, communicates with others—nearby neighbors or others that were close and eventually moved away—through connections between an axon and the dendrite of another cell. These connections or synapses (Fig. 1.3) are discontinuities where the signal is transmitted by complicated sets of varying electrical impulses involving proteins and specific neurotransmitters interacting with small receptor centers. The number of these connections per neuron is very variable but always high, typically of the order of 10⁵ in humans, so it is generally not useful to imagine groups of disjointed neurons because, although there are well-differentiable areas in brain tissue, connectivity is always extraordinarily high.

The real situation is complicated in practice owing to the coexistence of neurons of diverse shapes and differences from one animal to another and between different areas of the same animal. In any case, one can speak of a meaningful identity that essentially distinguishes, which is also interesting, this system from a modern computer. The nervous system contains a number of units, typically between 10⁹ and 10¹¹, that is many orders of magnitude greater than that in the computer, and each biological unit is slower—it reacts to a stimulus on a time scale in the range of 10⁻³ s, whereas those in an electronic system react in 10⁻⁹ s—but the former is connected to many more units, with thousands of other neurons. These facts, given the speed, power, and versatility that the brain has, still unbeatable by the best machines in many of its functions, reveal the importance of the brain's computational strategy based on an intimate and dynamic cooperation between its units.

Today it is clear why some seemingly excessive mathematical simplifications of the concept of a neuron—such as imagining each of them as a binary variable entity—are, however, useful to capture the essence of the implications of cooperative processes in neurology and psychology. This is familiar in physics, where molecular details may be irrelevant to many material properties, and in sociology, where birds and fish exhibit the same flock effects and real traffic is very independent of the drivers’ personalities. Of course, the complicated reality of the processes inside the neuron can play a significant role, as we will see, but more determinant is the role of synapses—a designation that in this context usually applies to the entire connection, from the axon of the presynaptic neuron to a dendrite of the postsynaptic neuron (Fig. 1.3). To this contributes the fact that the (irregular) electrochemical pulses or action potentials are constantly transmitted through these connections with extraordinary frequency, up to about 100 times per second.

The appearance of eukaryotic cells was a great qualitative step in the “long night of evolution.” The genetic material, primitively dispersed in the (prokaryotic) cells, was organized into chromosomes to form a nucleus separated by a membrane from the rest of the cytoplasm, and key molecular processes in the metabolism were also confined in well-defined structures (organelles). These changes facilitated a better use of energy as well as reproduction through meiosis, that is, double division and subsequent recombination of the ancestral genetic material. A different cell type had thus emerged, and new paths opened. In fact, another substantial evolutionary leap could then occur: the emergence of multicellular organisms. And these were apt to tolerate with certain probability two main transformations: differentiation and morphogenesis. It had become possible that, from a primitive cell, many different types of cells with varied functions could arise. The contest between such a variety would lead, through additional developments, to the formation of the most complex organisms.

Cellular differentiation has taken a long time. Today it seems natural to distinguish in our body the skin, bone, muscle, neurons … but when the explosion of diversity occurred in the Cambrian, 570 million years ago, there were only a few kinds of cells incapable of the complexity we enjoy. It took 100 million years that we could distinguish a hundred cell types, and today we recognize more than 200 different from each other. It is not well known how the origin of the first neuron occurred, but it is likely that it arose from structural transformations of superficial cells, the epithelial ones, which in hydras show certain characteristics typical of neurons.

Cells surround their cytoplasm with a membrane composed of a double layer of lipids. This prevents free flow, but the membrane is also dotted with proteins that operate as pores or channels through which nutrients, ions, waste, and so on can be exchanged to allow easy interaction with other cells. The extracellular environment usually contains a high concentration of sodium chloride in solution and relatively low concentrations of calcium (Ca⁺⁺), potassium (K⁺), and chloride (Cl⁻). In its interior, on the contrary, there is usually a high concentration of K⁺ and Cl⁻ and a low concentration of Na⁺. There are two immediate causes for the existence of these gradients in most eukaryotic cells. One is that the pores give the membrane a permeability up to 100 times greater for K⁺ than for sodium and other ions. The second cause is a certain protein that, acting as a pump, expels sodium from the cellular interior while introducing potassium. These processes, responsible for maintaining the cellular ionic composition, involve specific proteins that are synthesized using the cell's genetic information. The existence of these proteins in the cell membrane is the result of millions of years of evolution in which many other cells lacking these genetics disappeared.

It has been said that delving into the biomolecular details of the neuron, despite their relevance and the attention that they have received to date, cannot clarify the essence of the mental functions that interest us. However, it is necessary to know well what a neuron can do and what its limits are. The basic properties of a neuron should be specified from the beginning as simply and accurately as possible. In the 1940s, McCulloch, Pitts, and others, inspired by this strategic search for the fundamental characteristics of the neuron, deciphered how to simplify its concept. Bypassing its intricate structure, they interpreted the neuron as an elementary switch. According to this, its main function would be to “shoot” or fire when the sum of the signals that reach it exceeds a characteristic threshold; otherwise, it is at “rest.” Devices were built with this idea and interconnected sets of them were tested in various ways to assess their ability to solve logical problems. These seminal studies have allowed us to conclude with confidence that, as regards various phenomena due to cooperation among many, neurons can be imagined, without prejudice, as binary variables, that is, “devices” with only two possible states or values. This degree of simplification may seem surprising, but it should be noted that, in the presence of collaboration, the properties of the individuals can turn out to be practically irrelevant. On the other hand, nature tends to that simplicity. In fact, the digital transmission of ones and zeros is much more reliable and simple than the analog case—in which real numbers with an infinite number of possible values would be transmitted. And this is even more pressing if there is propagation through a large complicated architecture, such as that of the nervous system, and it is necessary to reach remote areas anywhere in the body, all in the presence of constant natural disturbances.

The binary image of the neuron, thus simplified, has been perfected by providing it with details that we wish to correspond with mechanisms—say, at the level between microscopic and mesoscopic—that, observed in real neurons, have been thought to exert a qualitative influence on mental functions. Some familiar proposals are,⁴ in chronological order, those of Hodgkin and Huxley, who studied the propagation of electrical signals in squid giant axons; the model of Bernard Katz, subsequently simplified by Richard FitzHugh and Jin-Ichi Nagumo, including details of the synaptic connections; and those of Catherine Morris and Harold Lecar, which combine previous ideas. In Chapters 6 and 7, we will study in detail the consequences of assuming two of these “mathematical neurons,” namely, those known as integrate-and-fire (alternatively, sum-and-shoot) neurons and FitzHugh–Nagumo neurons. Two cooperative models are used to evaluate these cases, so that their peculiarities become explicit, and their respective “performances” are compared with those of a binary neuron and, using experimental data, a real neuron.

There is a kind of artisanship today that allows the representation, with fidelity, through circuitry and differential equations, any type of hypothesis regarding the details of the neuron. This process sometimes consists, as illustrated in Fig. 1.4, of measuring the electrical properties at different points of the neuronal morphology and combining this information with related chemical data and resonance images. A computer program then translates all of this into a set of (RC) electrical circuits, each representing the membrane properties of a segment of the neuron, connected by resistors. The resulting circuitry can then be easily translated into a system of mathematical equations, or a Monte Carlo setup, which is explored under various hypotheses using powerful mathematical and computational methods—a long road since Cajal was searching (with limited means) structures that appeared before his eyes, trying to imagine how the transmission of information occurred through that seemingly capricious network. Nowadays, partly in the context of the discipline known as statistical physics and based on precise experimental observations to which we refer later, there is a growing understanding of the organization and emergent behavior of large interconnected sets of neurons that has resulted from the study of mathematical metaphors, whose essence and consequences we describe in Chapters 2–7.

Any reader who, familiar with the neuron, attempts to seek more global information will soon encounter cognitive neuroscience, which aims to describe the areas involved in and the dynamics underlying perception and processing in the brain. In such studies, a person is subjected to stimuli designed with the purpose of evoking specific behaviors, and the neurophysiological changes that occur in each case are monitored. In practice, these studies involve a group of individuals that is as large as possible so that the average observation is significant.

A distant antecedent to this approach (to which we will return) is a certain historical tendency to characterize the thing as a mosaic of pieces that can be distinguished from each other. For example, following ancient mystics, the physician Franz Joseph Gall founded phrenology, which postulates that distinct areas of the brain are associated with various “psychic powers” (Fig. 1.5). This recognized the brain as the organ of the mind and its areas, which were not predetermined but supposed to be modifiable through development and education, as having specific functions. Another familiar and primitive, though partially well grounded, image of this type is Brodmann's map (Fig. 1.5), which, subsequently completed by others, is still mentioned. The idea in this case is that the observation of certain sets of cells informs about the specific function of each of the areas, which can thus be distinguished. Associations of this type are accepted today, but the practice suffers from ambiguities and inaccuracies that prevent sufficient scientific confidence in the method.

The use of new techniques—mainly, functional magnetic resonance imaging (fMRI), magnetic encephalography (MEG), and electroencephalography (EEG)—now permits the stimulation of individual parts of the mind such as those mentioned to elucidate a significant portion of the anatomical substrates of many high cognitive operations. These experiments may now affect both relatively simple brain functions, including visual image processing, and more sophisticated ones, such as those related to speech and pain, and the regions involved in various emotions have thus been identified. Figure 1.6 shows the rapid growth of studies using these techniques, compared with the relative stagnation in the number of results reported using Freud's ideas and psychoanalysis.

As a result of these efforts and other complementary ones that we will be describing, hundreds of brain zones can now be characterized, which are separately identifiable although strongly interconnected, each with a typical surface area of a few tens of square centimeters, traversed by networks and containing hundreds of millions of nerve cells (Chapter 7). But surely this is not enough for the demanding reader, eager to understand what global properties are behind the extraordinary connections between neurons and between these different areas.