Our brain is severely handicapped for facing the challenges presented by the society of information in which we enter. The shortcomings are found at the level of perception of the external world, in our feeble capacity to handle numbers and in our inability to spontaneously think in logical terms.
14.2.1 Increments of cognition
I resume: The mathematical expertise and cognizance of nothingness acquired by the Mayas in the New World were not exploited further in that region of the globe. In the Old World, the Sumerians and the Babylonians developed mathematical tools. The subsequent attempt of the Assyrians to investigate in depth problems of division and multiplication was destroyed in ovo by the destruction of their civilization but the Babylonians eventually mastered the concept of nothingness, around the 3rd century BC. Alexander sent the Babylonian clay tablets bearing the sign of zero to Greek centers of research. These adopted the concept for their astronomical computations but declined to apply it to other fields. Despite the fact that the Greeks, in particular Archimedes, had adopted the heliocentric hypothesis in astronomy, they rejected the notion of actual (physical) infinity, which demanded from them an effort of imagination that was, at that time, not possible. This notion surfaced again with the priest Giordano Bruno (1548-1600), who was burned, not for this claim but for his religious deviancies. The Greeks also knew of potential (mathematical) infinity but could not handle it (e.g. the paradox of Zeno).
The concept of null made its way to India and to Islam, where geometry and algebra were integrated. This remarkable achievement was not exploited further by these cultures. The null concept was adopted by the industrious North Italian city-states and the whole of Christendom contributed thereafter to the unification of the various mathematical disciplines with the development of the notion of potential infinity. Within the Christian realm, England provided the cultural environment most propitious for the development of a mathematical spirit focused on practical applications and the evolvement of a culture based on machinism and sciences. The trend was picked up by Germany but quenched there in the twentieth century by two crippling wars, in favor of the US. Calculus allowed the evolvement of computers, the backbones of the thinking brain, dominated by the Anglo-Saxons, sensu largo. France produced and still produces excellent mathematicians but the managerial elite of the country, as a general rule, dwarfs their skills.
Our brain possesses 100 billion neurons and executes every second between 1013 and 1019 elementary operations. Yet, the power of the brain for numerical calculus is ridiculously weak. The human brain is not comparable to a computer. The performances of our best mathematicians pale compared with those of our pocket calculators.
We organize and visualize numbers in a logarithmic way from the left to the right (those civilizations that write from right to left visualize numbers from right to left): we have a clear idea of the place of the small numbers along the visualized line but, as soon as we reach numbers higher than about 100, the distinction between the numbers becomes blurred. We see immediately that 5 is inferior to 9 but to grade 127649 versus 125649 is more difficult. This linear, oriented, deformed representation of numbers cannot be reprogrammed. A second shortcoming of our brain is that, despite its complexity, it is not able to reliably execute chains of operations. Whereas a few tens of neurons would be sufficient to effectuate complex mathematical calculations, our brain does not have these neurons and, to solve mathematical problems, engages in a complex process involving billions of neurons. The problem is aggravated by the very short-term memory of humans: usually, we are able to retain 7 numbers (the Chinese retain about 9) during about 2 seconds. Chimps possess a better short-term memory than American students. Finally, there is no doubt that gender plays a role in mathematical skills for the accomplishment of certain cerebral tasks. Men are superior to women as far as spatial orientation is concerned: they find their way easier, which is important when treating geometrical notions or designing architectural objects.
In short, we have and will forever have difficulties in memorizing an agenda, verify our banking accounts, find back our way, optimize a road by looking at a map, evaluate the lapse of time with precision, all tasks in which accomplishment we are embarrassingly clumsy.
14.2.3 Errors in perception
The human species, like all other animal species, has devised sensory organs geared to the immediate perception of our environment, and adequate response to its challenges. The human brain has evolved to treat vital problems: analyze signals received by our senses, coordinate our movements and communicate with other members of the human species and with other animal species as dogs, horses, elephants. We very easily commit errors when relying on our senses. Visual errors of perception are easily induced. These two examples are well known:
The two horizontal lines have an identical length, the two small circles have the same diameter, although our perception of their size is different. Such errors are also found when the senses of taste and smell are solicited.
14.2.4 Logical reasoning
According to Jean Piaget (1896 – 1980), a biologist who turned psychologist at the university of Geneva, logic is the optimal form of biological adaptation. Aristotle pointed out that the essence of human reasoning is the “logos”, which was, according to him, the conjunction of logical reason and language. Language is an essential component of human reasoning. On these assumptions, Aristotle devised the “Organon”, which is a system of correct reasoning. Our capacity to think in a correct way depends on our capacity to name objects and manipulate concepts in a correct way. Piaget discovered that the logical thought evolves from birth until adolescence. Information becomes logically coordinated in 14-15 years old adolescents. However, Descartes showed that adult Man does not naturally and spontaneously think in logical terms. The average adult human being commits quite easily errors in reasoning that stray away from logic. Adults make errors of deduction in a systematic way, which need to be corrected by a learning process.
Here are two examples of bias in reasoning:
1A. If a (red) square is positioned left on a blackboard, there is obligatorily a (yellow) circle on its right.
2A. If asked to select, among a number of forms and colors, the two that correspond to this statement, none of us will make a mistake. We all place a (yellow) circle to the right of the (red) square, as depicted here.
The challenge to correct reasoning is the following question:
1B. If there is no (red) square positioned left on the board, then there is a (yellow) circle on the right.
2B. If asked to select on the board, among a number of forms (and colors), the two that disprove this rule, 90% of adult human beings will again point out a (red) square left of a (yellow) circle because most humans remain hooked on the perception of the forms and colors mentioned (red square and (yellow) circle), forget that the proposition 1B is a negation, and also forget that they must disprove it in 2B. The logical mind, i.e. about 10% of the adult world population, will choose “no (red) square” on the left, and add to the right a “no (yellow) circle”, for example he will position a (blue) hexagon left of a (black) rectangle.
Another indication of shortcoming of our reasoning capabilities is:
1C. With 4 cards on a table, bearing the signs Autumn, Winter, Summer and Spring on their visible face, turn the 2 cards needed to show that, if there is an Autumn on the visible side, then there is a Summer on the other side.
1D. Most of us asked to solve this test of Wason will start by turning the card bearing an Autumn and verify that the hidden side really bears a Summer. This first move is correct. Thereafter, about 90% of the adult subjects will turn the card bearing visibly the sign Summer, to verify that the hidden other side is an Autumn. This second move is wrong: either the second card with a visible Summer has indeed an Autumn on the reverse side, and the rule is not disproved or else it bears a Spring but this does not invalidate the rule either. However, if the card bearing a visible Spring has an Autumn on its hidden side, then the rule is wrong. It is this card that needed to be verified.
How come that 90% of the adult humans choose the wrong card? It is because our brains work on economy. To solve the problem, we rely on the occipital and temporal parts of our brain, which correspond to vision and to a silent lecture of the enounced rules. During this silent lecture, the subject focuses on the words that evoke the colors, shapes, space and numbers, and not on logical connections. Our posterior brain focuses on “square”, “red”, “Summer”, “left” etc. and we forget the instructions given by the logical rule. We are geared to respond to the immediate perception of the external world, and this system is often very efficacious, but it is not adapted to abstract reasoning, hence we commit errors although persuaded that the answer we gave was the correct one.
After being shown where the error was, we do not improve in our rational thinking and do the same error again when the same type of problems props up again. The best way to improve the access to a logical response, managed by the frontal lobe, with the result that the errors of interpretation do not occur anymore, is to inhibit the activity of the posterior parts of the brain. The deductive logic demands an inhibition of the perception, i.e. an abstraction. Paradoxically, this is achieved by appealing to emotion. Contrary to the opinion of Piaget, the human brain is not a cold and logical calculator. A. Damasio has shown that emotion aids in logical reasoning. Evolution has molded the brain in such a way that it feels the emotions necessary to inhibit non-adapted responses to environmental challenges that compromise survival (chapter 6 develops this subject). The teaching of the errors made in the exercise of logical reasoning is efficacious when the teaching is charged with an emotional content. When the subject who made an error is duly warned of the traps hidden in a question, when his attention is drawn on the fallacies that present impulsive perceptive connections, the teaching is fruitful in 90% of the cases and the frontal lobe becomes systematically involved in the solving of logical problems, with an abandon of the assistance of the posterior lobes.
Some civilizations (e.g. France) have opted for a teaching of deductive logical rules that relies on a cold abstract expose dissociated from any emotional content. Few students submitted to this drill will be able to overcome the errors of deductive logic this teaching is supposed to prevent. They will persevere in error although persuaded that their answer to the challenge is the correct one. In contemporary France, facing tremendous economic development problems, it is currently asserted that the elites tried during the last 30 years everything that did not work. This is because they are unable to overcome errors of deductive logic. Other civilizations will not appeal at all to deductive rules of reasoning. Mindless teaching of texts assimilated by reliance on memory unchallenged by emotion, characterize stereotyped social conducts that may be laden with abhorrent features.