10 • The True Origins of the Mathematical Description of the Universe Having described my brain-based hypothesis for the generation for time and space, I can now move on to discuss another key mental abstraction em- ployed by the True Creator of Everything to build a tangible account of reality and the external world. To begin this discussion, I need to pose a very basic question: Where does mathematics come from? Essentially, this question is at the core of another famous inquiry, one that puzzled not only Albert Einstein himself but also several leading mathemati- cians of the twentieth century. For example, in his Richard Courant’s lecture in mathematical sciences delivered at New York University, the mathemati- cian and physics Nobel laureate Eugene Wigner referred to the “unreasonable eff ectiveness” of mathematics in explaining the outside world. At the root of this puzzle is the repeated demonstration, over the past four centuries and change, that mathematical objects and formulations, as we saw above, seem to describe with great accuracy the behavior of natural phenomena in the uni- verse that surrounds us. The astonishment that recurring verifi cations of this claim caused in many of the most brilliant minds that contributed to the quan- tum revolution is exemplifi ed by another wonderful statement by Wigner, as quoted by Mario Livio in Is God a Mathematician? “The miracle of the ap- propriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or worse, to our pleasure, even though per- haps also to our baffl ement, to wide branches of learning.” According to the braincentric cosmology, to solve this mystery one has to begin by identifying the true creator of mathematics, the “language” multiple 220 Y7643-Nicholelis.indb 220 9/20/19 7:26 AM mathematical description of the universe 221 human brainets have created, groomed, and promoted as the best grammar to generate a comprehensive and accurate description of the cosmos. It is not a secret to anyone that the majority of professional mathematicians believe that mathematics has an existence of its own in the universe, which means that it is totally independent of the human brain and mind. Mathemati- cians hold that theory mainly as a matter of professional expediency, because that allows them to have a better grip on the domain in which they work. Yet taken to the limit, this view would basically imply that all mathematics we know emerged as the product of pure discovery by its practitioners. Members of this intellectual camp are usually named Platonists because they defend the existence of Platonic mathematics. For the Platonists, there is no doubt that God—if he exists—is a member of their brotherhood. Ironic as it may sound, Kurt Gödel, the man who demonstrated the inherent incompleteness of axi- omatic formal systems, was a devoted Platonist himself. On the other extreme of this discussion, cognitive neuroscientists and psychologists, such as George Lakoff and Rafael Núñez, almost consensually refute the Platonistic view of mathematics. Instead, they argue forcibly, and with lots of experimental evidence to back their claims, that mathematics is another pure creation of the human brain. Consequently, they believe that all mathematics is invented in our minds and then used to generate a descrip- tion of natural phenomena occurring in the outside world, or even to predict the occurrence of events not yet observed. In the introduction to their Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, Lakoff and Núñez state, “All that is possible for human beings is an understanding of mathematics in terms of what the human brain and mind aff ord. The only conceptualization that we can have of mathematics is a hu- man conceptualization. Therefore, mathematics as we know it and teach it can only be humanly created and humanly conceptualized mathematics.” They continue: “If you view the nature of mathematics as a scientifi c question, then mathematics is mathematics as conceptualized by human beings using the brain’s cognitive mechanisms.” Thus, in addressing the essential question of why mathematicians and physicists have been able to use mathematics, time after time, to formulate comprehensive and precise theories about the universe, Lakoff and Núñez do not hesitate in replying: “Whatever fi t there is between mathematics and the world occurs in the minds of scientists who have observed the world closely, learned the appropriate mathematics well (or invented it), and fi t them together (often eff ectively), using their all-too-human minds and brains.” According to Y7643-Nicholelis.indb 221 9/20/19 7:26 AM 222 ma thematical description of the universe this view, there is no doubt what the origin of mathematics is: mathematics comes from us or, more precisely, from the type of brain and mind we have. As discussed by Mario Livio in Is God a Mathematician?, over the years, many distinguished mathematicians have broken ranks with their brother- hood to publicly defend the notion that mathematics is a human creation, brewed and packed inside our brains. For example, the distinguished British- Egyptian mathematician Michael Atiyah, a Fields and Copley Medal winner, believed: “If one views the brain in its evolutionary context then the mysteri- ous success of mathematics in the physical sciences is at least partially ex- plained. The brain evolved in order to deal with the physical world, so it should not be too surprising that it has developed a language, mathematics, that is well suited for the purpose.” Atiyah had no qualms about openly admitting that “even a concept as basic as that of the natural numbers was created by humans, by abstracting elements of the physical world.” Interestingly, the view that defends brain-built mathematics frontally chal- lenges Albert Einstein’s famous aphorism: “The most stunning thing about the universe is that it can be understood.” When examined from the point of view of an evolution-built, human brain–based mathematics, Einstein’s aston- ishment is unwarranted. Indeed, as the computer scientist Jef Raskin points out, “The groundwork for mathematics had been laid down long before in our ancestors, probably over millions of generations.” As cited in Livio’s book, Raskin argues that mathematics had to be consis- tent with the physical world and, as such, it is a human-created tool that serves to describe the universe that exists outside our heads. Therefore, there is no big mystery why mathematics off ers a good fi t for the surrounding world, simply because it was this world and all its peculiar features that led to the embedding of the primitives inside our brains that resulted in the emergence of logic and mathematics in the fi rst place. The evolutionary nature of mathematics is strongly supported by the dem- onstration that other animals, including other vertebrates, mammals, and our close ancestors, monkeys and apes, also express rudimentary mathematical skills, particularly numerical abilities. Lakoff and Núñez list a series of com- pelling examples collected over the past six decades. For example, rats can be trained to press a lever a specifi c number of times to obtain a food re- ward. Rodents also learn to estimate a fi nite number through their perception of a sequence of tones or light fl ashes, demonstrating that they have some sort of general brain-generated number estimation capability that is sensory- modality independent. Y7643-Nicholelis.indb 222 9/20/19 7:26 AM mathematical description of the universe 223 The experimental evidence also indicates that nonhuman primates are better “mathematicians” than rats. For example, wild rhesus monkeys seem to exhibit a level of arithmetic profi ciency that rivals that of human infants. Other studies have shown that chimpanzees can perform sum operations that involve the use of fractions, such as one-quarter, one half, and three-quarters; when presented with one-quarter of a fruit (apple) and a glass half fi lled with a colored liquid, a chimp would invariably select three-quarters as the answer for this mathematical puzzle. In summary, there is a consensus that, unlike those of humans, the brains of rodents and primates are not equipped to express mathematic skills that go beyond some elementary primitives. As such, they cannot create an abstract description of the natural world as we do. For over half a century now, neuroscientists have realized that individual neurons in the primary visual cortex of mammals and primates exhibit the ex- quisite property of fi ring maximally when lines of light presented at diff erent orientations, or even moving bars, are placed inside the neuron’s visual recep- tive fi eld. That suggests to me that the primitives of geometry, like straight lines, were imprinted in the brains of animals during the evolutionary process as a result of their interactions with the external environment. And since this imprinting yielded a considerable evolutionary advantage, it has been passed from generation to generation and from species to species until it found itself hosted deep in the visual cortex of our own human brains. So far I have talked about mammals and primates. However, a couple of years ago, Ronald Cicurel brought to my attention a video he watched during a scientifi c conference. The video describes the mating ritual the Japanese puff er fi sh performs at the bottom of the ocean to attract females. This tiny fi sh, which is naturally almost invisible in the bluish ocean waters, expends a full week to get a single date—working twenty-four hours a day, seven days a week, without a break—to complete his geometrical masterpiece.