BRAIN AND AI Angel Garrido Departamento de Matemáticas Fundamentales, Facultad de Ciencias de la UNED, Paseo Senda del Rey 9. 28040-Madrid, Spain; E-Mail: [email protected] Abstract: From ancient times, the history of human beings has developed by a succession of steps and sometimes jumps, until reaching at the relative sophistication of the modern brain and culture. Researchers are attempting to create systems that mimic human thinking, understand speech, or beat the best human chess player. Understanding the mechanisms of intelligence, and creating intelligent artefacts are the twin goals of Artificial Intelligence (AI). Great mathematical minds have played a key role in AI in recent years; to name only a few, Janos Neumann (also known as John von Neumann), Konrad Zuse, Norbert Wiener, Claude E. Shannon, Alan M. Turing, Grigore Moisil, Lofti A. Zadeh, Ronald R. Yager, Michio Sugeno, Solomon Marcus, or Lászlo A. Barabási. Introducing the study of AI is not merely useful because of its capability for solving difficult problems, but also because of its Mathematical nature. It prepares us to understand the current world, enabling us to act on the challenges of the future. Introduction The Mind and Brain can be thought of as computational systems — but what kinds of computations do they carry out, and what kinds of mathematics can best characterize these computations? The historical origin of Artificial Intelligence as a scientific field is usually established at the Darmouth Conference (1956). In that year, John McCarthy coined the term, defined as “the science and engineering of making intelligent machines”. But this definition does not cover the actual breadth of the field. AI is multi-connected with many other fields, such as Neuroscience or Philosophy; and we can trace its origins further back, to arcane origins, perhaps to Plato, Raymond Lully (Raimundo Lulio, in Spanish), G. W. Leibniz, Blaise Pascal, Charles Babbage, Leonardo Torres Quevedo, etc., with their attempts to create thinking machines. A suggestive definition of the field would be to say that it is the area of Computer Science that focuses on creating machines that can engage on behaviours that humans consider intelligent. The history of AI field is long and fruitful; just recall topics as diverse and important as the famous Turing test, the Strong Vs Weak AI discussion, the Chinese Room argument, and so on. And modern AI has spanned more than fifty years now. Frequently, AI requires Logic. But Classical Logics show too many insufficiencies [7, 8], that have made necessary to introduce more sophisticated tools, such as Fuzzy Logic, Modal Logic, Non- Monotonic Logic. Indeed, Mathematics can be thought of as a mere instance of First-Order Predicate Calculus, and therefore, a part of applied Monotonic Logic. The limitations of classical logic reasoning, and the clear advantages of Fuzzy Logic, are discussed later in this paper. Among the things that AI needs to implement as representation are Categories, Objects, Properties, Relations, and so on. And all of these are connected to Mathematics [1-6]; they are, as well, very good and illustrative examples, in the context of education. For instance, it is possible to show Fuzzy Sets together with the usual sets, also called Crisp, or Classical Sets, as a particular case; or to introduce concepts and strategies from Discrete Mathematics, as the convenience of using Graph Theory tools on many fields. The problems in AI can be classified in two general types: Search Problems and Representation Problems. Then, we have Logics, Rules, Frames, Nets, as interconnected models and tools, by graphs. As it is easy to see, all of them are very mathematical topics. The origin of ideas about thinking machines [2, 7], and the mechanisms through which the human brain works; the possibility of mimicking its behaviour if we create some computational structure similar to the neuron, or perhaps the neural system, its synapses or connections between neurons, to produce what is called a Neural Network… Rather than Science Fiction, or the plot of a film, these are real-world subjects of study, and they have been so for many years. And the interest in them has increased the near past. The central purpose of AI would be to create an admissible model for human knowledge. Its subject is, therefore, “pure form”. We try to emulate the way of reasoning of a human brain. Research directed to this goal can only happen in a succession of approximating steps, but the attempts proceed always in this sense. Initially, AI worked over idealizations of the real world. Its natural fields were, therefore, “formal worlds”. Search procedures operated in the Space of States, which contains the set of all states (or nodes, in the case of representation by graphs), that we can obtain when we apply all the available operators. Many early AI programs used the same basic algorithm. To achieve some goal (winning a game or proving a theorem), they proceeded step by step towards it (by making each time a move or a deduction) as if searching through a maze, backtracking whenever they reached a dead end. This paradigm was called “reasoning as search”. Studying Artificial Intelligence is interesting not only because its potential to tackle many open problems, both inside the field and in application to others scientific areas, and even the study of the humanities, but also because it is a new and very creative branch of Mathematics, and it prepares us to understand the current world, enabling us to act on the challenges of the future. Ray Kurzweil (RK, by acronym) is one of the most brilliant and active current minds, in the field of AI. This is an inventor and a soothsayer, or diviner of the future of technology, on which has made many predictions (see, for instance, his book The Age of Spiritual Machines), most of which have been met. It becomes a kind of Jules Verne´s reported. Among his most notable works include: - The Singularity is Near. It refers to time (the `singularity´) in which the machines will reach and surpass the power of human thought: he figure in 1945. - How to Create a Mind? On the functioning of the brain (especially the structure of the neocortex), and how it could imitate or simulate reach into the computer. In 1990 he predicted that a computer could defeat a world chess champion in 1998, and a year before coming to that date, as did the DEEP BLUE, IBM, playing against Garry Kasparov; or defeat a world champion in GO, more complex play, by Deep Mind. Also predicted the exponential growth of the WWW, previously only used by some people in `academia´. This and his other predictions have been performing like that in 2000 would be available as of prosthetic limbs that allow paraplegics walk, which is already used, for example, US Army veterans. Also the appearance of `automatic´ driver able to bring himself automobiles. And getting Google. Among his many inventions, we could mention the first electronic reader for the blind people, or speech recognition system which resulted in the SIRI. Also the first digital scanner. It has created business and has sold and then created others. Currently, RK is head of research at Google, in San Francisco. RK said, in his book How to Create a Mind?, “There is now a grand project under way involving many thousands of scientists and engineers working to understand the best example we have of an intelligent process: the human brain. It is arguably the most important effort in the history of human- machine civilization”… “reverse-engineering the human brain may be regarded as the most important project… The goal … is understand precisely how the human brain works, and then to use these revealed methods to better understand ourselves, to fix the brain when needed and … to create even more intelligent machines. Keep in mind that greatly amplifying a natural phenomenon is precisely what engineering is capable of doing. As an example, consider the rather subtle phenomenon of Bernoulli´s Principle, which states that there is slightly air pressure over a moving curved surface than over a moving flat one. The mathematics of how Bernoulli´s Principle produces wing lift is still not yet fully settled among scientists, yet engineering has taken this delicate insight, focused its powers, and created the entire world of aviation. His project is to come to understand what human language means. Because when you write an article you are not creating a collection of interesting words. Is that you have something to say, and Google is being devoted to intelligently organize and process all the information. The message of our paper is information. We want the computer to read everything available on the Web, and all pages of each of the existing books, to become able to maintain an intelligent dialogue with the user, as well as to be able to answer your questions... Google will know the answer to your question even before you ask it... In a recent interview (2015) RK was asked by the difference between a human brain and a computer. He replied that “a computer is not able to do two things at once. Just last, but does it very quickly and very accurately. Make billions of operations per second, and just wrong. The brain is a bit contrary. Just make a few operations per second; this makes it slower than the computer. “And when will this be possible?”, they asked. “We have no long said to reach that point. I wrote it would take a computer capable of performing 100 trillion and 100,000 trillion operations per second for `recreate´ the human brain.