Mathematics, the Physical World, Information and Mind
This section includes the intertwining of three important questions related to the physical universe and the mind.
The first question is the nature of mathematics. Mathematics is “unreasonably effective” in producing theories that very accurately describe parts of the universe that are impossible for us to actually experience through our own senses. The equations scientists produce describe photons, neutrinos, quarks, gluons, and the big bang with unbelievable accuracy. The question related to the mind is where does math come from. Is it invented by the human mind, or somehow discovered in the human mind? Is it sculpture and art, or is it mining?
The second question is the nature of information. Increasingly scientists at all levels are noticing the importance of information. In fact, there are now substantial theories in physics that information could be the very basis of energy and matter. Some of this theory comes from the recent understanding of black holes and the search for a quantum computer. In biology the codes for the sequences of DNA are a form of digital information. Significantly, information is also perceived by the mind and used in every detail of human culture. How does the mind relate to this information throughout the universe?
The third question is the relation of certain basic laws of physics and the mind. The laws of physics must be relevant to mind, since mind is part of the universe. Thermodynamics, relativity and quantum mechanics are all now targets to describe mind in nature. Since most of biology is focused on the very small molecular processes, it is natural for quantum mechanics to be a strong focus of theories related to biology and mind. If cells have proto mind, then how is this influenced by quantum mechanics?
One book that deals with all three questions is Cognitive Biology by Gennaro Auletta. Gennaro Auletta synthesizes neuroscience, cognitive science, philosophy, quantum mechanics, information theory and more in an elaborate study of how the brain functions, and what it has to do with information in the universe. This 800-page book filled with basic science and mathematical formulas is a tremendous resource in understanding perception, and brain function. It gives a detailed description of quantum mechanics and how it relates to physical theories of information. The book then connects this understanding with a detailed analysis of neuroscience and cognitive science. Professor Auletta concludes with an opinion somewhat similar to the eminent physicist Roger Penrose, discussed later in this section, that there are three worlds that overlap, that is, the world of ideas, the physical world and the mental world. In the Penrose model the world of ideas maps to the physical world, which maps to the mental world, which maps back to the idea world. In Auletta’s model each of the three worlds overlaps somewhat with the other two, but in a way where all three do not overlap at once.
Many major philosophers and some major mathematicians have argued about the nature of mathematics. Most do not agree and present many different theories. Hilbert, unsuccessfully, tried to unify mathematics into a coherent logical system. He believed in the reality of the axiomatic method, but not a full platonic reality, which exists out of space and time. Gödel, who proved that there are inherent limitations to axiomatic proofs, believed in a modified platonic reality of mathematics. Penrose professes a platonic truth to mathematic principles. Others believe mathematics reflects grounding in our human experience, starting from bodily sensations and including cultural influences.
Books mentioned here touch on the question but do not answer it. Some of these books explain how mathematicians work, and what it is like to discover/create mathematical systems and proofs. The book Is God a Mathematician? by Mario Livio gives a grand history of mathematics, but does not answer the question. In the end he assumes it is partly discovered and partly invented.
The Number Sense: How the Mind Creates Mathematics is written by a cognitive neuroscientist describing the increasing research into abilities of animals, children and adults to form a theory of innate “number sense”. In The Mathematician’s Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them by David Ruelle, a distinguished professor of mathematics writes about mathematicians and how they work. He doesn’t arrive at a conclusion of whether it comes from a platonic realm, or from the brain, but he does imply that cultural influences might affect the intuition of certain mathematicians. The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose is outspoken about his belief that mathematics is discovered from a platonic realm, which can be accessed by mind. The book Plato’s Ghost: The Modernist Transformation of Mathematics is an encyclopedic summary of many philosophical views about mathematics. He traces cultural influences on the development of mathematics from Kant to the present. Important in this discussion is the nature of logic and how it relates to the universe and to human cognition. Kurt Gödel and the Foundations of Mathematics: Horizons of Truth by Matthias Baaz, Christos H. Papadimitriou, Hilary W. Putnam and Dana S. Scott is a multi author collection about the implications of Gödel’s theorem on the philosophy of mathematics and physics.
Studying mathematics many years ago I was struck by comments of several great physicists searching for mathematical formulations to describe their theories. I was surprised that they were searching for beautiful equations and had not realized that one of the basic notions sometimes used in mathematics is that the simpler and more elegant equation is probably the better one. One of the most poignant descriptions of this search for the beautiful theory is from Steven Weinberg’s haunting book Dreams of a Final Theory. The search for symmetry in the universe, and the importance of symmetry breaking has been part of the pursuit for a beautiful mathematical theory of physical reality. There are other books that also wonderfully describe this unusual characteristic of physics and mathematics including Fearful Symmetry: The Search for Beauty in Modern Physics and Deep Down Things: The Breathtaking Beauty of Particle Physics by Bruce A. Schumm.
Information theory began as a mathematical description of how to transport bits of information efficiently, which was used to develop modern telecommunications. More recently physics has begun to theorize about a much greater importance for information as part of basic definitions of energy and matter in the descriptions of black holes and quantum computers. Only very recently did the multi authored book on this subject Information and the Nature of Reality edited by Paul Davies and Niels Henrik Gregersen first outline this field for those who are not experts in advanced physics. Three other books discuss the history of this field in books that most can understand: Information: The New Language of Science by Hans Christian Von Baeyer, The Information: A History, a Theory, a Flood by James Gleick, and Information: A Very Short Introduction (Very Short Introductions) by Luciano Floridi.
Quantum mechanics has unique characteristics that would make a non-scientist wonder if it has something to do with mind. At the size of electrons, quarks, and photons, a unit of matter seems to exist in many places at once, communicate instantly at any distance, and have all possibilities for future movement available at the same moment, all of which are intuitively like our subjective experience of how the mind functions. Unfortunately, none of these strange properties of matter have been proven to have anything to do with the properties of the mind.
The proven counter intuitive properties of matter in quantum mechanics include superposition, coherence, entanglement, and tunneling.
Superposition is the idea that all future possible movements of a piece of matter exist all at once in the present moment in the mathematical form called the wave function. Coherence is a state where all parts of a system stay in perfect sync without any clear reason. Entanglement is when two particles are forever connected such that changing one changes the other instantly, no matter how far away they are. Tunneling relies on the fact that matter is both a particle and a wave. Matter’s waviness allows its exact location to be dispersed such that parts of it could be on both sides of a wall. This allows particles to sneak through barriers as if slithering through wormholes to get around energy and material barriers. None of these have been proven to have anything to do with mind.
Some believe that quantum mechanics implies that an observer might be integral to how matter and energy function in the universe, helping to spawn consciousness theories. For example, an observer is needed to interpret whether light is functioning as a wave or a particle, by first asking the question as to which it is and then devising an experiment to find out. A second example involves the fact that the wave function gives a very specific reading on where a particle is located, only after a specific question is asked. Otherwise it remains ambiguous.
Many physicists and philosophers have attempted to find a connection of quantum effects and mind including Penrose’s specific theory of quantum effects in the microtubules that make up the structure of the neuron. But the real test will be to find proven examples of quantum effects in biology, and specifically examples related to mind in biology.
The first accessible multi-authored book that attempts to outline possible quantum effects in biology is Quantum Aspects of Life by Derek Abbott, Paul C. w. Davies and Arun K. Pati. While this is an excellent recent book, since it has been published more specific examples have already been found. (See post on Quantum weirdness and the mind.) Perhaps the clearest discussion on the ways that the observer seems to be important in quantum mechanics is the Quantum Enigma: Physics Encounters Consciousness by Bruce Rosenblum and Fred Kuttner. This is an excellent book that has been used as textbook in college courses.
The Age of Entanglement: When Quantum Physics Was Reborn by Louisa Gilder is an excellent historical account of the discoveries of these unusual properties of matter. The book Cognitive Biology: Dealing with Information from Bacteria to Minds by Gennaro Auletta is written by a philosopher who is expert in quantum theory. It describes a theory of quantum affects as a basis for mind throughout biology. Two other books are written by well-known physicists and profess theories of how quantum effects are directly related to mind in nature: Mindful Universe: Quantum Mechanics and the Participating Observer by Henry P. Stapp and Consciousness and the Universe: Quantum Physics, Evolution, Brain & Mind by Roger Penrose, Stuart Hameroff, Henry P. Stapp. The latter book is an encyclopedic multi authored book with a wide range of theories as to how quantum mechanics is related to the mind. Roger Penrose’s theory of quantum computers being a computation source for the brain in the neuron’s microtubule structure is highlighted in the first article. William Byers excellent book The Blind Spot: Science and the Crisis of Uncertainty (Apr 17, 2011) elaborates on many aspects of the illusion of scientific certainty considering the problems of human subjectivity in science and the importance of ambiguity in scientific theory.