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Webinar on Mind, Thinking & Creativity

Webinar on Mind, Thinking & Creativity
March 9, 2016 at 4 pm GMT (11 am EST, 5 pm CET, 9:30 pm IST)

WAAS and WUC conducted a webinar on March 9, 2016 in preparation for the upcoming course on Mind, Thinking and Creativity at IUC Dubrovnik on April 12-15.

Mind is humanity’s highest developed instrument for seeking knowledge. It is an instrument with remarkable capabilities and characteristic limitations. What we commonly call knowledge consists of word symbols and concepts based on implicit social and psychological constructions and values. As photographs and movies are images of reality rather than reality itself, mind perceives sense impressions, formulates thoughts and utilizes images and symbols to represent a reality it cannot directly grasp. Individuals perceive, interpret and comprehend their experiences as reality at both the personal and societal level. In planning and proposing recipes and blueprints for governance and managing change, decision makers and experts often take little notice of the extent to which prevailing concepts are influenced by the particular way in which individuals, communities, societies and cultures construe what they call reality. Social reality rarely conforms to or even approximates the neat categories, distinctions, differences, oppositions and contradictions by which mind characterizes it in social theory.

The insufficiency in our conceptual knowledge of social reality is itself an expression and result of more fundamental limitations in the ways we understand and utilize the human mind and the mental processes on which that knowledge is based. The course on Mind, Thinking and Creativity will explore the characteristics of mental knowledge and thought processes, types of thinking, the character of rational thought, the mental and social construction of knowledge, deep thinking, creativity and genius.

Our guest speaker of the webinar was William Byersauthor of Deep Thinking, The Blind Spot and How Mathematicians Think. Byers is a Canadian mathematician who has made important original contributions to our understanding of how the mind thinks, creativity, the process of formulating new conceptual paradigms, limits to rationality, the intrinsic uncertainty of all knowledge, the relative roles of ambiguity, logic and paradox in thinking, and artificial intelligence. 

In Deep Thinking, Byers explains that there is more than one way to think. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning. Deep thinking is a different and more basic way of using the mind. It results in the discontinuous “aha!” experience, which is the essence of creativity. It is at the heart of every paradigm shift or reframing of a problematic situation.

The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Deep thinking can be found whenever one conceptual system morphs into another.

“Deep thinking is the result of ambiguity. An ambiguity causing a distress that results in creativity to relieve us and lifts us to a next level of consciousness. It is the essence of a baby learning to speak as well as the essence of evolution over millions or years. It is Byers' conviction that progress and creativity is the result of conflicting situations, ambiguity, and uncertainty, not only in mathematics, but for science in general and it is even the essence of being, the motor of evolution in general.”

-- Adhemar Bultheel, European Mathematical Society

“Byers says, scientists need to recognize "uncertainty, incompleteness, and ambiguity, the ungraspable, the blind spot, or the limits to reason." These blind spots are embedded in the scientific method, because the world itself is ambiguous and cannot be seen clearly. Scientists ignore this at their peril. Ancient Greek mathematics, for instance, suffered from a refusal to accept the ambiguous concept of the square root of 2.”

--Publishers Weekly

 "Is the idea that anything can be determined with absolute certainty an illusion? . . . Byers incorporates many brilliant thinkers and seminal scientific breakthroughs into his discussion, offering the cogent, invigorating argument that only by embracing uncertainty can we truly progress."

--Kirkus Reviews

"The myth of absolute predictability has polluted our society and led to a lack of flexibility and imagination. Byers takes on the difficult challenge of formulating a better worldview, in effect a new kind of philosophy of science and mathematics that emphasizes creativity and wonder. He sees more deeply than others into the profoundly and richly ambiguous nature of mathematical and scientific concepts."

--Gregory J. Chaitin, author of Thinking about Gödel and Turing

"This is an extremely ambitious book. In addition to science and mathematics, Byers brings to bear insights from literature, philosophy, religion, history, anthropology, medicine, and psychology. The Blind Spot breaks new ground, and represents a major step forward in the philosophy of science. The book is also a page-turner, which is rare for this topic."

--Joseph Auslander, professor emeritus, University of Maryland

"Science deals in certainties, right? Wrong, says Montreal-based mathematician William Byers. . . . He contends that this view is wide of the mark and dangerous, influenced by the human need for everything to be 'certain'."

--Alison Flood, Wired


Deep Thinking: What Mathematics Can Teach Us About the Mind

  1. Any simulation, no matter how brilliant in conception, is qualitatively different from what it simulates.  65 
  2. Deep thinking is not analytic. It is not only involved in the creation of the conceptual system but also in the student’s re-creation of it.  76
  3. “Deep thinking” is a way to talk in concrete terms about the gap between machine and human intelligence.  77
  4. A paradigm of deep thinking is the conceptual reframing that occurs when a child moves from the world of counting numbers to the world of fractions.  79
  5. Machine intelligence is not human intelligence, machine learning is not human learning.  83
  6. Our culture’s capacity to sustain innovation and people’s ability to adjust successfully to a world in which change is not only continuous but also accelerating, depends on society’s ability to conceptualize the difference between machine and human intelligence.  91
  7. An algorithm cannot generate creativity. In fact the reverse is true—creativity is what produces algorithms.  98
  8. Deep thinking is involved in moving from one conceptual system to another. The two systems are incompatible from one point of view yet, in other, they have a hierarchical relationship, which integrates them with one another.  123
  9. The ability to hold two contradictory ideas in the mind without flinching is the essential element in creative activity. This “Deep learning” is the kind of learning that arises from deep thinking. It is to be found in the learning of concepts and conceptual systems but especially in the development of new conceptual systems.  144
  10. All scientific and mathematical theories are constrained by the fact that we describe the world by means of a conceptual system.  157
  11. Rational thinking consists of a sequence of propositions arranged in a logical order that is organized so that each step follows from the preceding one by means of the rules of logical inference…There are other ways of using the mind, which are neither rational nor sequential. “Deep thinking” is the name that I am giving to a kind of non-sequential thinking.  176 Non-rational thinking would appear to be amorphous and vague precisely because we are used to identifying thought with rationality.  178
  12. Deep thinking includes a discontinuous leap that gets you very excited because it gives you a vision of an entirely new world.  344
  13. The change from one conceptual system to its successor is radical because the new way and the old way of seeing the world are incompatible with one and this incompatibility is the reason why conceptual change is discontinuous—it is very difficult to hold both views at the same time. It is the need to resolve the incompatibility that powers deep thinking whether it comes in the guise of development, conceptual learning, or major breakthroughs in the progress of science.  414
  14. Deep thinking is always generated by something that is problematic. This problem may manifest itself as an ambiguity, an incompatibility, or even a contradiction.  452
  15. Deep thinking always involves an element of discontinuity— either get it or you don’t. It involves an insight, a leap to a new point of view.  459
  16. Certainty, on the other hand, is only to be found within an established conceptual system… Moving from one conceptual system to another inevitably necessitates stepping into the realm of the uncertain.  462
  17. All systems of thought are incomplete, as Gödel taught us, and this incompleteness can be thought of as an inevitable residue of uncertainty.  466
  18. Deep thinking involves reframing, that is, coming to look at a given situation in an entirely new way.  469
  19. The intriguing thing about conceptual systems is that they possess both a subjective and an objective dimension.  531
  20. Concepts have their meaning conferred upon them by the system of which they form a part. It is the conceptual system that is crucial and thus I have made it my point of entry.  534
  21. Most people believe that what they see is independent of the fact that they see it; they imagine that it is possible to separate the content of what they see from the window through which they see it. This is the same as believing that one’s knowledge is distinct from one’s “knowing,” the cognitive mechanisms through which that knowledge is known. This belief informs the requirement that a scientific result must be “objective”—independent of the observer. If the scientific conclusion depends on the operative scientific paradigm—the lens through which it is viewed—then the very nature of “objectivity” must be reconsidered.  553
  22. Knowing and knowledge are intertwined so tightly that they can only be pried apart in an artificial manner and at a cost of distorting the system that is being studied.  559
  23. The word “objective” can be used in two different ways. The first is “not dependent on personal opinion or prejudice,” while the second is “independent of mind.” The system of concepts is objective in the first sense but not the second.  582
  24. The objectivity that we claim for mathematical and scientific results is relative objectivity.  589
  25. Euclidean and non-Euclidean geometry are not only different mathematical systems but are also different conceptual systems.  592
  26. Data means nothing on its own and cannot be understood.  605
  27. The painting only makes sense when the observer of the painting, whose eye makes the painting come alive, is considered along with the two-dimensional canvas painting; it is only implied. In an analogous way learning does not only involve some body of objective material but also the point of view that an individual brings to the material. Just as every observer brings their history and entire being to their viewing of the picture so we bring all of our cultural and conceptual baggage to every situation of learning.  612
  28. A scientific experiment is not just something that can be held at arm’s length and examined at a distance. Every situation is not real unless it is viewed. Another way to say this is that the complete description of a scientific experiment (or anything else) must include a point of view, a way of looking at the phenomenon, which is what a conceptual system provides.  621
  29. To change conceptual systems, the old system, the old world, must lose its compelling power to define reality and be replaced by an entirely new way of seeing the world.  649
  30. Actually there are (at least) two distinct modes of “doing” mathematics and science. The first involves working within a fixed paradigm and the second involves replacing one paradigm by another. The dominant mode of thinking in the former situation consists of continuous, analytic thought.  759
  31. There remain intrinsic limitations to our ability to “objective” situation, which is an abstraction that does not really exist. The real world is intimately tied to, and ultimately is inseparable from, the lens through which it is viewed.  766
  32. Conceptual systems by their very nature are subject to change and development.  768
  33. Neither mathematics nor science deals in permanent and unchanging truth.
  34. Technology is always attempting to replicate aspects of intelligence and deep thinking. Of course this could be said of any conceptual system. And this attempt is always doomed to fail in an absolute sense even though some of the attempts are extraordinary.  815
  35. Closed systems can never capture the fundamental openness of deep thinking for the simple reason that once it is reified it is constrained.  818
  36. Paradigm change necessarily involves a discontinuous jump. Reality is singular and each paradigm evokes its own reality.  837
  37. A scientist never really gives up the paradigm within which she has been trained. What happens is that a new generation grows up within a new paradigm and the old generation retires or dies off. For the most part the researcher spends her time making continuous computations within an unchanging conceptual system.  839
  38. Geo-centered, helio-centered, or without a physical center represent three profoundly different ways of living in the world. The loss of an external center, which comes about with the dominance of the scientific worldview, may well have contributed to the alienation, anxiety, and general angst that are so common in the modern world.  897
  39. The student is not wrong or stupid; she is living in a different mathematical world.  1024
  40. Discontinuities and incompatibilities are an irreducible part of the world. The world cannot be described by a single, rational conceptual system, scientific or otherwise, because you must deal with the problems that inevitably develop within any system and give rise to new systems.  1036
  41. Actually no system of thought is really concrete; they are all abstract. It is more useful to think about going from one conceptual system to another.  1118
  42. Modern mathematics, pure and applied, still has not reconciled the differences between the discrete and the continuous.  1170
  43. The process of mathematical and scientific discovery consists of an alternation between insight and logical derivation. The latter seemingly has the last word. Thus many people have concluded that formal logic is the only way of using the mind that matters in mathematics whereas, in practice, what matters is getting the idea, the productive way of looking at the problem.  1197
  44. Mathematics is not (merely) logical; its essence is deep thinking!  1199
  45. Deep thinking involves freeing the mind from its constraints—seeing beyond the  current paradigm and reframing the situation.  1202
  46. Deep thinking has no single location where it begins and it certainly does not have a definitive end. It is pure process—  1206
  47. Establishing the relationship between deep thinking and formal thought we are addressing the intrinsic limits of computation.  1210
  48. In deep thinking the mind is used in a manner that is fundamentally different from the way it is used in the everyday thought of adults but also from the way the mind is used in the analytic thought of scientific and mathematical theory and discourse.  1213
  49. Conceptual change is the most significant and radical instance of deep thinking. Its nature is completely different than that of deductive reasoning.  1250
  50. People tend to think that a proposition in mathematics is either right or wrong because they see the whole thing happening within a fixed conceptual system.  1257
  51. Continuous thought follows the rules of formal or informal logic. Thus we believe that a question cannot have two contradictory answers, that is, an answer is either right or wrong. 1282
  52. To move on, our fixation with our present views must be broken down.  1314
  53. All scientific theories are incomplete and approximate. They may function well at the centre of the domain that they describe but tend to break down at the boundaries. 1325
  54. The new system does not eradicate the old. On the one hand the new and the old are incompatible with one another. On the other the two systems can be integrated.  1336
  55. Obviously deep thinking involves one’s conscious self but it is also evident that there are elements of it that are not conscious.  1370
  56. Jacques Hadamardi in his treatise on creativity in mathematics and explains why insight, when it comes, often seems like it is discovered serendipitously and feels like it comes from sources that are outside of the self.  1371
  57. Deep thinking and creativity are, I would argue, the essence of mind.  1381
  58. Learning, “the way the world changes our mind,” and creativity, the way “our minds … change the world,” involve the same basic mechanism, namely, deep thinking.  1394
  59. Consciousness evolves—both historically and developmentally. However it is important to remember that the earlier and more basic forms of consciousness do not disappear.  1401
  60. Most people can be trained to be creative and this training will necessarily include accessing forms of consciousness that are characteristic of childhood.  1404
  61. The whole is greater than the sum of its parts and its properties cannot be anticipated from the properties of the parts.  1481
  62. There is a tendency for the analytic to deny the existence of the synthetic. 1516
  63. Understanding is the creative core of learning—what real education is all about. “Understanding” is a creative process that is discontinuous. There is no algorithmic way of attaining understanding. Understanding and coming up with an idea are both creative processes that involve both the synthetic and the analytic.  1557
  64. The vital step in the creative process involves holding two contradictory ideas in the mind simultaneously.  Thus creativity depends on duality and conflict.  1645
  65. If we attempt to reduce learning or creativity to an exclusively left-hemispheric activity we will inevitably miss its essence.  1736
  66. New conceptual learning can only occur after the individual has escaped from his operative mindset.  1773
  67. Real science is “deep science”; real mathematics is “deep mathematics.” They both involve both hemispheres, both analytic and synthetic thought but the life of the subject—creating and learning—resides in the right hemisphere and in synthetic thought.  1812
  68. Creativity is learning in its most profound sense.  1928
  69. The setting for creative experience is allowing oneself to accept, without resistance, the entire situation complete with its non-logical elements.  2118
  70. Idea is “that which reveals relations within phenomena.”  2144
  71. There is No Formula for Creativity. There can be no technique for creativity because any activity generated by a technique or formula is not creative.  2167
  72. It is impossible to decide to let go. The injunction “let go,” like the injunction “be spontaneous,” is paradoxical in a way that reminds me of the “liar’s paradox”— “this sentence is false.”  2240 If you let go because of a decision to let go then you would not be letting go at all. The opposite of letting go is following some rule or formula, which is what you would be doing if you could decide to let go.  2242
  73. If creativity cannot be produced by formula or technique then it must be a free creation of the mind—truly original with no direct line that connects it to what came before.  2277
  74. The evolution of life and the evolution of the cosmos consist of episodes of marvelous creativity that could not have been predicted a priori.  2279
  75. What is it that gives data significance? What transforms it into knowledge? Can data be understood or, rather, what is the relationship between information and understanding?  2349
  76. Information is not knowledge, much less understanding.  2358
  77. Understanding, for example, is a relationship between the person and the subject. It is neither totally objective nor is it totally subjective.  2362
  78. Human beings are not machines and the mind is not a computer—the computer arose out of a series of acts of creativity and not vice-versa.  2369
  79. Invention of reason is a creative breakthrough on the highest level but maintaining that logical inference is creative is a profound error. 2382
  80. Belief that learning is primarily about the acquisition of facts is fundamentally flawed.  2416
  81. Knowledge must involve patterns or relationships between individual facts.  2425
  82. Machines live in a universe of data; but the existence of knowledge necessitates a human presence.  2438
  83. There is a tendency in the modern world to reduce all knowledge to data and this is done by completely suppressing the “knower.”  2450
  84. Knowledge only comes alive when it is understood.  2468
  85. Many persist in thinking that education involves acquiring objective and timeless knowledge.  2490
  86. I think of the acquisition of data and skills, not as real education but as the mere beginning of real education. Real education involves the acquisition of knowledge and understanding, which both include an important element of creativity.  2581
  87. Education involves replacing one conceptual system by another. This last step is the key, and most difficult, aspect of education. 2597
  88. Learning is not just about acquiring knowledge, skill, concepts, or even conceptual systems. It is also about moving from one way of thinking about a situation to another, more complex, way of thinking.  2598
  89. When we come to see learning as a spectrum we will also see creativity in the same way. When all learning is seen to contain elements of creativity then it cannot help but transform our view of what education should be. 2614
  90. Learning is not an industrial process and the industrial metaphor is a bad one. Learning how to learn, and the joy of learning, comes from accessing the domain of knowing.  2625
  91. The existence of obstacles is an essential feature of education, which is often ignored.  2673
  92. Learning inevitably begins by admitting your own ignorance,  you have to “not understand” before you can hope to understand.  2716
  93. Learning is natural and inevitable. There is really no stasis, no time when we are in a state of permanent equilibrium. Either we are growing and learning, or we are in a state of decline and decay.  2828
  94. No one can learn for someone else. You cannot magically impart understanding to another. Learning, as I have repeatedly stressed, is intrinsically difficult.  2864
  95. To appreciate the value of having a human being teaching a class we must look on the teacher as a facilitator of “deep learning.”  2907
  96. I laugh when I hear people placing their hopes for the future of education on educational apps for the smart phone or tablet computer. I, too, find myself captivated by technological innovation but let us not allow the novelty of the latest technological gadget to blind us to what is essential. You can have great teaching without gadgets and poor teaching with the best equipment in the world. In fact technology is often as much a distraction as it is an aid. 3127
  97. Our vital need as a society is for “deep learning” and to get there we need “deep teaching.”  3131
  98. Real mathematics is alive and it is the mind that gives it life!  3591
  99. If transcendence is to be found anywhere it is within change and not by replacing change with a theoretical framework that will never change. In mathematics as in science and in life, evolution will ultimately have the final word.  3642
  100. We tend to think that Ramanujan was so creative despite his lack of formal training but maybe it was precisely that lack of training (and also the particular form of his religious beliefs) that made him such an original mind.  3709

The Blind Spot: Science and the Crisis of Uncertainty

  1. A better way to think about the present situation is that what looks like a series of disparate crises is really one crisis that manifests itself in various ways—one all-encompassing crisis that arises from inner contradictions that are inherent in modern culture. 7
  2. The Blind Spot refers to an intrinsic and inevitable limitation to scientific theories and even to scientific concepts. 81
  3. All of the crises mentioned here can be traced back, in one way or another, to the point of view of the science of certainty. 82
  4. The two approaches to science that I discuss in this book divide up neatly in this regard; the first attempts to deny or eliminate uncertainty, the second takes uncertainty as an inevitable fact of life, as an opportunity, and considers how best to work with it. 84
  5. we must learn to “think outside the box.” A certain ideology of science and technology constitutes the proverbial “box” in this instance, and we must get outside of it if we hope to deal with the present situation. 88
  6. And yet science is a human activity, an activity pursued by human beings. This is an obvious statement but it bears repeating since part of the mythology of science is precisely that it is independent of human beings, independent of mind and intelligence. 98
  7. Most often we think of scientific thinking as rational thinking characterized by clarity and logic. Are these the only characteristics of scientific thinking? Are they even the most important ways in which scientists think? 102
  8. This blind spot arises out of human consciousness itself, and is rooted in the biology of the brain.
  9. Ambiguity is seen to be unexpectedly present in much of mathematics and science. 126
  10. Science is motivated by a desire to unify our experience of the world and to unify ourselves with the world. 136 Einstein talked about his feeling that “behind anything that can be experienced there is something that the mind cannot grasp and whose beauty and sublimity reaches us only indirectly and as a feeble reflection.”2 The “blind spot” is my name for those things that are real but which the mind cannot grasp and thus cannot capture through words, symbols, or equations. 152
  11. A drunken man has lost his house keys and is searching for them under a streetlight. A policeman approaches and asks what he is doing. “Looking for my keys,” he says. “I lost them over there.” And he points down the street. “So why are you looking for them here?” “Because the light here is so much better,” the man replies. 159
  12. Our brain provides us with the illusion that there is no visual blind spot, so our rational intelligence—through its insistence on consistency and completeness—hides the blind spot from our consciousness. 178
  13. There exists an intrinsic limitation to what can be known through science. The existence of that which is real but cannot be understood poses a major challenge to our usual way of thinking about the world and to our thinking about the relationship between human beings and the natural world. 202
  14. Some things cannot be put into words because doing so is only an approximation to the real situation. The verbal or symbolic formulation captures some aspects of the situation but is not identical to it. There is a question regarding the relationship between the definition and the thing being defined. 223
  15. To insist on a one-to-one correspondence between words and reality protects us from the self-referential spiral that is inherent in human self-consciousness, the ambiguity that lies at the heart of the human condition. 229
  16. Trying to understand something often means trying to give it a definition, yet (as in the case of infinity or randomness) another definition is always possible. Each definition structures a certain field of mathematical or scientific thought. Certainly one definition may be better than another but even an excellent definition does not capture the informal domain out of which it emerges. It structures the informal situation. 294
  17. “Understanding” demands placing something in a context. 299
  18. Each subject we explore should be thought of more as a “field” (like an energy field in physics) than a fixed and definite object. A field does not have a fixed objective meaning. It is much much larger than that. 311
  19. The entire world of science is grounded in human consciousness and rationality. 318
  20. The existence of the “ungraspable” implies that there are intrinsic limitations to the cultural project of reducing reality to rationality. 319
  21. The ungraspable refers to a quality of intrinsic incompleteness that is inevitably associated with the conceptual. 370
  22. Many people will be surprised by the assertion that some things cannot be understood. 371
  23. That which is real but inexpressible is not something vague or mystical; it is something that is immediate and simple. It is the ground out of which the concept arises. 397
  24. Science derives from a source that is not accessible to science. 401
  25. Sources of creativity are by definition unknown, inevitably outside of the present conceptual universe. 410
  26. The unknown is the matrix out of which creativity is born. 411
  27. Creativity has its origins neither in the natural world nor in the world of concepts—it involves much more than the mere shuffling of well-defined conceptual categories as a computer would do. 413
  28. Concepts are the results of acts of creativity and not the other way around. 415
  29. Science is not identical to reality; science is a description of reality. 416
  30. The first thing that is necessary is to break the mistaken identification of science with reality. 418
  31. It is necessary to differentiate between science and the mythology of science. 420
  32. Just as the brain renders invisible the physiological blind spot and gives the illusion that the visual field is continuous and complete, so the mythology of science has the function of hiding from view the holes in the fields of consciousness and rationality. 422
  33. The “blind spot” I am talking about is an inevitable consequence of our rational consciousness. 425
  34. What is the assumption of rationality, the assumption of logical consistency if not the mind’s way of “filling in” the holes in our rational universe. 429
  35. When we look for this blind spot intellectually, it seems to disappear and so we must infer its existence in an indirect manner. 431
  36. Yet rationality is itself the result of an act of creativity and so cannot be used to explain the origins of the extraordinary creativity of science. 439
  37. The uncertainty of the unknowable is deeply unsettling to the analytic intelligence. 481
  38. I am not saying that there is anything wrong with logic, analytic thinking, or the intellect, but they do have a tendency to take over, to insist on being the sole arbiter of reality. 491
  39. To use words to point beyond words; to use well-formulated sentences to point out that there exist aspects of reality that are not captured by well-formulated sentences is a form of mental judo. 498
  40. If we were talking about music, everyone would recognize the difference between the music itself and a description of the music. So it is with science and the natural world that science describes. 500
  41. It is as though one part of us knows but cannot speak, while the other speaks very well but inevitably misses that unmediated connection with things that is the content of the deepest form of knowing. 517
  42. What is missing from most scientific discussions is the role of the scientist as a subjective participant in the scientific enterprise. 519
  43. Reason is grounded in one modality of human consciousness and thus is inevitably blind to other ways of knowing. 522
  44. The major scientific breakthroughs in the last century that all point in one way or another to limits on what we can know. 533
  45. Modern science contains a new way of looking at reality, and what is distinctive about the new view is the emergence of these limits—limits to reason, to deductive systems, to certainty, and to objectivity. 535
  46. The discovery of uncertainty is like a canary in a coal mine. 541
  47. It is through mathematics that we can best study the strengths and weaknesses of this mode of thinking. 549
  48. Mathematics is the traditional bastion of reason and absolute certainty. 551
  49. Morris Kline, in the introduction to Mathematics: The Loss of Certainty, says, “It is now apparent that the concept of a universally accepted, infallible body of reasoning—the majestic mathematics of the 1800s and the pride of man—is a grand illusion. 552
  50. Uncertainty and doubt concerning the future of mathematics have replaced the certainties and complacency of the past.” 554
  51. Uncertainty has entered mathematics in many different guises. An early shock was the creation of non-Euclidean geometries. For millennia, people had looked to Euclidean geometry as the quintessence of certain knowledge and it was the way that the mind was used in geometry—deductive logical reasoning—that seemingly brought elusive certainty within the grasp of humankind. 557
  52. Not only were the results of Euclidean geometry thought to be certain, they also seemed to reflect the very structure of physical reality. The deductive axiomatic method that Euclid introduced was the method for arriving at certainty both about the results themselves and about the properties of the natural world.
  53. The real numbers settled certain questions of the deepest mathematical and scientific importance, but these very successes opened the door to a whole series of seemingly paradoxical situations that threatened to destabilize mathematics. All of this contributed to a loss of faith in the objective and absolute certainty of mathematics. 667
  54. The gap between certainty and truth had now been revealed for all to see. 687
  55. Certainty is not to be confused with truth. 710
  56. Many explicit mathematical questions can be shown to be undecidable. 721
  57. Incompleteness and the undecidable are different ways in which the blind spot finds its way into science. They indicate that there are limits to what can be achieved through a certain kind of thinking. Such limits are today firmly established as part of the intellectual landscape. However, their implications are still far from having been assimilated into the general culture. 745
  58. The classical ideal of complete, objective, and absolutely certain knowledge has been lost. The ability of reason to “capture” the world has been put in doubt. 781
  59. Many of the great theories of modern science testify to the fact that uncertainty is an irreducible feature of the world. 789
  60. A classical, deterministic science is a science of stasis. It misses the essence of life, namely dynamic change. It would seem that it is precisely the life sciences in which the need for a new perspective is most compelling. 793
  61. Every crisis has within it the seeds of rebirth, and this particular crisis carries the potential for a revolutionary new way to imagine the world, the role of human beings, and the nature of the mind. 804
  62. The loss of certainty can be seen as the end of the world, or—as I have repeatedly said—it can be seen as an opening to a new way of thinking about science. 804
  63. One of the factors that characterize this moment in history is our civilization’s current confrontation with problems of such complexity and urgency that we find ourselves paralyzed. These include economic problems, vast population growth, scarcity of food and clean water, depletion of energy sources coupled with the insatiable desire of people in developing countries like China and India to share in the promised land of middle class life and the consumer economy. The problems are so vast, and the proposed solutions so stopgap, that even thinking about the problem becomes painful and seemingly futile. 807
  64. The present world crisis, for that is what it is, will not be resolved by “business as usual,” by applying techniques and strategies that have brought on the situation we are in.
  65. We must find a way to approach our cultural blind spots, to face uncertainty with courage, to confront our own powerlessness in the face of what I have been calling the ungraspable without becoming paralyzed. 813
  66. Our situation contains elements of the paradoxical—it is the successes of the scientific method that have brought us face to face with its limitations, just as it is the complexity of the global financial community that has brought on the present economic meltdown. 815
  67. Facing the situation authentically will evoke the creative intelligence that we desperately need at the present time. 819
  68. What are the implications for science and society of the existence of a blind spot that cannot be captured by systematic thought? 824
  69. Uncertainty and incompleteness are the price we pay for creativity—in fact, for being alive. 826
  70. These two points of view lead to two different orientations toward the entire scientific enterprise. One I shall call the “science of certainty,” and the other the “science of wonder.” They differ in many ways, but one crucial difference involves their attitude toward the uncertainty and incompleteness. 829
  71. The demand for absolute certainty is more characteristic of a mythology of science, a view that one finds more often in technology than in pure science. It is a distortion of pure science, a distortion that, as we shall see, has the potential to create a lot of damage. 832
  72. “Romanticism as a cultural force is generally regarded as intensely hostile to science, its ideal of subjectivity eternally opposed to that of scientific objectivity. But I do not believe this was always the case, or that the terms are mutually exclusive. The notion of wonder seems to be something that once united them, and can still do so.” 846
  73. Wonder has never been absent from science, but it disappears when we turn science into something mechanical, or use it as a way of achieving total control over nature or society. 848
  74. Einstein’s most enigmatic and delightful statements, “The most beautiful experience we can have is the mysterious. It is the fundamental emotion that stands at the cradle of true art and science.” 854
  75. A discussion of science should properly be based on the centrality of wonder, mystery, and creativity. 858
  76. The misconception that the “science of certainty” is identical to science has contributed to many of society’s current problems. 863
  77. The science of wonder has room for both certainty and uncertainty. 867
  78. Creativity is connected to, even based upon, illumination. Where does illumination come from? What are its sources? 879
  79. Science has been called the religion of our time. Religion once provided what science provides today—a vast mythological structure that contains an explanation of the cosmos and the particular role of human beings in that cosmos. 900
  80. Science provides the sense that the universe is a coherent, connected, and meaningful entity—a sense of the unity of things. This sense of coherence is powerful and important even if most people believe it is merely a subjective sensation and therefore a derivative feeling of secondary importance. 902
  81. Coherence is important precisely because it has both subjective and objective dimensions; because it is related to and accompanies the acts of creativity. The sense of wonder often accompanies the sudden appearance of a sense of coherence. 905
  82. Coherence results from acts of creativity, but coherence is itself a sense that unifies the natural world with the human mind as it grapples with, and attempts to make sense of, that world. Thus, coherence, and therefore creativity, is something that transcends classical objectivity and subjectivity. 911
  83. The problem here is that the argument is mistakenly about the content of science versus the content of religion. Einstein’s “cosmic religious feeling” is meant to bridge that particular gap—to show that the highest form of religious feeling is to be found in science as well as religion.
  84. “Cosmic religious feeling” is the unifying context from which both science and religion emerge and is intrinsically connected to creativity. 931
  85. Cosmic religious feeling is both an inspiration for, and a result of, creative activity in science. 935
  86. In Einstein’s view, science and religion both arise out of this common ground—the same cosmic religious feeling. 948
  87. Normally in any description of science, we proceed by assuming that the objective theory can stand independently of any “subjective” component—this is considered to be the very defining characteristic of science. 971
  88. Viewing science as a field of creative endeavor will allow us to think of science in a radically new light, 974
  89. There would be no science without human creativity and that creativity should be part and parcel of what we are referring to when be we talk about science. 988
  90. Perhaps Einstein should be taken more seriously when he senses that there is an intelligence that is revealed in the workings of the universe. It is not that human intelligence creates an order in what is essentially a chaotic domain but that some intelligence or “mind” is an intrinsic aspect of reality. What a radical challenge to our usual way of seeing things! The scientist reveals that universal mind to us, but that mind is there independent, in some sense, of the individual. 993
  91. This intelligence appeared to be independent of the individual personality, independent of anything that is personal. What is exciting and so mysterious is that this “mind …in the world” is reflected in the human mind. This larger external intelligence is accessible to human intelligence. This is the true mystery of science. Creativity is not the imposition of arbitrary patterns on the world.

All superscripts denote the text location in the Kindle e-book edition


William Byers
Professor Emeritus in Mathematics and Statistics, Concordia University, Canada


Garry Jacobs
Chief Executive Officer, WAAS


Carlos Blanco
Professor of Philosophy, Pontifical University of Comillas, Spain


Bohdan Hawrylyshyn
President, Foundation Vidrodgenia, Geneva


Winston Nagan
Professor of Law, University of Florida; Chair of Board, WAAS


Zbigniew Bochniarz
Affiliated Professor of Econ., University of Washington, USA


Stefan Brunnhuber
Medical Dir. & Chief Medical Off., Diakonie Hospital, Germany


Rodolfo Fiorini
Academic Scientist, Politecnico di Milano, Italy


Mario Hytten
CEO, Planetaire AB, Captimax Sports Media Ltd, Sweden


Zdravko Radman
Professor of Philosophy, Institute of Philosophy, Croatia


Herwig Schopper
Former Director General of CERN, Geneva


Alberto Zucconi
President, Person-Centered Approach Institute, Italy

1. What is pushing individuals to become deep thinkers, to discover a new conceptual system, and to overcome contradicting and differing issues in encountering them? Some individuals can do, and others cannot.  What is an element/factor that enables some individuals to become more creative?

WB: First of all creativity is not so much something that you decide to do consciously in order to become rich or famous or get promoted. On the contrary it is something that the individual is compelled to do pushed along by a motivation that the person may not even be conscious of.  I would say that being creative is an expression of our deepest nature.  So I would turn the question around and ask why it is that not everyone is creative.  This may be because most of us are too comfortable with who we are, what we have, and what we believe uncritically to be the case.  We live in a bubble within which we are quite at home.  Disturbing that comfortable world takes courage because you must be prepared to live with unpleasant tension and cognitive dissonance.  It is disorienting and a kind of suffering.


2. You mentioned that a new conceptual system is emerging among the digital natives along with technological innovation. How would you describe this new conceptual system? Are new technologies enabling young people to be more creative?

WB:  No, I said that each major technological change brings about a new (technological) conceptual system.  Does it help young people to be more creative?  Remember that I associated creativity with changing CSs.  Having a new CS surely means that you look at things in a way that is different than previous generations do but that does not necessarily make you creative.  In fact people today tend to be the slaves of their technologies and so may not have the time for the concentrated immersion in a problem that is a prerequisite for creativity.


3. Deep thinking – in contrast to analytical thinking, is it more like an experiential and embodied knowledge?  Anthropologists conduct fieldwork to understand culture and human behaviors of the topic of interest from informants’ point of view.  In design field, researchers observe and interview people to find insights into a product/service that they are developing.  In both instances, researchers are trying to obtain the perspectives of the insiders to gain a deeper understanding of the topic/object of research.

WB: DT often is generated by an ambiguous situation in which there are two different points of view (c.f. Koestler on Creativity) that conflict with one another.  In the situations you have described there are clearly these two different viewpoints—insiders and researchers— so the problem is not only understanding the other point of view but developing a point of view that includes the culture of the insiders but is expressible in the language and culture of the researcher.  To bridge that gap requires a creative response.


4. IT industry is looking into human’s biological and physiological data using sensors to investigate human conditions and their interactions with the environment. All the data will be converted into numbers, and sent to a digital and analytical system. In that sense, these data may not be able to enhance deep thinking and creativity. To make these inventions (Virtual Reality, auto-driving cars, AI, etc. ) more creative, what is necessary in addition to algorithm, a conceptual system based on rationality?

WB:  I think of the inventions you mention as extensions of our society's present conceptual system.  A self-driving car is interesting and new but it is not a very creative idea.  You wouldn't say, "Wow! I've never thought of it that way."  It's easy to imagine a self-driving car.  The problems are technical and complicated but not radical.  We know we can do it and will do it sooner or later.  

As I said I think that the title AI is a misnomer.  I don't see how an AI program can be creative when it is necessarily embedded in an analytic paradigm and creativity, real creativity, requires one to step outside of the analytic mind.  

Nevertheless there can be creativity within a CS.  Writing a paper in mathematics or science should involve creativity within these Ss.  But even here the research must be based on an original idea.  Where does that idea come from?  Often from finding a new way to look at the situation, i.e. reframing.  Getting a new idea does not come from a logical analysis or by crunching data alone.  It comes from absorbing yourself in the problem for a long period of time and then stepping back from the problem, going for a walk, or taking a nap.  Then the promising idea pops into your head sometimes crystallized by a random event that has no obvious connection to your problem.  This is thinking outside the box.  You can't force it to happen but it does often happen when the mind is ripe and open.