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The human endeavors collectively characterized today as science undoubtedly constitute one of the grandest and most distinctive achievements of our species. Indeed, along with artistic expressions in the visual and musical spheres, science may be deemed a defining characteristic of Homo sapiens.

In the pages that follow, I shall discuss and explore the nature and the limits of our scientific knowledge. My focus is on science—that is, on our attempts to ascertain the truth about our physical environment and to understand the phenomena we observe, directly and indirectly, in the world. I have only occasional things to say about technology—meaning the skills to predict, control and manipulate the physical world around us to and for our benefit. I certainly do not mean to suggest that technology is of lesser importance; the practical consequences of our technological endeavors on the lives of human beings have been nothing short of stupendous. Indeed, much of the prestige attached to science and scientists in our modern world is undoubtedly a reflection of the acknowledged significance of man’s technological achievements.

But, science is distinct from technology; it is different in its objectives and its methodologies. Sometimes, technological advances have been a result of scientific discovery; sometimes, technological advances have preceded and even prompted scientific progress, presenting the challenge of understanding and explaining why the technological achievement actually worked. However, questions about the extent to which new scientific theories resulted in technological innovation or important new theories followed the achievements of practical inventors are not relevant to the issues pursued herein.

The point that I seek to establish in the following pages is that despite the astonishing achievements and practical consequences of technology, science has been remarkably unsuccessful. Upon a close examination, the lack of actual knowledge about and real understanding of the deeper fundamentals about reality seem to be among the more striking and surprising characteristics of modern science.

Let me quickly add that this fact is not bad news. To the contrary, it is a fundamental source of wonder—one consequence of mystery—and the stimulus of our continuing quest to discover. It is the reason that science is neither dead nor done, and probably never will be. For me, it is a cause for hope and motivation and an inspiration for creativity. How much we do not know is good news.

The reader may immediately wonder whether working scientists share the view here expressed about the limits of our scientific knowledge. Numerous important scientists have paid at least lip-service to the belief that what is yet to be discovered by science is far greater than what we currently know. Indeed, such an observation by one of the fathers of modern science, Galileo Galilei, working in the first half of the seventeenth century, has been recently paraphrased as follows: “[H]owever much we discover about the building-blocks of life, what we do not know will always be infinitely greater than what we know. All our brilliant detective work amounts to no more than a little gloss on the shining masterwork of creation.” Harry Eyres, “How to Cultivate a Growth Industry,” FT.com, October 15, 2010.

Similarly, over 300 years later, Nobel laureate physicist Robert Laughlin wrote: “Even this room is teeming with things we do not understand. Only people whose common sense has been impaired by too much education cannot see it. The idea that the struggle to understand the natural world has come to an end is not only wrong, it is ludicrously wrong. We are surrounded by mysterious physical miracles, and the continuing, unfinished task of science is to unravel them.” A Different Universe (2005), p.218. And physicist David Deutsch has proclaimed: “Never before in the history of human thought has it been so obvious that our knowledge is tiny and our ignorance vast.” The Beginning of Infinity (2011) p.449. (Some such comments are just dramatic embellishment, of course. For example, utilizing the mathematical construct of infinity, Deutsch reasons that human knowledge is necessarily at the beginning of its achievements, since any specified point is, by definition, “at the beginning of infinity.” See, e.g., id., pp.164–95, 196.)

Many leading scientists, however, have expressed over the centuries quite different views. Several notables have declared that the tasks of science were soon to be largely completed. Such an attitude was arguably pervasive in the late nineteenth century. At the conclusion of that century, astronomer Simon Newcomb, physicist Albert Michelson and physicist William Thomson (Lord Kelvin), concluded—and announced to the world—that the end of scientific discovery was sufficiently near that most of the remaining tasks would be more akin to cleanup than revolutionary advance. See, e.g., Rupert Sheldrake, The Science Delusion: Freeing the Spirit of Inquiry (2012), p.19. Curiously, that attitude did not fully disappear despite the dramatic scientific upheavals of the first half of the twentieth century. For example, John Horgan, then a senior science writer at Scientific American, published a book in 1977 called The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age. Based on interviews with many leading scientists, he advanced this thesis: “If one believes in science, one must accept the possibility—even the probability—that the great era of scientific discovery is over. …Further research may yield no more great revelations or revolutions, but only incremental returns.” Indeed, one of the original celebrity-scientists, Carl Sagan, prophesized as recently as 1979 that the process of discovery was almost complete:

“This book is written just before—at most, I believe, a few years or a few decades before—the answers to many of these vexing and awesome questions on origins and fates are pried loose from the cosmos. …Had we been born fifty years later, the answers would, I think, already have been in. …In all of the four-billion-year history of life on our planet, in all of the four-million-year history of the human family, there is only one generation privileged to live through that unique transitional moment: that generation is ours.”Broca’s Brain: Reflections on the Romance of Science (1979), p.xv.

I am, in fact, of that very generation of which Sagan writes and, of course, we are now almost four decades into the future that he was imagining. And, this book discusses most of the same “fundamental” and “awesome questions” to which he refers:

“questions on the origins of consciousness; life on our planet; the beginnings of the Earth; the formation of the Sun; the possibility of intelligent beings somewhere up there in the depths of the sky; as well as, the grandest inquiry of all—on the advent, nature and ultimate destiny of the universe.”Id., p.xiii.

Yet, as you might have guessed, the answers are not yet in. Not even close. You younger readers were not, in fact, born too late to experience the wonder and mystery or to partake of the process of discovery. Indeed, I believe that the same will be true for your children (and theirs).

Since the late twentieth century, the most common attitude among scientists about the state of science seems to be to acknowledge the proposition that the search for the truth about the physical world may never result in a declaration of complete victory, but to believe that in general we are continually getting closer and closer. That view is one of the things that I hope to put at issue in the reader’s mind.

In recent years, some leading scientists have begun to raise the rather different question of whether science is actually capable of ever explaining everything about our world. For example:

 Retired professor of mathematics William Byers asserts that there are “fundamental limits” to reason and human understanding, the fact of which was fully discovered in the twentieth century. He writes, “The discovery of … ‘limits to reason’ is in many ways the key scientific discovery of the twentieth century, one that our society has still not fully assimilated.” The Blind Spot: Science and the Crisis of Uncertainty (2011), p.4.

 John D. Barrow, Research Professor of Mathematical Sciences at Cambridge University, has expressed skepticism about the possibility of achieving a “theory of everything,” i.e., an underlying and unifying theory that would combine a theory of gravity (such as general relativity) and quantum mechanics and, then, all the rest of science: “The process of discovery could continue indefinitely either because the complexity of Nature is truly bottomless or because we have chosen a particular way of describing Nature which, while being as accurate as we desire, is none the less at best always but an asymptotic approximation that only an infinite number of refinements could make correspond exactly to reality. More pessimistically, our human frame and its evolutionary past may have placed real limits upon the concepts that we can accommodate.” Theories of Everything: The Quest for Ultimate Explanation (2005), p.2.

 Cambridge University Professor of Cosmology Martin Rees, Astronomer Royal and Baron Rees of Ludlow, has speculated that “some aspects of reality—a unified theory of physics, or a full understanding of consciousness—might elude us simply because they’re beyond human brains… Perhaps complex aggregations of atoms, whether brains or machines, can never understand everything about themselves.” From Here to Infinity (2011), pp.110–11

 Oxford University Professor of Mathematics Roger Penrose, in speculating about the ultimate “theory of everything,” has suggested that there might be a level of understanding on which Truth, Beauty and Good are all reflected. “There may be a sense in which the three worlds [mental perceptions, the physical world and the world of mathematical forms] are not separate at all, but merely reflect, individually, aspects of a deeper truth about the world as a whole of which we have little conception at the present time.” The Road to Reality: A Complete Guide to the Laws of the Universe (2005), pp.22–3. But, such a "deeper truth" is not likely to look like science as we know it.

The simple fact may be that there are things that are very real about the Universe in which we participate that are not susceptible to explanation by science as we know it. If so, there will be some important things that necessarily elude scientific explanation. This is an important issue. I shall end on (but not try to answer) the question, many pages from now, in a discussion of the science of human consciousness and the much and long debated issue of free will.

Irrespective of the answer to this ultimate question, it is important to recognize the fundamental limits of our current understanding and knowledge of the world around us. It is not just the matter of what new discoveries are to be made at the fringes of our existing knowledge, but of how much of what we think we already know will turn out to be wrong. Thus, it is essential—and scientific—to remain constantly open-minded and skeptical.

Some leading scientists and historians of science have made this point quite forcefully. The renowned twentieth century theoretical physicist Richard Feynman “recognized—as scientist and as philosopher—that the chain of explanation never ends; it never really reaches an anchor. ...Physicists had hands-on experience with uncertainty, and they learned how to manage it. And to treasure it—for the alternative to doubt is authority, against which science had fought for centuries. ‘Great value of a satisfactory philosophy of ignorance,’ Feynman jotted on a sheet of notepaper one day, ‘teach how doubt is not to be feared but welcomed.’” James Gleick, in the Introduction to Richard Feynman, The Character of Physical Law (1994) (originally published by The British Broadcasting Corporation in 1965), pp.viii, x. Daniel B. Botkin, in a recent Op-ed column in the Wall Street Journal, also invokes Feynman in cautioning about absolutism in scientific debates: “How about a little agnosticism in our scientific assertions—and even, as with Richard Feynman, a little sense of humor so that we can laugh at our errors and move on? We should all remember that Feynman also said, ‘If you think that science is certain—well that’s just an error on your part.’” “Absolute Certainty is Not Scientific,” Opinion, The Wall Street Journal, December 2, 2011.

In the words of Joseph Bronowski: “Science is a very human form of knowledge. We are always at the brink of the known, we always feel forward for what is to be hoped. Every judgment in science stands on the edge of error, and is personal. Science is a tribute to what we can know even though we are fallible. [But, nonetheless, scientists need always to heed the words of] Oliver Cromwell: ‘I beseech you …think it possible you may be mistaken.’” The Ascent of Man (1973), p.374.

There has, in fact, even been some relatively recent academic interest expressed in the importance of ignorance. Columbia University professor of neuroscience Stuart Firestein describes a course that he began teaching in 2006 entitled Ignorance. Ignorance: How It Drives Science (2012). The New York Times reports that a professor of surgery at the University of Arizona, Marlys H. Witte, began teaching, despite some resistance, a class entitled “Introduction to Medical and Other Ignorance” in the mid-1980s. James Holmes, “The Case for Teaching Ignorance,” The New York Times, August 24, 2015. Holmes adds that “The study of ignorance…is in its infancy.” In his book, Firestein stresses how what we do not know frames the questions asked by science and that the evidence of good answers or discoveries is the new questions that those discoveries reveal. He even praises the process of writing grant applications because that process focuses on the unknown and how one might go about finding answers. Ignorance, p.59.

Of course, working scientists are focused on and engaged in, and sometimes obsessed by, their efforts to advance the particular fields that they have chosen. That focus is good. What they do is noble and represents some of the best of human activity and aspiration—the quest for knowledge and the need for understanding. The fact, as I attempt to demonstrate in the following chapters, that they fail to “know,” and seem doomed never really to “understand,” is irrelevant. The striving itself is worthy. See, e.g., Albert Camus, The Myth of Sisyphus and Other Essays (1991) (translation by Justin O’Brian), p.123: “The struggle itself toward the heights is enough to fill a man’s heart. One must imagine Sisyphus happy.”

With regard to the inspiration that can be generated by the efforts of those who strive to create something beyond themselves, Lord Rees has used the example of Ely Cathedral, arising out of the fens of East Anglia. He spoke in tribute to those who “built this cathedral—pushing the boundaries of what was possible. Those who conceived it knew that they wouldn’t live to see it finished. Their legacy still elevates our spirit, nearly a millennium later.” From Here to Eternity, p.150. The dignity and grandeur of the quest matter.

In the opening chapters, I shall discuss the philosophy of science, focusing on theories of knowledge and proof, and then the nature and role of mathematics. Next, I review some methodological debates that arose among economists during the twentieth century, which I find to be suggestive of the nature of these problems in the social sciences and to be a potentially more accessible context in which to present the philosophical and methodological issues. Awareness of the philosophical underpinnings of the methods and methodologies employed by natural scientists and social scientists provides, I believe, significant insights into the discussions of the state of scientific knowledge in the various fields addressed below. (As stated by the nineteenth century economist John Neville Keynes [the father of the better known twentieth century economist John Maynard Keynes]: “In the long run, time cannot but be saved by making a preliminary study of the instruments of investigation to be used, the proper way of using them, and the kinds of things that they are capable of yielding. For in so far as methods of reasoning are employed without due regard to the conditions of their validity, the results gained must likewise be of uncertain validity….” The Scope and Method of Political Economy (1891), p.4.)

With this background, I go on to look at major issues in biology (as reflected in Darwinian theory), physics, particle physics and quantum mechanics, cosmology and neuroscience, trying to span the traditional sciences as well as the newer areas of scientific investigation. We shall see that most areas of science began as what we would generally call philosophy, then with the introduction of empirical analysis and the extensive use of mathematics became more and more like the modern concept of science. That trend continues, leading in the last century to the enthusiastic speculation that someday, even someday soon, “science” might encompass everything and explain it all and, more recently, to this century’s apparently increasing minority concern that perhaps science will not do so in the end, because science (as we know it) cannot do so.

But, in all events, science is a continuing source of wonder. We will continue to be awed by the creativity, the beauty and the elegance of the theoretical edifices that man has been able to erect to date in his search to understand the world in which we live. And, we should also marvel at and be inspired by how much we simply still do not understand.