Tantalizing Ambiguity

There is something wrong with science. Promises of big breakthroughs that could fundamentally change our understanding of reality have burned brightly for a little while during the past three decades, only to quietly fade away or sputter out. Remember when mapping the human genome was going to revolutionize medicine and lead to cures for everything from cancer to dementia? Or when radio telescopes set up to search for extra­terrestrial intelligence in the 1960s evoked dreams of contact with alien life forms? The Human Genome Project wrapped up in 2003 with no revolution in sight. And last year, SETI’s 42 radio telescopes were temporarily mothballed without evidence that there is anyone else out there.

Even scientists and mathematicians who only a few years ago thought they had finally grasped the Holy Grail of science—a Theory of Everything—with string theory have watched a favoured theory founder on a combination of mathematical complexity and unprovability. The resulting disappointment has spawned a number of books by scientists and mathematicians wondering just what is wrong with science. Why, in more than 30 years, have there been no fundamental breakthroughs in the science that describes our reality?

Lee Smolin, a physicist at the Perimeter Institute, bemoaned this troubling lack of progress in The Trouble with Physics: The Rise of String Theory, the Fall of a Science and What Comes Next. His solution to ending this intellectual drought was a call for more scientists who are “the visionaries, the seers, who can see through unjustified but universally held assumptions and ask new questions.” Of course, he added, these are exactly the innovative thinkers who are typically relegated to the fringes of mainstream science, or excluded altogether.

“If our generation of theorists,” said Smolin, “has failed to make a revolution, it is because we have organized the academy in such a way that we have few revolutionaries, and most of us don’t listen to the few we have.”

The international science community took direct aim at bureaucratic, risk-averse research funding agencies, blaming them for suffocating revolutionary thinking. Governments in Canada, the United States, the United Kingdom and Europe responded to the chorus of criticism by setting up programs specifically to fund the kind of high-risk research that holds the potential for major breakthroughs and revolutionary thinking. But just as new funding streams were being implemented, the economic crisis in 2008 hit, and funding agencies were left scrambling to safeguard funding for mainstream research, never mind anything revolutionary.

Even as scientists continue to ponder the problems within their own profession, they are under attack from the outside. Biblical creationists have grabbed hold of the uncertainties and gaps in evolutionary theory to trivialize it as a theory full of holes. Critics of climate change science have highlighted the uncertainties and assumptions in climate change research as part of an assault on scientists and scientific methodology. In these attacks, there is an underlying element of anger directed at science, as if science has failed society because it is not living up to its proper role of providing the safety and security of certainty.

Byers, an emeritus mathematician at Concordia University in Montreal, argues that because science plays such a large role in modern civilization, a basic misunderstanding of the nature of science reaches far and deep into modern society. The problem? People expect science to provide them with the comfort of certainty, which Byers argues science simply cannot do. Yet scientists, the media and the public seem to buy happily into the idea that certainty in science and mathematics is not only possible but necessary, thus creating a giant philosophical blind spot that masks a scientific schizophrenia.

Indeed, Byers makes it clear that science has become entrapped in a mythology that it is certain, objective, unambiguous and independent of human beings. And people gravitate to careers in science and mathematics precisely because they are seeking to satisfy the human need for certainty. But if society has charged science with the responsibility of providing a complete description of reality, Byers says, society and science must necessarily incorporate all that is excluded from classical science—subjectivity, ambiguity and the fact that scientific explanations are invented, created and designed by real, live human beings.

“The problem,” says Byers, “lies not with science but with the point of view that I call the ‘science of certainty,’ a particular approach to science in which the need for certainty, power, and control are dominant … It is this mythology that is called upon when some governments, administrators, and businessmen misuse science to justify their questionable practices.”

One such questionable practice with far-­reaching implications is the assumption of mathematical certainty in the uncertain world of Wall Street, a comforting notion that algorithms, mathematical formulas and equations provide an objective truth in the high-stakes gambling of stocks and bonds. People have convinced themselves that complex mathematical instruments can somehow insert predictability into the seeming randomness of the stock market. Of course, we all saw how well that particular illusion worked out for them (and for our own investments), but the high-stakes brokers and bankers have no intention of giving up their highly lucrative mathematical magic.

“If certainty in the financial world is unobtainable,” says Byers, “it is still possible to package the illusion of certainty and use it to make money. The package consists of precisely those algorithms and equations, not science but the mythology of science, not certainty but pseudo-certainty. The more complex the package and the more arcane the mathematics, the better.”

In their yearning for certainty, says Byers, people have paid a high price, ceding the value of their intuition, insight and judgement in deference to complex mathematical formulas. And that leads directly to the impoverishment of scientific ­creativity.

And therein lies a quite suitable answer to the question of what exactly is the problem with science. Science has attempted to strip the subjective human element from scientific activity. That is why almost all published research papers are written without the use of personal pronouns. “I” and “we” are absent from the description of science. One does not say “I poured the solution into the beaker”; rather, “the solution was poured into the beaker.” Journal editors insist on it, and that helps sustain the illusion that science is free of the participation of fallible humans.

Society (and scientists) subscribes to an idealized version of a scientist who, Byers notes, is “an impartial and omniscient observer, a kind of God, standing outside of the phenomenal universe and observing its patterns and regularities.” This description evokes the image of serious men and women in white lab coats carrying clip boards and taking careful notes as they walk slowly around the outside of the universe, observing it as if it were an enormous ant farm. Yet real, human scientists are somehow expected to treat the real world as if they are not actual, active participants in that same reality.

Byers is pushing for a new view of science that does not pretend that the subjectivity of the human experience, with all its messy and wonderful complexity, is somehow not part of the very reality scientists are trying to describe. He proposes another point of view for science, a “science of wonder,” which he also calls a “science of creativity,” where uncertainty and ambiguity leave space for bold leaps into the unknown.

While his goal is certainly ambitious—“nothing less than to formulate a new paradoxical, but fecund, basis for considering the nature of scientific activity—a new kind of philosophy of ­science”—Byers is rather gentle in advocating his new philosophy. He is aware of the need to prepare the ground well so as not to alarm those for whom certainty is important for their sense of security.

The Blind Spot is aimed at intelligent laypersons and at scientists. Byers’s earlier book How Mathematicians Think: Using Ambiguity, Contradiction and Paradox to Create Mathematics sparked considerable discussion among mathematicians. This time, Byers is taking the gospel to science and society.

Byers spends a lot of time in the first two thirds of The Blind Spot carefully explaining the fundamental ambiguity that underlies both science and mathematics. For instance, he shakes up our general acceptance that mathematics is an exercise of calculation by introducing people who perceive numbers quite differently. Mathematical savant Daniel Tammet simply “knows” solutions without performing any calculations at all. According to Tammet, numbers appear to him with colours, textures and sounds, and when he wants, for instance, to multiply two large numbers, he “sees” the two numbers as opposite each other and then the solution appears in the space between them.

In the last third of his book, Byers is in full swing, offering a veritable banquet of tasty intellectual treats to chew on and mull over. For instance, after repeatedly warning that the pursuit of scientific certainty requires a “neurotic” suppression of the very human conflict between object and subject, mind and body, observer and participant, Byers offers a place for certainty. Humans, he says, have a strong sense—a certainty—that there is a natural harmony and unity that pervades the universe, and that the conviction that the natural world is comprehensible and ordered is what drives scientific research.

What is missing from Byers’s wide-ranging critique of the “science of certainty” is any discussion of how philosophies such as realism and logical positivism have fed into this view of science. Nor does he explicitly mention the standard practice in science of using an idealized representation of a problem to simplify it and make it easier to solve.

Since the time of Galileo, scientists have been reframing problems by knowingly and deliberately paring away the ambiguities of complicated and messy real-world problems, turning them into tidier, unambiguous, “in an ideal world” versions. This practice took a new twist in the early 1900s when the few physicists who also had mathematical training turned to complex (and complicated) mathematical techniques to help them understand the mysterious quantum world of atoms. It worked so well that by the time I took up physics in the 1990s mathematics had become the most powerful tool in a scientist’s repertoire, and one that has infiltrated just about every discipline, no matter how poor the fit.

We students were always looking for ways to eliminate the ambiguities in our assignments so they would fit neatly into one of the multitude of equations in our student bible, Schaum’s Mathematical Handbook of Formulas and Tables. And the more advanced the physics, the greater the imperative to reframe the problem to fit the mathematical tools, even if those tools seemed to have little correlation with the physical reality we were trying to describe. I was trained to think of mathematics as a logical, rational and unambiguous method of describing patterns in the universe. That is its great value. No one told us mathematics is itself full of ambiguity.

Byers’s book is not likely to shock scientists who acknowledge the uncertainty underlying their work, and most accept that their favoured theories are provisional and are likely to be overturned at some point. Scientists may, however, recoil at how effectively Byers manages to undermine faith in the tools of mathematics.

Scientists and mathematicians can argue quite rightly that the classical model of science has been remarkably effective. The many great technological and scientific advances in our world today are proof of that. But perhaps the reason there have been no major breakthroughs for some time is that the science of certainty has reached the limits of its effectiveness. Maybe it is time for some new thinking.

The Blind Spot is an intellectually satisfying read. I found myself repeatedly putting the book down and taking time to think through a large number of different ways of looking at science that I had not considered before. Byers admits that the very act of writing this book has enriched his own view of science, consolidating a shift away from the power of logic and the potential of a grand theory of everything that so entranced him for most of his career. I too am changed by this book, by the very act of pondering Byers’s ideas and arguments. Perhaps that is the highest praise that an author can receive, that his work has changed people’s thinking.

What Byers is proposing is revolutionary and he is certainly challenging unjustified but universally held assumptions. The question now is how many other people will listen to him.