Yet contradiction and paradoxes have a hallowed place in intellectual history. First of all, contradiction is highly instructive simply because it forces us to think further and deeper. It reveals a discrepancy in our understanding of the world which needs to be resolved and encourages scientists to perform additional experiments and decisive calculations to settle the matter. It is only when scientists observe contradictory results that the real fun of discovery begins. It’s the interesting paradoxes and the divergent conclusions that often point to a tantalizing reality which is begging to be teased apart by further investigation.
Let's consider that purest realm of human thought, mathematics. In mathematics, the concept of proof by contradiction or reductio ad absurdum has been highly treasured for millennia. It has provided some of the most important and beautiful proofs in the field, like the irrationality of the square root of two. In his marvelous book "A Mathematician's Apology", the great mathematician G H Hardy paid the ultimate tribute to this potent weapon:
"Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game."However, the great ability of contradiction goes far beyond opening a window into abstract realms of thought. Twentieth-century physics demonstrated that contradiction and paradoxes constitute the centerpiece of reality itself. At the turn of the century, it was a discrepancy in results from blackbody radiation that sparked one of the greatest revolutions in intellectual history in the form of the quantum theory. Paradoxes such as the twin paradox are at the heart of the theory of relativity. But it was in the hands of Niels Bohr that contradiction was transformed into a subtler and lasting facet of reality which Bohr named 'complementarity'. Complementarity entailed the presence of seemingly opposite concepts whose co-existence was nonetheless critical for an understanding of reality. It was immortalized in one of the most enduring and bizarre paradoxes of all, wave-particle duality. Wave-particle duality taught us that contradiction is not only an important aspect of reality but an indispensable one. Photons of light and electrons behave as both waves and particles. The two qualities seem to be maddeningly at odds with each other. Yet both are absolutely essential to grasp the essence of physical reality. Bohr codified this deep understanding of nature with a characteristically pithy statement- "The opposite of a big truth is also a big truth". Erwin Schrödinger followed up on his own disdain for complementarity by highlighting an even more bizarre quantum phenomenon- entanglement- wherein particles that are completely separated from each other are nonetheless intimately connected; by doing this Schrödinger brought us the enduring image of a cat helplessly trapped in limbo between a state of life and death.
The creative tension created by seemingly contradictory phenomena and results has been fruitful in other disciplines. Darwin was troubled by the instances of altruism he observed in the wild; these seemed to be contradicting the ‘struggle for existence’ which he was describing. It took the twentieth century and theories of kin selection and reciprocal altruism to fit these seemingly paradoxical observations into the framework of modern evolutionary theory. The history of organic chemistry is studded by efforts to determine the molecular structures of complex natural products like penicillin and chlorophyll. In many of these cases, contradictory proposed structures like those for penicillin spurred intense efforts to discover the true structure. Clearly, contradiction is not only a vital feature of science but it is also a constant and valuable companion of the process of scientific discovery.
These glittering instances of essential contradiction in science would seem perfectly at home with the human experience. While contradiction in science can be disturbing and ultimately rewarding, many religions and philosophies have come to savor this feature of the world for a long time. The Chinese philosophy of Yin and Yang recognizes the role of opposing and contrary forces in sustaining human life. In India, the festival celebrating the beginning of the Hindu new year includes a ritual where every member of the family consumes a little piece of sweet jaggery (solidified sugarcane juice) wrapped in a bitter leaf of the Neem tree (which contains the insecticide azadirachtin). The sweet and bitter are supposed to exemplify the essential combination of happy and sad moments that are necessary for a complete life. Similar paradoxes are recognized in Western theology, for instance pertaining to the doctrines of the Trinity and the Incarnation.
The ultimate validation of contradiction however is not through its role in life or in scientific truth but through its role as an insoluble part of our very psyche. We all feel disturbed by contradiction, yet how many of us think we hold perfectly consistent and mutually exclusive beliefs in our own mind about all aspects of our life? You may love your son, yet his egregious behavior may lead you to sometimes (hopefully not often) wish he had not been born. We often speak of 'love-hate' relationships which exemplify opposing feelings toward a loved one. If we minutely observe our behavior at every moment, such observation would undoubtedly reveal numerous instances of contradictory thoughts and behavior. This discrepancy is not only an indelible part of our consciousness but we all realize that it actually enriches our life, makes it more complex, more unpredictable. It is what makes us human.
Why would contradictory thinking be an important part of our psyche? I am no neuroscientist, but I believe that our puzzlement about contradiction would be mitigated if we realize that we human beings perceive reality by building models of the world. It has always been debatable whether the reality we perceive is what is truly 'out there' (and this question may never be answered); what is now certain is that neural events in our brains enable us to build sensory models of the world. Some of the elements in the model are more fundamental and fixed while others are flexible and constantly updated. The world that we perceive is what is revealed to us through this kind of interactive modeling. These models are undoubtedly some of the most complex ever generated, and anyone who has built models of complex phenomena would recognize how difficult it is to achieve a perfectly logically consistent model. Model building also typically involves errors, of which some may accumulate and others may cancel. In addition models can always be flawed because they don't include all the relevant elements of reality. All these limitations lead to models in which a few facts can appear contradictory, but trying to make these facts consistent with each other could possibly lead to even worse and unacceptable problems with the other parts of the model. Simply put, we compromise and end up living with a model with a few contradictions in favor of a model with too many. Further research in neuroscience will undoubtedly shed light on the details of model building done by the brain, but what seems unsurprising is that these models contain some contradictory worldviews which nonetheless preserve their overall utility.
Yet there are those who would seek to condemn such contradictory thinking as an anomaly. In my opinion, one of the most prominent examples of such a viewpoint in the last few years has been the criticism of religious-minded scientists by several so-called 'New Atheists' like Richard Dawkins and Sam Harris. The New Atheists have made it their mission to banish what they see as artificial barriers created between science and religion for the sake of political correctness, practical expediency and plain fear of offending the other party. There is actually much truth to this viewpoint, but the New Atheists seem to take it beyond its strictly utilitarian value.
A case in point is Francis Collins, the current director of the NIH. Collins is famous as a first-rate scientist who is also an ardent Catholic. The problem with Collins is not that he is deeply religious but that he tends to blur the line between science and religion. A particularly disturbing instance is a now widely discussed set of slides from a presentation where he tries to somehow scientifically justify the existence and value of the Christian God. Collins's conversion to a deeply religious man when he apparently saw the Trinity juxtaposed on his view of a beautiful frozen waterfall during a hike is also strange, and at the very least displays a poor chain of causation and inadequate critical thinking.
But all this does not make Collins any less of an able administrator. He does not need to mix science with religion to justify his abilities as a science manager. To my knowledge there is not a single instance of his religious beliefs dictating his preference for NIH funding or policy. In practice if not in principle, Collins manages to admirably separate science from storytelling. But the New Atheists are still not satisfied. They rope in Collins among a number of prominent scientists who they think are 'schizophrenic' in conducting scientific experiments during the week and then suspending critical thinking on Sundays when they pray in church. They express incredulity that someone as intelligent as Francis Collins can so neatly compartmentalize his rational and 'irrational' brain and somehow sustain two completely opposite - contradictory - modes of thought.
For a long time I actually agreed with this viewpoint. Yet as we have seen before, such seemingly contradictory thinking seems to be a mainstay of the human psyche and human experience. There are hundreds of scientists like Collins who largely manage to separate their scientific and religious beliefs. Thinking about it a bit more, I realized that the New Atheists' insistence on banishing perfectly mutually exclusive streams of thinking seems to go against a hallowed principle that they themselves have emphasized to no end- a recognition of reality as it is. If the New Atheists and indeed all of us hold reality to be sacrosanct, then we need to realize that contradictory thinking and behavior are essential elements of this reality. As the history of science demonstrates, appreciating contradiction can even be essential in deciphering the workings of the physical world.
Now this certainly does not mean that we should actively encourage contradiction in our thinking. We also recognize the role of tragedy in the human experience, but few of us would strive to deliberately make our lives tragic. Contradictory thinking should be recognized, highlighted and swiftly dealt with, whether in science or life. But its value in shaping our experience should also be duly appreciated. Paradox seems to be a building block in the fabric of the world, whether in the mind of Francis Collins or in the nature of the universe. We should in fact celebrate the remarkable fact that the human mind can subsume opposing thoughts within its function and still operate within the realm of reason. Simply denying this and proclaiming that it should not be so would mean denying the very thing we are striving for- a deeper and more honest understanding of reality.