What We Cannot Know

What We Cannot Know: Explorations at the Edge of Knowledge
by Marcus du Sautoy

Review by Dr Pingali Gopal
(Blog site at pingaligopi.wordpess.com)


Science has achieved a lot; and it promises to do so in the future. The spirit of scientific enquiry based on theory and experiment is the bedrock on which humanity has progressed. The humans have this unique thirst to know which set them apart from other conscious beings. The spirit of knowledge and enquiry has made our lives comfortable over so many centuries. It has its own detractors. Science has given us the atom bomb too and the methods of mass destruction. Maybe, science has also equipped us with destroying ourselves. But, the fact remains that scientific enquiry will never stop so long as humans are alive, because the spirit of knowing more about the world is one of the prime movers in the individual and the collective scheme of things. However, there comes a point when the scientists must give up, put their hands up in despair, and shout,’ We cannot go any further’. There are certain edges beyond which everything is in a state of permanent fog and a mist. The author calls them the ‘known unknowns’. The book is a brilliant exposition of these edges of science which are beyond the grasp of the human mind presently.

But one can never say never, as the author gives the example of the famous Auguste Comte who in the middle of the 19th century said emphatically, shaking the table with the strongest fist, that the chemical composition of the stars can never be found out. Famous last words, one can say, as he has been proved very wrong. Similarly, there may come a time when some of the edges may be cleared of the mist beyond; but, the prospects look a little bleak.

The author starts off with his casino dice and makes Chaos Theory as the first of his known unknowns. The author is sad that he can never make a prediction where his dice will fall even if the dice is fair; he has knowledge about the initial state; and he has a hold of all the equations. Newton gave us this fantastic predictable world where if the initial conditions of the Universe or for that matter any system are known; and the laws and equations are plugged in, the future state can be clearly known at any point of time. In short, the world is predictable if there is complete knowledge of the existing state. But, alas, Chaos theory was a nail in the coffin of this hopeful proposition. The catch was the state of initial conditions. That can never be known to perfection. Starting with Poincaré, Chaos theory now establishes the fact that the initial state can never be known to perfection. The result is extremely sensitive to the initial conditions, and a change at the 50th decimal place can bring gross changes in the outcome. There is no way to predict which way the smoke will go once an incense stick is lighted. Light up 1000 incense sticks in the same conditions, and the smoke will take a different direction. The imperfectability of knowledge of the initial state translates that we can never know the future and the past too. There are biological chaotic systems too where an additional animal in the system can create a havoc in the dynamic systems or create a stable species environment. The smallest change in the initial set up can lead to extremely divergent final outcomes. It is frustrating for the scientists perhaps to deal with such theories; but Chaos theory is now accepted as mainstream. The elements of Chaos theory have been aptly summarized in the famous statement that the fluttering of a butterfly in New York can set off a storm somewhere across the globe.

The next great unknown comes with the divisibility of matter. The Greeks thought the atoms were the smallest building blocks beyond which we cannot divide any further. The atom however was only a concept till the 19th and the early 20th century, but later it was visualised more clearly by science and experiments. The atoms were discovered to have protons, neutrons, and electrons as its constituents. The atoms were no longer the basis of matter. The discovery of the sub-atomic particles is one of the most fascinating stories in the history of science. The experiments were truly breath-taking and offer an example of the triumph of the human mind. But, the celebrations did not last long. We now have the quarks as the ultimate constituents of matter and the scientists have apparently reached a dead end in the divisibility of matter. The LHC (Large Hadron Collider) is discovering a new sub-atomic particle a day almost, but as far as the final divisibility of matter, we perhaps cannot see beyond the quarks, which now take the place of the ultimate building blocks of matter. The present technology does not allow us to go beyond them. There are other fundamental particles being speculated, the string being the primary one. Strings are one dimensional strings of an extremely tiny magnitude vibrating in 11 dimensions and giving rise to the entire building of matter. The size of atoms is 0.1 to 0.5 nanometers (1 × 10-10 m to 5 × 10-10 m). The quarks measure smaller than 43 billion-billionths of a centimetre (0.43 x 10−16 cm). Hold your breath here- the strings are speculated to measure 10-33 centimeters, or about a millionth of a billionth of a billionth of a billionth of a centimeter. We need extremely high energy particle colliders to prove the existence of strings which are presently existing as mathematical models only. The major problem with string theory is that it is not provable to be right and it can neither be proved wrong. Science progresses by an important concept called falsifiability. If a theory can be proved wrong, it is termed as proper science. The string theory has become a theory of anything and everything; and there is no force presently in the world which can say that it is wrong. Hence, there is this great unknown when we go into the microscopic world as what really constitutes the basic stuff of matter. Does it end with quarks or does the quarks have some more ingredients of which it is made off? Our energies to discover them are not enough. The LHC is running out of funds too.

The physics of the sub-atomic world or quantum physics has been tested to the extreme and it is working to fantastic precisions. However, such is the great unknown discovered by the great Heisenberg that it is difficult even today after so many decades for physicists to accept that. The uncertainty principle simply states the fact by an equation that the momentum and position of a particle can never be both known with perfection. There is a trade-off between the two. If one has a grip on the velocity of the particle, the information on the position is lost; and, when the position is known, the momentum is completely unknown. It is a disturbing prediction, but one that has stood the test of time. This has formed the bedrock of quantum physics and its myriad applications, but it is certainly one of the big known unknowns of physics today. The position and its speed of a particle can never be known together. The trapping of a bee in a shrinking box is given as a pictorial representation of this concept; as the position of the bee becomes increasingly specified, the speed at which it is buzzing becomes hazier. We must learn to live with that.

The span of the Universe is the biggest unknowns today in the realm of physics. Is it truly infinite? Is it expanding forever? Does it have an end? Science is probably giving up on this question, as the observable horizon is reached. Beyond the horizon, there is this unobservable universe from where the information cannot even reach us due to the limiting factor of the speed of light. The dark energy is accelerating the expansion of universe and there will be a time when there will just a vast emptiness. The elementary particles will stand alone and maybe will become the seed of the next universe. Universe started at the time of Big Bang about 14 billion years ago, and the biggest unknowns of science is the question of time before the event. A question which does not apparently make any sense. To question what was before the Big-Bang is met with a studied silence. Physics is now asking the question now; and the mainstream physics accepts the question a little valid. A few decades earlier, a similar question to a cosmologist would be responded by a telephone call to the mental asylum to pack the questioner off for the rest of his life! Now, we have the speculation of multiverse theory where our universe is one of the infinite of the universes which has certain parameters allowing life. There is nothing special about the constants of physical matter of our universe. All possible values are possible. We are just in one of the universes which has those parameters; and which has supported life and intelligence to the extent that we can ask the question of why the universe is the way it is.

Time is a very difficult concept to come to grips with. The finite speed of light is the factor for causing a good amount of confusions in the concepts of past, present, and future. Suppose an observer is standing at a point C which is equidistant from his perspective from planet A and planet B. Now consider that planet A explodes and after a few years’ planet B explodes. For the observer at C, planet A has exploded before planet B. Now, far off on Earth, if light from B reaches us earlier than light from A, and we make the valid observation that B exploded earlier. The point is, we are right and so is the person at the point C who has completely a different view. In this relative world, past, present, and the future cease to have any absolute claimants and everything is relative.

The nature of time and space; and its nature at the start of the universe and in the black holes is an unknown which physics is trying to reconcile with a quantum gravity theory. The quantum gravity theory is still in progress for decades. Whether it will be sorted out or a new theory will come up is something which science does not seem to know presently. He quotes Julian Barbour, who has come up with the fantastic theory that time does not exist at all! It is exciting that such thoughts are being propagated in the realm of physics. In the new theory, changing events define time, and it does not exist as such. There are an infinite series of ‘Nows’ where things are just arranged in a static matter. There is no motion at all. It is radical for physics, but hardly for Advaitic Vedanta. Advaita always insisted on that the time is simply a concept of the mind. There is only one present in which the future and the past are simply superimposed. Highly prophetic are the words of Swami Vivekananda who insisted that science will and must reconcile and agree with Advaita one day. It will never be the other way around.

The author then tackles the tricky issue of Consciousness. One has the access to high technology today like the EEG, fMRI, and PET scanners which give extraordinary anatomical and functional imaging of the human brain. But, is it ever possible to know what a person is thinking by the patterns established on the imaging sequences? The author says it is difficult. It is perhaps impossible to get into another person’s brain and say for sure what the person is thinking. Free-will is then tackled. Are we truly free? Again, the answer seems to be in the negative. We think we have a free choice, but stunning experiments have shown that it is an illusion too. The decisions to act in a manner is made some six seconds before one’s cortex thinks of doing an action. There is something higher than the brain, and this something is the big unknown of physics and biology. Is it Consciousness? Is it the same for everyone? Physics has reached a dead end when it comes to the question of ‘Who is the I in the I?’ Research is on frantically as Consciousness studies are considered respectable now in contrast to the olden days. Again, Vedanta seems to have the last word. Consciousness is God, it says. It is the state transcending all states, and the entire world is just a superimposition on that state which is a state where there is no time or space. The Universe, its sequences of past, present, and the future are simply non-existent like a dream. Cause and effect are dreamlike with no reality to them. Science is again coming near those kind of thoughts; the truth which has always been revealed by our masters since Vedic times. The Rishis and the seers perhaps have been true all along.

In the final chapter, the author comes to the fascinating Gödel’s theorem, which seem to have profound implications in mathematics. As I understood it, a mathematical system like the number theory has some axioms to begin with, the truth of which is considered a given. A huge system of proofs and theorems are built on those basic axioms. But, Gödel showed that using the same system, the truth of the axioms can never be proved right. The truth of the base is something forever beyond our knowledge systems. Apparently, this is a theorem of enormous implications. Being a non-mathematician, I had a little difficulty in following this end chapter as he waxes eloquent. However, the concept of a limiting knowledge which cannot be overcome in the domain of something so rigid and deterministic as mathematics is something which fascinates the author.

The author ends the book with this segment and one is surely wanting more. The pure lyricism in the prose is a joy extraordinary. There might be a few places where the reader might be a bit lost, but one gets the gist of the book very clearly as the beauty of various fields of science amply blossom under the author’s pen. It is a book for every lover of science and for every lover of the English language.

The author claims to be an atheist, but some of the edges of science seem to me clearly coming in the ambit of Vedantic philosophy. It always surprises me no end that many top-notch scientists and physicists in the Western world must turn to atheism to do their science. The history of western science is almost a persistent clash with and fear of the religious authority. Of course, there are some great exceptions of priest-scientists, but the overall picture is that of an antagonism. Indians had and probably will never have such issues in the pursuit of the so called ‘secular fields’ of science, technology, medicine, engineering, and others. They have been as much spiritualized in the Indian context as the arts have been. The goddess in the temple can inspire the deepest poetry of Kalidas or the most profound mathematics of Ramanujam. The realization of the lower and the higher realms of knowledge makes this clearly possible. As I always say, there is no dichotomy when the chairman of ISRO breaks a coconut at Tirupati before the launch of the high technology rockets.  Unfortunately, most of the western scientists equate religion with the Abrahamic religions only. I wish they only read the works of Swami Vivekananda, Ramana Maharishi, or even the modern writers like Dennis Waite to have an inkling of Advaitic thought. I am perfectly sure that they will change their opinions and will attest to the famous statement of Swami Vivekananda that Science will meet Vedanta one day in its quest for Unity. Vedanta perhaps is the destination of science.

Buy from Amazon US
Buy from Amazon UK

One thought on “What We Cannot Know

  1. Thank you Dennis for posting this Review of a Mathematician’s 2016 book crystal gazing the future of science.

    Our Congratulations and also thanks to the Reviewer, Dr. Pingali Gopal who is a well-qualified surgeon for his comprehensive sum up of the material presented in the book and adding his own thoughtful comments from a Vedantic perspective.

    We look forward to many more of Dr. Pingali’s articles on this subject of Advaita and Science.


Leave a Reply