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What We Cannot Know

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du Sautoy, What We Cannot Know, Kindle ed., 2016

This is perhaps the best book about the history and philosophy of science I have ever read—and, having taught the subject at the university level for a number of years, I have read quite some. The author is a professor of mathematics at Oxford. In 2008 the University appointed him to the Simonyi Professorship for the Public Understanding of Science, which was all but tantamount to launching him into a new career. Judging by this book, he has done so with great success indeed.

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To start at the beginning, the great strength of science has always been its ability to predict what given certain conditions, will happen in the future. On such and such a day, at such and such an hour, in such and such a place, there will be an eclipse lasting so and so many minutes or hours. Mix stuff X with stuff Y, and the outcome will be an explosion. So far, so good. In the hands of the philosopher Karl Popper (1892-1994) this ability to predict has been turned into the test as to whether or not a proposition or theory is scientific, an idea to which any modern scientist who hopes to publish his work must subscribe.

Enter chaos theory. Developed from the 1960s on, it centers on the question why many major physical events—tornadoes, for example, or earthquakes—are so devilishly hard to predict. The answer? Because, in many systems, very small initial changes can sometimes lead to enormously different outcomes. As, for example, when a buttery flapping its wings in Beijing combines with any number of other factors, some great some small, to cause a tornado in Florida. Another example, central to du Sautoy’s book, is provided by the throwing of a dice (or multiple dice, but there is no need to go into that here). No knowledge we can obtain, however accurate and however detailed, is ever likely to tell us which face a dice is going to land on the next time we throw it. Instead, all we can hope for is a statistic—namely that, assuming the dice is perfectly balanced and as we keep throwing it again and again, on the average one out of six throws will result in a six.

Next, what is the universe made of? The Greek philosopher Democritus believed it was material (that is why we call him a materialist). Using a knife to cut it up, the outcome would be smaller and smaller pieces of matter until, finally, we would find ourselves dealing with indivisible, a-tomos in Greek, particles forming the building blocks of the universe. Two and a half millennia have passed, and we still do not know whether he was right. On one hand particles much smaller than the atom—protons, neutrons, electrons, neutrinos, positrons, muons, bosons, quarks, and many others—have been discovered and keep being discovered, leading to the question whether the quest will ever end. On the other, of many if not all these particles it is not at all clear whether they are in fact particles. They are perhaps best described as flashes of light (electromagnetic waves) appearing now here, now there; in other words, as waves.

Much worse still, there is the Uncertainty Principle. First pronounced by Werner Heisenberg back in 1927, it tells us that we cannot know both the location of a particle and its momentum; the reason being that any attempt to focus on one of these qualities will cause the other to change. So much for determinism at the smallest level of them all.

Still staying with the universe, we want to know more about its genesis, its qualities, its size (if it has a size), and its ultimate fate. It is not that we have not been making progress; even as I write, man-made machines are exploring the surface of Mars. Whereas the philosopher Auguste Comte (1798-1857) once declared that we would never know what the oh-so-remote stars are made of, now spectroscopy enables us to do exactly that even for those that are billions of lightyears away. But other questions remain. Assuming that the Big Bang really did take place and is not a convenient fiction as the aether used to be, what exactly was it that “exploded”? What, if anything, did it explode into? Will the expansion of the universe that the Big Bang initiated go on forever, or will it one day come to an end and reverse itself, leading to a Big Crunch? Is our universe the only one that exists, or are there others? How about the possibility that other universes exist, not simultaneously but sequentially, one after another, each preceded by its own Big Bang and each ending in its own Big Crunch? Either way, are the remaining universes we are talking about subject to the same physical and mathematical laws as ours is? Or are they entirely different? Will we ever be able to observe them and communicate with them? In that case, will we benefit from doing so or will the outcome be our annihilation?

Starting at least as far back as Parmenides in the sixth century BCE, is has been widely believed that only God can create something out of nothing, Does that mean that the Big Bang, assuming it ever took place, provides proof of His existence? And what is this God? Is he eternal? If not, when and how did He come into being? Is He separate from the universe, or are the two one and the same? Was his creation of the Big Bang a one-time act, or did He go on interfering with the universe ever after? Can we communicate with him?

The Big Bang is supposed to have taken place, and the universe come into being, approximately 13.7 billion years ago. Referring to time, what does that mean? Did time exist before the Big Bang? Or didn’t it? What is time, anyhow? Does it have an objective existence the way space and mass do (at least du Sautoy does not seem to question their existence, though others have done so)? Or is it, to speak with Stephen Hawking, simply that which certain of our instruments measure?

And how about life? Many other researchers have worked on this question, trying to imagine, and to a very limited extent model, the conditions that might have led to its rise. However, for du Sautoy it seems to be of secondary importance, given that he only devotes remarkably little space to it. With him it is as if the mapping of DNA, and our ability–as exemplified, some say, by China’s modifying some genes so as to create the corona virus—to manipulate it to some extent, has solved the most important mysteries of all. Never mind that, so far, no one has been able to create even the simplest forms of life in a test tube; nor explain, for example, how a fetus develops from a blastula into a fully formed baby.
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As if to compensate for this, du Sautoy delves quite deeply into another aspect of life: namely, the fact that we are conscious, aware of our own existence, and capable of experiencing things. Precisely what is this consciousness? Are we the only animals who possess it? If not, how far “down the ladder of life” do we have to go before we hit on creatures that do not have it? Do primates have it? Do snails? Can there be such a thing as life that does not have consciousness as manifested, if not in the form of launching into a dialogue with itself, at any rate by the ability to feel some kind of pain? Looking at the problem from its other side, will we ever be able to build a conscious computer? Or must we forever put up with one that behaves as if it were conscious?

Closely tied to the question of consciousness is that of the free will. On its supposed existence rests our entire society; our education, our religion, our law (or, before we had law, taboos which individuals did or did not violate), our system of justice. Some would say that this applies to all societies; a society that does not assume that we are autonomous beings, at least so some extent, is inconceivable. But does the free will really exist? Or is it, as not just some ancient authors but some modern brain scientists as well claim, just an illusion? And if illusion it is, what are the implications for the abovementioned social phenomena? Will future criminals, tried for theft e.g, be able to save their hide by claiming that it was not them but the neurons in their brains that committed it? Suppose we succeed in building a computer possessing, as part of its consciousness, a free will; when it comes to law and justice will we treat it as we do humans?

Finally, math. In any inquiry into natural science, math makes a good starting point. That is because, starting at least as far back as Galileo, and in some ways going all the way to Pythagoras two millennia earlier, mathematics is the one great pillar on which all the natural sciences rest. So astronomy, so cosmology, so physics, and so chemistry; and so, increasingly, biology too. Wherever math reigns, we feel that we have reached some kind of unique insight or understanding. Wherever it does not, the mysterious quality known as “scientific” is either present only to a limited extent or altogether absent.

The difficulty is that, contrary to the usual view of math as the one science that can yield certainty, math itself is not without its problems. First, as du Sautoy himself is at pains to emphasize, much of it deals with things that do not really exist. Not just irrational numbers and imaginary numbers but perfect circles, straight lines, points that have no dimensions, movements proceeding in straight lines and at constant speeds, and much more. Second, there is the much-discussed, but so far unanswered, question why such artificial creations and abstractions should not only fit the physical world with which we are familiar but provide the best tools for analyzing it; in other words, why nature should allow herself to be governed by mathematics in these and other things.

Third, it has been shown—by Kurt Goedel, Einstein’s constant companion at Princeton during Einstein’s last years—that any mathematical system will necessarily contain propositions that are self-contradictory, unprovable, or both. Such as can only be resolved by drawing on propositions taken from outside that system, where the game starts afresh. No Baron von Muenchhausen pulling himself up by his bootstraps, in other words. To use another metaphor, it is as if we were living inside a Russian doll. No sooner do we succeed in gaining what we think is a complete understanding the innermost one than we discover that surrounding it on all sides is another doll; and so on and so on in a succession of dolls. One whose end, even assuming there is one, we cannot perceive.

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Goedel did not develop his theories in a vacuum. Just one day before he first announced them a famous German mathematician named David Hilbert, in an address to the Society of German Scientists and Physicians, claimed that “we must know/we shall know.” In other words, that everything is in principle knowable; and that, given sufficient genius and hard work, it will end up by becoming known.

Certainly he was not the first scientist to fall victim to that delusion, at least in certain fields and for a certain time. Prominent others before him were Albert Michelson, who first measured the speed of light while simultaneously showing that there was no such thing as ether in which it moved. And William Thomson, aka Lord Kelvin, who calculated the absolute freezing point. Nor was he the last. Both Stephen Hawking and Albert Einstein made similar claims. Hawking, in A Short History of Time when he wrote that the then current physicists’ model of the universe was getting so close to the ultimate truth as to leave fewer and fewer loose ends; Einstein, by famously claiming that “God does not play dice,” thus sticking to determinism and knowability as opposed to indeterminism and unknowability.

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My mother used to say that a single fool can ask more questions than ten wise people can answer. That is true; not are the abovementioned questions by any means the only ones du Sautoy discusses. As a layman reading the book, all I can say is that I emphatically did not feel that any of them—at any rate, those I was able to understand—were of the kind fools might ask. To the contrary: many go down to the core of our existence, and many have important practical implications. Even those that do not—e.g what time is and whether, before the Big Bang, there was such a thing—sounded interesting to my ears. One reason for this is because the author, an expert on mathematics as the science that seems to underlie all the rest, is uniquely qualified to look not just at one of them but at them all. Another, because he writes in a fluent, fairly light-headed way complete with just enough stories, anecdotes, and jokes to keep the reader asking for more.

As du Sautoy, in his last chapter, keeps telling us: It is the deficiencies of knowledge, and our attempts to obtain it, which make up the essence of life by endowing it with a sense of purpose.

Highly recommended.

What is Life?

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The question how dead matter could have given rise to conscious, sentient living beings such as ourselves has been preoccupying people for millennia past. So much so, indeed, that our inability to answer it remains one of the great constants of our history. Just think of the book of Genesis which has God first making man and then breathing into his nostrils “the breath of life.” Thereby turning him into “a living soul” out of whose rib He later fashioned a woman, too; meaning, perhaps, that the process by which Adam was created “out of the dust of the ground” was one of a kind which not even He could replicate

However, many of us moderns do not believe in God and may not even be familiar with the Bible. Let alone know what the Buddha, Plato, St. Augustine, Descartes, and many other philosophers and/or psychologists, biologists and computer engineers had to say about the matter and do so still. So I thought I would try to put together a short list of things which, by their presence or absence, will indicate whether X, or Y, or Z, is or isn’t alive. If not for the benefit others, at any rate for my own.

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  1. Cellular structure. Starting with germs—but not including viruses, which for that very reason are not always included under the rubric, life—all living matter is made up of cells. Cells fall into two basic types, prokaryotic and eukaryotic. Prokaryotic cells do not have a nucleus; eukaryotic ones do. Living organisms are built either of single cells, as bacteria and amoeba are, or of multiple ones.
  2. Self-repair. A cardinal quality only life has is its ability to repair itself. A locomotive, or an automobile, or a computer for that matter, cannot do this. Once something goes wrong, it will either stay wrong or get worse. Not so living organisms. A wound, provided it is not too serious, will start healing itself almost as soon as it is inflicted. Provided there is no infection, a hard object embedded in our flesh will be surrounded by scar tissue and can remain in place for many years without giving rise to any further trouble. In quite some animals even the loss of a tail, or tentacle, or limb, or teeth, will be compensated for by new growth. These are things no inanimate object, natural or artificial, can do. Or, presumably, will ever be able to do.
  3. Metabolism (from the Greek: beyond change); meaning, the sum total of life-sustaining chemical reactionsin organisms. It is generally divided into three parts. First, the conversion of food/fuel into energyon which all physiological processes run. Second, the conversion of food/fuel into building blocks for various kinds of tissue of which the body consists. And third, the elimination of wastes. These enzyme-catalyzed reactions allow organisms to grow, reproduce, maintain their structures, and respond to their environments. All living organisms necessarily have such chemical reactions; non-living ones do not.
  4. Growth. Given the opportunity, i.e food and a favorable environment, all living creatures grow. A chicken grows into a chick, a human baby into a man or woman many times its size and weight. This is not simply a matter of material being added from outside, as when two or more droplets, bubbles or particles merge during contact to form a single daughter droplet, bubble or particle. Nor of crystallization, as when a solution of certain materials, such as Epsom salt in boiling water, is allowed to cool, causing the salt atoms to run into each other and join together in a crystal. Rather, of a creature growing according to its own internal laws as embedded in its DNA.

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  5. Reproduction. Starting with germs and ending with trees and whales, what all living creatures have in common is their ability to reproduce, i.e make more or less faithful copies of themselves. Not so inanimate objects, not one of which has ever performed that feat. A spoon does not divide to form two spoons, a telephone does not become pregnant and give birth to another telephone. True, a three-dimensional printer can be used to produce as many copies as desired of many objects, parts of itself specifically included. Two printers can even made to work in tandem, producing parts that can then be used to build a third not identical to either of them. What they cannot do is assemble those parts until they form a third printer; that must be done by hand. As long as this is the case the story of the sorcerer’s apprentice, where a broom is first broken in two and then starts reproducing itself and refuses to stop, will remain just that—a story.
  6. Evolution. Reproduction means creating more organisms of the same kind. Not so evolution which, over time, results in the emergence of organisms that, on occasion, can be so different from the original as to be barely recognizable. As, for example, when terrestrial animals evolved out of maritime ones, birds, out of dinosaurs, and humans, out of some ape-like ancestor.
    Changes brought about by evolution are hereditary, which means that they are not simply the product of the natural environment and the organism’s attempt to adapt to it. As far as present-day scientific knowledge goes, what drives evolution is random changes (mutations). Such changes are brought about by errors in a creature’s DNA. The errors themselves can be caused by a. External factors, i.e certain chemicals or high energy particles hitting the DNA molecule in question; b. DNA’s failure to properly mate with its opposite number during conception; and c. DNA being an extremely complicated molecule, it may fail to replicate (copy) itself properly during cell division. Provided they are beneficial rather than harmful, in which case the creature that carries them will be selected out, a long sequence of such changes, known as genetic drift, can result in a new species emerging, at feat no non-living object has ever been able to emulate. That even applies to the so-called evolvabots built by robot-engineer John Long. Evolvabots do mimic some aspects of living systems such as sensing gradients, foraging, maneuvering, evading predators, and attacking prey. However, not one of them has ever changed themselves into something it was not
  7. Consciousness. Just what consciousness is no one knows. Starting with Democritus around 450 BCE, many philosophers and scientists have gone so far as to insist that it is an illusion and that, “in reality,” there is no such thing; all there is are patterns of electric (and chemical, a point that those who claim that brains are just computers often overlook) activity in the brain. However, few if any of them would agree that they themselves do not have it.
    Consciousness is what accounts for our ability to think—cogito ergo sum, as Descartes put it. Not just to answer questions, which properly programmed computers can do as well as, and much faster than, we, but to formulae them. Also, which may be even more important, to experience such feelings as awe, elation, fatigue, fear, joy, hatred, hunger, love, pain, pleasure, and any number of others right down to the end of the alphabet. Though one may doubt whether all these are present in all living creatures—whether, for example, germs can think and trees, experience fear—one thing seems abundantly clear: inanimate objects to not have it.
  8. Purposefulness. Two things can cause the status quo to change; a cause, and a purpose. A cause is exemplified by a push we get from behind, making us move, stagger or fall down. A purpose is something we first set up for ourselves and then, relying on our will, pursue. A cause works from the past into the present; a purpose, from the present into the future. A cause can affect both an inanimate object and a living one. Not so a purpose, which is limited to the latter alone. Whether all forms of life act on purpose we do not know. Some, however, clearly do.

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Conclusion: Note that each one of the above articles refers to an essential characteristic of life. Joined together in a single object, or contraption, or organism, they would actually be life. Yet we still do know how life grew out of inanimate matter. Let alone what it is. Whether or not it is based on ignorance or on fact, it is this gap which, by forcing us to resort to the idea of the free will, governs our systems of education, morality, justice, trade, and much more. As long as it persists, so will we.

Back to the Beginning

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Robert Lanza, Biocentrism: How Life and Consciousness are the Keys in Understanding the True Nature of the Universe, Kindle ed., 2010.

“In the beginning, God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the spirit of God moved upon the face of the waters.”

Starting at the time when those words were written down perhaps 2500-3000 years ago, human thought concerning the origins of the universe in which we live has essentially moved along two parallel tracks. One, which was associated with some versions of ancient Greek philosophical thought as well as with Hinduism right down to the present day, claimed that it has always existed and would always exist. The other, which is exemplified by the sentences from Genesis just quoted, was to assign its origin to some kind of conscious God (or gods) who, once He had made up His mind, created it just as a constructor designs a building and then does on to erect it.

Looking back over the three and half centuries since the scientific revolution of the seventeenth century, the outcome has been a kind of compromise. On one hand, few non-Hindus have accepted the idea that the world has always existed and will always go on existing in the same form. On the other, God has been banished from the discussion, at any rate as conducted among scientists as the most important purveyors of modern knowledge concerning questions of this kind. For example, Isaac Newton around 1700 still devoted as much attention to his theological works as he did to the laws of motion, gravitation, and optics. But when Napoleon in 1802 asked the famous physicist Pierre Laplace whether the existence of the observed universe did not prove that there was indeed a God he was told, “Sir, that is a hypothesis I do not require.”

Since then attempts to understand how the universe could have come into being without invoking the “hypothesis” in question have gone on and on. Laplace’s own answer, as set out in his writings, was that it had started out as a rotating nebula, or interstellar gas cloud. From there the planets and sun coalesced in accordance with the ordinary laws of gravity on one hand and mechanics on the other. Newton’s latest successor, Stephen Hawking, who incidentally is buried right next to him at Westminster Cathedral, argued that it was formed 13.8 billion years ago as a result of an imaginably enormous explosion popularly known as the big bang. However, there are many things this theory cannot explain. Asked what had exploded (impossible to say), why it had done so (for no known reason), what had existed before (a meaningless term) the explosion, and what the young universe, triggered by the explosion (of nothing), expanded into (also nothing), all Hawking could do was to shrug and declare that these questions and others like them were unanswerable. So precise, supported by so many equations. Yet so lacking, so unsatisfactory; it is enough to make one want to tear out one’s hair.

In other words, the scientists’ continuing efforts to do without Him, while admirable, have never been able to carry complete conviction. However often it was derided and dismissed, the idea that there must have been a creator of some kind could not be gotten rid of any more than the devil having been driven out through the door, could be prevented from returning by way of the window. He was, however, not God—a taboo term, since His existence could not be verified by any kind of observation or experiment—but consciousness.

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Starting at least as far back as Laplace—much earlier, if one cares to go back all the way to Epicurus—scientists have been arguing that consciousness grew out of the matter that preceded it. Not so, says Dr. Lanza: no natural process known to us could have performed that feat. Instead, he says, it was consciousness which gave rise to the world—so much so that, without the former, the latter could not even have existed.

To understand what he meant, take the popular riddle concerning a tree that has fallen in a forest with no one there to witness the fact. did it make a sound? Of course it did, say ninety-nine percent of those asked. Not so, say Dr. Lanza and a few others. The splintering of the trunk and its crash on the ground certainly gave rise to vibrations in the surrounding air. However, in the absence of anyone to receive those vibrations in his or her ears, transmit them by way of the acoustic nerves, and process them with the help of the brain, they would not have amounted to what we know as sound.

What applies to hearing applies equally well to our remaining senses. What the specialized neurons in the back of our brains register is not the world’s existing, objective, sound, light, and impact. On the contrary, light, impact, and sound are created by those neurons. To adduce another example, a single rainbow that can be seen by everyone who looks in the right direction at the right time does not exist. What does exist are trillions of raindrops. Each one carrying a potential rainbow; and all “waiting” to be discovered by animal sense organs and brains to be brought to bear on them. Instead of the internal and external world being separate and independent of one another, as Descartes would have it, they are merely two sides of the same coin. That, incidentally, is also the best available explanation for the riddle of quantum mechanics where, as far as we can make out, the speed and position of elementary particles seem to be determined by the fact that they are or are not observed.

This premise serves Dr. Lanza as the foundation on which to build everything else in the book, leading up to the conclusion that “the universe burst into existence from life [which is the seat of consciousness], not the other way around.” What I personally found most interesting in it is the following. We present-day humans are immensely proud of our scientific prowess. And rightly so, given that it has enabled us to study, and often gain some understanding of, anything from the bizarre submicroscopic world of elementary particles that exists right under our noses to gigantic galaxies more than thirty billion light years away. Dr. Lanza’s contribution is to point out that, without taking account of consciousness and the life with which it is inextricably tied, we shall never be able to understand reality as a whole. Some people might find this prospect disturbing. In so far as it means that there will never be a shortage of questions to explore and ponder, I personally find it comforting.

But isn’t consciousness, pure and unadulterated by a physical body, simply another word for God?