Tag: Alan Lightman

The Boundaries Between Science and Religion: Alan Lightman on Different Kinds of Knowledge

“The physical universe is subject to rational analysis and the methods of science. The spiritual universe is not. All of us have had experiences that are not subject to rational analysis. Besides religion, much of our art and our values and our personal relationships with other people spring from such experiences.”


Alan Lightman, whose beautiful meditation on our yearning for permanence in a universe that offers none, looks at the tension between science and religion in The Accidental Universe: The World You Thought You Knew.

In the essay, “The Spiritual Universe,” Lightman sets out to reconcile his personal struggle between religion and science. In so doing he sets out the necessary criteria for science to be compatible with religion:

The first step in this journey is to state what I will call the central doctrine of science: All properties and events in the physical universe are governed by laws, and those laws are true at every time and place in the universe. Although scientists do not talk explicitly about this doctrine, and my doctoral thesis adviser never mentioned it once to his graduate students, the central doctrine is the invisible oxygen that most scientists breathe. We do not, of course, know all the fundamental laws at the present time. But most scientists believe that a complete set of such laws exists and, in principle, that it is discoverable by human beings, just as nineteenth-century explorers believed in the North Pole although no one had yet reached it.

Our knowledge of scientific laws is provisional. We do not know all the laws but we believe in a complete set of them. We further believe, in principle anyway, that humans will uncover these laws. An example of a scientific law is the conservation of energy.

The total amount of energy in a closed system remains constant. The energy in an isolated container may change form, as when the chemical energy latent in a fresh match changes into the heat and light energy of a burning flame— but, according to the law of the conservation of energy, the total amount of energy does not change.

Even scientific laws that we already know about are updated and refined over time. Lightman offers the replacement of Newton's law of gravity (1687) by Einstein's deeper and more accurate law of gravity (1915). These revisions are part of the very fabric of science.

Next, Lightman provides a working definition of God.

I would not pretend to know the nature of God, if God does indeed exist, but for the purposes of this discussion, and in agreement with almost all religions, I think we can safely say that God is understood to be a Being not restricted by the laws that govern matter and energy in the physical universe. In other words, God exists outside matter and energy. In most religions, this Being acts with purpose and will, sometimes violating existing physical law (that is, performing miracles), and has additional qualities such as intelligence, compassion, and omniscience.

Lightman then offers a continuum of religious beliefs based on the degree to which God acts in the world. At one end is atheism — or denying the existence of god. Moving along the spectrum, we find deism, which was a prominent view in the seventeenth and eighteenth centuries that God created the universe but has not acted since this spark.

Voltaire was a deist. As God's role expands we find immanentism, which holds that God created the universe and its scientific laws. Under this view, God continues to act through the repeated application of those laws. We can probably put Einstein in the immanentism camp. (Philosophically both deism and immanentism are similar because God does not perform miracles.)

Opposite atheism lies interventionism. Most religions, including Christianity, Judaism, Islam, and Hinduism subscribe to this view, which is that God created the universe and its laws and occasionally violates the laws to create unpredictable results.

Lightman argues that all of these views, except interventionism, agree with science.

Starting with these axioms, we can say that science and God are compatible as long as the latter is content to stand on the sidelines once the universe has begun. A God that intervenes after the cosmic pendulum has been set into motion, violating the physical laws, would clearly upend the central doctrine of science.

Lightman cites Francis Collins, who offers some thoughtful advice on reconciling a belief in an interventionist God and science, or at least, deciding which to turn to for answers to the right kinds of questions. They are often very different.

“I’ve not had a problem reconciling science and faith since I became a believer at age 27 … if you limit yourself to the kinds of questions that science can ask, you’re leaving out some other things that I think are also pretty important, like why are we here and what’s the meaning of life and is there a God? Those are not scientific questions.

Under this reconciliation, miracles cannot be analyzed by the methods of science. This is an echo of Richard Feynman, who put it most clearly in one of his letters, saying that science only tells us if we do something then what will happen? Cause and effect. It doesn't give us any guidance on the question of should we do it?

Lightman, himself, falls in the atheist camp.

I am an atheist myself. I completely endorse the central doctrine of science. And I do not believe in the existence of a Being who lives beyond matter and energy, even if that Being refrains from entering the fray of the physical world. However, I certainly agree with (Other Scientists) that science is not the only avenue for arriving at knowledge, that there are interesting and vital questions beyond the reach of test tubes and equations. Obviously, vast territories of the arts concern inner experiences that cannot be analyzed by science. The humanities, such as history and philosophy, raise questions that do not have definite or unanimously accepted answers.

And yet we must believe in things we cannot (yet) prove. Lightman himself believes in the central doctrine which cannot be proven. At most we can only say there is no evidence to contradict it. This is what Karl Popper called real science – a process by which we hypothesize and then attack our hypotheses. A scientific “fact” is one that has stood up to extraordinary scrutiny.

With much of life, and much meaning in the world, there are often things outside of the scientific realm. These are worth considering.

I believe there are things we take on faith, without physical proof and even sometimes without any methodology for proof. We cannot clearly show why the ending of a particular novel haunts us. We cannot prove under what conditions we would sacrifice our own life in order to save the life of our child. We cannot prove whether it is right or wrong to steal in order to feed our family, or even agree on a definition of “right” and “wrong.” We cannot prove the meaning of our life, or whether life has any meaning at all. For these questions, we can gather evidence and debate, but in the end we cannot arrive at any system of analysis akin to the way in which a physicist decides how many seconds it will take a one-foot-long pendulum to make a complete swing. The previous questions are questions of aesthetics, morality, philosophy. These are questions for the arts and the humanities. These are also questions aligned with some of the intangible concerns of traditional religion.

Lightman recalls his time as a grad student in physics and the concept of a “well-posed problem” — a question with “enough clarity and precision that it is guaranteed an answer.” Put another way, scientists are trained not to “waste time on questions that do not have clear and definite answers.” And yet questions without clear and definite answers are sometimes just as important. Just because we can't apply the scientific method to them doesn't mean we shouldn't consider them.

[A]rtists and humanists often don’t care what the answer is because definite answers don’t exist to all interesting and important questions. Ideas in a novel or emotion in a symphony are complicated with the intrinsic ambiguity of human nature. That is why we can never fully understand why the highly sensitive Raskolnikov brutally murdered the old pawnbroker in Crime and Punishment, whether Plato’s ideal form of government could ever be realized in human society, whether we would be happier if we lived to be a thousand years old. For many artists and humanists, the question is more important than the answer.

The question is more important than the answer — just as the journey is more important than the destination and the process is more important than outcome.

As the German Poet Rainer Maria Rilke put it a century ago:  “We should try to love the questions themselves, like locked rooms and like books that are written in a very foreign tongue.”

“As human beings,” Lightman argues, “don’t we need questions without answers as well as questions with answers?”

The God Delusion, a widely read book by Richard Dawkins, uses modern tools to attack two common arguments for the existence of God: Intelligent Design (only an intelligent and powerful being could have designed the universe) and that only the action and will of God explains our morality and desire to help others. Dawkins convincingly shows that Earth could have arisen from the laws of nature and random processes, without the intervention of a supernatural and intelligent Designer. Our sense of morality and altruism could be a logical derivative of natural selection.

However, as Lightman reminds us, refuting or falsifying the arguments put forward to support a proposition does not necessarily falsify the proposition itself.

Science can never know what created our universe. Even if tomorrow we observed another universe spawned from our universe, as could hypothetically happen in certain theories of cosmology, we could not know what created our universe. And as long as God does not intervene in the contemporary universe in such a way as to violate physical laws, science has no way of knowing whether God exists or not. The belief or disbelief in such a Being is therefore a matter of faith.

Lightman is troubled by Dawkins' wholesale dismissal of religion.

Faith, in its broadest sense, is about far more than belief in the existence of God or the disregard of scientific evidence. Faith is the willingness to give ourselves over, at times, to things we do not fully understand. Faith is the belief in things larger than ourselves. Faith is the ability to honor stillness at some moments and at others to ride the passion and exuberance that is the artistic impulse, the flight of the imagination, the full engagement with this strange and shimmering world.

Indeed, William & Ariel Durant have argued that we need religion; it is part of our fabric of understanding and living in the world.


With that, Lightman brings the essay to a beautiful conclusion.

The physical and spiritual universes each have their own domains and their own limitations. The question of the age of planet Earth, for example, falls squarely in the domain of science, since there are reliable tests we can perform, such as using the rate of disintegration of radioactive rocks, to determine a definitive answer. Such questions as “What is the nature of love?” or “Is it moral to kill another person in time of war?” or “Does God exist?” lie outside the bounds of science but fall well within the realm of religion. I am impatient with people who, like Richard Dawkins, try to disprove the existence of God with scientific arguments. Science can never prove or disprove the existence of God, because God, as understood by most religions, is not subject to rational analysis. I am equally impatient with people who make statements about the physical universe that violate physical evidence and the known laws of nature. Within the domain of the physical universe, science cannot hold sway on some days but not on others. Knowingly or not, we all depend on the consistent operation of the laws of nature in the physical universe day after day— for example, when we board an airplane, allow ourselves to be lofted thousands of feet in the air, and hope to land safely at the other end. Or when we stand in line to receive a vaccination against the next season’s influenza.

Some people believe that there is no distinction between the spiritual and physical universes, no distinction between the inner and the outer, between the subjective and the objective, between the miraculous and the rational. I need such distinctions to make sense of my spiritual and scientific lives. For me, there is room for both a spiritual universe and a physical universe, just as there is room for both religion and science. Each universe has its own power. Each has its own beauty, and mystery. A Presbyterian minister recently said to me that science and religion share a sense of wonder. I agree.

The Accidental Universe is a mind-bending read on the known and unknowable, offering a window into our universe and some of the profound questions of our time.

Too Busy to Pay Attention to Life

“You act like mortals in all that you fear,
and like immortals in all that you desire.”
Lucius Annaeus Seneca


Alan Lightman, the physicist who brought us The Accidental Universe, has also written several works of fiction, including Einstein’s Dreams, presented as dreams Einstein might have had while working as a patent clerk in Switzerland in 1905. More philosophy than physics, the book is a collection of thought experiments about the concept of time. Each of the hypothetical scenarios is only a few pages long, but all provide food for thought. What if we knew when our time would end? What if there were no cause and effect to our actions? What if there was no past? No future? If we could freeze a moment in time, what moment would we choose? And, most critically, are we spending our finite allotment of time on this earth wisely?

In one of Einstein’s dreams, people live forever. In this world, the population is divided into the Nows and the Laters.

The Nows note that with infinite lives, they can do all they can imagine…Each person will be a lawyer, a bricklayer, a writer, an accountant, a painter, a physician, a farmer. The Nows are constantly reading new books, studying new trades, new languages. In order to taste the infinities of life, they begin early and never go slowly…They are the owners of the cafés, the college professors, the doctors and nurses, the politicians, the people who rock their legs constantly whenever they sit down.

The Laters reason that there is no hurry to begin their classes at university, to learn a second language, to read Voltaire or Newton, to seek promotion in their jobs, to fall in love, to raise a family. For all these things, there is an infinite span of time. In endless time, all things can be accomplished. Thus all things can wait. Indeed, hasty actions breed mistakes…The Laters sit in cafés sipping coffee and discussing the possibilities of life.

If you recognized yourself or the people in your life in these descriptions, it’s not surprising. People in this world of infinite time are strikingly familiar to us because we live our lives as if we are going to live forever. We bury our awareness of our mortality beneath our busyness or convince ourselves that there will be time to live the lives we want ‘later’. This is nothing new. Two thousand years ago, Seneca wrote:

What man can you show me who places any value on his time, who reckons the worth of each day, who understands that he is dying daily? For we are mistaken when we look forward to death; the major portion of death has already passed. Whatever years lie behind us are in death’s hands.

Too Busy to Pay Attention to Life

The Now personalities, the perpetually-busy, rushers-through of life, can be spotted in several of Einstein’s Dreams. A dream where “one may choose his motion along the axis of time”, illustrates the consequences of moving too quickly.

The woman catches her breath. She is fifty years old. She lies on her bed, tries to remember her life, stares at a photograph of herself as a child, squatting on the beach with her mother and father.

In another world, time passes more slowly for people in motion, but the faster people travel, the less happy they seem to be.

Because when two people pass on the street, each person perceives the other in motion, just as a man in a train perceives the trees to fly by his window. Consequently, when two people pass on the street, each sees the other’s time flow more slowly. Each sees the other gaining time. This reciprocity is maddening. More maddening still, the faster one travels past a neighbor, the faster the neighbor appears to be traveling.

These words strike a chord in today’s hectic, always-connected, world where we race from one commitment to the next, using our electronic devices along the way to maximize our productivity. But, as Seneca observes in On the Shortness of Life, multi-tasking only takes us further from our ultimate goal.

…no one pursuit can be successfully followed by a man who is preoccupied with many things…since the mind, when distracted, takes in nothing very deeply, but rejects everything that is, as it were, crammed into it. There is nothing the busy man is less busied with than living: there is nothing that is harder to learn.

We don’t slow down long enough to think. We're so focused on what's next that we rarely take the time to ask ourselves whether we’re living the life we want or if we’re even really present in the one we have.

Waiting for Life to Happen

Not everyone in Lightman’s tales is speeding through life. In one world, people get stuck in time.

In another house, a man sits alone at his table, laid out for two. Ten years ago, he sat here across from his father, was unable to say that he loved him…The man begins to eat, cannot eat, weeps uncontrollably. He never said that he loved him.

The tragedy of this world is that no one is happy, whether stuck in a time of pain or of joy. The tragedy of this world is that everyone is alone. For a life in the past cannot be shared with the present. Each person who gets stuck in time gets stuck alone.

In another of Einstein’s dreams, that will be painfully familiar to some, two couples are having dinner together, their conversation banal and meaningless.

For in this world, time does pass, but little happens. Just as little happens from year to year, little happens from month to month, day to day. If time and the passage of events are the same, then time moves barely at all…If a person holds no ambitions in this world, he suffers unknowingly. If a person holds ambitions, he suffers knowingly, but very slowly.

We can get stuck in the past, unable to let go of regret, or we can get stuck in a rut of routine, too uncertain of what the future might hold to risk chasing our dreams. Like the people in Dr. Seuss’s waiting place, we can end up ‘just waiting’…waiting for life to happen, passing our time in idle pursuits and telling ourselves that we’ll live the life we want when the mortgage is paid off or when the kids are grown or when we retire.

In On the Shortness of Life, Seneca writes:

How late it is to begin to live just when we must cease to live. What foolish forgetfulness of mortality to postpone wholesome plans to the fiftieth and sixtieth year, and to intend to begin life at a point to which few have attained!

Living a Life Less Short

Despite the title of his essay, Seneca argues that life is only as short as we choose to make it.

It is not that we have so little time but that we lose so much…the life we receive is not short but we make it so; we are not ill provided but use what we have wastefully.

In Moonwalking with Einstein, Joshua Foer suggests one way we can stretch out time.

Monotony collapses time; novelty unfolds it. You can exercise daily and eat healthy and live a long life, while experiencing a short one. If you spend your life sitting in a cubicle and passing papers, one day is bound to blend unmemorably into the next – and disappear. That’s why it’s important to change routines regularly, and take vacations to exotic locales, and have as many new experiences as possible that can serve to anchor our memories. Creating new memories stretches out psychological time, and lengthens our perception of our lives.

This also helps explain why time seems to move faster as we age. The older we become, the fewer novel experiences we tend to have.

In Lightman’s fictional worlds, the people who find contentment are those who learn to live in the moment. Staying in the present is surprisingly difficult to achieve, but practicing meditation and mindfulness can help us get there more often, and the reward when we do so is well worth the effort.

In the final dream of the book, time is a nightingale, as fleeting and elusive as the present moment.

On those occasions when a nightingale is caught, the catchers delight in the moment now frozen. They savor the precise placement of family and friends, the facial expressions, the trapped happiness over a prize or a birth or romance, the captured smell of cinnamon or white double violets. The catchers delight in the moment so frozen but soon discover that the nightingale expires, its clear, flutelike song diminishes to silence, the trapped moment grows withered and without life.

Einstein’s Dreams and Seneca’s essay On the Shortness of Life (also available free online) are both very quick reads. Reflecting on what they have to say is time well spent.

Our Yearning for Immortality: Alan Lightman on one of the most Profound Contradictions of Human Existence

Science does not reveal the meaning of our existence, but it does draw back some of the veils.


“Be not deceived,” Epictetus writes in The Discourses, “every animal is attached to nothing so much as to its own interest.” Few things are more in our nature than our yearning for permanence. And yet all evidence argues against us.

This profound human contradiction is what physicist Alan Lightman — the first person to receive dual appointments in sciences and humanities at MIT — explores in one of the essays in The Accidental Universe: The World You Thought You Knew.

Alan Lightman (Photo via MIT)
Alan Lightman (Photo via MIT)

The Accidental Universe

In the foreword to The Accidental Universe, Lightman tells a story of attending a lecture given by the Dalai Lama at the Massachusetts Institute of Technology. Among other things, the Dalai Lama spoke on the Buddhist concept of sunyata, which translates as “emptiness.” More specifically this doctrine means that objects in the physical universe are empty of inherent meaning — objects only receive meaning when we attach it to them with our thoughts and beliefs. This calls into question what is real.

As a scientist, I firmly believe that atoms and molecules are real (even if mostly empty space) and exist independently of our minds. On the other hand, I have witnessed firsthand how distressed I become when I experience anger or jealousy or insult, all emotional states manufactured by my own mind. The mind is certainly its own cosmos.

As Milton wrote in Paradise Lost, “It [the mind] can make a heaven of hell or a hell of heaven.”

In our constant search for meaning in this baffling and temporary existence, trapped as we are within our three pounds of neurons, it is sometimes hard to tell what is real. We often invent what isn’t there. Or ignore what is. We try to impose order, both in our minds and in our conceptions of external reality. We try to connect. We try to find truth. We dream and we hope. And underneath all of these strivings, we are haunted by the suspicion that what we see and understand of the world is only a tiny piece of the whole.


Science does not reveal the meaning of our existence, but it does draw back some of the veils.

We often think of the world as the totality of physical reality.

The word “universe” comes from the Latin unus, meaning “one,” combined with versus, which is the past participle of vertere, meaning “to turn.” Thus the original and literal meaning of “universe” was “everything turned into one.”

In the first essay “The Accidental Universe,” Lightman argues there is a possibility of multiple universes and multiple space-time continuums. But even if there is only a single universe, “there are many universes within our one universe, some visible and some not.” It all depends on your vantage point.

The challenge arises from explaining what we cannot see in a physical sense but can reason from deductions. We are like a pilot — relying our our incomplete mental instruments to guide us. We must believe what we cannot see and to a large extent we must believe what we cannot prove.

The Temporary Universe

In, The Temporary Universe, one of the best essays in the collection, Lightman sets out to explore our attachment to youth, immortality, and the familiar, despite their fleeting nature. The essay explores a profound contradiction of human existence — our longing for immortality.

I don’t know why we long so for permanence, why the fleeting nature of things so disturbs. With futility, we cling to the old wallet long after it has fallen apart. We visit and revisit the old neighborhood where we grew up, searching for the remembered grove of trees and the little fence. We clutch our old photographs. In our churches and synagogues and mosques, we pray to the everlasting and eternal. Yet, in every nook and cranny, nature screams at the top of her lungs that nothing lasts, that it is all passing away. All that we see around us, including our own bodies, is shifting and evaporating and one day will be gone. Where are the one billion people who lived and breathed in the year 1800, only two short centuries ago?


Physicists call it the second law of thermodynamics. It is also called the arrow of time. Oblivious to our human yearnings for permanence, the universe is relentlessly wearing down, falling apart, driving itself toward a condition of maximum disorder. It is a question of probabilities. You start from a situation of improbable order, like a deck of cards all arranged according to number and suit, or like a solar system with several planets orbiting nicely about a central star. Then you drop the deck of cards on the floor over and over again. You let other stars randomly whiz by your solar system, jostling it with their gravity. The cards become jumbled. The planets get picked off and go aimlessly wandering through space. Order has yielded to disorder. Repeated patterns to change. In the end, you cannot defeat the odds. You might beat the house for a while, but the universe has an infinite supply of time and can outlast any player.


We can't live forever. Our lives are controlled by our genes in each cell. The raison d'être for most of these genes is to pass on instructions for how to build.

Some of these genes must be copied thousands of times; others are constantly subjected to random chemical storms and electrically unbalanced atoms, called free radicals, that disrupt other atoms. Disrupted atoms, with their electrons misplaced, cannot properly pull and tug on nearby atoms to form the intended bonds and architectural forms. In short, with time the genes get degraded. They become forks with missing tines. They cannot quite do their job. Muscles, for example. With age, muscles slacken and grow loose, lose mass and strength, can barely support our weight as we toddle across the room. And why must we suffer such indignities? Because our muscles, like all living tissue, must be repaired from time to time due to normal wear and tear. These repairs are made by the mechano growth factor hormone, which in turn is regulated by the IGF1 gene. When that gene inevitably loses some tines … Muscle to flab. Vigor to decrepitude. Dust to dust.

Most of our bodies are in a constant cycle of dying and being rebuilt to postpone the inevitable. The gut is perhaps the most fascinating example. As you can imagine it comes in contact with a lot of nasty stuff that damages tissues.

To stay healthy, the cells that line this organ are constantly being renewed. Cells just below the intestine’s surface divide every twelve to sixteen hours, and the whole intestine is refurbished every few days. I figure that by the time an unsuspecting person reaches the age of forty, the entire lining of her large intestine has been replaced several thousand times. Billions of cells have been shuffled each go-round. That makes trillions of cell divisions and whispered messages in the DNA to pass along to the next fellow in the chain. With such numbers, it would be nothing short of a miracle if no copying errors were made, no messages misheard, no foul-ups and instructions gone awry. Perhaps it would be better just to remain sitting and wait for the end. No, thank you.

Despite the preponderance of evidence against it, our culture strives for immortality and youth. We cling to a past that was but a moment in time in Heraclitus river— photographs, memories of our children, old wallets and shoes. And yet this yearning for youth and immortality, the “elixir of life,” connects us to every civilization that has graced the earth. But it's not only our physical bodies that we want to remain young. We struggle against change — big and small.

Companies dread structural reorganization, even when it may be for the best, and have instituted whole departments and directives devoted to “change management” and the coddling of employees through tempestuous times. Stock markets plunge during periods of flux and uncertainty. “Better the devil you know than the devil you don’t.” Who among us clamors to replace the familiar and comfortable incandescent lightbulbs with the new, odd-looking, “energy-efficient” compact fluorescent lamps and light-emitting diodes? We resist throwing out our worn loafers, our thinning pullover sweaters, our childhood baseball gloves. A plumber friend of mine will not replace his twenty-year-old water pump pliers, even though they have been banged up and worn down over the years. Outdated monarchies are preserved all over the world. In the Catholic Church, the law of priestly celibacy has remained essentially unchanged since the Council of Trent in 1563.

I have a photograph of the coast near Pacifica, California. Due to irreversible erosion, California has been losing its coastline at the rate of eight inches per year. Not much, you say. But it adds up over time. Fifty years ago, a young woman in Pacifica could build her house a safe thirty feet from the edge of the bluff overlooking the ocean, with a beautiful maritime view. Five years went by. Ten years. No cause for concern. The edge of the bluff was still twenty-three feet away. And she loved her house. She couldn’t bear moving. Twenty years. Thirty. Forty. Now the bluff was only three feet away. Still she hoped that somehow, some way, the erosion would cease and she could remain in her home. She hoped that things would stay the same. In actual fact, she hoped for a repeal of the second law of thermodynamics, although she may not have described her desires that way. In the photograph I am looking at, a dozen houses on the coast of Pacifica perch right on the very edge of the cliff, like fragile matchboxes, with their undersides hanging over the precipice. In some, awnings and porches have already slid over the side and into the sea.

One constant over Earth's 4.5-billion-year history is upheaval and change.

The primitive Earth had no oxygen in its atmosphere. Due to its molten interior, our planet was much hotter than it is now, and volcanoes spewed forth in large numbers. Driven by heat flow from the core of the Earth, the terrestrial crust shifted and moved. Huge landmasses splintered and glided about on deep tectonic plates. Then plants and photosynthesis leaked oxygen into the atmosphere. At certain periods, the changing gases in the air caused the planet to cool, ice covered the Earth, entire oceans may have frozen. Today, the Earth continues to change. Something like ten billion tons of carbon are cycled through plants and the atmosphere every few years— first absorbed by plants from the air in the form of carbon dioxide, then converted into sugars by photosynthesis, then released again into soil or air when the plant dies or is eaten. Wait around a hundred million years or so, and carbon atoms are recycled through rocks, soil, and oceans as well as plants.

Eta Carinae
The Doomed Star, Eta Carinae, may be about to explode. But no one knows when – it may be next year, it may be one million years from now. Eta Carinae's mass – about 100 times greater than our Sun – makes it an excellent candidate for a full blown supernova. (Photo via NASA)

Shakespeare's Julius Caesar says to Cassius:

“But I am constant as the northern star,
Of whose true-fix'd and resting quality
There is no fellow in the firmament.”

We can forgive his lack of knowledge on modern astrophysics or the second law of thermodynamics. The North Star, like all stars, including the sun, is slowing dying as they consume fuel. They too will eventually explode or fade into the universe. The only reminders of existence will be cold embers floating in space.

The Three Signs of Existence

Buddhists have long been aware of the evanescent nature of the world.

Anicca, or impermanence, they call it. In Buddhism, anicca is one of the three signs of existence, the others being dukkha, or suffering, and anatta, or non-selfhood. According to the Mahaparinibbana Sutta, when the Buddha passed away, the king deity Sakka uttered the following: “Impermanent are all component things. They arise and cease, that is their nature: They come into being and pass away.” We should not “attach” to things in this world, say the Buddhists, because all things are temporary and will soon pass away. All suffering, say the Buddhists, arises from attachment.

If only we could detach. “But,” Lightman argues, “even Buddhists believe in something akin to immortality. It is called Nirvana.”

A person reaches Nirvana after he or she has managed to leave behind all attachments and cravings, after countless trials and reincarnations, and finally achieved total enlightenment. The ultimate state of Nirvana is described by the Buddha as amaravati, meaning deathlessness. After a being has attained Nirvana, the reincarnations cease. Indeed, nearly every religion on Earth has celebrated the ideal of immortality. God is immortal. Our souls might be immortal.

Lightman argues that either we are delusional or nature is incomplete. “Either I am being emotional and vain in my wish for eternal life for myself …. or there is some realm of immortality that exists outside nature.”

If the first alternative is right, then I need to have a talk with myself and get over it. After all, there are other things I yearn for that are either not true or not good for my health. The human mind has a famous ability to create its own reality. If the second alternative is right, then it is nature that has been found wanting. Despite all the richness of the physical world— the majestic architecture of atoms, the rhythm of the tides, the luminescence of the galaxies— nature is missing something even more exquisite and grand: some immortal substance, which lies hidden from view. Such exquisite stuff could not be made from matter, because all matter is slave to the second law of thermodynamics. Perhaps this immortal thing that we wish for exists beyond time and space. Perhaps it is God. Perhaps it is what made the universe.

Of these two alternatives, I am inclined to the first. I cannot believe that nature could be so amiss. Although there is much that we do not understand about nature, the possibility that it is hiding a condition or substance so magnificent and utterly unlike everything else seems too preposterous for me to believe. So I am delusional. In my continual cravings for eternal youth and constancy, I am being sentimental. Perhaps with the proper training of my unruly mind and emotions, I could refrain from wanting things that cannot be. Perhaps I could accept the fact that in a few short years, my atoms will be scattered in wind and soil, my mind and thoughts gone, my pleasures and joys vanished, my “I-ness” dissolved in an infinite cavern of nothingness. But I cannot accept that fate even though I believe it to be true. I cannot force my mind to go to that dark place.

“A man can do what he wants,” said Schopenhauer, “but not want what he wants.”

If we are stuck with mortality can we find a beauty in this on its own? Is there something majestic in the brevity of life? Is there a value we can find from its fleeting and temporary duration?

I think of the night-blooming cereus, a plant that looks like a leathery weed most of the year. But for one night each summer its flower opens to reveal silky white petals, which encircle yellow lacelike threads, and another whole flower like a tiny sea anemone within the outer flower. By morning, the flower has shriveled. One night of the year, as delicate and fleeting as a life in the universe.

The Accidental Universe is an amazing read, balancing the laws of nature and first principles with a philosophical exploration of the world around us.

The Honeybee Conjecture: What Is It About Bees And Hexagons?


Why is every cell in this honeycomb a hexagon?

More than 2,000 years ago, Marcus Terentius Varro, a roman citizen, proposed an answer, which ever since has been called “The Honeybee Conjecture.” He thought that if we better understood, there would be an elegant reason for what we see.

“The Honeybee Conjecture” is an example of mathematics unlocking a mystery of nature. And luckily, NPR, with the help of physicist/writer Alan Lightman, (who wrote The Accidental Universe: The World You Thought You Knew) helps explains Varro's hunch.

Why the preference for hexagons? Is there something special about a six-sided shape?

“It is a mathematical truth,” Lightman writes, “that there are only three geometrical figures with equal sides that can fit together on a flat surface without leaving gaps: equilateral triangles, squares and hexagons.”

So which to choose? The triangle? The square? Or the hexagon? Which one is best? Here's where our Roman, Marcus Terentius Varro made his great contribution. His “conjecture” — and that's what it was, a mathematical guess — proposed that a structure built from hexagons is probably a wee bit more compact than a structure built from squares or triangles. A hexagonal honeycomb, he thought, would have “the smallest total perimeter.” He couldn't prove it mathematically, but that's what he thought.

Compactness matters. The more compact your structure, the less wax you need to construct the honeycomb. Wax is expensive. A bee must consume about eight ounces of honey to produce a single ounce of wax. So if you are watching your wax bill, you want the most compact building plan you can find.

In 1999 Thomas Hales produced a mathematical proof, confirming that Varro was right.

Why are they all the same size?

For bees to assemble a honeycomb the way bees actually do it, it's simpler for each cell to be exactly the same. If the sides are all equal — “perfectly” hexagonal — every cell fits tight with every other cell. Everybody can pitch in. That way, a honeycomb is basically an easy jigsaw puzzle. All the parts fit.

Update: I ran across this interesting paper, which argues the honeybee comb have a circular shape at first and then transform into the hexagon.

We report that the cells in a natural honeybee comb have a circular shape at ‘birth’ but quickly transform into the familiar rounded hexagonal shape, while the comb is being built. The mechanism for this transformation is the flow of molten visco-elastic wax near the triple junction between the neighbouring circular cells. The flow may be unconstrained or constrained by the unmolten wax away from the junction. The heat for melting the wax is provided by the ‘hot’ worker bees.

Still Curious? Learn more about The Honeycomb Conjecture.