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Mathematician; Executive Director, Center for the Study of Language and Information, Stanford; Author, The

What is the nature of mathematics? Becoming a mathematician in the 1960s, I swallowed hook, line, and sinker the Platonistic philosophy dominant at the time, that the objects of mathematics (the numbers, the geometric figures, the topological spaces, and so forth) had a form of existence in some abstract ("Platonic") realm. Their existence was independent of our existence as living, cognitive creatures, and searching for new mathematical knowledge was a process of explorative discovery not unlike geographic exploration or sending out probes to distant planets.

I now see mathematics as something entirely different, as the creation of the (collective) human mind. As such, mathematics says as much about we ourselves as it does about the external universe we inhabit. Mathematical facts are not eternal truths about the external universe, which held before we entered the picture and will endure long after we are gone. Rather, they are based on, and reflect, our interactions with that external environment.

This is not to say that mathematics is something we have freedom to invent. It's not like literature or music, where there are constraints on the form but writers and musicians exercise great creative freedom within those constraints. From the perspective of the individual human mathematician, mathematics is indeed a process of discovery. But what is being discovered is a product of the human (species)-environment interaction.

This view raises the fascinating possibility that other cognitive creatures in another part of the universe might have different mathematics. Of course, as a human, I cannot begin to imagine what that might mean. It would classify as "mathematics" only insofar as it amounted to that species analyzing the abstract structures that arose from their interactions with their environment.

This shift in philosophy has influenced the way I teach, in that I now stress social aspects of mathematics. But when I'm giving a specific lecture on, say, calculus or topology, my approach is entirely platonistic. We do our mathematics using a physical brain that evolved over hundreds of thousands of years by a process of natural selection to handle the physical and more recently the social environments in which our ancestors found themselves. As a result, the only way for the brain to actually do mathematics is to approach it "platonistically," treating mathematical abstractions as physical objects that exist.

A platonistic standpoint is essential to doing mathematics, just as Cartesian dualism is virtually impossible to dispense with in doing science or just plain communicating with one another ("one another"?). But ultimately, our mathematics is just that: our mathematics, not the universe's.

Social psychologist, Hope College; author, Psychology, 8th edition

Reading and reporting on psychological science has changed my mind many times, leading me now to believe that 

• newborns are not the blank slates I once presumed,
• electroconvulsive therapy often alleviates intractable depression,
• economic growth has not improved our morale,
• the automatic unconscious mind dwarfs the controlled conscious mind,
• traumatic experiences rarely get repressed,
• personality is unrelated to birth order,
• most folks have high self-esteem (which sometimes causes problems),
• opposites do not attract,
• sexual orientation is a natural, enduring disposition (most clearly so for men), not a choice.

In this era of science-religion conflict, such revelations underscore our need for what science and religion jointly mandate: humility. Humility, I remind my student audience, is fundamental to the empirical spirit advocated long ago by Moses: "If a prophet speaks in the name of the Lord and what he says does not come true, then it is not the Lord's message." Ergo, if our or anyone's ideas survive being put to the test, so much the better for them. If they crash against a wall of evidence, it is time to rethink.

Researcher of Pirahã Culture; Chair of Languages, Literatures, & Cultures, Professor of Linguistics and Anthropology, Illinois State University

Homeopathic Bias and Language Origins

I have wondered why some authors claim that people rarely if ever change their mind. I have changed my mind many times. This could be because I have weak character, because I have no self-defining philosophy, or because I like change. Whatever the reason, I enjoy changing my mind. I have occasionally irritated colleagues with my seeming motto of 'If it ain't broke, break it.'

At the same time, I adhered to a value common in the day-to-day business of scientific research, namely, that changing one's mind is alright for little matters but is suspect when it comes to big questions. Take a theory that is compatible with either conclusion 'x' or conclusion 'y'. First you believed 'x'. Then you received new information and you believed 'y'. This is a little change. And it is a natural form of learning - a change in behavior resulting from exposure to new information.

But change your mind, say, about the general theory that you work with, at least in some fields, and you are looked upon as a kind of maverick, a person without proper research priorities, a pot-stirrer. Why is that, I wonder?

I think that the stigma against major mind changes in science results from what I call 'homeopathic bias' - scientific knowledge is built up bit by little bit as we move cumulatively towards the truth.

This bias can lead researchers to avoid concluding that their work undermines the dominant theory in any significant way. Non-homeopathic doses of criticism can be considered not merely inappropriate, but even arrogant - implying somehow that the researcher is superior to his or her colleagues, whose unifying conceptual scheme is now judged to be weaker than they have noticed or are been willing to concede.

So any scientist publishing an article or a book about a non-homeopathic mind-change could be committing a career-endangering act. But I love to read these kinds of books. They bother people. They bother me.

I changed my mind about this homeopathic bias. I think it is myopic for the most part. And I changed my mind on this because I changed my mind regarding the largest question of my field - where language comes from. This change taught me about the empirical issues that had led to my shift and about the forces that can hold science and scientists in check if we aren't aware of them.

I believed at one time that culture and language were largely independent. Yet there is a growing body of research that suggests the opposite - deep reflexes from culture are to be found in grammar.

But if culture can exercise major effects on grammar, then the theory I had committed most of my research career to - the theory that grammar is part of the human genome and that the variations in the grammars of the world's languages are largely insignificant, was dead wrong. There did not have to be a specific genetic capacity for grammar - the biological basis of grammar could also be the basis of gourmet cooking, of mathematical reasoning, and of medical advances - human reasoning.

Grammar had once seemed to me too complicated to derive from any general human cognitive properties. It appeared to cry out for a specialized component of the brain, or what some linguists call the language organ. But such an organ becomes implausible if we can show that it is not needed because there are other forces that can explain language as both ontogenetic and phlyogentic fact.

Many researchers have discussed the kinds of things that hunters and gatherers needed to talk about and how these influenced language evolution. Our ancestors had to talk about things and events, about relative quantities, and about the contents of the minds of their conspecifics, among other things. If you can't talk about things and what happens to them (events) or what they are like (states), you can't talk about anything. So all languages need verbs and nouns. But I have been convinced by the research of others, as well as my own, that if a language has these, then the basic skeleton of the grammar largely follows. The meanings of verbs require a certain number of nouns and those nouns plus the verb make simple sentences, ordered in logically restricted ways. Other permutations of this foundational grammar follow from culture, contextual prominence, and modification of nouns and verbs. There are other components to grammar, but not all that many. Put like this, as I began to see things, there really doesn't seem to be much need for grammar proper to be part of the human genome as it were. Perhaps there is even much less need for grammar as an independent entity than we might have once thought.

Student, MIT's Center for Bits and Atoms; Researcher, Internet 0, Fab Lab Thinner Clients for South Africa, Conformal Computing

Maybe MBAs Should Design Computers After All

Not that long ago, I was under the impression that the basic problem of computer architecture had been solved. After all, computers got faster every year, and gradually whole new application domains emerged. There was constantly more memory available, and software hungrily consumed it. Each new computer had a bigger power supply, and more airflow to extract the increasing heat from the processor.

Now, clock speeds aren't rising quite as quickly, and the progress that is made doesn't seem to help our computers start up or run any faster. The traditions of the computing industry, some going as far back as the first digital computers built by John von Neumann in the 1950s, are starting to grow obsolete. The slower computers seem to get faster, and the more deeply I understand the way things actually work, the more these problems become apparent to me. They really come to light when you think about a computer as a business.

Imagine if your company or organization had one fellow [the CPU] who sat in an isolated office, and refused to talk with anyone except his two most trusted deputies [the Northbridge and Southbridge], through which all the actual work the company does must be funneled. Because this one man — let's call him Bob — is so overloaded doing all the work of the entire company, he has several assistants [memory controllers] who remember everything for him. They do this through a complex system [virtual memory] of file cabinets of various sizes [physical memories], the organization over which they have strictly limited autonomy.

Because it is faster to find things in the smaller cabinets [RAM], where there is less to sift through, Bob asks them to put the most commonly used information there. But since he is constantly switching between different tasks, the assistants must swap in and out the files in the smaller cabinets with those in the larger ones whenever Bob works on something different ["thrashing"]. The largest file cabinet is humongous, and rotates slowly in front of a narrow slit [magnetic storage]. The assistant in charge of it must simply wait for the right folder to appear in front of him before passing it along [disk latency].

Any communication with customers must be handled through a team of receptionists [I/O controllers] who don't take the initiative to relay requests to one of Bob's deputies. When Bob needs customer input to continue on a difficult problem, he drops what he is doing to chase after his deputy to chase after a receptionist to chase down the customer, thus preventing work for other customers to be done in that time.

This model is clearly horrendous for numerous reasons. If any staff member goes out to lunch, the whole operation is likely to grind to a halt. Tasks that ought to be quite simple turn out to take a lot of time, since Bob must re-acquaint himself with the issues in question. If a spy gains Bob's trust, all is lost. The only way to make the model any better without giving up and starting over is to hire people who just do their work faster and spend more hours in the office. And yet, this is the way almost every computer in the world operates today.

It is much more sane to hire a large pool of individuals, and, depending on slow-changing customer needs, organize them into business units and assign them to customer accounts. Each person keeps track of his own small workload, and everyone can work on a separate task simultaneously. If the company suddenly acquires new customers, it can recruit more staff instead of forcing Bob to work overtime. If a certain customer demands more attention than was foreseen, more people can be devoted to the effort. And perhaps most importantly, collaboration with other businesses becomes far more meaningful than the highly coded, formal game of telephone that Bob must play with Frank, who works in a similar position at another corporation [a server]. Essentially, this is a business model problem as much as a computer science one.

These complaints only scratch the surface of the design flaws of today's computers. On an extremely low level, with voltages, charge, and transistors, energy is handled recklessly, causing tremendous heat, which would melt the parts in a matter of seconds were it not for the noisy cooling systems we find in most computers. And on a high level, software engineers have constructed a city of competing abstractions based on the fundamentally flawed "CPU" idea.

So I have changed my mind. I used to believe that computers were on the right track, but now I think the right thing to do is to move forward from our 1950s models to a ground-up, fundamentally distributed computing architecture. I started to use computers at 17 months of age and started programming them at 5, so I took the model for granted. But the present stagnation of perceptual computer performance, and the counter-intuitiveness of programming languages, led me to question what I was born into and wonder if there's a better way. Now I'm eager to help make it happen. When discontent changes your mind, that's innovation.

Physicist, MIT; Researcher, Precision Cosmology

Do we need to understand consciousness to understand physics?  I used to answer "yes", thinking that we could never figure out the elusive "theory of everything" for our external physical reality without first understanding the distorting mental lens through which we perceive it.

After all, physical reality has turned out to be very different from how it seems, and I feel that most of our notions about it have turned out to be illusions. The world looks like it has three primary colors, but that number three tells us nothing about the world out there, merely something about our senses: that our retina has three kinds of cone cells. The world looks like it has impenetrably solid and stationary objects, but all except a quadrillionth of the volume of a rock is empty space between particles in restless schizophrenic vibration. The world feels like a three-dimensional stage where events unfold over time, but Einstein's work suggests that change is an illusion, time being merely the fourth dimension of an unchanging space-time that just is, never created and never destroyed, containing our cosmic history like a DVD contains a movie. The quantum world feels random, but Everett's work suggests that randomness too is an illusion, being simply the way our minds feel when cloned into diverging parallel universes.

The ultimate triumph of physics would be to start with a mathematical description of the world from the "bird's eye view" of a mathematician studying the equations (which are ideally simple enough to fit on her T-shirt) and to derive from them the "frog's eye view" of the world, the way her mind subjectively perceives it. However, there is also a third and intermediate "consensus view" of the world. From your subjectively perceived frog perspective, the world turns upside down when you stand on your head and disappears when you close your eyes, yet you subconsciously interpret your sensory inputs as though there is an external reality that is independent of your orientation, your location and your state of mind. It is striking that although this third view involves both censorship (like rejecting dreams), interpolation (as between eye-blinks) and extrapolation (like attributing existence to unseen cities) of your frog's eye view, independent observers nonetheless appear to share this consensus view. Although the frog's eye view looks black-and-white to a cat, iridescent to a bird seeing four primary colors, and still more different to a bee seeing polarized light, a bat using sonar, a blind person with keener touch and hearing, or the latest robotic vacuum cleaner, all agree on whether the door is open.

This reconstructed consensus view of the world that humans, cats, aliens and future robots would all agree on is not free from some of the above-mentioned shared illusions. However, it is by definition free from illusions that are unique to biological minds, and therefore decouples from the issue of how our human consciousness works. This is why I've changed my mind: although understanding the detailed nature of human consciousness is a fascinating challenge in its own right, it is not necessary for a fundamental theory of physics, which need "only" derive the consensus view from its equations.

In other words, what Douglas Adams called "the ultimate question of life, the universe and everything" splits cleanly into two parts that can be tackled separately: the challenge for physics is deriving the consensus view from the bird's eye view, and the challenge for cognitive science is to derive the frog's eye view from the consensus view. These are two great challenges for the third millennium. They are each daunting in their own right, and I'm relieved that we need not solve them simultaneously.

Neuroscientist, Stanford University, Author, A Primate's Memoir

Well, my biggest change of mind came only a few years ago. It was the outcome of a painful journey of self-discovery, where my wife and children stood behind me and made it possible, where I struggled with all my soul, and all my heart and all my might. But that had to do with my realizing that Broadway musicals are not cultural travesties, so it's a little tangential here. Instead I'll focus on science.
I'm both a neurobiologist and a primatologist, and I've changed my mind about plenty of things in both of these realms. But the most fundamental change is one that transcends either of those disciplines — this was my realizing that the most interesting and important things in the life sciences are not going to be explained with sheer reductionism.

A specific change of mind concerned my work as a neurobiologist.

This came about 15 years ago, and it challenged neurobiological dogma that I had learned in pre-school, namely that the adult brain does not make new neurons. This fact had always been a point of weird pride in the field — hey, the brain is SO fancy and amazing that its elements are irreplaceable, not like some dumb-ass simplistic liver that's so totally fungible that it can regrow itself. And what this fact also reinforced, in passing, was the dogma that the brain is set in stone very early on in life, that there's all sorts of things that can't be changed once a certain time-window had passed.

Starting in the 1960's, a handful of crackpot scientists had been crying in the wilderness about how the adult brain does make new neurons. At best, their unorthodoxy was ignored; at worst, they were punished for it. But by the 1990's, it had become clear that they were right. And "adult neurogenesis" has turned into the hottest subject in the field — the brain makes new neurons, makes them under interesting circumstances, fails to under other interesting ones.

The new neurons function, are integrated into circuits, might even be required for certain types of learning. And the phenomenon is a cornerstone of a new type of neurobiological chauvinism — part of the very complexity and magnificence of the brain is how it can rebuild itself in response to the world around it.

So, I'll admit, this business about new neurons was a tough one for me to assimilate. I wasn't invested enough in the whole business to be in the crowd indignantly saying, No, this can't be true. Instead, I just tried to ignore it. "New neurons", christ, I can't deal with this, turn the page. And after an embarrassingly long time, enough evidence had piled up that I had to change my mind and decide that I needed to deal with it after all. And it's now one of the things that my lab studies.

The other change concerned my life as a primatologist, where I have been studying male baboons in East Africa. This also came in the early 90's. I study what social behavior has to do with health, and my shtick always was that if you want to know which baboons are going to be festering with stress-related disease, look at the low-ranking ones.  Rank is physiological destiny, and if you have a choice in the matter, you want to win some critical fights and become a dominant male, because you'll be healthier. And my change of mind involved two pieces.

The first was realizing, from my own data and that of others, that being dominant has far less to do with winning fights than with social intelligence and impulse control. The other was realizing that while health has something to do with social rank, it has far more to do with personality and social affiliation — if you want to be a healthy baboon, don't be a socially isolated one. This particular shift has something to do with the accretion of new facts, new statistical techniques for analyzing data, blah blah. Probably most importantly, it has to do with the fact that I was once a hermetic 22-year old studying baboons and now, 30 years later, I've changed my mind about a lot of things in my own life.

Science Writer; Consultant; Lecturer, Copenhagen; Author, The Generous Man

Permanent Reincarnation

I have changed my mind about my body. I used to think of it as a kind of hardware on which my mental and behavioral software was running. Now, I primarily think of my body as software. 

My body is not like a typical material object, a stable thing.  It is more like a flame, a river or an eddie. Matter is flowing through it all the time. The constituents are being replaced over and over again.

A chair or a table is stable because the atoms stay where they are. The stability of a river stems from the constant flow of water through it.

98 percent of the atoms in the body are replaced every year. 98 percent! Water molecules stays in your body for two weeks (and for an even shorter time in a hot climate), the atoms in your bones stays there for a few months. Some atoms stay for years. But almost not one single atom stay with you in your body from cradle to grave.

What is constant in you is not material. An average person takes in 1.5 ton of matter every year as food, drinks and oxygen. All this matter has to learn to be you. Every year. New atoms will have to learn to remember your childhood.

These numbers has been known for half a century or more, mostly from studies of radioactive isotopes. Physicist Richard Feynman said in 1955: "Last week's potatoes! They now can remember what was going on in your mind a year ago."

But why is this simple insight not on the all-time Top 10 list of important discoveries? Perhaps because it tastes a little like spiritualism and idealism? Only the ghosts are for real? Wandering souls? 

But digital media now makes it possible to think of all this in a simple way. The music I danced to as a teenager has been moved from vinyl-LPs to magnetic audio tapes to CDs to Pods and whatnot. The physical representation can change and is not important — as long as it is there. The music can jump from medium to medium, but it is lost if it does not have a representation. This physics of information was sorted out by Rolf Landauer in the 1960'ies. Likewise, out memories can move from potato-atoms to burger-atoms to banana-atoms. But the moment they are on their own, they are lost.

We reincarnate ourselves all the time. We constantly give our personality new flesh. I keep my mental life alive by making it jump from atom to atom. A constant flow. Never the same atoms, always the same river. No flow, no river. No flow, no me.

This is what I call permanent reincarnation: Software replacing its hardware all the time. Atoms replacing atoms all the time. Life. This is very different from religious reincarnation with souls jumping from body to body (and souls sitting out there waiting for a body to take home in).

There has to be material continuity for permanent reincarnation to be possible. The software is what is preserved, but it cannot live on its own. It has to jump from molecule to molecule, always in carnation.

I have changed my mind about the stability of my body: It keeps changing all the time. Or I could not stay the same.

Research Professor, Department of Anthropology, Rutgers University; Author,
Why We Love

Planned Obsolescence?  The Four-Year Itch

When asked why all of her marriages failed, anthropologist Margaret Mead apparently replied, "I beg your pardon, I have had three marriages and none of them was a failure."  There are many people like Mead.  Some 90% of Americans marry by middle age.  And when I looked at United Nations data on 97 other societies, I found that more than 90% of men and women eventually wed in the vast majority of these cultures, too.  Moreover, most human beings around the world marry one person at a time: monogamy.  Yet, almost everywhere people have devised social or legal means to untie the knot.  And where they can divorce — and remarry — many do.

So I had long suspected this human habit of "serial monogamy" had evolved for some biological purpose.  Planned obsolescence of the pairbond?  Perhaps the mythological "seven-year itch" evolved millions of years ago to enable a bonded pair to rear two children through infancy together.  If each departed after about seven years to seek "fresh features," as poet Lord Byron put it, both would have ostensibly reproduced themselves and both could breed again — creating more genetic variety in their young.

So I began to cull divorce data on 58 societies collected since 1947 by the Statistical Office of the United Nations.  My mission: to prove that the "seven year itch" was a worldwide biological phenomenon associated in some way with rearing young.  

Not to be.  My intellectual transformation came while I was pouring over these divorce statistics in a rambling cottage, a shack really, on the Massachusetts coast one August morning.  I regularly got up around 5:30, went to a tiny desk that overlooked the deep woods, and poured over the pages I had Xeroxed from the United Nations Demographic Yearbooks.  But in country after country, and decade after decade, divorces tended to peak (the divorce mode) during and around the fourth year of marriage.  There were variations, of course.  Americans tended to divorce between the second and third year of marriage, for example.  Interestingly, this corresponds with the normal duration of intense, early stage, romantic love — often about 18 months to 3 years.  Indeed, in a 2007 Harris poll, 47% of American respondents said they would depart an unhappy marriage when the romance wore off, unless they had conceived a child.

Nevertheless, there was no denying it:  Among these hundreds of millions of people from vastly different cultures, three patterns kept emerging.  Divorces regularly peaked during and around the fourth year after wedding.  Divorces peaked among couples in their late twenties.  And the more children a couple had, the less likely they were to divorce: some 39% of worldwide divorces occurred among couples with no dependent children; 26% occurred among those with one child; 19% occurred among couples with two children; and 7% of divorces occurred among couples with three young.

I was so disappointed.  I mulled about this endlessly.  My friend used to wave his hand over my face, saying, "Earth to Helen; earth to Helen."  Why do so many men and women divorce during and around the 4-year mark; at the height of their reproductive years; and often with a single child?  It seemed like such an unstable reproductive strategy.  Then suddenly I got that "ah-ha" moment:  Women in hunting and gathering societies breastfeed around the clock, eat a low-fat diet and get a lot of exercise — habits that tend to inhibit ovulation.  As a result, they regularly space their children about four years apart.  Thus, the modern duration of many marriages—about four years—conforms to the traditional period of human birth spacing, four years. 

Perhaps human parental bonds originally evolved to last only long enough to raise a single child through infancy, about four years, unless a second infant was conceived.  By age five, a youngster could be reared by mother and a host of relatives. Equally important, both parents could choose a new partner and bear more varied young.

My new theory fit nicely with data on other species.  Only about three percent of mammals form a pairbond to rear their young.  Take foxes.  The vixen's milk is low in fat and protein; she must feed her kits constantly; and she will starve unless the dog fox brings her food.  So foxes pair in February and rear their young together.  But when the kits leave the den in mid summer, the pairbond breaks up.  Among foxes, the partnership lasts only through the breeding season.  This pattern is common in birds.  Among the more than 8,000 avian species, some 90% form a pairbond to rear their young.  But most do not pair for life. A male and female robin, for example, form a bond in the early spring and rear one or more broods together.  But when the last of the fledgling fly away, the pairbond breaks up. 

Like pair-bonding in many other creatures, humans have probably inherited a tendency to love and love again—to create more genetic variety in our young.  We aren't puppets on a string of DNA, of course.  Today some 57% of American marriages last for life.  But deep in the human spirit is a restlessness in long relationships, born of a time long gone, as poet John Dryden put it, "when wild in wood the noble savage ran."

Science writer; Contributing Editor, Astronomy Magazine

The Myth Of The "Open Mind"

When I was 21, I began working for the Union of Concerned Scientists (UCS) in Cambridge Massachusetts. I was still an undergraduate at the time, planning on doing a brief research stint in energy policy before finishing college and heading to graduate school in physics. That "brief research stint" lasted about seven years, off and on, and I never did make it to graduate school. But the experience was instructive nevertheless.

When I started at UCS in the 1970s, nuclear power safety was a hot topic, and I squared off in many debates against nuclear proponents from utility companies, nuclear engineering departments, and so forth regarding reactor safety, radioactive wastes, and the viability of renewable energy alternatives. The next issue I took on for UCS was the nuclear arms race, which was equally polarized. (The neocons of that day weren't "neo" back then; they were just cons.) As with nuclear safety, there was essentially no common ground between the two sides. Each faction was invariably trying to do the other in, through oral rhetoric and tendentious prose, always looking for new material to buttress their case or undermine that of their opponents.

Even though the organization I worked for was called the Union of Concern Scientists, and even though many of the staff members there referred to me as a "scientist" (despite my lack of academic credentials), I knew that what I was doing was not science. (Nor were the many physics PhD's in arms control and energy policy doing science either.) In the back of my head, I always assumed that "real science" was different — that scientists are guided by facts rather than by ideological positions, personal rivalries, and whatnot.

In the decades since, I've learned that while this may be true in many instances, oftentimes it's not. When it comes to the biggest, most contentious issues in physics and cosmology — such as the validity of inflationary theory, string theory, or the multiverse/landscape scenario — the image of the objective truth seeker, standing above the fray, calmly sifting through the evidence without preconceptions or prejudice, may be less accurate than the adversarial model of our justice system. Both sides, to the extent there are sides on these matters, are constantly assembling their briefs, trying to convince themselves as well as the jury at large, while at the same time looking for flaws in the arguments of the opposing counsel.

This fractionalization may stem from scientific intuition, political or philosophical differences,  personal grudges, or pure academic competition. It's not surprising that this happens, nor is it necessarily a bad thing. In fact, it's my impression that this approach works pretty well in the law and in science too. It means that, on the big things at least, science will be vetted; it has to withstand scrutiny, pass muster.

But it's not a cold, passionless exercise either. At its heart, science is a human endeavor, carried out by people. When the questions are truly ambitious, it takes a great personal commitment to make any headway — a big investment in energy and in emotion as well. I know from having met with many of the lead researchers that the debates can get heated, sometimes uncomfortably so. More importantly, when you're engaged in an epic struggle like this — trying, for instance, to put together a theory of broad sweep — it may be difficult, if not impossible, to keep an "open mind" because you may be well beyond that stage, having long since cast your lot with a particular line of reasoning. And after making an investment over the course of many years, it's natural to want to protect it. That doesn't mean you can't change your mind — and I know of several cases where this has occurred — but, no matter what you do, it's never easy to shift from forward to reverse.

Although I haven't worked as a scientist in any of these areas, I have written about many of the "big questions" and know how hard it is to get all the facts lined up so that they fit together into something resembling an organic whole. Doing that, even as a mere scribe, involves periods of single-minded exertion, and during that process the issues can almost take on a life of their own, at least while you're actively thinking about them. Before long, of course, you've moved onto the next story and the excitement of the former recedes. As the urgency fades, you start wondering why you felt so strongly about the landscape or eternal inflation or whatever it was that had taken over your desk some months ago.

It's different, of course, for researchers who may stake out an entire career — or at least big chunks thereof — in a certain field.  You're obliged to keep abreast of all that's going on of note, which means one's interest is continually renewed. As new data comes in, you try to see how it fits in with the pieces of the puzzle you're already grappling with. Or if something significant emerges from the opposing camp, you may instinctively seek out the weak spots, trying to see how those guys messed up this time.

It's possible, of course, that a day may come when, try as you might, you can't find the weak spots in the other guy's story. After many attempts and an equal number of setbacks, you may ultimately have to accede to the view of an intellectual, if not personal, rival. Not that you want to but rather because you can't see any way around it. On the one hand, you might chalk it up as a defeat, something that will hopefully build character down the road. But in the grand scheme of things, it's more of a victory — a sign that sometimes our adversarial system of science actually works.

Physicist; Albert Einstein Professor of Science, Princeton University; Coauthor, Endless Universe: A New History of the Cosmos

What created the structure of the universe?

Most cosmologists would say the answer is "inflation," and, until recently, I would have been among them. But "facts have changed my mind" — and I now feel compelled to seek a new explanation that may or may not incorporate inflation.

The idea always seemed incredibly simple. Inflation is a period of rapid accelerated expansion that can transform the chaos emerging from the big bang into the smooth, flat homogeny observed by astronomers. If one likens the conditions following the bang to a wrinkled and twisted sheet of perfectly elastic rubber, then inflation corresponds to stretching the sheet at faster-than-light speeds until no vestige of its initial state remains. The "inflationary energy" driving the accelerated expansion then decays into the matter and radiation seen today and the stretching slows to a modest pace that allows the matter to condense into atoms, molecules, dust, planets, stars and galaxies.

I would describe this version as the "classical view" of inflation in two senses. First, this is the historic picture of inflation first introduced and now appearing in most popular descriptions. Second, this picture is founded on the laws of classical physics, assuming quantum physics plays a minor role. Unfortunately, this classical view is dead wrong. Quantum physics turns out to play an absolutely dominant role in shaping the inflationary universe. In fact, inflation amplifies the randomness inherent in quantum physics to produce an universe that is random and unpredictable.

This realization has come slowly. Ironically, the role of quantum physics was believed to be a boon to the inflationary paradigm when it was first considered twenty-five years ago by several theorists, including myself. The classical picture of inflation could not be strictly true, we recognized, or else the universe would be so smooth after inflation that galaxies and other large-scale structures would never form. However, inflation ends through the quantum decay of inflationary energy into matter and radiation. The quantum decay is analogous to the decay of radioactive uranium, in which there is some mean rate of decay but inherent unpredictability as to when any particular uranium nucleus will decay. Long after most uranium nuclei have decayed, there remain some nuclei that have yet to fission.

Similarly, inflationary energy decays at slightly different times in different places, leading to spatial variations in the temperature and matter density after inflation ends. The "average" statistical pattern appears to agree beautifully with the pattern of microwave background radiation emanating from the earliest stages of the universe and to produce just the pattern of non-uniformities needed to explain the evolution and distribution of galaxies. The agreement between theoretical calculation and observations is a celebrated triumph of the inflationary picture.

But is this really a triumph? Only if the classical view were correct. In the quantum view, it makes no sense to talk about an "average" pattern. The problem is that, as in the case of uranium nuclei, there always remain some regions of space in which the inflationary energy has not yet decayed into matter and radiation at all. Although one might have guessed the undecayed regions are rare, they expand so much faster than those that have decayed that they soon overtake the volume of the universe. The patches where inflationary energy has decayed and galaxies and stars have evolved become the oddity — rare pockets surrounded by space that continues to inflate away.

The process repeats itself over and over, with the number of pockets and the volume of surrounding space increasing from moment to moment. Due to random quantum fluctuations, pockets with all kinds of properties are produced — some flat, but some curved; some with variations in temperature and density like what we observe, but some not; some with forces and physical laws like those we experience, but some with different laws. The alarming result is that there are an infinite number of pockets of each type and, despite over a decade of attempts to avoid the situation, no mathematical way of deciding which is more probable has been shown to exist.

Curiously, this unpredictable "quantum view" of inflation has not yet found its way into the consciousness of many astronomers working in the field, let alone the greater scientific community or the public at large.

One often reads that recent measurements of the cosmic microwave background or the large-scale structure of the universe have verified a prediction of inflation. This invariably refers to a prediction based on the naïve classical view. But if the measurements ever come out differently, this could not rule out inflation. According to the quantum view, there are invariably pockets with matching properties.

And what of the theorists who have been developing the inflationary theory for the last twenty-five years? Some, like me, have been in denial, harboring the hope that a way can be found to tame the quantum effects and restore the classical view. Others have embraced the idea that cosmology may be inherently unpredictable, although this group is also vociferous in pointing how observations agree with the (classical) predictions of inflation.

Speaking for myself, it may have taken me longer to accept its quantum nature than it should have, but, now that facts have changed my mind, I cannot go back again. Inflation does not explain the structure of the universe. Perhaps some enhancement can explain why the classical view works so well, but then it will be that enhancement rather than inflation itself that explains the structure of the universe. Or maybe the answer lies beyond the big bang. Some of us are considering the possibility that the evolution of the universe is cyclic and that the structure was set by events that occurred before the big bang. One of the draws of this picture is that quantum physics does not play the same dominant role, and there is no escaping its predictions of the uniformity, flatness and structure of the universe.

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